Sudheer Venna

Big Ideas Math Book Answers has created a sequence of lessons in all the chapters. Get Big Ideas Math Answers Grade K Chapter 12 Identify Three-Dimensional Shapes on this. This pdf link will make understanding concepts of 3-Dimensional shapes so easy. The 3-D shapes are cone, cylinder, cube, cuboid, etc. So following the Big Ideas Math Answers Grade K Chapter 12 Identify Three-Dimensional Shapes is necessary to get notified of the topics. So it will be easy for you to understand the concepts behind each and every lesson.

Big Ideas Math Book Grade K Answer Key Chapter 12 Identify Three-Dimensional Shapes

The topics covered in this chapter are Vocabulary, Two- and Three-Dimensional Shapes, Cubes and Spheres etc. So, Download Big Ideas Math Answers Grade K Chapter 12 Identify Three-Dimensional Shapes PDF for free. For more practice questions simply go to the performance task and cumulative practice which is given at the end of the chapter. Just click on the below-attached links and start your preparation from now.

Vocabulary

• Identify Three-Dimensional Shapes Vocabulary

Lesson: 1 Two- and Three-Dimensional Shapes

• Lesson 12.1 Two- and Three-Dimensional Shapes
• Two- and Three-Dimensional Shapes Homework & Practice 12.1

Lesson: 2 Describe Three-Dimensional Shapes

• Lesson 12.2 Describe Three-Dimensional Shapes
• Describe Three-Dimensional Shapes Homework & Practice 12.2

Lesson: 3 Cubes and Spheres

• Lesson 12.3 Cubes and Spheres
• Cubes and Spheres Homework & Practice 12.3

Lesson: 4 Cones and Cylinders

• Lesson 12.4 Cones and Cylinders
• Cones and Cylinders Homework & Practice 12.4

Lesson: 5 Build Three-Dimensional Shapes

• Lesson 12.5 Build Three-Dimensional Shapes
• Build Three-Dimensional Shapes Homework & Practice 12.5

Lesson: 6 Positions of Solid Shapes

• Lesson 12.6 Positions of Solid Shapes
• Positions of Solid Shapes Homework & Practice 12.6

Chapter 12: Identify Three-Dimensional Shapes

• Identify Three-Dimensional Shapes Performance Task
• Identify Three-Dimensional Shapes Activity
• Identify Three-Dimensional Shapes Chapter Practice

Identify Three-Dimensional Shapes Vocabulary

Directions:
Circle each can. Draw a square around each box. Count and write how many of each two-dimensional shape you draw.

Answer:

Answer:

Answer:

Answer:

Lesson 12.1 Two- and Three-Dimensional Shapes

Explore and Grow

Directions:
Circle any triangles, rectangles, squares, hexagons, and circles you see in the picture. Use another color to circle any objects in the picture that match the blue shapes shown. Tell what you notice about each shape.

Answer:

two-dimensional
rectangle
circle
triangle
hexagon
Total11 shapes
three-dimensional
cylinder
sphere
cube
cone
Total 8 shapes
Explanation:
A two-dimensional shape is a shape that has length and width but no depth. … A circle is one example of a two-dimensional shape. Example Two. A rectangle is another example of a two-dimensional shape.

Triangles, Rectangles, Squares, Hexagons, and Circles all these shapes are all 2-D shapes.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width, and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
All the objects in the picture represent the 3-D shapes so, they are circled with a different color.

Think and Grow

Directions:
Circle any three-dimensional shapes. Draw rectangles around any two-dimensional shapes. Tell why your answers are correct.

Answer:

two-dimensional
rectangle
circle
three-dimensional
cylinder
sphere
cuboid
cone
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Apply and Grow: Practice

Directions:
1 – 4 Circle any three-dimensional shapes. Draw rectangles around any two-dimensional shapes. Tell why your answers are correct.

Question 1.

Answer:

two-dimensional
rectangle
circle
three-dimensional
cylinder
cube
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangles.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Question 2.

Answer:

two-dimensional
circle
square
hexagon
three-dimensional
sphere
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Question 3.

Answer:

two-dimensional
Triangle
three-dimensional
Cuboid
Triangle prism
Cone
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Question 4.

Answer:

two-dimensional
0
three-dimensional
Cylinder
Sphere
Cone

Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Think and Grow: Modeling Real Life

Directions:
Circle any shapes in the picture that are solids. Draw rectangles around any shapes in the picture that are flats. Count and write how many solids and flats you find.

three-Dimensional
________
– – – – – – – –
________

two-dimensional
________
– – – – – – – –
________

Answer:

two-dimensional
Rectangles
Total 7 flat surfaces
three-dimensional
Cubes
Sphere
Cone
Cylinder
Total 8 solids
Explanation:
Solid figures are three-dimensional. A face is a flat surface of a solid.

Two- and Three-Dimensional Shapes Homework & Practice 12.1

Directions:
1 – 3 Circle any three-dimensional shapes. Draw rectangles around any two-dimensional shapes. Tell why your answers are correct.

Question 1.

Answer:

two-dimensional
Triangle
Square
three-dimensional
Cylinder
Sphere
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Question 2.

Answer:

two-dimensional
Hexagon
Circle
three-dimensional
Cube
Cone
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Question 3.

Answer:

two-dimensional
Rectangle
Square
three-dimensional
Cube
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Directions:
4 and 5 Circle any three-dimensional shapes. Draw rectangles around any two-dimensional shapes. Tell why your answers are correct. 6 Circle any three-dimensional shapes in the picture. Count and write the number. Draw rectangles around any two-dimensional shapes in the picture. Count and write the number.

Question 4.

Answer:

two-dimensional
Circle
three-dimensional
Cylinder
Sphere
Cone
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Question 5.

Answer:

two-dimensional
Rectangle
Circle
Triangle
three-dimensional
Cube
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Question 6.

Answer:

Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Lesson 12.2 Describe Three-Dimensional Shapes

Explore and Grow

Directions:
Cut out the Roll, Stack, Slide Sort Cards. Sort the cards into the categories shown.

rolls

stacks

slides

Answer:

Think and Grow

Directions:

• Look at the solid shape on the left that rolls. Circle the other solid shapes that roll.
• Look at the solid shapes on the left that stack. Circle the other solid shapes that stack.
• Look at the solid shape on the left that slides. Circle the other solid shapes that slide.

Answer:

Explanation:
Solid shapes that can roll are circled with Brown.
Solid shapes that can slide are circled with Yellow.
Solid shapes that can stack are circled with Blue.

The object which has a flat surface can slide. Example Rectangle, cube, cuboid, cylinder shapes.
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.
Shapes with a curved face can roll. Example sphere , cylinder , cone shape.

Apply and Grow: Practice

Directions:
1 Look at the solid shape on the left that rolls. Circle the other solid shapes that roll. 2 Circle the solid shapes that roll and slide. 3 Circle the solid shapes that stack and slide. 4 Circle the solid shape that does not stack or slide.

Question 1.

Answer:

Given:
The cylinder can roll,roll and slide, stack and slide
The cube can slide and stack.
The sphere can only roll.

Explanation:
The object which has a flat surface can slide. Example Rectangle, cube, cuboid, cylinder shapes.
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.
Shapes with a curved face can roll. Example sphere, cylinder, cone shape.

Question 2.

Answer:

Given:
The cylinder can roll, stack and slide, roll and slide
Cone can roll, roll and slide.
The cube can slide and stack.
Explanation:
Solid shapes that can roll are circled with Brown.
Solid shapes that can slide are circled with Yellow.
Solid shapes that can stack are circled with Blue.

The object which has a flat surface can slide. Example Rectangle, cube, cuboid, cylinder shapes.
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.
Shapes with a curved face can roll. Example sphere, cylinder, cone shape.

Question 3.

Answer:

Given:
A ball that represents a Sphere. The ball can only roll.
A wooden log which represent cylinder. Log can roll, roll and slide, stack and slide.
The wooden box which represents cube. The box can slide and stack.
Hat represent cone. hat can roll, roll and slide.

Explanation:
Solid shapes that can roll are circled with Brown.
Solid shapes that can slide are circled with Yellow.
Solid shapes that can stack are circled with Blue.
The object which has a flat surface can slide. Example Rectangle, cube, cuboid, cylinder shapes.
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.
Shapes with a curved face can roll. Example sphere, cylinder, cone shape.

Question 4.

Answer:

Given:
The ball which represents Sphere. The ball can only roll.
Glue stick which represents cylinder. Glue stick can roll,roll and slide, stack and slide.
The box which represents cube. Box can slide and stack.
Birthday Hat represents cone. Birthday hat can roll, roll and slide.

Explanation:
Solid shapes that can roll are circled with Brown.
Solid shapes that can slide are circled with Yellow.
Solid shapes that can stack are circled with Blue.
The object which has a flat surface can slide. Example Rectangle, cube, cuboid, cylinder shapes.
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.
Shapes with a curved face can roll. Example sphere, cylinder, cone shape.

Think and Grow: Modeling Real Life

Directions:
You stack the 3 objects shown. Write 1 below the object you place at the bottom of the stack, write 2 below the object you stack next, and write 3 below the object you stack last. Tell why you chose this order.

Answer:

Given:
cylinder shaped Oats box and piggy bank. Oats box and piggy bank can roll, roll and slide, stack and slide.
cube shaped Cardboard box and a Wooden box . A cardboard box and a Wooden Box can slide and stack.
cone shaped Party hats. Party hats can roll, roll and slide.

Explanation:
The object which has a flat surface can slide. Example Rectangle, cube, cuboid, cylinder shapes.
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.
Shapes with a curved face can roll. Example sphere , cylinder , cone shape.

Describe Three-Dimensional Shapes Homework & Practice 12.2

Directions:
1 Look at the solid shapes on the left that stack. Circle the other solid shapes that stack. 2 Look at the solid shape on the left that rolls. Circle the other solid shapes that roll. 3 Look at the solid shape on the left that slides. Circle the other solid shapes that slide.

Question 1.

Answer:

Explanation:
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.

Question 2.

Answer:

Explanation:
Shapes with a curved face can roll. Example sphere, cylinder, cone shape.

Question 3.

Answer:

Explanation:
The object which has a flat surface can slide. Example Rectangle, cube, cuboid, cylinder shapes.

Directions:
4 Circle the solid shapes that roll and stack. 5 Circle the solid shapes that stack and slide. 6 Circle the solid shape that does not roll. 7 You stack the 3 objects shown. Write 1 below the object you place at the bottom of the stack, write 2 below the object you stack next, and write 3 below the object you stack last. Tell why you chose this order.

Question 4.

Answer:

Cylinder shaped objects can roll and slide.

Explanation:
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.
Shapes with a curved face can roll. Example sphere, cylinder, cone shape.

Question 5.

Answer:

Given:
Cube shaped objects can slide and stake.
Cylinder shaped objects can roll and slide.

Explanation:
The object which has a flat surface can slide. Example Rectangle, cube, cuboid, cylinder shapes.
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.

Question 6.

Answer:

Given:
Cube shaped objects can slide and stake. Cube shaped solids that does not roll.

Explanation:
The object which has a flat surface can slide. Example Rectangle, cube, cuboid, cylinder shapes.
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.

Question 7.

Answer:

Explanation:
In the figure given we have 2 cylinder shaped objects and 1 cone shaped object.
Cylinders can stack, slide and roll. So, I used both the cylinder shaped objects at the bottom.
Cone can roll and slide. As cones shaped figures can not be stacked I used at the top.

Lesson 12.3 Cubes and Spheres

Explore and Grow

Directions:
Cut out the Cube and Sphere Sort Cards. Sort the cards into the categories shown.

Answer:

Think and Grow

Directions:
Circle the cube. Draw a rectangle around the sphere. Tell why your answers are correct.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges.

Apply and Grow: Practice

Directions:
1 Circle the cube. Draw a rectangle around the sphere. Tell why your answers are correct. 2 – 4 Circle any object that looks like a cube. Draw a rectangle around any object that looks like a sphere. Tell why your answers are correct.

Question 1.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges.

Question 2.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges.

Question 3.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges.

Question 4.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges.

Think and Grow: Modeling Real Life

Directions:
Use Make a Cube to build your own number cube. Draw the shape of the flat surfaces of your cube. Count and write the number of flat surfaces.

________
– – – – – – – –
________ flat surfaces
Answer:

Cubes and Spheres Homework & Practice 12.3

Directions:
1 – 3 Circle the cube. Draw a rectangle around the sphere. Tell why your answers are correct.

Question 1.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges

Question 2.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges

Question 3.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges

Directions:
4 – 6 Circle any object that looks like a cube. Draw a rectangle around any object that looks like a sphere. Tell why your answers are correct. 7 Draw the shape of the flat surfaces of a die. Count and write the number of flat surfaces.

Question 4.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges

Question 5.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges

Question 6.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges.

Question 7.

Answer:

Explanation:
Dice is similar to a cube.
A cube is a region of space formed by six identical square faces joined along their edges.

Lesson 12.4 Cones and Cylinders

Explore and Grow

Directions:
Cut out the Cone and Cylinder Sort Cards. Sort the cards into the categories shown.

Answer:

Think and Grow

Directions:
Circle the cone. Draw a rectangle around the cylinder. Tell why your answers are correct.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Apply and Grow: Practice

Directions:
1 Circle the cone. Draw a rectangle around the cylinder. Tell why your answers are correct. 2 – 4 Circle any object that looks like a cone. Draw a rectangle around any object that looks like a cylinder. Tell why your answers are correct.

Question 1.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Question 2.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Question 3.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Question 4.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Think and Grow: Modeling Real Life

Directions:
Use Make a Cylinder to build a can of vegetables. Draw the shape of the flat surfaces of your can. Count and write the number of flat surfaces.

__________
– – – – – – – – – –
__________ flat surfaces
Answer:

Cones and Cylinders Homework & Practice 12.4

Directions:
1 – 3 Circle the cone. Draw a rectangle around the cylinder. Tell why your answers are correct.

Question 1.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Question 2.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Question 3.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Directions:
4 – 6 Circle any object that looks like a cone. Draw a rectangle around any object that looks like a cylinder. Tell why your answers are correct. 7 Draw the shape of the flat surface of a cone. Count and write the number of flat surfaces.

Question 4.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Question 5.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Question 6.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Question 7.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

Lesson 12.5 Build Three-Dimensional Shapes

Explore and Grow

Directions:
Use your materials to build one of the three-dimensional shapes shown. Circle the three-dimensional shape that you build.

Answer:

Think and Grow

Directions:

• Use your materials to build the 2 shapes shown.
• Connect the 2 shapes that you build, as shown.
• Tell what solid shape you build.

Answer:
Cube

Apply and Grow: Practice

Directions:
1 – 3 Use your materials to build the solid shape shown. 4 Use your materials to build a solid shape that has 6 square, flat surfaces. Circle the shape you build.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Think and Grow: Modeling Real Life

Directions:

• Use your materials to build the castle tower in the picture.
• Circle the solid shapes that you use to build the tower.

Answer:

Explanation
The above figure represent a cylinder base with cone on the top.

Build Three-Dimensional Shapes Homework & Practice 12.5

Directions:
1 and 2 Use your materials to build the solid shape shown. 3 Use your materials to build the solid shape that has a curved surface and only 1 flat surface. Circle the shape you build. 4 Use your materials to build a solid shape that has no flat surfaces. Circle the shape you build.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Directions:
5 Use your materials to build the totem pole in the picture. Circle the solid shapes that you use to make the totem pole.

Question 5.

Answer:

Explanation:
The above totem is a stack of three shapes. The bottom is in the shape of a Cube. The middle is in the shape of a Cylinder. The top is in the shape of a Cone.

Lesson 12.6 Positions of Solid Shapes

Explore and Grow

Directions:
Place a counter beside the bench. Place a counter in front of the tree. Place a counter next to below the stairs. Place a counter the baby swing.

Answer:

Think and Grow

Directions:

• Circle the object that looks like a cylinder that is next to the table. Draw a line through the object that looks like a cone that is below the shelf. Draw a rectangle around the object that looks like a sphere that is above the table.
• Circle the object that looks like a cube that is behind the shovel. Draw a line through the object that looks like a cylinder that is beside the tree. Draw a rectangle around the object that looks like a sphere that is in front of the tree.

Answer:

Apply and Grow: Practice

Directions:
1 Circle the object that looks like a cylinder that is behind a paper cup. Draw a line through the object that looks like a sphere that is above the napkin dispenser. Draw a rectangle around the object that looks like a cone that is below a glass cup. 2 Circle the object that looks like a cone that is beside the log. Draw a line through the object that looks like a sphere that is above the log. Draw a rectangle around the object that looks like a cone that is in front of the log.

Question 1.

Answer:

Question 2.

Answer:

Think and Grow: Modeling Real Life

Directions: Use the City Scene Cards to place the objects on the picture.

• Place a dog in front of the boy crossing the street.
• Place a tree beside the building that looks like a cube.
• Place an object that looks like a sphere above the buildings. Place that object behind a cloud.
• Place an object that looks like a cone below the traffic light.
• Place a streetlight next to the girl on the sidewalk.

Answer:

Positions of Solid Shapes Homework & Practice 12.6

Directions:
1 Circle the object that looks like a sphere that is beside the pool. Draw a line through the object that looks like a cone that is next to the ball. Draw a rectangle around the object that looks like a cylinder that is behind the block.

Question 1.

Answer:

Directions:
2 Circle the object that looks like a cone that is above the stuffed animal. Draw a line through the object that looks like a cylinder that is in front of the stuffed animal. Draw a rectangle around the object that looks like a cube that is below the stuffed animal. 3 Use the Construction Scene Cards to place the objects on the picture. Place a building below the object that is shaped like a cube. Place a tree beside that building. Place a blimp the traffic cone. Place a truck in front of the traffic cone.

Question 2.

Answer:

Question 3.

Answer:

Identify Three-Dimensional Shapes Performance Task

Directions: 1 You pick up trash in the park. Draw lines to match each item with its correct recycling bin.

• The object that rolls but does not stack that is in front of the lamppost goes in the yellow bin.
• The object below the bench that does not roll goes in the blue bin.
• The object that has 1 flat surface that is behind an object that looks like a cylinder goes in the green bin.
• The object that stacks, slides, and rolls that are above an object that looks like a cube goes in the orange bin.
• The object in front of the tree that rolls and has 2 flat surfaces goes in the green bin.
• The object next to the tree that stacks and slides and has only flat surfaces goes in the green bin.
• The object that has a curved surface that does not stack that is beside the tree goes in the blue bin.
• The object that slides and rolls that is next to an object that has 6 flat surfaces goes in the blue bin.

Question 1.

Answer:

Identify Three-Dimensional Shapes Activity

Solid Shapes: Spin and Cover
Directions:
Take turns using the spinner to find which type of three-dimensional shape to cover. Use a counter to cover an object on the page. Repeat this process until you have covered all of the objects.

Answer:

Identify Three-Dimensional Shapes Chapter Practice

Directions:
1 and 2 Circle any three-dimensional shapes. Draw rectangles around any two-dimensional shapes. Tell why your answers are correct. 3 Look at the solid shape on the left that rolls. Circle the other solid shapes that roll. 4 Circle the solid shapes that stack and slide.

12.1 Two- and Three-Dimensional Shapes

Question 1.

Answer:

two-dimensional
rectangle
circle
three-dimensional
Sphere
cube
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

Question 2.

Answer:

two-dimensional
Triangle
three-dimensional
Cylinder
Cone
Explanation:
A two-dimensional shape is a shape that has length and width but no depth.
Examples: Circle, Triangle, Rectangle, Squares, Hexagons.
2-D shapes have been shaped with rectangle.
A three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Examples: Sphere, Torus, Cylinder, Cone, Cube, Cuboid, Triangular Pyramid, Square Pyramid.
3-D shapes have been shaped with circle.

12.2 Describe Three-Dimensional Shapes

Question 3.

Answer:

Explanation:
Shapes with a curved face can roll. Example sphere , cylinder , cone shape

Question 4.

Answer:

Explanation:
The object which has a flat surface can slide. Example Rectangle, cube, cuboid, cylinder shapes.
Shapes with a flat face can stack. Example Cube, Rectangle, Cylinder shape.

Directions:
5 Circle the cube. Draw a rectangle around the sphere. Tell why your answers are correct. 6 Circle any object that looks like a cube. Draw a rectangle around any object that looks like a sphere. Tell why your answers are correct. 7 and 8 Circle any object that looks like a cone. Draw a rectangle around any object that looks like a cylinder. Tell why your answers are correct.

12.3 Cubes and Spheres

Question 5.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges.

Question 6.

Answer:

Explanation:
A sphere is a round, ball-shaped solid. It has one continuous surface with no edges or vertices.
A cube is a region of space formed by six identical square faces joined along their edges.

12.4 Cones and Cylinders

Question 7.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Question 8.

Answer:

Explanation:
A Cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

A Cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.

Directions:
9 Use your materials to build the solid shape shown. 10 Use your materials to build a shape that has a curved surface and 2 flat surfaces. Circle the shape you build. 11 Use your materials to build the elf in the picture. Circle the solid shapes that you use to make the elf.

12.5 Build Three-Dimensional Shapes

Question 9.

Question 10.

Answer 9 – 10 :

Question 11.

Answer:

Directions:
12 Circle the object that looks like a cylinder that is below the hat. Draw a line through the object that looks like a cone that is beside the cooler. Draw a rectangle around the object that looks like a cylinder that is in front of the hat. 13 Circle the object that looks like a sphere that is above the cone. Draw a line through the object that looks like a cylinder that is next to the cone. Draw a rectangle around the object that looks like a sphere that is behind the cone.

Question 12.

Answer:

Question 13.

Answer:

Final Words:

You can learn the difference between 2-D and 3-D shapes from here. Write your new ideas on your book and solve the problems in own way. Also create questions on your own and try to understand the concepts in depth. We hope the given info is helpful for all the students of Grade K. If you have any doubts regarding the concept you can post the comments in the below-mentioned comment box. Hope this Big Ideas Math Grade K Solution Key helps you to score good marks in the exams.

Are you feeling difficulty while preparing for the 12th Chapter Solve Length Problems? Then stay tuned to this page. Here we are giving the Big Ideas Math Answers Grade 2 Chapter 12 Solve Length Problems. Students can download the Big Ideas Math Answers Grade 2 Chapter 12 Solve Length Problems pdf for free of cost.

Big Ideas Math Book 2nd Grade Answer Key Chapter 12 Solve Length Problems

Students can check out the topic-wise questions and solutions of Big Ideas Math Book Grade 2 Chapter 12 Solve Length Problems. The different lessons of BIM Grade 2 Chapter 12 Solve Length Problems are Solve Length Problems Vocabulary, Use a Number Line to Add and Subtract Lengths, Problem Solving: Length, Problem Solving: Missing Measurement, and Practice Measurement Problems.

Make use of Big Ideas Math 2nd Grade 12th Chapter Solve Length Problems Answer Key during your practice sessions. Make the most out of them and score better grades in your exams. Students can access whichever topic they feel like preparing by click on the quick links listed below. You will be directed to the chosen link.

Vocabulary

• Solve Length Problems Vocabulary

Lesson: 1 Use a Number Line to Add and Subtract Lengths

• Lesson 12.1 Use a Number Line to Add and Subtract Lengths
• Use a Number Line to Add and Subtract Lengths Homework & Practice 12.1

Lesson: 2 Problem Solving: Length

• Lesson 12.2 Problem Solving: Length
• Problem Solving: Length Homework & Practice 12.2

Lesson: 3 Problem Solving: Missing Measurement

• Lesson 12.3 Problem Solving: Missing Measurement
• Problem Solving: Missing Measurement Homework & Practice 12.3

Lesson: 4 Practice Measurement Problems

• Lesson 12.4 Practice Measurement Problems
• Practice Measurement Problems Homework & Practice 12.4

Chapter: 12 – Solve Length Problems

• Solve Length Problems Performance Task
• Solve Length Problems Activity
• Solve Length Problems Chapter Practice
• Solve Length Problems Cumulative Practice

Solve Length Problems Vocabulary

Organize It
Use the review words to complete the graphic organizer.

Answer :

Explanation :
Bar model can be defined as a pictorial representation of a number in the form of bars or boxes used to solve number problems.

Define It
Match the review word to its model.

Answer :

Lesson 12.1 Use a Number Line to Add and Subtract Lengths

Explore and Grow

Your goldfish is 4 centimetres long. It grows 6 more centimetres. Use the number line and your ruler to show how long the goldfish is now.

Answer :
Length of the gold fish = 4 centimetres
Increased length of gold fish = 6 centimetres
Length of gold fish now = 4 + 6 = 10 centimetres  .

Explanation:
Draw an arrow from 0 to 4 to represent 4. Then draw an arrow 6 units to the right representing adding +6.
So, 4 + 6 =0

What is the same about your ruler and the number line? What is different?
_________________________
_________________________
_________________________
_________________________
Answer:
A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
Ruler a straight strip, typically marked at regular intervals and used to draw straight lines or measure distances.

Show and Grow

Question 1.
You swim 15 meters and take a break. Then you swim 10 meters. How many meters do you swim?

Answer:
Distance covered while swimming = 15 meters
Distance covered while swimming after break = 10 metresters .
Therefore, 25 meters traveled in swimming

Explanation :
Draw an arrow from 0 to 10 to represent 10. Then draw an arrow 15 units to the right representing adding +15.
So, 10 + 15 = 25

Question 2.
A ribbon is 16 yards long. You cut off 7 yards. How long is the ribbon now?

Answer:
Length of the ribbon = 16 yards
Decreased in the length of the ribbon = 7 yards
Length of the ribbon now = 16 – 7 = 9 yards .

Explanation :
Draw an arrow from 0 to 16 to represent 16. Then draw an arrow 7 units to the left representing Subtracting -7.
So, 16  – 7 = 9

Apply and Grow: Practice

Question 3.
A snake is 24 inches long. It sheds 14 inches of its skin. How much skin does it not shed?

Answer:
Length of the snake = 24
Length of snake sheds = 14
Length of the snake didn’t shed = Total Length – shed length = 24 – 14 = 10 inches

Explanation :
Draw an arrow from 0 to 24 to represent 24. Then draw an arrow 14 units to the left representing Subtracting 10
So, 24 – 14 = 10 inches .

Question 4.
A photo is 15 centimetres long. You cut off 3 centimetres from the left and 3 centimetres from the right. How long is the photo now?

Answer:
Length of the photo = 15 centimetres
Length of the photo cut from left = 3 centimetres
Length of the photo cut from right = 3 centimetres
Length of the photo now = 15 – 3 – 3 = 15 – 6 = 9 centimetres

Question 5.
Structure
Write an equation that matches the number line.

Answer:

Explanation :
Draw an arrow from 0 to 11 to represent 11. Then draw an arrow 6 units to the right representing adding 6 and draw an arrow 3 units to the left representing subtracting 3 .
So, 11 + 6 – 3 = 14 .

Think and Grow: Modeling Real Life

You want to make a bracelet that is 6 inches long. You make 4 inches before lunch. You make 2 inches after lunch. Did you finish the bracelet?

Model:

Did you finish? Yes No
Answer:
Length of the bracelet = 6 inches
Length of the bracelet made before lunch = 4 inches.
Length of the bracelet made after lunch = 2 inches.
Total Length of the bracelet made = 4 + 2 = 6 inches .
Yes , it is finished

Explanation :
Draw an arrow from 0 to 4 to represent 4. Then draw an arrow 2 units to the right representing adding 2
So, 4 + 2 = 6 inches .

Show and Grow

Question 6.
You are painting a fence that is 24 feet long. You paint 10 feet on Saturday. You paint 13 feet on Sunday. Did you finish painting the fence?

Answer:
Length of the total fencing = 24 feet
Length of the fence painted on Saturday = 10 feet
Length of the fence painted on Sunday = 13 feet
Total length of the fencing painted = 10 + 13 = 23 feet.
No painting of fencing is not finished as it is painted 23 feet . still 1 feet left to paint ( 24 – 23 = 1 feet )

Explanation :
Draw an arrow from 0 to 10 to represent 10. Then draw an arrow 13 units to the right representing adding 13
So, 10 + 13  = 23 feet .

Question 7.
DIG DEEPER!
You throw a disc 9 meters. On your second throw, the disc travels 3 meters more than your first throw. How many meters did the disc travel in all?

______ meters
Answer:
Length of the first disc thrown = 9 metres
Length of the disc travels in second throw = 3 meters more than your first throw = 9 + 3 = 12
Total length the disc travels in first and second throw = 9 + 12 = 21 meters .

Explanation :
Draw an arrow from 0 to 9 to represent 9. Then draw an arrow 12 units to the right representing adding 12
So, 9 + 12  = 21 meters .

Use a Number Line to Add and Subtract Lengths Homework & Practice 12.1

Question 1.
You kick a ball 13 yards. Your friend kicks it back 9 yards. How far is the ball from you now?

Answer:
Distance traveled by ball when i kicked the ball  = 13 yards
Distance traveled by ball when my friend kicked the ball = 9 yards back ward = -9 yards.
Distance of ball from me now = 13 yards – 9 yards = 4 yards.

Explanation :
Draw an arrow from 0 to 13 to represent 13. Then draw an arrow 9 units to the left representing Subtracting 9
So, 13- 9 = 4 yards .

Question 2.
Your shoelace is 20 inches long. Your friend’s is 4 inches longer than yours. How long is your friend’s shoelace?

Answer:
Length of my shoelace = 20 inches
Length of my friend’s shoelace = 4 inches longer than me = 4 + 20 = 24 inches.

Explanation :
Draw an arrow from 0 to 20 to represent 20. Then draw an arrow 4 units to the right representing adding 4
So, 20 + 4 = 24 inches .

Question 3.
Structure
One power cord is 7 feet long. Another power cord is 5 feet long. Use the number line to find the combined length of the power cords.

Answer:
Length of power cord = 7 feet
Length of another power cord = 5 feet
Total length of both cords = 7 + 5 = 12 feet

Explanation :
Draw an arrow from 0 to 7 to represent 7. Then draw an arrow 5 units to the right representing adding 5
So, 7 + 5  =12 feets .

Question 4.
Modeling Real Life
A worker needs to pave a bike path that is 25 feet long. He completes 13 feet on Monday and 11 feet on Tuesday. Did he complete the paving?

Answer:
Length of the bike path = 25 feet
length paved on Monday = 13 feet
Length paved on Tuesday = 11 feet
Total length paved on Monday and Tuesday = 13 + 11 = 24 feet
1 feet is less to complete the length of bike path . So, Paving is not completed .

Explanation :
Draw an arrow from 0 to 13 to represent 13. Then draw an arrow 11 units to the right representing adding 11
So, 13+ 11  = 24 feets .

Question 5.
DIG DEEPER!
You throw a baseball 5 yards. On your second throw, the baseball travels 2 yards more than your first throw. How many yards did the baseball travel in all?

_______ yards
Answer:
Distance traveled by a base ball = 5 yards
Distance traveled by a base ball in second throw = 2 yards more than your first throw = 5 + 2 = 7 yards .

Explanation :
Draw an arrow from 0 to 5 to represent 5. Then draw an arrow +2 units to the right representing adding 2
So, 5 + 2  = 7 yards .

Review & Refresh

Compare
Question 6.

Answer:
210 = 200 + 10

Question 7.

Answer:
532 = 500 + 20 + 3

Lesson 12.2 Problem Solving: Length

Explore and Grow

How much longer is the red ribbon than the blue ribbon?

______ inches
Answer:

Show and Grow

Question 1.
An orange fish is 10 centimeters long. A yellow fish is 35 centimeters long. A red fish is 19 centimeters long. How much longer is the yellow fish than the red fish?


Answer:
Length of Orange fish =  10 centimeters
Length of Yellow fish = 35 centimeters
Length of red fish  = 19 centimeters
length of yellow fish is how much longer than the red fish = 35 – 19 = 16 centimeters

Apply and Grow: Practice

Question 2.
A green scarf is 60 inches long. An orange scarf is 45 inches long. A red scarf is 36 inches long. How much longer is the green scarf than the red scarf?

______ inches
Answer:
Length of green scarf = 60 inches
Length of Orange scarf = 45 inches .
Length of Red scarf = 36 inches .
Length of green scarf is how much longer than red scarf = 60 – 36 = 24 inches .

Question 3.
DIG DEEPER!
A pink ribbon is 90 centimeters long. A purple ribbon is 35 centimeters long. A blue ribbon is46 centimeters long. How much longer is the pink ribbon than the total length of the purple and blue ribbons?

_______ centimeters
Answer:
Length of pink ribbon = 90 centimeters
Length of purple ribbon = 35 centimeters
Length of blue ribbon = 46 centimeters
The total length of the purple and blue ribbons = 35 + 46 = 81  centimeters.
Length of pink ribbon is how much longer than the total length of the purple and blue ribbons = 90 – 81 = 9 centimeters

Question 4.
Structure
How much taller is Student 3 than the shortest student?

________ inches
Answer:
Taller student is student 3 = 53 inches .
Shorter student is student 2 = 48 inches .
Taller Student is how much taller than shorter student = 53 – 48 = 5 inches .

Think and Grow: Modeling Real Life

You hop 27 inches and then 24 inches. Your friend hops 3 inches less than you. How far does your friend hop?
Think: What do you know? What do you need to find?
Model:
_______ inches
Answer:
Length hoped by me is 27 and 24 inches = 27 + 24 = 51 inches
Length hoped by my friend = 3 inches less than me = 51 – 3 = 48 inches .

Show and Grow

Question 5.
You throw a ball 36 feet and then 41 feet. Your friend throws a ball 5 feet farther than you. How far does your friend throw the ball?

______ feet
Answer:
Distance traveled by ball in first throw = 36 feet
Distance traveled by ball in Second throw = 41 feet
Total Distance traveled by balls = 36 + 41 = 77 feet
Distance traveled by ball when my friend throws = 5 feet farther than me = 77 + 5 = 82 feet .

Question 6.
DIG DEEPER!
A black horse runs 53 meters and then 45 meters. A brown horse runs 62 meters and then 31 meters. Which horse ran the longer distance in all? How many more meters did the horse run?

Black horse Brown horse
_________ more meters
Answer:
Distance traveled by black horse is 53 meters and then 45 meters. = 53 + 45 = 98 meters
Distance traveled by Brown horse is 62 meters and then 31 meters = 62 + 31 = 93 meters
Black Horse runs longer distance than brown horse
Black horse travels 98 – 93 = 5 meters more than brown horse .

Problem Solving: Length Homework & Practice 12.2

Question 1.
The distance to the principal’s office is 24 yards. The distance to the bathroom is 15 yards. The distance to your teacher’s desk is 2 yards. How much farther away is the principal’s office than the bathroom?

_______ yards
Answer:
The distance to the principal’s office = 24 yards
The distance to the bathroom = 15 yards
The distance to your teacher’s desk = 2 yards

The principal’s office is 9 yards farther away than the bathroom .

Question 2.
YOU BE THE TEACHER
You launch a rocket 63 meters. Your friend launches it 28 meters, and your cousin launches it 86meters. Your cousin says that he launches the rocket 58 meters farther than you. Is he correct? Explain.

Answer:
Distance traveled by my rocket = 63 meters
Distance traveled by my friend rocket = 28 meters
Distance traveled by my cousin’s rocket = 86 meters
Distance differences between my rocket and my cousins rocket = 86 – 63 = 23 meters .
My Rockets is 23 meters farther than my cousin rocket not 58 meters.
So above statement is wrong .
Explanation :
Distance differences between my rocket and my cousins rocket = 86 – 63 = 23 meters .
My Rockets is 23 meters farther than my cousin rocket not 58 meters.

Question 3.
Modeling Real Life
You create a drawing that is 15 centimeters long and then add on 7 more centimeters. Your friend creates a drawing that is 3 centimeters longer than yours. How long is your friend’s drawing?

_______ centimeters
Answer:
Length of my Drawing = 15 centimeters
Length of my drawing after adding 7 centimeters = 15 + 7 = 22 centimeters
Length of my Friends drawing = 3 centimeters longer than my drawing = 22 + 3 = 25 centimeters
Therefore length of my friend’s drawing = 25 centimeters .

Question 4.
DIG DEEPER!
A frog hops 36 inches and then 22 inches. A toad hops 14 inches and then 43 inches. Which animal hopped the longer distance in all? How many more inches did the animal hop?
Frog Toad
________ more inches
Answer:
Distance hopped by frog is 36 inches and then 22 inches. = 36 + 22 = 58 inches .
Distance hopped by toad is 14 inches and then 43 inches = 14 + 43 = 57 inches .
Frog hopped more distance than toad
Difference of distance hopped by frog and toad = 58 – 57 = 1 inch .

Review & Refresh 

Question 5.
635 + 10 = ______
635 + 100 = _____
Answer:
635 + 10 = 645
635 + 100 = 735
Explanation :
The ones digit remains the same when you add ten. The tens digit increases by 1 every time you add ten
The ones digit remains the same and the tens digit remains the same when you add hundred. The hundred digit increases by 1 every time you add hundred

Question 6.
824 + _____ = 924
824 + _____ = 834
Answer:
824 + 100 = 924
824 + 10 = 834
Explanation :
The ones digit remains the same when you add ten. The tens digit increases by 1 every time you add ten
The ones digit remains the same and the tens digit remains the same when you add hundred. The hundred digit increases by 1 every time you add hundred

Question 7.
309 + _____ = 409
309 + _____ = 319
Answer:
309 + 100 = 409
309 + 10 = 319
Explanation :
The ones digit remains the same when you add ten. The tens digit increases by 1 every time you add ten
The ones digit remains the same and the tens digit remains the same when you add hundred. The hundred digit increases by 1 every time you add hundred

Lesson 12.3 Problem Solving: Missing Measurement

Explore and Grow

You and your friend each have a piece of yarn. The total length of both pieces is 16 centimeters. Use a ruler to measure your yarn. Then draw your friend’s yarn.

Answer:

Explain how you found the length of your friend’s yarn.
_______________________
_______________________
_______________________
Answer:
Total Length of the yarn  = 16 centimeters
Length of my yarn = 7.8 centimeters .
Length of my friend’s yarn = 16 – 7.8 =  8.2 centimeters

Show and Grow

Question 1.
A rope is 31 meters long. You cut a piece off. Now the rope is 14 meters long. How much rope did you cut off?

So, ? = ______.
______ inches
Answer:
Length of the rope = 31 meters
Length of the rope after cut off = 14 meters.
Length of the cut off rope = 31 – 14 = 17 meters .

Apply and Grow: Practice

Question 2.
A celery stalk is 20 centimeters long. You cut off the leaves. Now it is 13 centimeters long. How much did you cut off?

______ centimeters
Answer:
Length of celery stalk = 20 centimeters
Length of celery stacking after chopping the leaves = 13 centimeters .
Length of the chopped leaves = 20 – 13 = 7 centimeters .

Question 3.
Descartes walked some and then ran 39 yards. He went a total of 75 yards. How far did he walk?
______ yards
Answer:
Total Distance traveled by Descartes = 75 yards
Distance traveled by running = 39 yards
Distance Traveled by walking = 75 – 39 = 36 yards

Question 4.
Your coat zipper is 18 inches long. The zipper gets stuck at 11 inches. How much of the zipper will not zip?

_____ inches
Answer:
Length of coat zipper = 18 inches
Length of zipper got stuck = 11 inches
Length of zipper will not zip = 18 – 11 = 7 inches .

Question 5.
Number Sense
The path to school is 181 meters long in all. How long is the missing part of the path?

_______ meters
Answer:
Total path to school = 181 meters
The path from the house to first turn = 74 meters
The path from the first turn to the second turn = 86 meters.
Path from second turn to school is missing = 181 – 74 – 86 = 181 – 160 = 21 meters

Think and Grow: Modeling Real Life

You make a paper chain that is 8 feet long. You add 7 feet of chain to the end. Then 6 feet of the chain breaks off. How long is the chain now?
Think: What do you know? What do you need to find?

_____ feet
Answer:
Length of paper chain = 8 feet
Length of chain added in the end = 7 feet .
Length of chain broken = 6 feet
Total length of the chain now = 8 + 7 – 6 = 15 – 6 = 9 feet .
Explanation :

Show and Grow

Question 6.
You build a tower that is 48 centimeters tall. You add 34 centimeters to the tower height. Your tower breaks and 29 centimeters fall off. How tall is your tower now?
______ centimeters
Answer:
Height of the tower = 48 centimeters
Height added to the tower = 34 centimeters
Total Height of the tower now = 48 + 34 = 82 centimeters .
Height at which tower broken = 29 centimeters
Height of the tower after broken = 82 – 29 = 53 centimeters

Question 7.
A football team is 78 yards away from scoring. They gain 15 yards on the first play and 21 yards on the second play. How far is the team from scoring now?

_______ yards
Answer:
The distance of foot ball team from scoring = 75 yards
Distance gain in first play = 15 yards
Distance gain in second play = 21 yards.
Distance of foot ball team from scoring now = 75 – 15 – 21 = 39 yards .

Problem Solving: Missing Measurement Homework & Practice 12.3

Question 1.
A piece of fabric is 36 inches long. Another piece is 18 inches long. What is the total length of both pieces of fabric?

_____ inches
Answer:
Length of first fabric = 36 inches
Length of second fabric = 18 inches
Total length of both fabrics = 36 + 18 = 54 inches.

Question 2.
A rose is 61 centimeters long. You cut off some of the stem. Now it is 48 centimeters long. How much did you cut off?

______ Centimeters
Answer:
Length of rose = 61 centimeters
Length of rose after chopping stem = 48 centimeters .
Length of chopped stem = 61 – 48 = 13 centimeters .

Question 3.
Number Sense
Newton’s balloon is 18 inches long. Descartes’s balloon is 23 inches long. Your friend’s balloon is 12 inches long. Which sentences are true?

Newton’s balloon is 6 inches longer than your friend’s.
Your friend’s balloon is 11 inches longer than Descartes’s.
Descartes’s balloon is 5 inches longer than Newton’s.
Answer:
Statement 1 is true and Statement 3 is true
Length of Newton’s balloon =18 inches
Length of Descartes’s balloon = 23 inches .
Length of  my Friend’s balloon = 12 inches .
Explanation :
Statement 1 :
Newton balloon and my friends balloon difference in length = 18 – 12 = 6 inches.
It means Newton balloon is 6 inches longer than my friend balloon .
Statement 2 :
Descartes balloon and my friends balloon difference in length= 23 – 12 = 11 inches .
Descartes balloon is 11 inches longer than my friends balloon .
so statement is wrong .
Statement 3 :
Descartes balloon and newtons balloon difference in length = 23 – 18 = 5 inches.
Descartes balloon is 5 inches longer than newton balloon .
Statement is true .

Question 4.
DIG DEEPER!

Answer:
Equation 3 is true

Question 5.
Modeling Real Life
A piece of wood is 16 feet long. You cut off 6 feet, but it is still too long. You cut off 2 more feet. How long is the piece of wood now?

______ feet
Answer:
Length of wood = 16 feet
Length of wood chopped = 6 feet
Length of wood chopped again = 2 feet
Length of wood after chopping = 16 – 6 – 2 = 16 – 8 = 8 feet .

Review & Refresh

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Lesson 12.4 Practice Measurement Problems

Explore and Grow

Newton’s piece of string is 24 centimeters long. He gives Descartes 12 centimeters of the string. How long is the string that Newton has left? Draw a picture and write an equation to solve.

______ cm
Answer:
Length of Newton’s peice of string = 24 centimeters
Length of string given to Descartes = 12 centimeters
Length of string left over with Newton = 24 – 12 = 12 centimeters .
24 – 12 = 12 is the equation .

Compare the lengths of string. Is one longer, or are they the same length? Explain.

__________________________
__________________________
Answer:

Both the lengths are same
Newton’s length = Descarte’s length = 12 centimeters .

Show and Grow

Question 1.
Your blanket is 66 inches long. Your friend’s blanket is 9 inches longer than yours. How long is your friend’s blanket?

So, ? = ______
_____ inches
Answer:
Length of my blanket = 66 inches
Length of my friend’s blanket = 9 inches longer than yours. = 66 + 9 = 75 inches
My friends blanket is 9 inches longer than my blanket .

Apply and Grow: Practice

Question 2.
A blue whale is 31 meters long. A humpback whale is 16 meters long. How much longer is the blue whale than the humpback whale?

_____ meters
Answer:
Length of blue whale = 31 meters
Length of hump back whale = 16 meters
Differences in the length of blue whale and hump back whale = 31 – 16 = 15 meters.
Length of blue whale is 15 meters longer than hump back whale .

Question 3.
Newton runs 450 meters. Descartes runs 25 meters less than Newton. How far do they run in all?

______ meters
Answer:
Distance traveled by Newtons in running= 450 meters
Distance traveled by Descartes in running= 25 meters less than Newton = 450 – 25 = 425 meters .
Total Distance traveled by Newton and Descartes = 450 + 425 = 875 meters .

Question 4.
Reasoning
Solve the problem below two different ways.
You want to read 100 books during the school year. You read 25 books in the fall and 54 books in the winter. How many books do you still need to read?
______ books
Answer:
Total Number of books to read = 100 books
Number of books read in fall = 25 books
Number of books read in winter = 54 books
Number of books still needed to read = 100 – 25 – 54 = 100 – 79 = 21 books

Think and Grow: Modeling Real Life

A yellow subway train is 18 meters longer than a blue subway train. The yellow subway train is 92 meters long. How long is the blue subway train?

Equation:
______ meters
Answer :
Length of yellow subway tarin = 92 meters .
Length of yellow subway train = 18 meters longer than a blue subway train
Length of blue subway train = 92 – 18 = 74

Show and Grow

Question 5.
A brown rabbit hops 24 inches less than a white rabbit. The brown rabbit hops 48 inches. How many inches does the white rabbit hop?
_____ inches
Answer:
Distance traveled by brown rabbit by hopping = 24 inches less than a white rabbit
Distance traveled by brown rabbit = 48 inches .
Distance traveled by white rabbit = 48 + 24 = 72 inches

Question 6.
Your kite string is 47 yards long. You tie 6 yards of string to the end. Now your kite string is 21 yards longer than your friend’s kite string. How long is your friend’s kite string?

_______ yards
Answer:
Length of the kite  string = 47 yards
Length attached to kite in the end = 6 yards
Length of my kite string now =47 + 6 = 53 yards
Length of my kite string= 21 yards longer than your friend’s kite string
Length of my friend’s kite string = 53 – 21 = 32 yards .

Practice Measurement Problems Homework & Practice 12.4

Question 1.
A swimming pool is 28 feet long. The pool cover is 32 feet long. How much longer is the pool cover?

So, ? = ______
_____ feet
Answer:
Length of swimming pool = 28 feet
Length of pool cover = 32 feet
Difference of length in pool and pool cover = 32 – 28 = 4 feet
So, the pool cover is 4 feet longer than pool

Question 2.
Writing
Write and solve a word problem about the colored pencils.

Answer:
Which color pencil is longer and how much centimetres it is longer from shorter pencil ?
Explanation :
The length of green pencil = 8 cm
The length of red pencil = 11 cm
The length of blue pencil = 15 cm
green pencil is the shorter pencil
Blue pencil is the longer pencil
Differences in the lengths of blue and green pencils = 15 – 8 = 7 cms
The blue pencil is 7 cms longer than green pencil .

Question 3.
Modeling Real Life
You cast out your fishing line 14 yards less than your friend. Your friend casts out her line 33 yards. How many yards do you cast out your fishing line?

______ yards
Answer:
length of my friend’s fishing line = 33 yards
length of my fishing line= 14 yards less than my friend’s
Length of my fishing line= 33 – 14 = 19 yards

Question 4.
Modeling Real Life
Your nightstand is 24 inches tall. You put a 20-inch lamp on it. Now your nightstand and lamp are 19 inches taller than your bed. How tall is your bed?

______ inches
Answer:
Height of my nightstand = 24 inches
Height of the lamp = 20 inch
Height of nightstand and lamp = 24 + 20 = 42 inches.
Height of bed = nightstand and lamp are 19 inches taller than your bed.
Height of bed = 42 – 19 = 23 inches .

Review & Refresh

Question 5.
Write the number in expanded form and word form.
645
______ + ____ + ______ _________
Answer:
645 = 600 + 40 + 5
Explanation :
Six hundred and forty five represents six hundreds plus four tens and five ones
When numbers are separated into individual place values and decimal places is called expanded form

Question 6.
Write the number in standard form and word form.
800 + 60 + 2
_____ _______________________
Answer:
862
Explanation:
eight hundred and sixty two = 8 hundreds plus 6 tens and 2ones .
When numbers are separated into individual place values and decimal places is called expanded form

Solve Length Problems Performance Task

Question 1.
A recorder is 1 foot long. A clarinet is 24 inches long. Which instrument is longer? How much longer is the instrument?


Recorder Clarinet
_____ inches
Answer:
Length of the Recorder = 1 foot = 12 inches
Length of the clarinet = 24 inches
Clarinet is longer
Difference in the length of clarinet and Recorder = 24 – 12 = 12 inches .
Clarinet is 12 inches longer than Recorder .

Question 2.
A piano has 27 more keys than a keyboard. There are 52 white keys and 36 black keys on a piano.
a. How many keys are on the keyboard?

_____ keys
Answer :
Number of white keys on piano = 52
Number of black keys on piano = 36
Total Number of keys on piano = 52 + 36 = 88 keys
piano has 27 more keys than a keyboard
Number of keys on key board = 88 – 27 = 61 keys .

b. The number of black keys on the piano is equal to the number of white keys on the keyboard. How many black keys are on the keyboard?
______ black keys
Answer:
Number of black keys on piano = 36 = number of white keys on keyboard
Number of black keys on keyboard = 61 – 36 = 25 keys .

Question 3.
A drum set has drums and cymbals on stands.
a. The cymbals are 77 centimeters from the ground. You raise the stand 18 centimeters. The cymbals are now 23 centimeters higher than one of the drums. What is the height of the drum?

_______ centimeters
Answer :
Length of cymbals from ground = 77 centimeters .
Length of the stand = 18 centimeters .
Length of cymbals now = 77 + 18 = 95 centimeters
cymbals are now 23 centimeters higher than one of the drums.
Height of the drums = 95 – 23 =72 centimeters .

b. Another drum is 60 centimeters from the ground. You raise it 12 centimeters. Are both drums the same height?
Yes No
Answer:
Height of the drum = 60 centimeters
Height of the drum raised = 12 centimeters.
Height of the drum now = 60 + 12 = 72 centimeters .
Both the drums are at equal heights of 72 centimeters
Yes, both drums have the same height .

Solve Length Problems Activity

Draw and Cover
To Play: Players take turns. On your turn, pick a Draw and Cover Card and solve. Then cover the sea turtle that has the answer. Continue playing until all sea turtles are covered.

Solve Length Problems Chapter Practice

12.1 Use a Number Line to Add and Subtract Lengths

Question 1.
You throw a ball 12 yards. Your friend throws it back 8 yards. How far is the ball from you now?

Answer:
Distance traveled by ball when thrown by me= 12 yards
Distance traveled by my friend after throwing = – 8 yards. ( – represents back direction )
Distance of ball far from me  = 12 – 8 = 4 yards.

Explanation:
Draw an arrow from 0 to 12 to represent 12. Then draw an arrow 4 units to the left representing subtracting 4.
So, 12 – 8 = 4 yards .

12.2 Problem Solving: Length

Question 2.
Your cat’s first collar was 6 inches long. Now your cat has a collar that is 13 inches long. Your puppy’s collar is 11 inches long. How much longer is your cat’s collar now?

Answer:
Length of cat first collar = 6 inches
Length of cat collar now  = 13 inches .
Difference in cat collar now and first collar = 13 – 6 = 7 inches
Cat collar is 7 inches longer than first collar

12.3 Problem Solving: Missing Measurement

Question 3.
You must be 54 inches tall to ride a roller coaster. At 8 years old, you were 48 inches tall. You grow 3 inches the next year. How much more do you still need to grow to be able to ride the roller coaster?

______ inches
Answer:
Required Height to ride a aroller coaster = 54
My Height at the age of 8 yaers = 48 inches.
Next year my height = 48 + 3 = 51 inches.
Height required more for me to ride a roller coaster = 51 – 48 = 3 inches

Question 4.
Number Sense
A car tire is 61 centimeters tall. A truck tire is 84 centimeters tall. A monster truck tire is167 centimeters tall. Which sentences are true?
The car tire is 23 centimeters taller than the truck tire.
The truck tire is 83 centimeters shorter than the monster truck tire.
The monster truck tire is 106 centimeters taller than the car tire.

Answer:
Statements 2 and 3 are true .
Length of car tire = 61 centimeters
Length of truck tire = 84 centimeters
Length of monster truck = 167 centimeters
Explanation:
Statement 1:
Car tire and truck tire difference in lengths = 84 – 61 = 23 centimeters
Truck tire is 23 centimeters  longer than car tire
Statement is false
Statement 2 :
Truck tire and monster tire lengths differences = 167 – 84 = 83 centimeters
The truck tire is 83 centimeters shorter than the monster truck tire.
Statement is true .
Statement 3 :
Monster truck and car tire lengths differences = 167 – 61 = 106 centimeters
The monster truck tire is 106 centimeters taller than the car tire.
Statement is true .

12.4 Practice Measurement Problems

Question 5.
A kangaroo jumps 24 feet. A frog jumps 19 feet less than the kangaroo. How far does the frog jump?

______ feet
Answer:
Height of kangaroo jump = 24 feet
Height of frog jump = 19 feet less than the kangaroo. = 24 – 19 = 5 feet

Question 6.
A store owner wants to add on to the parking lot to make it 38 meters long. It is currently 21 meters long. How many meters does the store owner want to add?
_____ meters
Answer:
Length of parking after adding parking = 38 meters
Current length = 21 meters
Increase in the length = 38 – 21 = 17 meters .

Solve Length Problems Cumulative Practice

Question 1.
Which expressions have a sum less than 12?

Answer:
Expressions : 5 + 3 , 1 +0 and 4 +6
Explanation :
5 + 3 = 8
4 + 6 = 10
1 + 0 = 1
7 + 8 = 15

Question 2.
Find each difference.

Answer:

Question 3.
A blue sailboat is 44 feet long. A white sailboat is 36 feet long. A green sailboat is 22 feet long. Which sentences are true?

Answer:
Statement 2 and 3 are true .
Length of blue sail boat = 44 feet
Length of white sail boat = 36 feet
Length of green sail boat = 22 feet
Explanation:
Statement 1 :
Difference of blue and green sail boat = 44 – 22 = 22 feet
The blue sail boat is 22 feet longer than green boat .
Statement 1 is wrong .
Statement 2 :
Difference of white and green sail boat = 36 – 22 = 14 feet.
The green sail boat is 14 feet shorter than white sail boat .
Statement 2 is true .
Statement 3 :
Difference of blue and green sail boat = 44 – 22 = 22 feet
The green sail boat is 22 feet shorter than blue boat .
Statement 3 is true .
Statement 4 :
Difference of blue and white sail boat = 44 – 36 = 8 feet
The blue sail boat is 8 feet longer than white sail boat .
Statement 4 is wrong .

Question 4.
What is the value of the underlined digit?
739

Answer:
3 tens

Question 5.
Use mental math to solve.
403 – 10 = ______
898 – 100 = _____
640 – 10 = ______
204 – 10 = ______
843 – _____ = 833
_______ – 100 = 731
Answer:
403 – 10 = 393
898 – 100 = 798
640 – 10 = 630
204 – 10 = 194
843 – 10 = 833
831- 100 = 731

Question 6.
The cracker is about 2 inches long. What is the best estimate of the length of the cracker box?

Answer:
Length of cracker = 2 inches
The best estimate of the length of the cracker box = 3 inches

Question 7.
You take 14 pictures on Friday. You take 20 more on Saturday. Your friend takes 34 pictures in all on Friday and Saturday. How many pictures did you and your friend take in all?

Answer:
Number of pictures taken on Friday by me= 14 pictures
Number of pictures taken on Saturday by me= 20 more on Saturday = 20 pictures
Number of pictures taken by friend on Friday and Saturday = 34 pictures
Total Number of pictures taken by me and my friend = 14 + 20 + 34 = 68 pictures

Question 8.
Which expressions are equal to 245 + 386?

Answer:
245 + 386 = 631
Expression  are 631 and 200 + 300 + 40 + 80+ 5 + 6
Explanation :
631
500 + 130 + 11 = 630 + 11 = 641
200 + 300 + 40 + 80+ 5 + 6 = 500+120+11 = 620 +11 = 631
500 + 120 + 5 = 625

Question 9.
Newton runs 7 yards, takes a break, and runs 3 more yards. Which number line shows how many yards Newton runs?

Answer:
Distance traveled by Newton =7 yards
Distance traveled by newton after break = 3 yards
Total Distance Traveled by Newton = 7 + 3 = 10 yards
Picture 4 represents correct .

Explanation :
in picture 4 the distance traveled by newton will be shown where the arrow ends at 10 .

Question 10
Find the sum.

Answer:

Question 11.
Find each difference.
80 – 53 = ?
79 – 13 = ?
90 – 32 = ?
64 – 40 = ?
Answer:
80 – 53 = 27
79 – 13 = 66
90 – 32 = 58
64 – 40 = 24

Question 12.
Complete the sentences using centimeters or meters.
A teacher’s desk is about 2 ________ long.
A paper clip is about 8 ________ long.
A carrot is about 12 _________ long.
A boat is about 20 _______ long.
Answer:
A teacher’s desk is about 2 meters long.
A paper clip is about 8 centimeters long.
A carrot is about 12 centimeters long.
A boat is about 20 meters long.

Final Words:

We wish that the data mentioned here about Big Ideas Math Answers Grade 2 Chapter 12 Solve Length Problems are helpful for the students. You can complete the homework and assignments easily by downloading Big Ideas Math Book Grade 2 Chapter 12 Solve Length Problems Answer Key PDF. If you have any doubts, then please leave a comment below. Bookmark our site to get the solutions for other chapters of grade 2.

The download pdf link of Big Ideas Math Grade 1 Answer Key Chapter 3 More Addition and Subtraction Situations is available on this page. This pdf includes the fundamentals of addition and subtraction in multiple methods. Thus, the students who want to improve their math skills must solve the questions given in the Big Ideas Math Answers Grade 1 Ch 3 More Addition and Subtraction Situations.

Big Ideas Math Book 1st Grade Answer Key Chapter 3 More Addition and Subtraction Situations

As per the student’s understanding level, only these Big Ideas Math Answers Grade 1 Chapter 3 More Addition and Subtraction Situations are designed and helping them to learn all primary mathematical concepts in a simple way. Learn the basic concepts of addition and subtraction from our Big Ideas Math Book 1st Grade Answers Chapter 3 More Addition and Subtraction Situations. Check out the topics covered in this chapter from the below section.

• More Addition and Subtraction Situations Vocabulary

Lesson 1: Solve Add To Problems with Start Unknown

• Lesson 3.1 Solve Add To Problems with Start Unknown
• Solve Add To Problems with Start Unknown Practice 3.1

Lesson 2: Solve Take From Problems with Change Unknown

• Lesson 3.2 Solve Take From Problems with Change Unknown
• Solve Take From Problems with Change Unknown Practice 3.2

Lesson 3: Solve Take From Problems with Start Unknown

• Lesson 3.3 Solve Take From Problems with Start Unknown
• Solve Take From Problems with Start Unknown Practice 3.3

Lesson 4: Compare Problems: Bigger Unknown

• Lesson 3.4 Compare Problems: Bigger Unknown
• Compare Problems: Bigger Unknown Practice 3.4

Lesson 5: Compare Problems: Smaller Unknown

• Lesson 3.5 Compare Problems: Smaller Unknown
• Compare Problems: Smaller Unknown Practice 3.5

Lesson 6: True or False Equations

• Lesson 3.6 True or False Equations
• True or False Equations Practice 3.6

Lesson 7: Find Numbers That Make 10

• Lesson 3.7 Find Numbers That Make 10
• Find Numbers That Make 10 Practice 3.7

Lesson 8: Fact Families

• Lesson 3.8 Fact Families
• Fact Families Practice 3.8

Performance Task

• More Addition and Subtraction Situations Performance Task
• More Addition and Subtraction Situations Chapter Practice
• More Addition and Subtraction Situations Cumulative Practice 1 – 3

More Addition and Subtraction Situations Vocabulary

Organize It

Review Words:
count on
number line

Use the review words to complete the graphic organizer.

Answer:

Define It

Use your vocabulary cards to identify the words.

Answer:

Lesson 3.1 Solve Add To Problems with Start Unknown

Explore and Grow

Use counters to model each problem.

Answer:

Explaination:
Given Sum is 5 and a addend of 2. So, to get the sum 5 we need to count 3 more from 2.
2 + 3 = 5.

Answer:

Explaination:
Given 5 as sum and an addend 2. To get the sum 5 we need to count 3 more from 2.
3 + 2 = 5

Show and Grow

Question 1.

_______ + 5 = 8
Answer:
3 + 5 = 8

Explaination:
Given: 8 as sum and an addend 5. To get the sum 8 we need to add 3 more to 5.
3 + 5 = 8

Question 2.

_______ + 2 = 8
Answer:
1 + 2 = 3

Explaination:
Given: 3 as sum and an addend 2. To get the sum 3 we need to add 1 more to 2.
1 + 2 = 3

Apply and Grow: practice

Question 3.

_________ + 3 = 7
Answer:

Explaination:
Given: 7 as sum and an addend 3. To get the sum 7 we need to add 4 more to 3.
4 + 3 = 7

Question 4.

_______ + 8 = 10
Answer:

Explaination:
Given: 10 as sum and an addend 8.  We need to add 2 more to 8 to get 10 as sum.
2 + 8 = 10.

Question 5.
_______ + 4 = 9
Answer:
5 + 4 = 9
Explaination:
Given: 9 as sum and an addend 4. To get the sum 9 we need to add 5 more to 4.
5 + 4 = 9

Question 6.
_________ + 0 = 5
Answer:
5 + 0 = 5
Explaination:

Adding 0 to any number gives the sum as the number itself.
Given: 5 as sum and an addend 0.
so we add 5 to get the sum 5.

Question 7.
MP Structure
Circle the equation that matches the model.

8 + 2 = 10            2 + 6 = 8
2 + 2 = 4             4 + 6 = 10
Answer:


Explaination :
There are 2 counters in 1st  box and 6 counters in 2nd box.
Total number of boxes = 2
Add the number of boxes=
2 + 6 = 8.

Think and Grow: Modeling Real Life

There are some ladybugs. 2 more join them. Now there are 9. How many ladybugs were there to start?

Model:

Addition equation:
______ ladybugs.
Answer:

Addition equation: 7 + 2 = 9

There were 7 ladybugs at the start.
Explaination:

given

Show and Grow

Question 8.
You have some books. You get 4 more books. Now you have 10. How many books did you have to start?

Model:

Addition equation:

_________ books
Answer:

Addition equation: 6 + 4 = 10

I have to start with 6 books.

Solve Add To Problems with Start Unknown Practice 3.1

Question 1.

________ + 5 = 10
Answer:

5 + 5 = 10

Question 2.

_________ + 1 = 4
Answer:

3 + 1 = 4

Question 3.
_________ + 2 = 7
Answer:
5 + 2 = 7

Question 4.
_________ + 3 = 9
Answer:
6 + 3 = 9

Question 5.
MP Structure
Circle the equations that match the model.

6 + 1 = 7                      4 + 2 = 6
3 + 4 = 7                      1 + 5 = 6
Answer:

Question 6.
Modeling Real Life
There are some hippos. 6 more join them. Now there are 9. How many hippos were there to start?

___________ hippos
Answer:
Total number of hippos = 9
Number of hippos joined = 6
Number of hippos at the start are 3

Review & Refresh

Question 7.
There are 8 on a free.
5 fall off.
How many are left?

________ – ________ = _________
Answer:
Number of leaf on the trees = 8
Number of fallen leafs = 5
Total number of leafs left on the tree=
8 – 5 = 3 leafs left.

Question 8.
You have 3 .
You lose 1 .
How many im – 19 do you have left?
________ – ________ = _________
Answer:
Number of balls i have = 3
Number of balls i lose = 1
Total number of left with me =
3 – 1 = 2 balls left.

Lesson 3.2 Solve Take From Problems with Change Unknown

Explore and Grow

Use counters to model each problem.

Answer:

Answer:

Show and Grow

Question 1.

7 – _____ = 2
Answer:

7 – 5 = 2

Question 2.

5 – ______ = .3
Answer:

5 – 2 = 3

Apply and Grow: Practice

Question 3.

8 – ______ = 2
Answer:

8 – 6 = 2

Question 4.

9 – ______ = 6
Answer:

9 – 3 = 6

Question 5.
3 – _______ = 0
Answer:
3 – 3 = 0

Question 6.
10 – ________ = 5
Answer:
10 – 5 = 5

Question 7.
MP Repeated Reasoning
Match each model with its correct equation.
Answer:

Answer:

Think and Grow: Modeling Real Life

You have 9 coins. You toss some of them into a fountain. You have 5 left. How many coins did you toss?

Model:

Subtraction equation

________ coins.
Answer:
Total number of coins i have = 9 coins
Number of coins left with me = 5 coins
Number of coins i tossed in fountain = 9 – 5 = 4 coins

Show and Grow

Question 8.
You have 8 crayons. You lose some of them. You have 2 left. How many crayons did you lose?

Model:

Subtraction equation:

__________ crayons
Answer:
Total number of crayons = 8
Number of crayons left after loosing = 2
Number of crayons left = 8 – 2 = 6

Solve Take From Problems with Change Unknown Practice 3.2

Question 1.
8 – ? = 4
8 – ______ = 4
Answer:

Question 2.
7 – ? = 3

7 – ______ = 3
Answer:

Question 3.
5 – _______ = 4
Answer:
5 – 1 = 4

Question 4.
6 – ______ = 6
Answer:
6 – 0 = 6

Question 5.
MP Repeated Reasoning
Match each model with its correct equation.

Answer:

Question 6.
Modeling Real Life
You have 10 toys. Your friend borrows some of them. You have 7 left. How many toys did your friend borrow?

________ toys
Answer:

Total number of toys = 10
Number of toys left after borrowing = 7
Number of toys my friend borrowed = 10 – 7 = 3 toys.

Review & Refresh

Question 7.
You have 6
You buy 3 more .
How many do you have now?
_______ + _______ = ______
Answer:
Number of banana’s i have = 6
Number of banana’s bought = 3
Total number of banana’s= 6 + 3 = 9 banana’s.

Question 8.
You have .
You buy 1 more .
How many do you have now?
_______ + _______ = ______
Answer:
number of bat i have =1
number of more bat i bought = 1
total number of bat i have = 1 + 1 = 2 bats.

Lesson 3.3 Solve Take From Problems with Start Unknown

Explore and Grow

Use counters to model each problem.

3 + 4 = _______

_____ – 3 = 4

Answer:

3 + 4 = 7
7 – 3 = 4

Show and Grow

Question 1.
? – 2 = 4

Think 2 + 4 = _______.
So, ______ – 2 = 4
Answer:

Think 2 + 4 = 6.
So, 6 – 2 = 4

Question 2.
? – 1 = 1

Think 1 + 1 = _______.
So, ______ – 1 = 1
Answer:

Think 1 + 1 = 2.
So, 2 – 1 = 1.

Apply and Grow: Practice

Question 3.
? – 2 = 5

Think 2 + 5 = _______.
So, ______ – 2 = 5
Answer:

Think 2 + 5 = 7.
So, 7 – 2 = 5

Question 4.
? – 3 = 6

Think 3 + 6 = _______.
So, ______ – 3 = 6.
Answer:

Think 3 + 6 = 9.
So, 9 – 3 = 6.

Question 5.
? – 4 = 1
Think 4 + 1 = _______.
So, ______ – 4 = 1.
Answer:
Think 4 + 1 = 5.
So, 5 – 4 = 1.

Question 6.
? – 6 = 4
Think 6 + 4 = _______.
So, ______ – 6 = 4.
Answer:
Think 6 + 4 = 10.
So, 10 – 6 = 4.

Question 7.
MP Structure
Circle the equations that match the model.

8 – 2 = 6                  8 + 2 = 10
6 – 2 = 4                  2 + 6 = 8
Answer:

Think and Grow: Modeling Real Life

A group of students are at a playground. 2 of them leave. There are 8 left. How many students were there to start?

Model:

Subtraction equation:

__________ students
Answer:

Number of students leave = 2
Number of students remaining = 8
Total number of students = 8 + 2 = 10 students.
subtraction equation: 10 – 2 = 8.

Show and Grow

Question 8.
You have some strawberries. You eat 9 of them. You have 0 left. How many strawberries did you have to start?

Model:

Subtraction equation:

_________ strawberries
Answer:

Number of strawberries i ate = 9
Number of strawberries left after eating = 0
Total number of strawberries i had at the start = 9 + 0 = 9 strawberries.
Subtraction equation: 9 – 9 = 0.

Solve Take From Problems with Start Unknown Practice 3.3

Question 1.
? – 7 = 2

Think 7 + 2 = _______.
So, ______ – 7 = 2.
Answer:

Think 7 + 2 = 9.
So, 9 – 7 = 2.

Question 2.
? – 2 = 8

Think 2 + 8 = _______.
So, ______ – 2 = 8.
Answer:

Think 2 + 8 = 10.
So, 10 – 2 = 8.

Question 3.
? – 3 = 0
Think 3 + 0 = _______.
So, ______ – 3 = 0.
Answer:
Think 3 + 0 = 3.
So, 3 – 3 = 0.

Question 4.
? – 2 = 0
Think 2 + 6 = _______.
So, ______ – 2 = 6.
Answer:
Think 2 + 6 = 8.
So, 8 – 2 = 6.

Question 5.
MP Structure
Circle the equations that match the model.

8 – 1 = 7 9 + 1 = 10
9 – 8 = 1 8 + 1 = 9
Answer:

Question 6.
Modeling Real Life
There are some people on a trolley. 4 of them exit. There are 4 people left. How many people were on the trolley to start?

__________ people
Answer:

Number of people who exit the trolley = 4
Number of people left on trolley = 4
Total number of people on the trolley = 4 + 4 = 8

Review & Refresh

Question 7.
There are 5 blue balloons and 3 red balloons. How many more blue balloons are there?

________ – _________ = ________ more blue balloons
Answer:
Given
Blue Balloons = 5
Red Balloons = 3
5 – 3 = 2 more blue balloons are there.

Lesson 3.4 Compare Problems: Bigger Unknown

Explore and Grow

Use counters to model the story.

Newton has 5 balls. Descartes has 2 more balls than Newton. How many balls does Descartes have?

Answer:
Number of balls with newton = 5
Number of balls with Descartes = 5 + 2 = 7.

Show and Grow

Question 1.
Your friend has 7 trading cards. You have 3 more than your friend. How many trading cards do you have?

7 + _______ = _______ trading cards
Answer:

7 + 3 = 10 trading cards.

Apply and Grow: Practice

Question 2.
Your friend has I soccer ball. You have 2 more than your friend. How many soccer balls do you have?


1 + _______ = _______ soccer balls
Answer:

1 + 2 = 3 soccer balls

Question 3.
Your friend swims 4 more laps than you. You swim 3 laps. How many laps does your friend swim?


_______ + _______ = _______ laps
Answer:

Question 4.
MP Precision
Your friend catches 5 more fish than you. You catch 2 fish. How many fish does your friend catch? Circle the bar model that matches the problem.

Answer:

Think and Grow: Modeling Real Life

Your friend has 1 yellow flower and 2 red flowers. You have 3 more flowers than your friend. How many flowers do you have?

Model:

Addition equation:

________ flowers
Answer:
Model:

Addition equation: 3 + 3 = 6 flowers.

Show and Grow

Question 5.
Your friend has 6 gray shirts and 2 blue shirts. You have 2 more shirts than your friend. How many shirts do you have?

Model:

Addition equation:

_________ shirts
Answer:

Addition equation: 8 + 2 = 10 shirts

Compare Problems: Bigger Unknown Practice 3.4

Question 1.
You have 3 key chains. Your friend has 5 more than you. How many key chains does your friend have?

3 + ______ = ______ key chains
Answer:

3 + 5 = 8 key chains

Question 2.
You have 8 more bracelets than your friend. Your friend has 2 bracelets. How many bracelets do you have?


_______ + ______ = ______ bracelets
Answer:

2 + 8 = 10 bracelets.

Question 3.
MP Precision
You have 1 seashell. Your friend has 8 more than you. How many seashells does your friend have? Circle the bar model that matches the problem.

Answer:

Question 4.
Modeling Real Life
Your friend has 2 comic books and 2 mystery books. You have 3 more books than your friend. How many books do you have?

_________ books
Answer:

4 + 3 = 7 books.

Review & Refresh

Question 5.
There are 2 blue crayons and 6 red crayons. How many fewer blue crayons are there?

_______ – ______ = _______ fewer blue crayons
Answer:
Number of red crayons = 6
Number of blue crayons = 2
Number of fewer blue crayons = 6 – 2 = 4 blue crayons.

Lesson 3.5 Compare Problems: Smaller Unknown

Explore and Grow

Use counters to model the story.

Newton has 5 treats. Descartes has 2 fewer treats than Newton. How many treats does Descartes have?

Answer:
Number of treats with newton = 5
Number of treats with Descartes = 5 – 2 = 3.

Show and Grow

Question 1.
Your friend has 8 stones. You have I fewer than your friend. How many stones do you have?


_______ – _______ = ________ stones
_______ + _______ = ________ stones
Answer:

8 – 1 = 7 stones
7 + 1 = 8 stones

Apply and Grow Practice

Question 2.
You blow 5 bubbles. Your friend blows 2 fewer than you. How many bubbles does your friend blow?


_______ – _______ = ________ bubbles
_______ + _______ = ________ bubbles
Answer:

5 – 2 = 3 bubbles
3 + 2 = 5 bubbles.

Question 3.
You have 3 fewer oranges than your friend. Your friend has 9 oranges. How many oranges do you have?


_______ ○ ______ = _______ oranges
Answer:

9 – 3 = 6 oranges

Question 4.
DIG DEEPER!
Complete the bar model. Do both equations match the bar model?

Answer:

Both the equations matches.

Think and Grow: Modeling Real Life

Your friend has 2 blue markers and 7 yellow I markers. You have 5 fewer markers than your friend. How many markers do you have?

Model:

Equation:

_________ markers
Answer:

Equation: 9 – 5 = 4
I have 4 markers

Show and Grow

Question 5.
Your friend has 6 tennis balls and I baseball. You have 2 fewer balls than your friend. How many balls do you have?

Model:

Equation:

_________ balls
Answer:

Equation: 7 – 2 = 5

I have 5 balls

Compare Problems: Smaller Unknown Practice 3.5

Question 1.
Your friend has 9 awards. You have 5 fewer than your friend. How many awards do you have?


______ – _____ = _____ awards
______ + _____ = _____ awards
Answer:

9 – 5 = 4 awards
4 + 5 = 9 awards

Question 2.
Your friend finds 2 fewer bugs than you. You find 4 bugs. How many bugs does your friend find?


_______ ○ ______ = _______ bugs
Answer:

4 – 2 = 2 bugs
My friend found 2 bugs.

Question 3.
MP Reasoning
Complete the bar model. Circle the equation that matches the bar model.

Answer:

Question 4.
Modeling Real Life
Your friend has 8 black cats and 2 orange cats. You have 7 fewer cats than your friend. How many cats do you have?

_______ cats
Answer:

Number of cats my friend have= 8 + 2 = 10 cats
Number of cats i have = 10 – 7 = 3

Review & Refresh

Question 5.
Write the numbers of shirts and shorts. Are the numbers equal? Circle the thumbs up for yes or the thumbs down for no.

Answer:

Lesson 3.6 True or False Equations

Explore and Grow

Color the flowers that have a sum or difference of 6.

Answer:

Show and Grow

Is the equation true or false?

Question 1.

Answer:

Question 2.

Answer:

Apply and Grow: Practice

Is the equation true or false?

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

10 – 4 = 6
6 – 0 = 6

Question 6.

Answer:

5- 2 = 3
7 – 4 = 3

Question 7.

Answer:

Question 8.

Answer:

Question 9.
MP Number Sense
Circle all of the equations that are true.

Answer:

Think and Grow: Modeling Real Life

You have 7 marbles. You lose 2 of them. Your friend has 4 marbles and finds 3 more. Do you and your friend have the same number of marbles?

Equation:

Answer:
Number of marbles I have = 7 – 2 = 5
Number of marbles my friend have = 4 + 3 = 7
Equation:

Show and Grow

Question 10.
You have I balloon. You blow up 3 more. Your friend has 5 balloons. I of your friend’s balloons pops. Do you and your friend have the same number of balloons?

Equation:

Answer:
Number of balloons i have= 1 + 3 = 4
Number of balloons my friend have = 5 – 1 = 4
Equation:

True or False Equations Practice 3.6

Is the equation true or false?

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.
MP Number Sense
Circle all of the equations that are false.

Answer:

Question 6.
Modeling Real Life
You have 5 crayons. You find 3 more. Your friend has 7 crayons and finds I more. Do you and your friend have the same number of crayons?


Answer:
Number of crayons with me = 5 + 3 = 8
Number of crayons with my friend = 7 + 1 = 8

Review & Refresh

Question 7.
Circle the triangles.

Answer:

Lesson 3.7 Find Numbers That Make 10

Explore and Grow

Place some red counters on the ten frame. Add yellow counters to fill the frame. Write an equation to match.

Answer:

Show and Grow

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Apply and Grow Practice

Question 5.

4 + _____ = 10
Answer:

Question 6.

7 + _____ = 10
Answer:

Question 7.
1 + _____ = 10
Answer:
1 + 9 = 10

Question 8.
8 + _____ = 10
Answer:
8 + 2 = 10

Question 9.
_____ + 2 = 10
Answer:
8 + 2 = 10

Question 10.
_____ + 5 = 10
Answer:
5 + 5 = 10

Question 11.
_____ + 3 = 10
Answer:
7 + 3 = 10

Question 12.
_____ + 0 = 10
Answer:
10 + 0 = 10

Question 13.
DIG DEEPER!
Match the numbers that have a sum of 10.

Answer:

Think and Grow: Modeling Real Life

There are 7 jump ropes. Your teacher buys some more. Now there are 10. How many jump ropes did your teacher buy?

Model:

Addition equation:

________ jump ropes
Answer:
Number of jump ropes= 7
Teacher bought some ropes and total = 10
Number of ropes teacher brought = 10 – 7 = 3

Addition equation: 7 + 3 = 10

3 jump ropes.

Show and Grow

Question 14.
There are 2 penguins. Some more join them. Now there are 10. How many more penguins joined them?

Model:

Addition equation:

________ penguins
Answer:
Number of penguins at present= 2
Total number of penguins = 10
Number of penguins joined = 10 – 2 = 8

Addition equation: 2 + 8 = 10

8 penguins joined.

Find Numbers That Make 10 Practice 3.7

Question 1.

8 + _______ = 10
Answer:

Question 2.

1 + _______ = 10
Answer:

Question 3.
10 + _______ = 10
Answer:
10 + 0 = 10

Question 4.
5 + _______ = 10
Answer:
5 + 5 = 10

Question 5.
_______ + 4 = 10
Answer:
6 + 4 = 10

Question 6.
_______ + 0 = 10
Answer:
10 + 0 = 10

Question 7.
DIG DEEPER!
Match the numbers that have a sum of 10.

Answer:

Question 8.
Modeling Real Life
You have 3 baseball cards. Your friend gives you some more. Now you have 10. How many baseball cards did your friend give you?

________ baseball cards
Answer:
Number of baseball cards with me= 3
Total number of baseball cards i have = 10
Number of baseball cards given by my friend = 10 -3 = 7 cards.

Review & Refresh

Find the sum. Then change the order of the addends. Write the new addition problem.

Question 9.

Answer:

Question 10.

Answer:

Lesson 3.8 Fact Families

Explore and Grow

Use linking cubes to model the equations.

Show and Grow

Question 1.
Complete the fact family.

1 + 8 = ______                          9 – ______ = ______

______ + ______ = ______            9 – ______ = ______
Answer:

1 + 8 = 9                         9 – 8 = 1

8 + 1 = 9                         9 – 1 = 8

Apply and Grow: Practice

Complete the fact family.

Question 2.

4 + 2 = ______                              6 – ______ = ______

______ + ______ = ______                6 – ______ = ______
Answer:

4 + 2 = 6                             6 – 2 = 4

2 + 4 = 6                             6 – 4 = 2

Question 3.

3 + 6 = ______                                 ______ – 6 = 3

______ + ______ = ______                   ______ – ______ = ______
Answer:

3 + 6 = 9                                9 – 6 = 3

6 + 3 = 9                                9 – 3 = 6

Question 4.
7 + 1 = ______                                   ______ – 7 = _______

______ + ______ = ______                    ______ – 1 = ______
Answer:

7 + 1 = 8                                   8 – 7 = 1

1 + 7 = 8                                   8 – 1 = 7

Question 5.
DIG DEEPER!
Cross out the equation that does not belong in the fact family.
5 + 3 = 8             5 – 3 = 2
3 + 5 = 8             8 – 5 = 3
Answer:
5 + 3 = 8
3 + 5 = 8             8 – 5 = 3

Think and Grow: Modeling Real Life

You have 3 puppets. Your friend has 7 puppets. How many fewer puppets do you have?

Model:

Equation:

________ fewer puppets
Answer:
Number of puppets i have = 3
Number of puppets my friend have = 7
Difference between puppets between me and my friend:

Equation: 7 – 3 = 4

I have 4 fewer puppets.

Show and Grow

Question 6.
There are 2 spoons and 8 forks. How many more forks are there?

Model:

Equation:

________ more forks
Answer:
Number of spoons = 2
Number of forks = 8
difference between spoons and folks:
Equation: 8 – 2 = 6

There are 6 more forks.

Fact Families Practice 3.8

Question 1.

1 + 5 = ______                          6 – ______ = _______

______ + ______ = ______            6 – ______ = ______
Answer:

1 + 5 = 6                         6 – 5 = 1

5 + 1 = 6                         6 – 1 = 5

Question 2.
3 + 7 = ______                          ______ – 7 = 3

______ + ______ = ______            ______ – _______ = ______
Answer:

3 + 7 = 10                          10 – 7 = 3

7 + 3 = 10                          10 – 3 = 7

Question 3.
Complete the fact family.
3 + 0 = ______                           ______ – 3 = _______

______ + ______ = ______             ______ – 0 = ______
Answer:

3 + 0 = 3                           3 – 3 = 0

0 + 3 = 3                           3 – 0 = 3

Question 4.
DIG DEEPER!
Cross out the equation that does not belong in the fact family.
6 + 4 = 10               10 – 6 = 4
4 + 6 = 10                6 – 4 = 2
Answer:
6 + 4 = 10               10 – 6 = 4
4 + 6 = 10

Question 5.
Modeling Real Life
There are 7 fish and 2 frogs. How many fewer frogs are there?

________ fewer frogs
Answer:
Number of fish = 7
Number of frogs = 2
Difference between frogs and fish = 7 – 2 = 5.
There are 5 fewer frogs.

Review & Refresh

Circle the objects that holds more.

Question 6.

Answer:

Question 7.

Answer:

More Addition and Subtraction Situations Performance Task

Question 1.
You and your friend bake banana bread and raisin bread. You have 8 loaves of bread. 3 of them are raisin bread. Your friend has 10 loaves of bread. 6 of them are banana bread. How many more loaves of banana bread does your friend have than you?

_______ loaf
Answer:
Total number of bread loaves i have = 8.
Number of raisin breads i have = 3.
Number of banana breads i have = 8 – 3 = 5.
Total number of bread loaves my friend have = 10.
Number of banana bread my friend have = 6.
Difference between the banana breads is : 6 – 5 = 1.
My friend have 1 more loaves of banana bread than me.

Question 2.
You give away 3 loaves of banana bread and 3 loaves of raisin bread. Your friend gives away 1 more loaf of bread than you. How many loaves of bread does your friend give away?

_______ loaves
Answer:
Number of banana bread loaves i gave away = 3
Number of raisin bread loaves i gave away = 3
Total number of bread loaves i gave away = 3 + 3 = 6.
The number of bread loaf my friend gave away is 1 more then = 6 + 1 = 7.
My friend gave away 7 loaves of bread.

Question 3.
You and your friend make boxes of muffins. Does each box have the same number of muffins?

Yes              No
Answer:
Number of muffins in the boxes i make = 3 + 7 = 10.
Number of muffins in the boxes my friend make = 5 + 4 = 9.
Difference between the muffins = 10 – 9 = 1
NO  the boxes does not have same number of muffins.

More Addition and Subtraction Situations Chapter Practice

Solve Add To Problems with Start Unknown Homework & Practice 3.1

Question 1.
? + 4 = 6

_______ + 4 = 6
Answer:

2 + 4 = 6

Question 2.
? + 2 = 8

_______ + 2 = 8
Answer:

6 + 2 = 8

Solve Take From Problems with Change Unknown Homework & Practice 3.2

Question 3.
5 – ? = 4

5 – ______ = 4
Answer:

5 – 1 = 4

Question 4.
7 – ? = 7

7 – ______ = 7
Answer:

7 – 0 = 7

Solve Take From Problems with Start Unknown Homework & Practice 3.3

Question 5.
? – 6 = 3

Think 6 + 3 = ______.
So, ______ – 6 = 3.
Answer:

Think 6 + 3 = 9.
So, 9 – 6 = 3.

Question 6.
? – 3 = 1

Think 3 + 1 = ______.
So, ______ – 3 = 1.
Answer:

Think 3 + 1 = 4.
So, 4 – 3 = 1.

Question 7.
MP Structure
Circle the equation that matches the model.

6 – 6 = 0 4 – 2 = 2 6 – 2 = 4
Answer:

Compare Problems: Bigger Unknown Homework & Practice 3.4

Question 8.
Your friend has 3 stickers. You have 4 more than your friend. How many stickers do you have?

Answer:

Compare Problems: Smaller Unknown Homework & Practice 3.5

Question 9.
Your friend has 5 stuffed animals. You have 2 fewer than your friend. How many stuffed animals do you have?

Answer:

Question 10.
Modeling Real Life Your friend has 4 dogs and 2 cots. You have I fewer pet than your friend. How many pets do you have?

Answer:

True or False Homework & Practice 3.6

Is the equation true or false?

Question 11.

Answer:

Question 12.

Answer:

Question 13.
MP Number Sense
Circle all of the equations that are true.

Answer:

Find the number That Make 10 Homework & Practice 3.7

Question 14.

3 + _______ = 10
Answer:

Question 15.

6 + _______ = 10
Answer:

Fact Families Homework & Practice 3.8

Question 16.
Complete the fact family.
8 + 1 = _______                         ________ – 8 = 1
________ + _______ = _______      _______ – _______ = ______
Answer:
8 + 1 = 9                         9 – 8 = 1
1 + 8 = 9                         9 – 1 = 8

Question 17.
Modeling Real Life
There are 2 slides and 6 swings on a playground. How many more swings are there?

__________ more swings
Answer:
Number of slides = 2
Number of swings = 6
Number of more swings = 6 – 2 = 4 more swings.

More Addition and Subtraction Situations Cumulative Practice 1 – 3

Question 1.
Shade the circle next to the answer.
4 + 4 = ______
○ 4
○ 6
○ 9
○ 8
Answer:

Question 2.
Shade the circle next to the addition equation that you can use to solve 8 – 3.
○ 8 + 3 = 11
○ 3 + 5 = 8
○ 1 + 8 = 9
○ 5 + 2 = 7
Answer:

Question 3.
Circle the equation that matches the bar model.

Answer:

Question 4.
You take 10 pictures. Your friend takes 3 pictures. Shade the circle next to the equation that shows how many more pictures you take.

○ 3 + 3 = 6
○ 10 – 3 = 7
○ 10 + 3 = 13
○ 3 – 1 = 2
Answer:

Question 5.
Shade the circle next to the number that completes the addition equation.
________ + 7 = 9

○ 1
○ 2
○ 3
○ 4
Answer:

Question 6.
There are 6 .
3 more join them.
How many are there now?
_________ + __________ = _________
Answer:
Number of = 6
Total number of = 6 + 3 = 9

Question 7.
Is each equation true or false?

Answer:

Question 8.
Use the picture to write a subtraction equation.

________ – 0 = _______
Answer:

5 – 0 = 5

Question 9.
You have 8 beads. 5 are orange. The rest are blue. Shade the circles next to the equations that describe the beads.

○ 3 + 5 = 8
○ 8 – 2 = 6
○ 4 + 4 = 8
○ 8 – 5 = 3
Answer:

Question 10.
Use the numbers shown to write two equations.

Answer:
Given   3     8     5
3 + 5 = 8      5 + 3 = 8

Question 11.
Shade the circle next to the equation that does not belong in the fact family.

○ 3 + 1 = 4
○ 4 – 3 = 1
○ 1 + 3 = 4
○ 3 – 1= 2
Answer:

Question 12.
There are 3 rabbits. 3 more join them. Shade the circle next to the equation that shows how many rabbits there are in all.

○ 3 + 2 = 5
○ 3 + 4 = 7
○ 4 + 1 = 5
○ 3 + 3 = 6
Answer:

Conclusion:

Hope you are all satisfied with the answers provided in the Bigideas Math Grade 1 Chapter 3 More Addition and Subtraction Situations. Get different methods to solve the problems in our Big Ideas Math Solution Key 1st Grade Chapter 3 More Addition & Subtraction Situations. Thus, the students who are interested to learn the basics quickly can follow the methods given here.

Hello Students!!! Are you looking for Grade 2 Chapter 6 Fluently Subtract within hundred Answers? If yes, then our guess is correct. Here we have given a detailed explanation for every concept of BIM 2nd Grade 6th Chapter Fluently Subtract within 100 Book. Students are advised to practice all the topics covered in this chapter to score good marks in the exam. Also, download Big Ideas Math Answers Grade 2 Chapter 6 Fluently Subtract within 100 Answer Key PDF for making a better preparation plan.

Big Ideas Math Book 2nd Grade Answer Key Chapter 6 Fluently Subtract within 100

This free Big Ideas Math Grade 2 Chapter 6 Fluently Subtract within 100 Solutions helps the students to complete their homework and assignments easily. Refer to Big Ideas Math Book Grade 2 Chapter 6 Fluently Subtract within 100 Answer Key to prove yourself good in the practice tests and surprise tests. After solving this chapter, the students can be able to identify subtraction patterns, show regrouping, model subtraction problems, and explain which strategy is used to find the difference of numbers.

The various topics included in this answer key are Fluently Subtract within 100 Vocabulary, Model and Regroup to Subtract, Use Models to Subtract a One-Digit Number from a Two-Digit number, Use Models to Subtract Two-Digit Numbers, Use Models to Subtract Two-Digit Numbers, Use Addition to Check Subtraction, Practice Two-Digit Subtraction, and More Problem Solving: Subtraction. The performance task included at the end will help you to check your skills. As per your convenience, we have given the links according to the topics given in the textbook. Click on the link and start your preparation.

Vocabulary

• Fluently Subtract within 100 Vocabulary

Lesson: 1 Model and Regroup to Subtract

• Lesson 6.1 Model and Regroup to Subtract
• Model and Regroup to Subtract Homework & Practice 6.1

Lesson: 2 Use Models to Subtract a One-Digit Number from a Two-Digit numbers

• Lesson 6.2 Use Models to Subtract a One-Digit Number from a Two-Digit numbers
• Use Models to Subtract a One-Digit Number from a Two-Digit numbers Homework & Practice 6.2

Lesson: 3 Use Models to Subtract Two-Digit Numbers

• Lesson 6.3 Use Models to Subtract Two-Digit Numbers
• Use Models to Subtract Two-Digit Numbers Homework & Practice 6.3

Lesson: 4 Use Models to Subtract Two-Digit Numbers

• Use Models to Subtract Two-Digit Numbers Homework & Practice 6.4

Lesson: 5 Use Addition to Check Subtraction 

• Use Addition to Check Subtraction Homework & Practice 6.5

Lesson: 6 Practice Two-Digit Subtraction

• Lesson 6.6 Practice Two-Digit Subtraction
• Practice Two-Digit Subtraction Homework & Practice 6.6

Lesson: 7 More Problem Solving: Subtraction

• Lesson 6.7 More Problem Solving: Subtraction
• More Problem Solving: Subtraction Homework & Practice 6.7

Performance Task

• Fluently Subtract within 100 Performance Task
• Fluently Subtract within 100 Activity
• Fluently Subtract within 100 Chapter Practice 6

Fluently Subtract within 100 Vocabulary

Organize It
Use the review words to complete the graphic organizer.

Answer:

Define It

Match.

Answer:

Lesson 6.1 Model and Regroup to Subtract

Explore and Grow

Model each problem. Make quick sketches to show how you found the difference.

Compare your quick sketches. What step did you use to find 21 − 6 that you did not use to find 19 − 6?

Answer:

The step in 21 − 6 that you did not use to find 19 − 6 is regrouping as 6 can be easily subtract from 9 but whereas 6 cannot be subtracted from 1 (21) so we need to regroup to subtract.

Show and Grow

Use models to subtract. Draw to show your work.

Question 1.

Answer:

Apply and Grow: Practice

Use models to subtract. Draw to show your work.

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.
Number Sense
Which numbers can you subtract from 44 without regrouping?

Answer:
3 and 4.

Think and Grow: Modeling Real Life

You have 42 craft sticks. You use 8 of them. How many craft sticks are not used?

Subtraction equation:

Answer:

Show and Grow

Question 6.
There are 74 people in a theater. 7 of them leave. How many people are left?

Answer:

People left from theater are 67.

Question 7.
DIG DEEPER!
You have 50 straws. You use some of them for a project. There are 44 left. How many straws did you use?

Answer:
Number of straws = 50.
Number of straws left = 44.
Number of used straws = 50 – 44. = 6 straws.

Model and Regroup to Subtract Homework & Practice 6.1

Use models to subtract. Draw to show your work.

Question 1.

Answer:

Question 2.

Answer:

Question 3.
YOU BE THE TEACHER
Is Newton correct? Explain.

Answer:
No, The answer is 22. after regrouping one from tens to ones . then in tens we will have 2 tens not 3 tens.

Question 4.
Modeling Real Life
You have 26 magnets. You put 9 of them on your refrigerator. How many magnets are not on the refrigerator?

Answer:
Number of magnets = 26.
Number of magnets on refrigerator = 9.
Number of magnets not on refrigerator = 26 – 9 = 15.

Question 5.
DIG DEEPER!
You have 83 cotton balls. You use some of them. There are 76 left. How many cotton balls do you use?

Answer:

Number of cotton balls = 83
Number of cotton balls left = 76.
Number of cotton balls used = 83 – 76 = 7.

Review & Refresh

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Lesson 6.2 Use Models to Subtract a One-Digit Number from a Two-Digit numbers

Explore and Grow

Make a quick sketch to find 41 − 3.

How do you regroup 4 tens and 1 one to subtract 3?
___________________________________
___________________________________
___________________________________

Answer:

We regroup one from tens to ones place then one tens will be subtracted from 4 tens so we have 3 tens remaining and in ones place we added 10 ones + 1 ones earlier .total 11 ones will be in ones place.Later we need to subtract 3 ones from 11 ones so we have 8 ones remaining after subtraction.

Show and Grow

Question 1.
31 – 4 = ?

Answer:

Question 2.
7 – 5 = ?

Answer:

Question 3.
88 – 9 = ?

Answer:

Question 4.
63 – 2 = ?

Answer:

Question 5.
90 – 8 = ?

Answer:

Question 6.
Number Sense
What one-digit numbers can you subtract from 24 without regrouping? Explain.
Answer:
The one digit which is less or equal to 4 can be used to subtract without regrouping are 1,2,3 and 4.

Think and Grow: Modeling Real Life

You catch 33 fish. You keep the state limit of 25. How many fish do you release?

Answer:

Show and Grow

Question 7.
The temperature this morning was 72 degrees. This afternoon, it is 67 degrees. How much did the temperature drop?

Answer:
Temperature in the morning= 72 degrees.
Temperature in the Afternoon= 67 degrees.
The Temperature drop= 72 – 67 =5 degrees.

Question 8.
DIG DEEPER!
You have a bowl of strawberries. You eat 7 of them. There are 19 left. How many strawberries were in the bowl to start?

Answer:
Number of strawberries left =19
Number of strawberries eaten = 7.
Total Number of strawberries = 19 + 7 = 26 strawberries.

Use Models to Subtract a One-Digit Number from a Two-Digit numbers Homework & Practice 6.2

Question 1.
\

Answer:

Question 2.

Answer:

Question 3.
YOU BE THE TEACHER
Is Descartes correct? Explain.

Answer:

Question 4.
Modeling Real Life
Descartes scores 8 more points than Newton. How many points did Newton score?

Answer:
Score of Descartes = 8 +Score of newton.
Score of Descartes = 97.
Score of newton = 97 – 8 =89.

Question 5.
DIG DEEPER!
There are some piñata toys on the ground. 6 of your friends each pick 1 up. There are17 left. How many toys were there to start?

Answer:
Total pinata toys picked by friends = 6 (6 friends picked 1 so 6 x 1 = 6 toys).
Toys left =17.
Total toys = 17 + 6 =23.

Review & Refresh

Break apart an addend to find the sum.

Question 6.

Answer:

Question 7.

Answer:

Lesson 6.3 Use Models to Subtract Two-Digit Numbers

Explore and Grow

Model the problem. Make a quick sketch to find 33 − 17.

Answer:

Show and Grow

Question 1.
55 – 18 = ?

Answer:

Question 2.
21 – 18 = ?

Answer:

Question 3.
44 – 29 = ?

Answer:

Question 4.
60 – 32 = ?

Answer:

Question 5.
75 – 21 = ?

Answer:

Question 6.
Number Sense
Use two of the numbers to write and solve a subtraction problem that requires regrouping

Answer:

Think and Grow: Modeling Real Life

You have 68 flowers. You give 17 to Newton. Then you give 14 to Descartes. How many flowers do you have left?

Subtraction problems:

Answer:

Show and Grow

Question 7.
There are 32 pretzels. You eat 11 of them. Your friend eats 12 of them. How many pretzels are left?

Answer:
Number of pretzels = 32.
Number of pretzels Eaten by me = 11.
Number of pretzels Eaten by my friend = 12.
Number of pretzels left = 32 – 11 – 12 = 9

Question 8.
Can you solve the problems on this page using addition and subtraction? Think: How do you know?

Answer:
Yes

Use Models to Subtract Two-Digit Numbers Homework & Practice 6.3

Question 1.
84 – 60 = ?

Answer:

Question 2.
40 – 15 = ?

Answer:

Question 3.
Number Sense
Which numbers can you subtract from 55 without regrouping?

Answer:
Numbers that can subtract from 55 without regrouping are 15 , 33 and 24.

Question 4.
Modeling Real Life
You and your friend have 38 cups of lemonade in all. You sell 14 cups. Your friend sells 16. How many cups are left?

Answer:
Total Number of Lemonade cups= 38.
Number of lemonade cups sold by me = 14.
Number of lemonade cups sold by my friend =16.
Number of cups left = 38 – 14 – 16 = 8.

Question 5.
Modeling Real Life
Your principal has 75 awards. She gives 25 to your class. Then she gives 34 to your friend’s class. How many awards are left?

Answer:
Number of Total Awards = 75.
Number of Awards given to my class = 25.
Number of Awards given to my friends class = 34.
Number of Awards left = 75 – 25 – 34 = 16.

Review & Refresh

Question 6.
A bookcase has 5 shelves. There are 3 plants on each shelf. How many plants are there in all?


Answer:
Each shelf has 3 plants
Total plants = 3 + 3 + 3 + 3 + 3= 15 Plants.

Use Models to Subtract Two-Digit Numbers Homework & Practice 6.4

Make quick sketches to find each difference.

31 – 3 =?

Answer:
31 – 23 = ?

How are the problems the same? How are they different?
_______________________________________
_______________________________________
_______________________________________

Answer:
The Minuend is the same for both the problems that is 31.
The Subtrahend are different for both the problems that is 3 and 23 .
Even the difference of both the problems are different that is 23 and 3 .

Show and Grow

Question 1.
52 – 19 = ?

Answer:

Question 2.
46 – 9 = ?

Answer:

Question 3.
60 – 21 = ?

Answer:

Question 4.
66 – 8 = ?

Answer:

Question 5.
84 – 2 = ?

Answer:

Question 6.
65 – 38 = ?

Answer:

Apply and Grow: Practice

Question 7.
58 – 22 = ?

Answer:

Question 8.
33 – 4 = ?

Answer:

Question 9.
22 – 15 = ?

Answer:

Question 10.
70 – 60 = ?

Answer:

Question 11.
43 – 26 = ?

Answer:

Question 12.
95 – 4 = ?

Answer:

Question 13.
Number Sense
Use the given numbers to complete the problem.

Answer:

Question 14.
DIG DEEPER!
Subtract a one-digit number from a two-digit number to complete the problem.

Answer:

Think and Grow: Modeling Real Life

You pick 19 yellow flowers and 24 purple flowers. You give 8 flowers away. How many flowers do you have left?

Step 1: Find the total number of flowers you picked.

Answer:

Step 2: Subtract the number of flowers you give away from your result in Step 1.

Answers:
8 Flowers.

Show and Grow

Question 15.
You bake 36 blueberry muffins and 36 banana nut muffins. You sell 47 muffins. How many muffins do you have left?

Answer:
Number of Blueberry muffins baked = 36.
Number of banana nut muffins baked = 36.
Total number of muffins = 36 + 36 = 72.
Number of muffins sold = 47.
Number of muffins left = 72 – 47 = 25.

Question 16.
There are 54 ladybugs. 7 fly away. Then 25 join. How many ladybugs are there now?

Answer:
Number of ladybugs = 54.
Number of bugs flew away = 7.
Number of bugs joined = 25.
Total number of bugs left = 54 – 7 + 25 =22.

Use Models to Subtract Two-Digit Numbers Homework & Practice 6.4

Question 1.
25 – 7 = ?

Answer:

Question 2.
65 – 35 = ?

Answer:

Question 3.
33 – 29 = ?

Answer:

Question 4.
80 – 53 = ?

Answer:

Question 5.
92 – 47 = ?

Answer:

Question 6.
56 – 4 = ?

Answer:

Question 7.
Writing
Write and solve a subtraction problem using 2 two-digit numbers. Write a story to match.

Answer:

From the above figure we observe that 86 is the minuend and 24 is the subtrahend.The difference is 62.
The 8 tens from minuend  have to subtract 2 tens from the subtrahend we get 6 tens in the difference . We have 6 ones in the minuend and we have to subtract 4 ones from subtrahend we get 2 ones in difference.
Therefore the difference is 6 tens and 2 ones = 62.

Question 8.
Modeling Real Life
You fill up 17 large water balloons and 24 small water balloons. You break 26 balloons. How many water balloons do you have left?

Answer:
Number of large water balloons = 17
Number of small water balloons = 24
Total number of balloons = 17 + 24 =41
Number of balloons broken = 26.
Number of balloons Remaining = 41 – 26 =15

Question 9.
Modeling Real Life
You have 45 rings. You throw 28 of them. You earn a bonus and get 15 more rings to throw. How many rings do you have now?

Answer:
Total Number of Rings = 45.
Number of rings threw = 28.
Number of Remaining Rings = 45 – 28 = 17.
Number of rings earned as Bonus = 15.
Total Number of Rings = 17 + 15 = 32.

Review & Refresh

Question 10.
How can you make a 10 to find 5 + 8?

Answer:
10 + 3

Lesson 6.5 Use Addition to Check Subtraction

Write the equation shown by each model.

How are the equations related?
__26 – ? =43____________________
__26 + 17 = ?____________________

Explain how you can check whether 24 – 13 = 11 is correct.
Answer:
Here when we add 13 + 11 we should get 24 then the answer is correct.

Show and Grow

Find the difference. Use addition to check your answer.

Question 1.

Answer:

Question 2.

Answer:

Apply and Grow: Practice

Find the Difference. Use addition to check your answer.

Question 3.
52 – 27 = ?

Answer:

Question 4.
76 – 58 = ?

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Question 9.
Reasoning
Newton uses 16 + 37 to check his answer to a subtraction problem. What two subtraction problems could he have solved?

Answer:

Think and Grow: Modeling Real Life

A joke book has 96 jokes. 58 are knock-knock jokes. The rest are riddles. How many riddles are there?

Answer:
The rest riddles are 38.

Show and Grow

Question 10.
A museum has 71 fossils. 47 are dinosaur fossils. The rest are fish fossils. How many fish fossils are there?

Answer:

Question 11.
There are 27 more countries in Europe than in North America. There are 50 countries in Europe. How many countries are there in North America?

Answer:
Countries in Europe = 50.
Countries in North America = 50 – 27 ( europe has 27 more than north america).
= 23 .

Use Addition to Check Subtraction Homework & Practice 6.5

Find the difference. Use addition to check your answer.

Question 1.
44 – 21 = ?

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.
Number Sense
Descartes subtracts to find 36 − 19. Which addition equation can he use to check his answer?

Answer:
36 -19 = 17
19 + 17 = 36

Question 7.
Modeling Real Life
A theme park has 62 rides. 45 of them are in the amusement park. The rest are in the water park. How many rides are in the water park?

Answer:
Number of rides in Theme park= 62
Number of rides in amusement park =45.
left over rides take place in water park
Number of rides in water park = 62 -45 = 17

Question 8.
Modeling Real Life
There are 58 more books in a library than in a classroom. There are 94 books in the library. How many books are in the classroom?

Answer:
Number of books in library = 94.
Number of books in class room = 94 – 58( 58 more books are there in classroom)
Number of books in class room = 36.

Review & Refresh

Use compensation to solve.

Question 9.
18 + 44 = _____

Answer:

Question 10.
63 + 27 = _____

Lesson 6.6 Practice Two-Digit Subtraction

Work with a partner. Choose different strategies to find 76 − 29.

Compare your strategy to your partner’s. Are your answers the same? Which strategy do you prefer? Why?

Answer:

I prefer Strategy – 2 as we can check the answer, which helps us to know whether the answer is correct or wrong.
Whatever the strategy may be the answer will be the same.

Show and Grow

Use any strategy to find the difference.

Question 1.
52 – 25 = _____

Answer:

Question 2.
78 – 56 = _____

Answer:

Question 3.
61 – 33 = ___

Answer:

Question 4.
83 – 37 = ___
Answer:

Question 5.
72 – 49 = __-
Answer:

Show and Grow

Question 1.
52 − 25 = __

Question 4.
83 − 37 = __

Question 5.
72 – 49 = __

Question 6.
45 – 39 = ___
Answer:

Question 7.
69 – 58 = ___
Answer:

Question 8.
94 – 45 = __
Answer:

Question 9.
86 – 48 = __
Answer:

Apply and Grow: Practice

Use any strategy to find the difference.

Question 10.
95 – 38 = __
Answer:

Question 11.
66 – 47 = ___
Answer:

Question 12.
58 – 6 = __
Answer:

Question 13.
81 – 35 = ___
Answer:

Question 14.
43 – 17 = ___
Answer:

Question 15.
37 – 8 = ___
Answer:

Question 16.
28 – 19 = ___
Answer:

Question 17.
72 – 30 = ___
Answer:

Question 18.
82 – 4 = __
Answer:

Question 19.
DIG DEEPER!
Fill in the missing digits.

Answer:

Question 20.
YOU BE THE TEACHER
Is Descartes correct? Explain

Answer:
Yes, You can verify your answer by adding 18 + 23 to get 41. if you wont 41 as your answer the sum is wrong.
18 + 23 = 41.

Think and Grow: Modeling Real Life

Is there a greater difference between the number of guests on Saturday and Sunday or on Sunday and Monday?

Answer:

Show and Grow

Question 21.
Is there a greater difference between the number of bagels sold on Sunday and Monday or on Monday and Tuesday?

Answer:

Practice Two-Digit Subtraction Homework & Practice 6.6

Use any strategy to find the difference.

Question 1.
34 – 26 = __

Answer:

Question 2.
75 – 47 = ___
Answer:

Question 3.
96 – 48 = __
Answer:

Question 4.
51 – 21 = ___
Answer:

Question 5.
23 – 16 = ___

Answer:

Question 6.
47 – 8 = ___
Answer:

Question 7.
25 – 3 = ___
Answer:

Question 8.
87 – 69 = ___
Answer:

Question 9.
48 – 29 = ___
Answer:

Question 10.
Number Sense
Find each missing number.

Answer:

Question 11.
Structure
Solve 31 − 14 two different ways.
Answer:

Question 12.
Modeling Real Life
Is there a greater difference between the number of animals adopted in December and January or in January and February?

Answer:

Review & Refresh

Question 13.

Answer:
2 + 8 =10
10 – 8 = 2

Question 14.

Answer:
5 + 6 = 11
11 – 6 = 5

Question 15.

Answer:
9 + 8 = 17
17 – 8 = 9.

Lesson 6.7 More Problem Solving: Subtraction

Explore and Grow

Model the story

Newton has 34 balloons. 18 fly away. How many balloons does Newton have left?

Answer:
Number of balloons = 34
number of balloons flew=18
Number of balloons left = 34 – 18 =16

Show and Grow

Question 1.
There are 27 more harmonicas than drums in a music room. There are 55 harmonicas. How many drums are there?

Answer:

Apply and Grow: Practice

Question 2.
There are 71 fish crackers. You eat 29 of them. Your friend eats 28. How many fish crackers are left?

Answer:
Number of Fish crackers = 71
Number of fish crackers eaten by me = 29
Number of fish crackers eaten by my friend = 28.
Number of fish crackers left = 71- 29 – 28 =14

Question 3.
Newton solves 16 more math problems than Descartes. Newton solves 34 math problems. How many math problems does Descartes solve?

Answer:
Problems solved by Newton =34.
Problem solved by Descartes = 34 – 16( as newton solves 16 problems more)
Problem solved by Descartes = 18

Question 4.
Number Sense
You have 78 tokens. Your friend gives you 14 more. You use 35 tokens. Use the given numbers to find how many tokens you have now.

Answer:

Think and Grow: Modeling Real Life

You see 20 elephants on a safari. You see 7 fewer giraffes than elephants. Then 5 of the giraffes leave the group. How many giraffes are left?

Answer:

Show and Grow

Question 5.
Your friend has 54 blocks. You have 18 fewer blocks than your friend. You use 29 blocks to make a tower. How many blocks do you have left?

Answer:
Number of Blocks with my friend = 54
Number of Blocks with me = 54 – 18 = 36
Number of blocks used by me to make a tower = 29.
Number of blocks left = 36 – 29 = 7 .

Question 6.
DIG DEEPER!
You had 19 almonds. You ate some. There are 11 left. Your friend ate 3 fewer almonds than you. How many almonds did your friend eat?

Answer:
Number of Almonds = 19.
Number of Almonds left = 11.
Number of Almonds eaten = 19 – 11 = 8.
Number of Almonds eaten by me = 8 – 3 = 5.
Number of Almonds eaten by my friend = 3.

More Problem Solving: Subtraction Homework & Practice 6.7

Question 1.
Some kids are at a trampoline park. 24 leave. There are 57 left. How many kids were there to start?

Answer:
Total Number of kids at a Trampoline park = X
Number of kids left the park = 24.
Number of kids remaining in the park = 57.
Total number of kids = 24 + 57 =81.

Question 2.
You have 62 dollars saved. You spend 37 dollars on a video game. Then you give 16 dollars to your friend. How many dollars do you have left?

Answer:
Total Number of Dollars = 62.
Number of dollars spend on video game = 37.
Number of dollars given to my friend = 16 .
Number of dollars left = 62 – 37 – 16 =9 .

Question 3.
Structure
You have 50 toothpicks. Your friend has 30 fewer toothpicks than you. Which picture shows how many toothpicks you and your friend have in all?

Answer:
Picture 2 is correct = 70 Toothpicks.
Number of tooth picks with me = 50.
Number of tooth picks with my friend = 50 – 30 = 20.
Total number of tooth picks = 50 + 20 = 70.

Question 4.
DIG DEEPER!
A museum has 12 dinosaur exhibits and some art exhibits. There are 34 exhibits in all. Then 3 more art exhibits are added. How many art exhibits are there now?

Answer:
Number of Dinosaur Exhibits = 12.
Total Number of Exhibits = 34
Number of Art Exhibits = 34 – 12 = 22
Number of Art Exhibits added = 3.
Total Number of Art Exhibits =22 + 3 = 25 .

Review & Refresh

Break apart the addends to find the sum.

Question 5.

Answer:

Question 6.

Answer:

Fluently Subtract within 100 Performance Task

Question 1.
Your class makes 53 paper snowflakes to decorate your classroom.
a. Your group makes 16 of them. How many snowflakes does the other group make?

Answer:
Total Number of paper snowflakes = 53.
Number of snow flakes made by my group =16.
Number of snowflakes made by other group = 53 – 16 = 37.

b. Your teacher hangs 49 of the snowflakes from the ceiling in an array with 7 equal rows. How many columns of snowflakes are there?

Answer:
Total Number snowflakes = 49.
Number of rows = 7.
Number of Columns = 49 ÷ 7 = 7.

c. Your teacher wants to hang one more equal row of snowflakes. Are there enough snowflakes? If so, how many extra snowflakes are there? If not, how many more snowflakes are needed?

Answer:
Number of snowflakes = 49.
One more row means 8 th row = 7 more snowflakes = 49 + 7 =56 snowflakes.
56 snowflakes are required we have only 49 snowflakes.
Therefore , more 7 snowflakes are required

Question 2.
Another class makes 75 paper snowflakes. 29 are white and some are blue. They make some more blue snowflakes. Now they have 61 blue snowflakes. How many more blue snowflakes did they make?

Answer:
Number of snowflakes = 75.
Number of white snowflakes = 29 .
Number of blue snowflakes = 75 – 29 = 46 .
Number of blue snowflakes made again = 61.
Total Number of Blue snowflakes = 61 + 46 = 107 .

Fluently Subtract within 100 Activity

To Play: Use Solve and Cover: Subtraction Cards. Place a Difference Card face up on each box. Place the stack of Problem Cards face down. Players take turns. On your turn, flip over a card from the stack. Solve the problem. Place the card on the difference. Play until all of the differences are covered.

Fluently Subtract within 100 Chapter Practice 6

6.1 Model and Regroup to Subtract

Question 1.
Use Models to Subtract. Draw to show your work.

Answer:

6.2 Use Models to Subtract a One-Digit Number from a Two-Digit Number

Question 2.
60 – 8 = ?

Answer:

Question 3.
74 – 3 = ?

Answer:

6.3 Use Models to Subtract Two-Digit Numbers

Question 4.
45 – 38 = ?

Answer:

Question 5.
74 – 27 = ?

Answer:

Question 6.
Number Sense
Use two of the numbers to write and solve a subtraction problem that requires regrouping.

Answer:
The two numbers that requires regrouping for subtraction are 63 – 45 = 18

6.4 Subtract from a Two-Digit Number

Question 7.
93 – 50 = ?

Answer:

Question 8.
57 – 28 = ?

Answer:

Question 9.
67 – 9 = ?

Answer:

6.5 Use Addition to Check Subtraction

Find the difference. Use addition to check your answer.

Question 10.
64 – 27 = ?

Answer:

Question 11.
86 – 36 = ?

Answer:

Question 12.

Answer:

Question 13.

Answer:

6.6 Practice Two-Digit Subtraction

Use any strategy to find the difference.

Question 14.
55 – 37 = ___
Answer:

Question 15.
60 – 20 = __
Answer:

Question 16.
39 – 3 = __
Answer:

6.7 More Problem Solving: Subtraction

Question 17.
Newton has some BINGO chips. He gives 25 of them away. He has 28 left. How many chips did he have to start?

Answer:

Question 18.
Number Sense
You have 35 balls. You use 18 of them. You win a bonus and get 10 more balls. Use the given numbers to find how many balls you have now.

Answer:

Question 19.
Modeling Real Life
A petting zoo has 27 sheep and some goats. There are 41 animals in all. Then 16 more goats are added. How many goats are there now?

Answer:
Total Animals = 41.
The number of sheep = 27.
A number of goat = ?
The number of goats = Total Animals – Number of sheep.
= 41 – 27 = 14
The number of goats added =16.
Total Number of goats= 14 + 16 = 30 goats.

Big Ideas Math 2nd Grade 6th Chapter Fluently Subtract within 100 Solution Key Pdf

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Big Ideas Math Answers Grade 4 Chapter 12 Use Perimeter and Area Formulas is the best source for students. Students can follow the step-by-step procedure to solve the problems. We have given a detailed explanation for every problem. Also, we included real-time examples to make the student’s preparation perfect. Get the free pdf Big Ideas Math Answers Grade 4 Chapter 12 Use Perimeter and Area Formulas to learn offline. Important notes provided for every concept where quick preparation is possible. So, immediately, begin your practice now and strengthen your knowledge.

Big Ideas 4th Grade Chapter 12 Use Perimeter and Area Formulas Math Book Answer Key

Easily improve your problem-solving skills with the help of Big Ideas Math Book 4th Grade Answer Key Chapter 12 Use Perimeter and Area Formulas. We have also included an additional practice section where you can test your knowledge and find out the difficult concepts for you. Concentrate on the difficult topics and become the expert on the complete concept. Easy learning and fast solving skills will come at the same place by using Big Ideas Math Grade 4 Chapter 12 Use Perimeter and Area Formulas Solution Key.

Lesson: 1 Perimeter Formula for a Rectangle

• Lesson 12.1 Perimeter Formula for a Rectangle
• Perimeter Formula for a Rectangle Homework & Practice 12.1

Lesson: 2 Area Formula for a Rectangle

• Lesson 12.2 Area Formula for a Rectangle
• Area Formula for a Rectangle Homework & Practice 12.2

Lesson: 3 Find Unknown Measures

• Lesson 12.3 Find Unknown Measures
• Find Unknown Measures Homework & Practice 12.3

Lesson: 4 Problem Solving: Perimeter and Area

• Lesson 12.4 Problem Solving: Perimeter and Area
• Problem Solving: Perimeter and Area Homework & Practice 12.4

Performance Task

• Use Perimeter and Area Formulas Performance Task 12
• Use Perimeter and Area Formulas Activity
• Use Perimeter and Area Formulas Chapter Practice

Lesson 12.1 Perimeter Formula for a Rectangle

Explore and Grow

Use color tiles to create a rectangle with a perimeter of 12 units. Compare your rectangle to your partner’s. How are they the same? How are they different?

How do you know that the perimeter of your rectangle is 12 units?

Answer:

The perimeter (P) of a rectangle = P=2l+2w( length=l ; width = w)

GIVEN: Perimeter of rectangle =12
P =2l + 2w
12= 2 (l + w)
12/2=l + w
6= l + w
Hence, the rectangle of my friend and mine are going to be same because perimeter given above is same for both the rectangle of us both.

The rectangle of mine is having a length of 3 units and width of 3 units.
Perimeter of my rectangle= (2 x l) + (2 x w)
P=(2 x 3) + (2 x 3)
P= 6 + 6
P= 12  units.
Here, my rectangle has 12  units perimeter. This is how I know my rectangle is having 12 units as its perimeter.

Structure
How is the perimeter of a rectangle related to its length and width?

Answer:
The perimeter (P) of a rectangle is given by the formula, P=2l+2w , where “l” is the length and “w” is the width of the rectangle.

Think and Grow: Use a Formula for Perimeter

Perimeter is the distance around a figure. A formula is an equation that uses letters and numbers to show how quantities are related. You can use a formula to show how the length, width, and perimeter of a rectangle are related.

Example
Find the perimeter of the rectangle.
The length is ___ feet and the width is __ feet.

P = (2 × l) + (2 × W) Formula for perimeter of a rectangle
= (2 × ___) + (2 × ___)
= __ + __
= ___
The perimeter is ___ feet.
ANSWER:

Given: Length of Rectangle = 24 feet
Width of Rectangle = 9 feet
FORMULA: Perimeter = (2 x l) + (2 x w)
P = (2 x 24) + (2 x 9)
P = 48 + 18
P = 66  feet.
Hence, the Perimeter of the rectangle = 66  feet.

Show and Grow

Find the perimeter of the rectangle.

Question 1.

Answer:
GIVEN: Length of rectangle = 16cm
Width of rectangle = 13 cm
Perimeter of the rectangle = (2 x l) + (2 x w)
P = ( 2 x 16) + ( 2 x 13 )
P = 32 + 26
P = 58  cm.
Hence, the perimeter of the rectangle = 58  cm.

Question 2.

Answer:
GIVEN: Length of the rectangle = 8 inches
Width of the rectangle = 4 (1/2) inches =9/2 = 4.5 inches
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2( 8 + 4.5 )
P = 2(12.5 )
P = 25 inches.
Hence, the perimeter of the rectangle = 25 inches.

Apply and Grow: Practice

Find the perimeter of the rectangle.

Question 3.

Answer:
GIVEN: Length of the rectangle = 54 yards
Width of the rectangle = 32 yards
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(54+32)
P= 2 x 86
P= 172 yards.
Hence, the perimeter of the rectangle =172 yards.

Question 4.

Answer:
GIVEN: Length of the rectangle =87 m
Width of the rectangle = 65 m
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P= 2(87+65)
P= 2 x 153
P= 306  m.
Hence, the perimeter of the rectangle = 306 m.

Question 5.

Answer:
GIVEN: Length of the rectangle = 49 inches
Width of the rectangle = 18 inches
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(49+18)
P =2 x 67
P =134 inches.
Hence, the perimeter of the rectangle = 134 inches.

Question 6.

Answer:
GIVEN: Length of the rectangle =11 cm
Width of the rectangle = 7 (3/10) cm = 73/10 cm =7.3 cm
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(11+7.3)
P = 2 x 18.3
P = 36.6  cm.
Hence, the perimeter of the rectangle = 36.6 cm.

Question 7.
You want to string lights around a rectangular room that is 12 feet long and 10 feet wide. How many feet of lights do you need?
Answer:
GIVEN: Length of the rectangle = 12 feet
Width of the rectangle = 10 feet
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(12+10)
P = 2 x 22
P = 44  feet
Hence, 44  feet of light is needed..

Question 8.
YOU BE THE TEACHER
Your friend finds the perimeter of the rectangle. Is your friend correct? Explain.

p = (2 × 13) × (2 × 5)
= 26 × 10
= 260  ft
Answer: GIVEN: Length of the rectangle = 13 feet
Width of the rectangle = 5 feet
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(13+5)
P = 2 x 18
P = 36 feet.
Hence, the perimeter of the rectangle = 36  feet.
Therefore my friend is wrong because his formula for finding perimeter of rectangle is wrong.
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)

Question 9.
DIG DEEPER!
You can use the formula for the perimeter of a rectangle to find the perimeter of the square. What other formula can you use to find the perimeter of the square?

Answer:
The perimeter of a square is the total length of the four equal sides of the square.
Perimeter of the square = 4 × s = 4 s
The perimeter of a rectangle is the total length of the two lengths and two widths of the rectangle.
If the length and width of a rectangle are l and w, then its perimeter = 2(l + w) units.
We cannot equate the perimeter of a rectangle to find the perimeter of the square because rectangle has length and width whereas square has four sides.
No, other ways are there find the perimeter of the square.

Think and Grow: Modeling Real Life

Example
In a video game, you make a rectangular castle that is 4 times longer than it is wide. What is the perimeter of the castle?

Multiply 4 and the width of the castle to find the length.
4 × 25 = ___
The length of the castle is ___ yards.

Answer:
GIVEN: Width of the rectangular castle  = 25 yards
Length of the rectangular castle = 4 times longer than it is wide =4 x 25 yards = 100 yards
Perimeter of the rectangle castle = (2 x l) + (2 x w) = 2( l + w)
P = 2 (100+25)
P = 2 x 125
P = 250  yards
Hence, Perimeter of the rectangle  castle= 250 yards.

Show and Grow

Question 10.
A teacher wants to put a border around a rectangular whiteboard. The whiteboard is 2 times longer than it is wide. What is the perimeter of the whiteboard?

Answer:
GIVEN: Width of the rectangular castle  =  1 m
Length of the rectangular castle = 2 times longer than it is wide = 2 x 1 m = 2 m
Perimeter of the rectangle castle= (2 x l) + (2 x w) = 2( l + w)
P = 2(2+1)
P = 2 x 3
P = 6 m
Hence, Perimeter of the rectangle castle = 6 m.

Question 11.
You want to put a ribbon border around each rectangular card. Which card requires more ribbon? How much more ribbon?

Answer:
GIVEN: FIRST RECTANGULAR CARD
Width of the rectangular card  =  18 cm
Length of the rectangular card =  18 cm
Perimeter of the rectangle card= (2 x l) + (2 x w) = 2( l + w)
P = 2(18+18)
P = 2 x 36
P = 72 cm.
SECOND RECTANGULAR CARD
Width of the rectangular card  =  14cm
Length of the rectangular card =  21 cm
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(21+14)
P = 2 x 35
P = 70  cm.
The FIRST RECTANGULAR CARD needs the more ribbon than SECOND RECTANGULAR CARD because FIRST RECTANGULAR CARD Perimeter = 72  cm and SECOND RECTANGULAR CARD Perimeter = 70 cm.
That means  difference in perimeter of FIRST RECTANGULAR CARD and the perimeter of SECOND RECTANGULAR CARD.
=72  cm – 70  cm
= 2  cm.

Question 12.
DIG DEEPER!
A rectangular flower bed has a length of 6 feet. The width is 48 inches shorter than the length. What is the perimeter of the flower bed?
Answer:
GIVEN:
Length of the rectangular bed = 6 feet
Width of the rectangular bed = 48 inches shorter than the length.
1 inch = 0.08333 feet
48inches = 48 x 0.0833 =  4 feet
Width of the rectangular bed =  4 feet
The perimeter of the  rectangular flower bed = (2 x l) + (2 x w) = 2( l + w)
P = 2(6+4)
P = 2 x 10
P = 20 feet.
Hence, the perimeter of the  rectangular flower bed = 20 feet.

Perimeter Formula for a Rectangle Homework & Practice 12.1

Find the perimeter of the rectangle.

Question 1.

Answer:
GIVEN: Length of the rectangle = 22 yards
Width of the rectangle = 18 yards
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(22+18)
P = 2 x 40
P = 80 yards.
Hence, the Perimeter of the rectangle = 80 yards.

Question 2.

Answer:
GIVEN: Length of the rectangle = 36 mm
Width of the rectangle = 25 mm
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(36+25)
P = 2 x 61
P =122 mm
Hence, the Perimeter of the rectangle = 122 mm.

Question 3.

Answer:
GIVEN: Length of the rectangle = 30 cm
Width of the rectangle = 14 cm
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(30+14)
P = 2 x 44
P = 88 cm
Hence, the Perimeter of the rectangle = 88 cm.

Question 4.

Answer:
GIVEN: Length of the rectangle = 12 (1/4) feet = 49/4 feet = 12.25 feet
Width of the rectangle = 8 feet
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(12.25 + 8)
P = 2 x 20.25
P = 40.5 feet
Hence, the Perimeter of the rectangle = 40.5feet.

Question 5.
Number Sense
What is the perimeter of a square tabletop with side lengths of 48 inches?
Answer:
GIVEN: Side of the square tabletop = 48 inches
Perimeter of the square = 4 x sides
P = 4 x 48
P = 192  inches.
Hence, Perimeter of the square tabletop = 192 inches.

Question 6.
Structure
Use the Distributive Property to write P = (2 × l) + (2 × w) another way.
Answer:
According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Perimeter of rectangle = (2 × l) + (2 × w)
P = 2(l + w)
Hence, According to distributive property,  the another way of the Perimeter of rectangle = 2(l + w).

Question 7.
Open-Ended
Draw a rectangle that has the same perimeter as the one shown, but different dimensions.

Answer:
GIVEN: Length of the rectangle = 50 m
Width of the rectangle = 25 m
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2( 50+25)
P = 2 x 75
P = 150 m.
MY FIGURE:

Length of the rectangle = 49m
Width of the rectangle = 26 m
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2( 49+26)
P = 2 x 75
P = 150 m.
Hence, the given rectangle Perimeter and my figure  Perimeter are the same of 150 m.

Question 8.
Modeling Real Life
A worker places tape around a rectangular shipping label that is 2 times longer than it is wide. How much tape does the worker need?

Answer:
GIVEN:
Width of the rectangle shipping label = 74 mm
Length of the rectangle shipping label = 2 times longer than it is wide =  2 x 74mm = 148mm
Perimeter of the rectangle = (2 x l) + (2 x w) = 2( l + w)
P = 2(148+74)
P = 2 x 222
P = 444  mm.
Hence, Perimeter of the rectangle shipping label = 444 mm.

Question 9.
Modeling Real Life
A coach is painting lines around the perimeter of two rectangular fields. Which field requires more paint?

Answer:
GIVEN: FIRST A COACH
Length of the rectangle field A = 100yards
Width of the rectangle field A =65 yards
Perimeter of the rectangle field A= (2 x l) + (2 x w) = 2( l + w)
P = 2( 100+65)
P =2 x 165
P = 230 yards
Length of the rectangle field B = 120yards
Width of the rectangle field B =53 1/3 yards = 160/3 = 53.3 yards
P = (2 x l) + (2 x w) = 2( l + w)
P = 2( 120+53.3)
P = 2 x 173.3
P = 346.6  yards
Hence, Perimeter of the rectangle field B is more than Perimeter of the rectangle field A
=346.6 – 230 = 116.6  yards.
Therefore, Perimeter of the rectangle field A requires more 116.6 square yards than Perimeter of the rectangle field B.

Review & Refresh

Write the first six numbers in the pattern. Then describe another feature of the pattern.

Question 10.
Rule: Subtract 11.
First number: 99
Answer:
Rule: Subtract 11.
GIVEN: First number = 99  in the pattern
Second number = 99-11= 88
Third number = 88-11= 77
Fourth number = 77-11 = 66
Fifth number = 66-11 = 55
Sixth number = 55-11 =44
Another feature of this pattern is that all the numbers are multiples of table 11.

Question 11.
Rule: Multiply by 5.
First number: 5
Answer: Rule: Multiply by 5.
GIVEN: First number = 5 in the pattern
Second number = 5 x5 =25
Third number = 25 x 5 = 125
Fourth number = 125 x 5= 625
Fifth number = 625 x 5 = 3125
Sixth number = 3125 x 5 = 15625
Another feature of this pattern is that all the numbers are multiples of table 5.

Lesson 12.2 Area Formula for a Rectangle

Explore and Grow

Use color tiles to create a rectangle with an area of 12 square units. Compare your rectangle to your partner’s. How are they the same? How are they different?

How do you know that the area of your rectangle is 12 square units?
Answer:

Hence, the rectangle of my friend and mine are going to be same because area = 12 square units given above is same for both the rectangle of us both.

Area of the rectangle =l x w , where “l” is the length and “w” is the width.
Length of the rectangle = 4units
Width of the rectangle = 3units
A = l x w
A = 4 x 3
A = 12 square units.
Hence, the Area of the rectangle = 12 square units.

Structure
How is the area of a rectangle related to its length and width?
Answer:
The area “A” of a rectangle is given by the formula, A=l x w , where “l” is the length and “w” is the width.

Think and Grow: Use a Formula for Area

Area is the amount of surface a figure covers. You can use a formula to show how the length, width, and area of a rectangle are related.

Example
Find the area of the rectangle.
The length is ___ inches and the width is ___ inches.
A = l × w Formula for area of a rectangle
= ___ × ___
= ___
The area is ___ square inches.

Answer:
GIVEN:
Length of the rectangle = 19 inches
Width of the rectangle = 14 inches
Area of the rectangle = l x w
A = 19 x 14
A = 266  square inches
Hence, the Area of the rectangle = 266  square inches.

Show and Grow

Find the area of the rectangle

Question 1.

Answer:
GIVEN:
Length of the rectangle = 6 m
Width of the rectangle = 4 m
Area of the rectangle = l x w
A = 6 x 4
A = 24 square m.
Hence, the are of the rectangle = 24 square m.

Question 2.

Answer:
GIVEN:
Length of the rectangle = 20 yards
Width of the rectangle = 12 yards
Area of the rectangle = l x w
A = 20 x 12
A = 240 square yards
Hence, the area of the rectangle = 240 square yards.

Question 3.

Answer:
GIVEN:
Length of the rectangle = 11 cm
Width of the rectangle = 7cm
Area of the rectangle = l x w
A = 11 x 7
A = 77 square cm
Hence, the area of the rectangle = 77 square cm.

Question 4.

Answer:
GIVEN:
Length of the rectangle =  5 feet
Width of the rectangle = 1 (1/2) feet = 3/2 feet = 1.5 feet
Area of the rectangle = l x w
A = 5 x 1.5
A = 7.5 square feet
Hence, the area of the rectangle = 7.5 square feet.

Apply and Grow: Practice

Find the area of the rectangle.

Question 5.

Answer:
GIVEN:
Length of the rectangle =  35 mm
Width of the rectangle = 32 mm
Area of the rectangle = l x w
A = 35 x 32
A = 1120 mm
Hence, the area of the rectangle = 1120 mm.

Question 6.

Answer:
GIVEN:
Length of the rectangle = 9 inches
Width of the rectangle = 4 (2/8) inches = 34/8 = 4.25 inches
Area of the rectangle = l x w
A = 9 x 4.25
A = 38.25 square inches
Hence, the area of the rectangle = 38.25 square inches.

Question 7.

Answer:
GIVEN:
Length of the rectangle =  8 feet
Width of the rectangle = 5 (1/2) feet =11/2 = 5.5 feet
Area of the rectangle = l x w
A = 8 x 5.5
A = 44 square feet
Hence, the area of the rectangle = 44 square feet.

Question 8.

Answer:
GIVEN:
Length of the rectangle = 79 cm
Width of the rectangle = 37 cm
Area of the rectangle = l x w
A = 79 x 37
A = 2923 square cm
Hence, the area of the rectangle = 2923 square cm.

Question 9.
You are installing wall-to-wall carpet in a rectangular bedroom that is 10 feet long and 9 feet wide. How many square feet of carpet do you need?
Answer:
GIVEN:
Length of the wall-to-wall carpet in a rectangular bedroom = 10 feet
Width of the wall-to-wall carpet in a rectangular bedroom = 9 feet
Area of the rectangle = l x w
A = 10 x 9
A = 90 square feet.
Hence, the area of the wall-to-wall carpet in a rectangular bedroom = 90 square feet
Therefore, 90 square feet of carpet is need.

Question 10.
YOU BE THE TEACHER
Newton says the area of the rectangle is 33 square meters. Descartes says the area is 33 meters. Who is correct? Explain.

Answer:
Length of the rectangle = 11 m
Width of the rectangle = 3 m
Area of the rectangle = l x w
A = 11 x 3
A = 33 square m
The area of the rectangle is 33 square meters.
Hence, Newton says correct not Descartes.

Question 11.
DIG DEEPER!
Write a formula for the area of a square that has a side length of s. Then use your formula to find the area of the square shown.

Answer:
Area of the square = 4 x sides = 4 x s
Given : side of the square = 12 yards
Area of the square = 4 x sides = 4 x s
A= 4 x 12
A = 48 square yards
Hence, the Area of the square = 48 square yards.

Think and Grow: Modeling Real Life

Example
The length of the rectangular dance floor is 6 feet longer than the width. What is the area of the dance floor?
Add 6 feet to the width to find the length.

Answer:
GIVEN: Width of rectangular dance floor = 24 feet
Length of the rectangular dance floor = 6 feet longer than the width = 24 +6 = 30 feet
Area of the  rectangular dance floor = l x w
A = 30 X 24
A = 720 square feet
Hence, the Area of the  rectangular dance floor = 720 square feet.

Show and Grow

Question 12.
A designer creates a rectangular advertisement for a website. The length of the advertisement is 1\(\frac{1}{2}\) centimeters longer than the width. What is the area of the advertisement?

Answer:
Length of the rectangular advertisement = 1\(\ frac {1}{2}\) centimeters longer than the width= 1(1 /2) cm + 7 cm = =3 / 2 cm + 7 cm = (1.5 + 7 )cm =8.5 cm
Width of the rectangular advertisement = 7 cm
Area of the  rectangular advertisement = l x w
A = 8.5 x 7
A = 59.5 cm
Hence, the Area of the  rectangular advertisement = 59.5 cm.

Question 13.
You create a mural using 4 rectangular posters that are each 4\(\frac{1}{4}\) feet long and 2 feet wide. You put the posters next to each other with no gaps or overlaps. What is the area of the mural?
Answer:
GIVEN:
Width of the rectangular posters=  2 feet
Length of the rectangular posters= 4\(\frac{1}{4}\) feet = 4 (1/4) feet = 17/4 feet = 4.25 feet
Area of the mural = l x w
A = 4.25 x 2
A =  8.5  square feet
Hence, the Area of the mural = 8.5 square feet.

Question 14.
DIG DEEPER!
Two rolls of wrapping paper have the same piece. The red roll is 3 feet wide and is 10 yards long when unrolled. The striped roll is 3\(\frac{1}{2}\) feet wide and 8 yards long when unrolled. Which roll is the better buy? Explain.
Answer:
GIVEN:
Width of Red roll =3 feet
CONVERTION : 1 YARD = 3 FEET
Width of Red roll =3 feet = 1 yard
Length of the red roll = 10 yards
Area of the red roll = l x w
A = 10 x 1
A = 10 square yards.
Area of the red roll = 10 square yards.
Width of striped roll = 3\(\frac{1}{2}\) feet = 3 1/2 feet = 3.5 feet.
CONVERTION : 1 YARD = 3 FEET
Width of striped roll = 3.5 feet
I yard = 3.5 feet
Width of striped roll = yard = 3.5 / 1 feet
Width of striped roll = 3.5 yard
Length of striped roll = 8 yards
Area of the striped roll = l x w
A = 3.5 x 8
A = 28 square yards.
Area of the striped roll = 28 square yards.
Its better to buy striped roll than red roll because u are going to get more.

Area Formula for a Rectangle Homework & Practice 12.2

Find the area of the rectangle

Question 1.

Answer:
GIVEN: Length of the rectangle = 8 m
Width of the rectangle = 7 m
Area of the rectangle = l x w
A = 8 x 7
A = 42 square m
Hence, Area of the rectangle = 42 square m.

Question 2.

Answer:
GIVEN: Length of the rectangle = 21 cm
Width of the rectangle = 9 cm
Area of the rectangle = l x w
A = 21 x 9
A = 189 square cm
Hence, Area of the rectangle = 189 square cm.

Question 3.

Answer:
GIVEN: Length of the rectangle = 56 yards
Width of the rectangle = 12 yards
Area of the rectangle = l x w
A = 56 x 12
A = 672 square yards
Hence, Area of the rectangle = 672 square yards.

Question 4.

Answer:
GIVEN:
Length of the rectangle = 10 (3/4) inches = 43/4 = 10.75 inches
Width of the rectangle = 6 inches
Area of the rectangle = l x w
A = 10.75 x 6
A = 64.5 square inches
Hence, Area of the rectangle = 64.5  square inches.

Question 5.
What is the area of the window?

Answer:
GIVEN:
Length of the window = 48 inches
Width of the window = 18 inches
Area of the window = l x w
A = 48 x 18
A = 864 square inches
Hence, the Area of the window = 864 square inches.

Question 6.
Structure
A rectangle has an area of 40 square feet. The dimensions are whole numbers. What are all of the possible dimensions of the rectangle?
Answer:
GIVEN:
Area of the rectangle = 40 square feet.
The whole numbers are the part of the number system in which it includes all the positive integers from 0 to infinity. These numbers exist in the number line.
Area of the rectangle = l x w
All of the possible dimensions of the rectangle =
40 =1 × 40
40 = 2 × 20
40 = 4 × 10
40 = 5 × 8.

Question 7.
Open-Ended
Draw a rectangle that has the same area as the one shown, but different dimensions.

Answer:
GIVEN:
Length of the rectangle = 40 mm
Width of the rectangle = 30 mm
Area of the rectangle = l x w
A = 40 x30
A = 1200 mm
Area of the rectangle = 1200 mm.

Length of my rectangle = 48 mm
Width of my rectangle = 25 mm
Area of my rectangle = l x w
A = 48 x 25
A = 1200 mm
Hence, the Area of my rectangle = 1200 mm.

Question 8.
Modeling Real Life
An interior designer says that a rug under a dining room table should be 4 feet longer and 4 feet wider than the table. What is the area of a rug a customer should buy for under the table?

Answer:
GIVEN:
Length of the dinning table = 6 feet
Width of the dinning table = 3feet
AS PER DESIGNER THE DINNING TABLE REQUIRED DIMENSIONS ARE AS BELOW:
Length should be 4 feet longer than table.
Length of the dinning table= 6 feet
Length of the rug = 6 feet + 4 feet = 10 feet
Width should be 4 feet wider than the table.
Width of the dinning table = 3feet
Width of the rug = 3 feet + 4 feet = 7 feet
Area of the rug = l x w
A = 10 x 7
A = 70 square feet.
Hence, the Area of the rug = 70  square feet.

Question 9.
DIG DEEPER!
A wolf hunts within a rectangular area that is 10 miles long and 5 miles wide. A cougar hunts within a rectangular area that is 8 miles long and 6 miles wide. Which animal hunts within a greater area? How much more area does the animal hunt in?
Answer:
GIVEN:
Length of the wolf hunts rectangular area=10 miles
Width of the wolf hunts rectangular area=5 miles
Area the wolf hunts rectangular area= l x w
A = 10 x 5
A = 50 square miles.
Area the wolf hunts rectangular area= 50 square miles.

Length of the cougar hunts rectangular area= 8 miles
Width of the cougar hunts rectangular area= 6 miles
Area of the cougar hunts rectangular area= l x w
A  = 8 x 6
A = 48 square miles
Area of the cougar hunts rectangular area= 48 square miles.

Hence, wolf hunts within a greater area than the cougar hunts.

Area the wolf hunts rectangular area= 50 square miles.
Area of the cougar hunts rectangular area= 48 square miles.
DIFFERENCE:
Area the wolf hunts rectangular area – Area of the cougar hunts rectangular area
= 50 square miles – 48 square miles
= 2 miles.
Therefore, Wolf hunts more of 2 square miles area than the cougar hunts.

Review & Refresh

Find the quotient.

Question 10.
70 ÷ 7 = __
Answer:
70 ÷ 7 = 10.
The quotient of 70 ÷ 7 = 10.

Question 11.
420 ÷ 6 = ___
Answer:
420 ÷ 6 = 70.
The quotient of 420 ÷ 6 = 70.

Question 12.
2,400 ÷ 8 = ___
Answer:
2,400 ÷ 8 = 300.
The quotient of 2,400 ÷ 8 = 300.

Lesson 12.3 Find Unknown Measures

Explore and Grow

For each row of the table, use color tiles to create the rectangle described. Then complete the table.

Answer:
GIVEN:

Area of the rectangle = 20 square units
length of the rectangle = 5 units
Width of the rectangle = ??
Let the Width of the rectangle be W
Area of the rectangle = l x w
=> 20 square units = 5units x W
=> 20 / 5 = W
=> 4 units =W
Width of the rectangle = 4 units

GIVEN:
Area of the rectangle = 24 square units
Length of the rectangle = ??
Let the Length of the rectangle = l
Width of the rectangle = 4 units
Area of the rectangle = l x w
=> 24 square units = l x 4units
=> 24 / 4= l
=> 6 units =l
Length of the rectangle = 6 units

GIVEN:
Perimeter of the rectangle = 20 units
Length of the rectangle = ??
Let the length of the rectangle be l
Width of the rectangle = 3 units
Perimeter of the rectangle = 2l x 2w = 2 (l + w)
20 = 2(l+ 3)
20 / 2= L + 3
10 = l + 3
10 – 3 =l
l =7 units.
The Length of the rectangle = 7 units.

GIVEN:
Perimeter of the rectangle = 24 units
Length of the rectangle = 8 units
Width of the rectangle = ??
Let the Width of the rectangle = w
Perimeter of the rectangle = 2l x 2w = 2 (l + w)
24 = 2 ( 8 + w)
24/2 =8 + w
12 = 8 + w
12 – 8 = w
w = 4units
Width of the rectangle = 4units.

The required table is as below:

Reasoning
Compare your strategy to your partner’s. How are they the same or different?
Answer:
The strategy of mine and my partner does not vary as both the required answers value is same.

Think and Grow : Find Unknown Measures

Example
The area of the rectangle is 36 square feet. Find the length.

Answer:
GIVEN:
Area of the rectangle = 36 square feet.
Length of the rectangle = l feet
Width of the rectangle = 3 feet
Area of the rectangle = l x w
36 = l x 3
36/3 = l
12 feet = l
Hence, the Length of the rectangle =12 feet

Example
The perimeter of the rectangle is 30 centimeters. Find the width.

Answer:
GIVEN:
Perimeter of the rectangle = 30 centimeters.
Length of the rectangle = 8 cm
Width of the rectangle = w cm
Perimeter of the rectangle = (2 x l) + ( 2 x w )
30 = ( 2 x 8) + (2 x w)
30 = 16 + 2w
30 – 16 = 2w
14 = 2w
14/2 = w
7 = w
Hence, the Width of the rectangle = 7 cm.

 

Show and Grow

Question 1.
Area = 75 square meters

Answer:
GIVEN:
Area of the rectangle = 75 square meters
Length of the rectangle = l m
Width of the rectangle = 5 m
Area of the rectangle =  l x w
75 = l x 5
75/5 = l
15 = l
Hence, the length of the rectangle = 15 m.

Question 2.
Perimeter = 42 inches

Answer:
GIVEN:
Perimeter of the rectangle = 42 inches
Length of the rectangle = 12 inches
Width of the rectangle = w inches
Perimeter of the rectangle = (2 x l) + ( 2 x w ) = 2 ( l + w )

Hence, the Width of the rectangle =  3.5 inches.

Apply and Grow: Practice

Find the unknown measure of the rectangle.

Question 3.
Area = 50 square millimeters

Answer:
GIVEN:
Area of the rectangle = 50 square millimeters
Length of the rectangle = l mm
Width of the rectangle = 2 mm
Area of the rectangle =  l x w
50 = l x 2
50/2 = l
25 = l
Hence, the length of the rectangle = 25 mm.

Question 4.
Perimeter = 30 centimeters

Answer:
GIVEN:
Perimeter of the rectangle = 30 centimeters
Length of the rectangle = 9 cm
Width of the rectangle = w cm
Perimeter of the rectangle = (2 x l) + ( 2 x w ) = 2 ( l + w )
30 = 2( 9+w )
30/2 = 9 + w
15 = 9 + w
15 – 9 = w
6 = w
Hence, the width of the rectangle = 6 cm.

Question 5.
Area = 240 square meters

Answer:
GIVEN:
Area of the rectangle =  240 square meters
Length of the rectangle = 80 m
Width of the rectangle =  w m
Area of the rectangle =  l x w
240 = 80 x w
240/80 = w
3 = w
Hence, the Width of the rectangle =  3 m.

Question 6.
Perimeter = 86 yards

Answer:
GIVEN:
Perimeter of the rectangle = 86 yards
Length of the rectangle = 23 yards
Width of the rectangle = w yards
Perimeter of the rectangle = (2 x l) + ( 2 x w ) = 2 ( l + w )
86 = 2( 23 + w)
86/2 = 23 +w
43 = 23 + w
43 – 23 = w
20 = w
Hence, the Width of the rectangle = 20 yards.

Question 7.
Perimeter 44 2/4 inches

Answer:
GIVEN:
Perimeter of the rectangle = 44 (2/4) inches = 90/4 = 22.5 inches
Length of the rectangle = l inches
Width of the rectangle = 8 (1/4) inches = 33/4 =  8.25 inches
Perimeter of the rectangle = (2 x l) + ( 2 x w ) = 2 ( l + w )
22.5 = 2( l+ 8.25)
22.5/2 = l + 8.25
11.25 = l + 8.25
11.25 – 8.25 = l
3.00 = l
Hence, the Length of the rectangle = 3 inches.

Question 8.
Area = 108 square feet

Answer:
GIVEN:
Area of the rectangle =  108 square feet
Length of the rectangle = l feet
Width of the rectangle =  9 feet
Area of the rectangle =  l x w
108 = l x 9
108/9 = l
12 = l
Hence, the Length of the rectangle = 12 feet.

Question 9.
DIG DEEPER!
What are the dimensions of Newton’s rectangle?

Answer:
Area of the Newton’s rectangle =  24 square meters
Let the Width of the Newton’s rectangle  be w m.
Length of the Newton’s rectangle = 2 meters longer than the width = 2 + w
Area of the Newton’s rectangle =  l x w
Factors of 24:
1 x 24 = 24 => 1 x ( 1 + 2 ) = 1 x 3= 3
2 x 12 = 24 =>2 x (2+2) =2 x 4 =8
3 x 8 = 24 =>3 x (3+2) = 3 x 5 = 15
4 x 6 = 24 => 4 x (4+2) = 4 x 6 = 24
The dimensions of Newton’s rectangle:
Width of the Newton’s rectangle = 4 m
Length of Newton’s rectangle = 4 + 2= 6 m
CHECK:
Area of of Newton’s rectangle =l x w
A = 4 x 6
A = 24 square meters.
Hence , the The dimensions of Newton’s rectangle = 4 m and 6 m.

 

Question 10.
DIG DEEPER!
The area of a square is 81 square centimeters. What is the perimeter of the square?
Answer:
GIVEN:
Area of a square = 81 square centimeters.
Area of a square  =s²  
81 = s²
√ 81 = s
9 = s
Side of the square = 9 cm
Perimeter of the square = 4x s
P= 4 x 9
P = 36 cm.
Hence, Perimeter of the square = 36 cm.

Think and Grow: Modeling Real Life

Example
The rectangular park has an area of 200 square yards. You kick a soccer ball straight across the width of the park. How far did you kick the soccer ball?
Use a formula to find the width.

Answer:
GIVEN:
Area of the rectangular park =200 square yards
Length of the rectangular park = 25 yards
Width of the rectangular park =w yards
Area of the rectangular park = l x w
200 = 25 x w
200/25 = w
8 = w
Hence, the Width of the rectangular park =9 yards.
Therefore, the soccer kicks the ball 8 yards far in the rectangular park.
Show and Grow

Question 11.
The rectangular parking spot has an area of 220 square feet. What is the length of the longest car that can fit in the parking spot?

Answer:
GIVEN:
Area of the rectangular parking spot = 220 square feet
Width of the rectangular parking spot = 10 feet
Length of the rectangular parking spot = l feet
Area of the rectangular parking spot = l x w
220 = l x 10
220/10 = l
22 = l
Hence, the Length of the rectangular parking spot = 22 feet.
Therefore , the length of the longest car that can fit in the parking spot is 22 feet.

Question 12.
You want to put a frame around the rectangular painting. The painting has a perimeter of 50 inches. How wide should the frame be?

Answer:
GIVEN:
Perimeter of the rectangular painting frame= 50 inches
Length of the rectangular painting  frame= 14 inches
Width of the rectangular painting frame= w inches
Perimeter of the rectangular painting = 2l + 2w = 2( l + w)
50 = 2(14+w)
50/2 = 14 + w
25 = 14 + w
25 – 14 =w
11 = w
Hence, the Width of the rectangular painting frame= 11 inches.

Question 13.
A rectangular zoo enclosure for a red panda has a perimeter of 116 meters. The length is 50 meters. What is the area of the enclosure?
Answer:
GIVEN:
Perimeter of the rectangular zoo = 116 meters
Length of the rectangular zoo = 50 meters
Width of the rectangular zoo = ??
Let the Width of the rectangular zoo = w meters
Perimeter of the rectangular painting = 2l + 2w = 2( l + w)
116 = 2( 50+ w)
116/2 = 50 + w
58 = 50 + w
58 – 50 = w
8 = w
Hence, the Width of the rectangular zoo = 8 meters
Area of the rectangular zoo =??
Area of the rectangular zoo = l x w
A = 50 x 8
A = 400 square meters
Therefore, the Area of the rectangular zoo = 400 square meters.

Question 14.
DIG DEEPER!
A rectangular patio at a restaurant has an area of 98 square feet. The dimensions of the patio are whole numbers. The length of the patio is 2 times the width. What are the dimensions of the patio?
Answer:
GIVEN:
Area of the rectangular patio = 98 square feet.
The dimensions of the patio are whole numbers.
The length of the patio is 2 times the width.
Let the Width of the rectangular patio be w feet.
=> Length of the the rectangular patio = 2 x w = 2w
Area of the rectangular patio = l x w
98 = (2w) x w
98 = 2w²
98/2 = w²
49 = w²
√ 49 = w
7 = w
Hence, the Width of the rectangular patio = 7 feet.
Length of the the rectangular patio = 2 x w = 2w= 2 x 7 = 14 feet
Therefore, the dimensions of the patio are 14 feet and 7 feet.

Find Unknown Measures Homework & Practice 12.3

Find the unknown measures of the rectangle.

Question 1.
Area = 63 square feet

Answer:
GIVEN:
Area of the rectangle = 63 square feet
Length of the rectangle = l feet
Width of the rectangle = 7 feet
Area of the rectangle = l x w
63 = l x 7
63/7 = l
9 = l
Hence, the Length of the rectangle = 9 feet.

Question 2.
Perimeter = 26 yards

Answer:
GIVEN:
Perimeter of the rectangle =  26 yards
Length of the rectangle = l yard
Width of the rectangle = 1 yard
Perimeter of the rectangle = 2l + 2w = 2 ( l + w)
26 = 2( l + 1)
26/2 = l +1
13 = l + 1
13 – 1 = l
12 = l
Hence, the Length of the rectangle = 12 yards.

Find the unknown measure of the rectangle.

Question 3.
Perimeter = 40 centimeters

Answer:
GIVEN:
Perimeter of the rectangle = 40 centimeters
Length of the rectangle =14 cm
Width of the rectangle = w cm
Perimeter of the rectangle = 2l + 2w = 2 ( l + w)
40 = 2( 14 + w)
40/2 =14 + w
20 = 14 + w
20 – 14= w
6 = w
Hence, the Width of the rectangle = 6 cm.

Question 4.
Area = 88 square millimeters

Answer:
GIVEN:
Area of the rectangle = 88 square millimeters
Length of the rectangle = l mm
Width of the rectangle = 8 mm
Area of the rectangle = l x w
88 = l x 8
88/8 = l
11 = l
Hence , the Length of the rectangle = 11 mm.

Question 5.
Area = 2,800 square meters

Answer:
GIVEN:
Area of the rectangle = 2,800 square meters
Length of the rectangle = l m
Width of the rectangle = 40 m
Area of the rectangle = l x w
2800 = l x 40
2800/40 = l
70 = l
Hence, the Length of the rectangle = 70 m.

Question 6.
Perimeter = 41 inches

Answer:
GIVEN:
Perimeter of the rectangle = 41 inches
Length of the rectangle =12 (4/8) inches = 100/8 = 12.5 inches
Width of the rectangle = w inches
Perimeter of the rectangle = 2l + 2w = 2 ( l + w)
41 = 2( 12.5 +w)
41/2 =12.5 + w
20.5 = 12.5 + w
20.5 – 12.5 = w
8 = w
Hence, the Width of the rectangle = 8 inches.

Question 7.
Structure
A rectangle has an area of 18 square inches and a perimeter of 18 inches. What are the dimensions of the rectangle?
Answer:
GIVEN:
Area of the rectangle = 18 square inches
Perimeter of the rectangle =18 inches.
LET, the Length of the rectangle be l inches
The Width of the rectangle be w inches.
FORMULA:
Area of the rectangle = l x w
18 = l x w
The dimensions of the rectangle :
18 = 1 x 18
18 = 2 x 9
18 = 3 x 6
Hence, the dimensions of the rectangle are (1,18);(2,9);(3,6) inches.

Question 8.
Modeling Real Life
The rectangular fire pit has a perimeter of 176 inches. What is the width of the fire pit?

Answer:
GIVEN :
Perimeter of the rectangular fire pit = 176 inches
Length of the rectangular fire pit = 50 inches
Width of the rectangular fire pit = ??
Let the Width of the rectangular fire pit be w inches.
Perimeter of the rectangular fire pit = 2l + 2w = 2(l + w)
176 = 2( 50 + w)
176/2 = 50 + w
88 = 50 + w
88 – 50 = w
35 = w
Hence, the Width of the rectangular fire pit =  35 inches.

Question 9.
A painting canvas has an area of 384 square inches. The length and width of the canvas are whole numbers. The length of the canvas is 8 inches greater than the width. What are the dimensions of the canvas?
Answer:
GIVEN:
Area of  the painting canvas = 384 square inches.
The length of the canvas is 8 inches greater than the width.
Let the Width of the painting canvas be w inches.
Area of  the painting canvas = l x w => 384 = l x w
384 = 1x 384 =>1 x (1 + 8) = 1 x 9 = 9
384 = 2 x 192 =>2 x (2+8) = 2 x 10 = 20
384 = 3 x 128 => 3 x (3 + 8) = 3 x 11 = 33
384 = 4 x 96 => 4 x (4 + 8) = 4 x 12 = 48
384= 6 x 64 => 6 x (6 + 8) = 6 x 14 = 84
384 = 8 x 48 => 8 x (8 + 8) =8 x 16 = 128
384 =12 x 32 =>12 x (12 + 8) = 12 x 20 = 240
384 =16 x 24 => 16 x (16 +8) = 16 x 24 = 384
Hence, The dimensions of the canvas=  (24,16) inches
Length of the canvas = 24 inches
Width of the canvas = 16 inches

Review & Refresh

Find the equivalent length.

Question 10.
35 ft = __ in.
Answer:
CONVERTION: 1 feet = 12 inches
35 feet = ?? inches
Let the unknown value be Y inches.
=>35 x 12 = 1 x Y
=>420 = 1 x Y
=> 420/1 = Y
=> 420 = Y
Hence, the unknown value = 420 inches.
35 feet = _420_ inches.

Question 11.
6 mi = __ yd
Answer:
CONVERTION: 1 mile =1760 yard
6 miles = ?? yard
Let the unknown value be X yards.
=> 1 x X = 1760 x 6
=> 1X = 10560
=> X = 10560/1
=> X = 10560
Hence, the unknown value be 10560 yards.
6 mi = _10560_ yd

Question 12.
17 yd = __ ft
Answer:
CONVERTION:
1 yard = 3 feet
17 yd = ?? feet
Let the unknown value be X feet.
=>1 x X = 3 x 17
=>1X = 51
=>X = 51/1
=> X = 51 feet
Hence, the unknown value be 51 feet.
17 yd = _51_ ft

Question 13.
4 yd = __ in.
Answer:
CONVERTION:
1 yard = 36 inches
4 yards = ?? inches
Let the unknown value be Y inches.
=> 1 x Y = 36 x 4
=> 1Y = 144
=> Y = 144/1
=> Y = 144
Hence, the unknown value be 144 inches.
4 yd = _144_ in.

Lesson 12.4 Problem Solving: Perimeter and Area

Explore and Grow

An office has a large rectangular window overlooking a city. Describe two methods for finding the area of the rectangular wall around the window.

Answer:
GIVEN:
Area of the inside window = l x w
Area of the outside wall = l x w
Area of the rectangular wall around the window = area of the outside wall – Area of the inside window
Hence, there is only one way to find the Area of the rectangular wall around the window.

Make Sense of Problems
Use one of your methods to estimate the area of a wall with a window.
Answer:
The area of the wall can be estimated to be twice the area of the window.

Think and Grow: Problem Solving: Perimeter and Area

Example
A rectangular board has an area of 1,700 square inches. You cut out a rectangular piece that is 10 inches long and 9 inches wide to make a carnival prop similar to the one shown. What is

Answer:
GIVEN:
Area of rectangular board =1,700 square inches
Length of the rectangular piece  cut = 10 inches
Width of the rectangular piece cut = 9 inches
Area of the rectangular piece cut = l x w
=>A = 10 X 9
=> A = 90 square inches
Area of the rectangular piece cut = 90 square inches.
Subtract Area of the cut out piece you cut out from the original area.
= 1700 square inches – 90 square inches
= 1610 square inches.
Hence, the Area of the area of the prop = 1610 square inches.

Understand the Problem
What do you know?

• The original board has an area of 1,700 square inches.
• The piece you cut out is 10 inches long and 9 inches wide.

What do you need to find?

• You need to find the area of the carnival prop.

Make a Plan

How will you solve?

• Find the area of the piece you cut out.
• Subtract the area of the piece you cut out from the original area.

Solve
Step 1: Find the area of the piece you cut out.

Step 2: Subtract the area of the you cut out piece you cut out from the original area.

The area of the prop is __ square inches.
Answer:
Area of rectangular board =1,700 square inches
Length of the rectangular piece  cut = 10 inches
Width of the rectangular piece cut = 9 inches
Area of the rectangular piece cut = l x w
=>A = 10 X 9
=> A = 90 square inches
Area of the rectangular piece cut = 90 square inches.
Subtract Area of the cut out piece you cut out from the original area.
= 1700 square inches – 90 square inches
= 1610 square inches.
Hence, the Area of the area of the prop = 1610 square inches

Show and Grow

Question 1.
Explain how you can check whether your answer above is reasonable.
Answer:
My above answer is reasonable because it satisfies.
Area of the area of the prop + Area of the cut out piece  =The Area of the outside rectangular
=>1610 square inches + 90 square inches
=>1700 square inches.
Hence, proved my answer is reasonable and correct.

Apply and Grow: Practice

Understand the problem. What do you know? What do you need to find? Explain.
Answer:
GIVEN:
Area of rectangular board =1,700 square inches
Length of the rectangular piece  cut = 10 inches
Width of the rectangular piece cut = 9 inches
This is known in the problem.
You need to find the area of the carnival prop.

Question 2.
A construction worker has 40 feet of caution tape. Is this enough tape to surround a rectangular region that is 120 inches long and 90 inches wide?
Answer:
GIVEN:
A construction worker has 40 feet of caution tape.
Length of the rectangular region = 120 inches
Width of the rectangular region = 90 inches
Perimeter of the rectangular region = 2l + 2 w = 2( l + w)
P = 2( 120 + 90)
P = 2 x 210
P = 420 inches.
CONVERTION: 1 inch = 0.8333 feet  or (1/12) feet
420 inches = ??
Let the unknown value be X feet
=> 1 x X = 420 x 1/12
=> 1X = 420/12
=> 1X = 35 feet.
The required tape to surround the rectangular region = 35 feet.
A construction worker has 40 feet of caution tape.
Therefore, the tape of construction worker bought will be enough to surround a rectangular region that is 120 inches long and 90 inches wide.

Question 3.
One ton of salt de-ices a rectangular section of a road that is 10,500 meters long and 3 meters wide. How many square meters does 6 tons of salt de-ice?
Answer:
GIVEN:
One ton of salt de-ices a rectangular section of a road
Length of the One ton of salt de-ices rectangular section of a road = 10500 meters
Width of the One ton of salt de-ices rectangular section of a road = 3 meters
Area of the One ton of salt de-ices rectangular section of a road = l x w
A = l x w
A = 10500 x 3
A = 31500 square meters
Area of the  One ton of salt de-ices rectangular section of a road = 31500 square meters.
Area of the 6 ton of salt de-ices rectangular section of a road  = ??
Area of the 6 ton of salt de-ices rectangular section of a road  = (Area of the one ton of salt de-ices rectangular section of a road) x 6
=> 31500 x 6
=> 189000 square feet.
Therefore, Area of the 6 ton of salt de-ices rectangular section of a road  = 189000 square feet.

Understand the problem. Then make a plan. How will you solve? Explain.

Question 4.
A worker installs fencing around two rectangular properties. One is 99 feet long and 80 feet wide. The other is95 feet long and 83 feet wide. Which property requires more fencing? How much more?
Answer:
GIVEN:
A worker installs fencing around two rectangular properties.
ONE RECTANGULAR PROPERTY
Length of the  one rectangular property = 99 feet
Width of the one rectangular property = 80 feet
Perimeter of the one rectangular property = 2l + 2w = 2( l + w)
P = 2 ( 99+ 80 )
P = 2 x 179
P = 358 feet
Perimeter of the one rectangular property = 358 feet.
OTHER RECTANGULAR PROPERTY
Length of the  other rectangular property = 95 feet
Width of the other rectangular property = 83 feet
Perimeter of the other rectangular property = 2l + 2w = 2( l + w)
P = 2 ( 95 + 83 )
P = 2 x 178
P = 356 feet
Perimeter of the other rectangular property = 356 feet
DIFFERENCE:
Perimeter of the one rectangular property – Perimeter of the other rectangular property
=> 358 – 356
=> 2 feet.
One rectangular property requires more fencing than the other rectangular property.
Therefore, 2 feet more it requires than the one rectangular property than the other rectangular property.

Question 5.
A roofer covers the rectangular roof with shingles. A chimney occupies a rectangular area that is 4 feet long and 2 feet wide. How many square feet of the roof are with shingles?

Answer:
GIVEN:
A roofer covers the rectangular roof with shingles.
Length of the rectangular area of chimney = 4 feet
Width of the rectangular area of chimney = 2 feet
Area of the rectangular area of chimney = l x w
A = 4 x 2
A = 8 square feet
Area of the rectangular area of chimney = 8 square feet.
Length of the rectangular roof = 60 feet
Width of the rectangular roof= 30 feet
Area of the rectangular roof = l x w
A = 60 x 30
A = 1800 square feet
Area of the rectangular roof = 1800 square feet.
Area of the roof are with shingles = Area of the rectangular roof – Area of the rectangular area of chimney
=> 1800 square feet – 8 square feet
=> 1792 square feet.
Area of the roof are with shingles = 1792 square feet.

Question 6.
You want to buy a cover for the lid of your laptop. Your laptop is 1\(\frac{1}{3}\) feet long and 1 foot wide. Which cover will fit best on your laptop?

Answer:
GIVEN:
Length of the Laptop = 1\(\frac{1}{3}\) feet long =1 (1/3) feet = 4/3 feet = 1. 33 feet.
Width of the laptop = 1 feet
Perimeter of the laptop =2l + 2w = 2( l + w)
P = 2( 1.33 + 1)
P =2 x 2.33
P = 4.66 feet
Perimeter of the laptop =4.66 feet.
CONVERTION:
1 feet = 12 inches
4.66 feet =??
=> 4.66 x 12
=> 55.92 inches
Hence, the perimeter of the laptop = 55.92 inches.
FIRST LAPTOP COVER :
Length of the first Laptop cover = 16 inches
Width of the first Laptop cover = 12 inches
Area of the first Laptop cover =  192 square inches
Perimeter of the first Laptop cover = 2l + 2w = 2( l + w)
P = 2( 16 + 12)
P = 2 x 28
P = 56 inches.
Perimeter of the first Laptop cover = 56 inches.
SECOND LAPTOP COVER :
Length of the second Laptop cover = 13 inches
Width of the second Laptop cover = 9 (3/4)inches = 39/4  inches = 9.75 inches
Area of the second Laptop cover =  126 (3/4) square inches
Perimeter of the second Laptop cover = 2l + 2w = 2( l + w)
P = 2( 13 +9.75 )
P = 2 x 22.75
P =  45.5 inches.
Perimeter of the second Laptop cover = 45.5 inches.
THIRD LAPTOP COVER
Length of the third Laptop cover = 14 (1/2) inches = 29/2  inches= 14.5 inches
Width of the third Laptop cover = 11 inches
Area of the third Laptop cover =  159 (1/2) square inches
Perimeter of the third Laptop cover = 2l + 2w = 2( l + w)
P = 2( 14.5 + 11 )
P = 2 x 25.5
P = 51 inches.
Perimeter of the third Laptop cover = 51 inches.
Therefore, first laptop cover will fit correctly to the laptop because cover size is more accurate size of 56 inches than other two laptop covers are lesser in size of the laptop size 55.92 inches.

Think and Grow: Modeling Real Life

Example
A worker wants to cover the miniature golf putting surface with artificial turf. The putting surface is in the shape of two rectangles. How much turf does the worker need?
Think: What do you know? What do you need to find? How will you solve?

Step 1: Divide the surface into two rectangles. Then find the area of each rectangle.

Answer:
GIVEN:

Divide the surface into two rectangles. Then find the area of each rectangle.

Length of the Rectangle A = 16 feet
Width of the Rectangle A = `4 feet
Area of the Rectangle A = l x w
A =16 x 4
A = 64 square feet
Area of the Rectangle A = 64 square feet.
Length of the Rectangle B = `10 feet
Width of the Rectangle B = `5 feet
Area of the Rectangle B = l x w
A = 10 x 5
A = 50 square feet
Area of the Rectangle B = 50 square feet.
ADDITION:
Area of the Rectangle A + Area of the Rectangle B
=> 64 square feet + 50 square feet
=> 114 square feet.
Hence, the workers need 114 square feet for artificial turf.

Question 7.
You want to install new carpet in the rectangular bedroom and the rectangular closet. How much carpet do you need to cover the floor?

Answer:
GIVEN:

Length of the rectangular bedroom = 20 feet
Width  of the rectangular bedroom = 10 feet
Area of the rectangular bedroom = l x w
A = 20 x 10
A = 200 square feet
Area of the rectangular bedroom = 200 square feet.
Length of the rectangular closet = 10 feet
Width  of the rectangular closet= 4 feet
Area of the rectangular closet = l x w
A = 10 x 4
A = 40 square feet
Area of the rectangular closet = 40 square feet.
ADDITION:
Carpet  needed to cover the floor = Area of the rectangular bedroom + Area of the rectangular closet.
=> 200 square feet + 40 square feet
=> 240 square feet.
Hence, the Carpet  needed to cover the floor = 240 square feet.

Question 8.
A gardener wants to enclose the garden with fencing. The garden is in the shape of two rectangles. How much fencing does the gardener need?

Answer:

Divide the surface into two rectangles.

Length of the Rectangle A = 8 yard
Width of the Rectangle A = 6 yard
Perimeter of the Rectangle A = 2l x 2w = 2( l + w)
P = 2( 8 + 6 )
P = 2 x 14
P = 28 yards
Perimeter of the Rectangle A = 28 yards.
Length of the Rectangle B = 10 yard
Width of the Rectangle B = 3 yard
Perimeter of the Rectangle B = 2l x 2w = 2( l + w)
P = 2( 10 + 3 )
P = 2 x 13
P = 26 yards
Perimeter of the Rectangle B = 26 yards.
Fencing the gardener needed = Perimeter of the Rectangle A + Perimeter of the Rectangle B
=> 28 yards + 26 yards
=> 54 yards.
Hence, the Fencing the gardener needed = 54 yards.

Problem Solving: Perimeter and Area Homework & Practice 12.4

Understand the problem. Then make a plan. How will you solve? Explain.

Question 1.
An indoor dog park has an area of 50,000 square feet. The owner creates a square welcome center inside the park that is 100 feet long. What is the area of the section that dogs can play in?

Answer:
GIVEN:

Area of the indoor dog park = 50,000 square feet.
The owner creates a square welcome center inside the park that is 100 feet long.
=> side of the square welcome center inside the park = 100 feet
Area of the square welcome center inside the park =  s x s
A = 100 x 100
A  = 10,000 square feet
Area of the square welcome center inside the park = 10,000 square feet.
Area of the section that dogs can play in = Area of the indoor dog park – Area of the square welcome center inside the park
=> 50,000 square feet – 10,000 square feet
=> 40,000 square feet.
Hence, the Area of the section that dogs can play in = 40,000 square feet.

Question 2.
You tile a hallway with square tiles that are 12 inches wide. You completely cover the hallway with 3 rows of 5 tiles. What is the area of the hallway?
Answer:
GIVEN:
Side of the square tiles = 12 inches
The hallway completely covered with 3 rows of 5 tiles.
Area of the square tiles hallway= s x s
A = 12 x 12
A = 144 square inches.
Hence, the Area of the square tiles hallway= 144 square inches.

Question 3.
Your friend makes a rectangular poster for a school play. The poster is 4 feet long and 3 feet wide. Ribbon costs $1 per foot. How much does it cost to add a ribbon border to the poster?
Answer:
GIVEN:
Length of the rectangular poster = 4 feet
Width of the rectangular poster = 3 feet
Perimeter of the rectangular poster = 2l +2w = 2(l + w)
P = 2 ( 4 + 3 )
P = 2 x 7
P = 14 feet
Perimeter of the rectangular poster = 14 feet.
Ribbon costs $1 per foot
Cost of the ribbon border to the poster = 14 feet x $1= $14
Therefore, the Cost of the ribbon border to the poster = $14.

Question 4.
Writing
Explain how you know when you need to find the perimeter or the area of a rectangle when solving a word problem.
Answer:
GIVEN:
Perimeter can be thought  as the length of the outline of a shape.
Area can be defined as the space occupied by a flat shape or the surface of an object.
On the above referred points,  I try to calculate the perimeter or the area of the rectangle when solving a word problem.

Question 5.
Modeling Real Life
Your teacher joins two rectangular tables for students to complete a craft. How much newspaper does your teacher need to cover the tops of the tables with no overlap and no paper hanging over the sides?

Answer:
GIVEN:

Divide the surface into two rectangles.

Length of the rectangle A = 72 inches
Width of the of the rectangle A = 30 inches
Perimeter of the rectangle A = 2l + 2w = 2( l + w)
P = 2( 72 + 30 )
P =  2 x 102
P = 204 inches
Perimeter of the rectangle A = 204 inches.
Length of the rectangle B = 60 inches
Width of the of the rectangle B = 30 inches
Perimeter of the rectangle B = 2l + 2w = 2( l + w)
P = 2( 60 + 30 )
P = 2 x 90
P = 180 inches
Perimeter of the rectangle B = 180 inches.
Newspaper needed to cover the tops of the tables with no overlap and no paper hanging over the sides = Perimeter of the rectangle A + Perimeter of the rectangle B
= 204 inches + 180 inches
= 384 inches.
Hence, the newspaper needed to cover the tables = 384 inches.

Question 6.
Modeling Real Life
A landscaper buys 2 bags of grass seed. Each bag covers 5,000 square feet. A rectangular lawn is 200 feet long and 40 feet wide. Does the landscaper have enough seed to cover the lawn once? twice? Explain.
Answer:
GIVEN:
A landscaper buys 2 bags of grass seed.
Area of the bags seed covers = 5000 square feet.
Length of the rectangular lawn = 200 feet
Width of the rectangular lawn = 40 feet
Area of the rectangular lawn = l x w
A = 200 x 40
A = 8000 square feet.
Area of the rectangular lawn = 8000 square feet.
The landscaper have enough seed to cover the lawn once only not twice because he has  bags which can cover only 5000 square feet not 8000 square feet rectangular lawn completely.

Review & Refresh

Multiply

Question 7.

Answer:
GIVEN:
= 2 x 1/4
= 1 x 1/2
= 1/2
= 0.5
Hence, = 0.5.

Question 8.

Answer:
= 12/5
= 2.4.
Hence, = 2.4.

Question 9.

Answer:
= 6 x 5/4
= 3 x 5/2
=15/2
= 7.5.
Hence, = 7.5.

Use Perimeter and Area Formulas Performance Task 12

Stop-motion animation videos are made by taking multiple photographs of an object. Each photograph shows the object in a slightly different position. When all of the photographs are combined into a video, the object appears to be moving.

1. You decide to make a stop-motion video. You make a background with an area of 12 square feet and a perimeter of 14 feet.
a. What are the dimensions of your background?
b. The part of the background in each photograph is 45 inches long and 30 inches wide. What is the perimeter of the background in each photograph?
c. What is the area of the background that is not in each photograph?
2. You take photographs for your video. Your video shows 15 photographs each second. How many photographs are in a 24-second video?
3. You start working on your animation at 3:05 P.M. and finish at 5:20 P.M. You spend equal amounts of time creating your background, taking photographs, and editing your video. How much time do you spend on each activity?
Answer:
GIVEN:
Area of the rectangular background= 12 square feet.
Perimeter  of the rectangular background = 14 feet.
1. a) All dimensions of the rectangular background =
Area of the rectangle = l x w
1 × 12 = 12.
2 × 6 = 12.
3 × 4 = 12.
The dimensions of the rectangular background = (1,12); (2,6);(3,4).
b) The Length of the background in each photograph = 45 inches The Width  of the background in each photograph =30 inches  The perimeter of the background in each photograph = 2l + 2w = 2(l + w)
P = 2 (45 + 30)
P = 2 x 75
P = 150 inches.
Hence, the perimeter of the background in each photograph = 150 inches.
2) 
GIVEN:
15 photograph taken in 1 second
=> ?? in 24 seconds
=> 24 x 15 = photographs taken in 24 seconds
=> 360 = photographs taken in 24 seconds
Hence, photographs taken in 24 seconds = 360.
3)
GIVEN:
Starting time on animation at 3:05 P.M.
Finishing time on animation at 5:20 P.M.
Time taken on each activity = Finishing time on animation – Starting time on animation
=> 5:20 P.M – 3:05 P.M
=> 2: 15 Hours
Hence, Time taken on each activity =2:15 Hours.

Use Perimeter and Area Formulas Activity

Area Roll and Conquer

Directions:

1. Players take turns rolling two dice.
2. On your turn, create a rectangle with the numbers on the dice as the length and width. Your rectangle cannot cover another rectangle.
3. Shade the rectangle in your color. Record the multiplication equation for the rectangle.
4. If you cannot create a rectangle on the board, then you lose your turn. Play 10 rounds, if possible.
5. The player with the greatest area covered wins!

Answer:
GIVEN:

1. Players take turns rolling two dice.

1)
2)

Length of the rectangle = 4 units
Width of the rectangle = 3 units.
3)
Equation of the rectangle = 4 x 3 = 12 square units.
4)   
5) 
The player with the greatest area covered wins!
Given Equation Area = 3 x 2 = 6 square units
My Equation Area= 4 x 3 =12 square units

Use Perimeter and Area Formulas Chapter Practice

12.1 Perimeter Formula for a Rectangle

Find the perimeter of the rectangle.

Question 1.

Answer:
GIVEN:
Length of the rectangle = 15 yard
Width of the rectangle = 13 yard
Perimeter of the rectangle = 2l + 2w = 2( l + w)
P = 2 (15 + 13)
P = 2 x 28
P = 56 yards
Hence, the Perimeter of the rectangle = 56 yards.

Question 2.

Answer:
GIVEN:
Length of the rectangle = 29 mm
Width of the rectangle = 23 mm
Perimeter of the rectangle = 2l + 2w = 2( l + w)
P = 2 ( 29 + 23)
P = 2 x 52
P = 104 mm
Hence, the Perimeter of the rectangle = 104 mm.

Question 3.

Answer:
GIVEN:
Length of the rectangle = 55 cm
Width of the rectangle = 46 cm
Perimeter of the rectangle = 2l + 2w = 2( l + w)
P = 2( 55 + 46)
P = 2 x 101
P = 202 cm
Hence, the Perimeter of the rectangle = 202 cm.

Question 4.

Answer:
GIVEN:
Length of the rectangle = 10 (2/12) feet = 20/12 = 1.67 feet
Width of the rectangle = 7 feet
Perimeter of the rectangle = 2l + 2w = 2( l + w)
P = 2(1.67 + 7)
P = 2 x 7.67
P = 15.34 feet
Hence, the Perimeter of the rectangle = 15.34 feet.

12.2 Area Formula for a Rectangle

Find the area of the rectangle.

Question 5.

Answer:
GIVEN:
Length of the rectangle =  58 m
Width of the rectangle = 37 m
Area of the rectangle = l x w
A = 58 x 37
A = 2146 square m.
Hence, the Area of the rectangle = 2146 square m.

Question 6.

Answer:
GIVEN:
Length of the rectangle = 13 (1/2) inches = 27/2 = 13.5 inches
Width of the rectangle = 7 inches
Area of the rectangle = l x w
A = 13.5 x 7
A = 94.5 square inches
Hence, the Area of the rectangle = 94.5 square inches.

Question 7.
A rectangle has an area of 60 square feet. The dimensions are whole numbers. What are all of the possible dimensions of the rectangle?
Answer:
GIVEN:
Length of the rectangle = l feet
Width of the rectangle = w feet
Area of the rectangle = 60 square feet
Area of the rectangle = l x w
All possible dimensions of rectangle =
60 = 1 x 60,
60 = 2 x 30,
60 = 3 x 20,
60 = 4 x 15
60 = 5 x 12,
60 = 6 x 10.
All possible dimensions of rectangle =(1,60);(2,30);(3,20);(4,15);(5,12);(6,10).

12.3 Find Unknown Measures

Find the unknown measure of the rectangle.

Question 8.
Area = 48 square yards

Answer:
GIVEN:
Area of the rectangle = 48 square yards
Length of the rectangle = l yards
Width of the rectangle = 3 yards
Area of the rectangle = l x w
48 = l x 3
48/3 = l
16 = l
Hence, the Length of the rectangle = 16 yards.

Question 9.
Perimeter = 90 centimeters

Answer:
GIVEN:
Perimeter of the rectangle = 90 centimeters
Length of the rectangle = l cm
Width of the rectangle = 12 cm
Perimeter of the rectangle = 2l + 2w = 2( l + w)
90 = 2( l + 12)
90/2 = l + 12
45 = l + 12
45 – 12 = l
33 = l
Hence, the Length of the rectangle = 33 cm.

Question 10.
Logic
What are the dimensions of Descartes’s rectangle?

Answer:
GIVEN:
Perimeter of the rectangle = 10 meters
Length and Width have a product = 6 square meters
=> l x w = 6 square meters
=> Area of the rectangle = l x w = 6 square meters.
All possible dimensions of the rectangle =
6 = 1 x 6
6 = 2 x 3.
Hence, All possible dimensions of the rectangle =(1,6);(2,3).

12.4 Problem Solving: Perimeter and Area

Question 11.
Modeling Real Life
You want to paint the wall. What is the area of the wall you will paint?

Answer:
GIVEN:
Length of the outer rectangle = 14 feet
Width of the outer rectangle = 10 feet
Area of the outer rectangle = l x w
A = 14 x 10
A = 140 square feet.
Area of the outer rectangle = 140 square feet.
Length of the inside rectangle = 4 feet
Width of the inside rectangle = 1(1/2) feet = 3/2 = 1.5 feet
Area of the inside rectangle = l x w
A = 4 x 1.5
A = 6 square feet.
Area of the inside rectangle = 6 square feet.
SUBTRACTION:
Area of the wall for paint = Area of the outer rectangle  – Area of the inside rectangle
= 140 square feet – 6 square feet.
= 134 square feet.
Hence, the Area of the wall for paint = 134 square feet.

Question 12.
A park director orders 360 feet of fencing. Does he have enough to surround the tennis court?

Answer:
GIVEN:
Fencing length park director ordered = 360 feet.
Length of the rectangle = 40 yards
Width of the rectangle = 20 yards
Perimeter of the rectangle = 2l + 2w = 2 ( l + w)
P= 2( 40 + 20)
P = 2 x 60
P = 120 yards
CONVERTION:
1 yard = 3 feet
120 yards = ??
=> 120 x 3
=> 360 feet.
Hence, the director ordered fencing  360 feet is enough for fencing the tennis court because the required court perimeter is same 360 feet.

Conclusion:

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