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## enVision Math Common Core 2nd Grade Answers Key Topic 5 Subtract Within 100 Using Strategies

**Essential Question:**

What are strategies for subtracting numbers to 100?

**enVision STEM Project: Heating, Cooling, and Subtraction**

Find Out Have an adult help you heat and cool water and other · materials. Find out if water and ice can change back and forth. Find out if heating and cooling an egg can change it back and forth.

Journal: Make a Book Show what you learn in a book. In your book, also:

- Tell about how heating and cooling are related
- Tell about how addition and subtraction are related

**Review What You Know**

**Vocabulary**

Question 1.

Circle each difference in the math problems shown below.

15 – 5 = 10

Answer:

Explanation:

In the above image we can observe two mathematical operations one is Subtraction and other is addition. Here we have to circle the difference in the above problems. By subtracting five from fifteen then the difference is 10. So draw a circle to the difference 10. By subtracting seven from the fourteen then the difference is 7. So draw a circle for 7. By adding 23 with 32 then the sum is 55. Here we are adding the two numbers so don’t draw a circle for 55.

Question 2.

Circle the statement if it describes mental math.

Math that is done with paper and pencil

Math that you can do in your head

Answer:

Explanation:

Mental math means the Math that we can do in our head. So draw a circle for Math that you can do in your head.

Question 3.

Circle the statement if it describes compatible numbers.

Numbers that are close to numbers that you want to add or subtract

Numbers that you can add or subtract using mental math

Answer:

Explanation:

In mathematics, compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally. Compatible numbers are close in value to the actual numbers that make estimating the answer and computing problems easier. We can round the numbers to the nearest ten, hundred, thousand or ten thousand to make them compatible numbers. So draw a circle for Numbers that are close to numbers that you want to add or subtract. Numbers that you can add or subtract using mental math.

**Addition and Subtraction Facts**

Question 4.

Complete the related addition and subtraction facts below.

You can use addition facts to help you subtract.

Answer:

Explanation:

In the above image we can observe two problems.

First one we have to perform addition operation. By adding six with seven then the sum is thirteen.

Second one we have to perform subtraction operation. Subtract seven from the thirteen then the difference is six.

Question 5.

Write each sum or difference.

Answer:

Explanation:

In the above image we can observe two arithmetical operations. The addition is taking two or more numbers and adding them together results sum. Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

First is addition operation. Add four with seven then the sum is eleven.

Second is subtraction operation. Subtract three from twelve then the difference is nine.

Third is addition operation. Add nine with six then the sum is fifteen.

Fourth is subtraction operation. Subtract eight from sixteen then the difference is eight.

**Math Story**

Question 6.

Tim has 25 stamps. Roy gives him 51 more stamps. How many stamps does Tim have now?

________ stamps

Answer:

25 + 51 = ?

25 + 51 = 76

Time have **76** stamps.

Explanation:

Tim has 25 stamps. Roy gives him 51 more stamps. Add 25 stamps with 51 stamps then the sum is 76 stamps. Now Tim have 76 stamps.

**Pick a Project**

PROJECT 5A

How much does the largest gopher tortoise weigh?

Project: Write a Story About a Tortoise

PROJECT 5B

How does the temperature change where you live?

Project: Create a Weather Report

PROJECT 5C

How many moons do some planets in our solar system have?

Project: Research and Compare Moons

**3-ACT MATH PREVIEW**

Math Modeling

Laundry Day

### Lesson 5.1 Subtract Tens and Ones on a Hundred Chart

**Solve & Share**

How can you use the hundred chart to help you find 57 – 23? Explain. Write an equation.

I can … use a hundred chart to subtract tens and ones.

Answer:

Explanation:

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Start at 57 then count back two tens and 3 ones then we land on 34. The difference is 34.

Visual Learning Bridge

Convince Me! How can you use a hundred chart to find 60 – 18?

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

Start at 60 and go up 1 row to 50 and to the left 8 spaces to the 42. The difference is 42.

Explanation:

18 comprises of 1 ten and 8 ones. So, we need to start at 60 and count back 1 ten and 8 ones.

After counting back 1 ten we will land at 50 from 60. Now we have to count back 8 ones from 50. Finally, we land on 42 which is the subtraction value.

**Guided Practice**

Subtract using the hundred chart. Draw arrows if you need to.

Question 1.

69 – 36 = ________

Answer:

69 – 36 = **33**

Explanation:

36 comprises of 3 tens and 6 ones. So, we need to start at 69 and count back 3 tens and 6 ones.

In the above image we can see that after counting back 3 tens we will land at 39 from 69. Now we have to count back 6 ones from 39. Finally, we land on 33 which is the subtraction value.

Question 2.

54 – 24 =________

Answer:

54 – 24 = **30**

Explanation:

24 comprises of 2 tens and 4 ones. So, we need to start at 54 and count back 2 tens and 4 ones.

In the above image we can see that after counting back 2 tens we will land at 34 from 54. Now we have to count back 4 ones from 34. Finally, we land on 30 which is the subtraction value.

Question 3.

________ = 65 – 34

Answer:

**31** = 65 – 34

Explanation:

34 comprises of 3 tens and 4 ones. So, we need to start at 65 and count back 3 tens and 4 ones.

In the above image we can see that after counting back 3 tens we will land at 35 from 65. Now we have to count back 4 ones from 31. Finally, we land on 31 which is the subtraction value.

Question 4.

47 – 22 = ________

Answer:

47 – 22 = **25**

Explanation:

22 comprises of 2 tens and 2 ones. So, we need to start at 47 and count back 2 tens and 2 ones.

In the above image we can see that after counting back 2 tens we will land at 27 from 47. Now we have to count back 2 ones from 27. Finally, we land on 25 which is the subtraction value.

**Independent Practice**

Subtract using the hundred chart. Draw arrows if you need to.

Question 5.

54 – 7 = ________

Answer:

54 – 7 = **47**

Explanation:

07 comprises of 0 tens and 7 ones. So, we need to start at 54 and count back 0 tens and 7 ones.

In the above image we can see that after counting back 0 tens we will land at 54 from 54. Now we have to count back 7 ones from 54. Finally, we land on 47 which is the subtraction value.

Question 6.

________ = 96 – 63

Answer:

**33** = 96 – 63

Explanation:

63 comprises of 6 tens and 3 ones. So, we need to start at 96 and count back 6 tens and 3 ones.

In the above image we can see that after counting back 6 tens we will land at 36 from 96. Now we have to count back 3 ones from 36. Finally, we land on 33 which is the subtraction value.

Question 7.

45 – 22 = ________

Answer:

45 – 22 = **23**

Explanation:

22 comprises of 2 tens and 2 ones. So, we need to start at 45 and count back 2 tens and 2 ones.

In the above image we can see that after counting back 2 tens we will land at 25 from 45. Now we have to count back 2 ones from 25. Finally, we land on 23 which is the subtraction value.

Question 8.

82 – 61 = ________

Answer:

82 – 61 = **21**

Explanation:

61 comprises of 6 tens and 1 ones. So, we need to start at 82 and count back 6 tens and 1 ones.

In the above image we can see that after counting back 6 tens we will land at 22 from 82. Now we have to count back 1 ones from 22. Finally, we land on 21 which is the subtraction value.

Question 9.

65 – 21 = ________

Answer:

65 – 21 = **44**

Explanation:

21 comprises of 2 tens and 1 ones. So, we need to start at 65 and count back 2 tens and 1 ones.

In the above image we can see that after counting back 2 tens we will land at 45 from 65. Now we have to count back 1 ones from 45. Finally, we land on 44 which is the subtraction value.

Question 10.

________ = 79 – 47

Answer:

**32** = 79 – 47

Explanation:

47 comprises of 4 tens and 7 ones. So, we need to start at 79 and count back 4 tens and 7 ones.

In the above image we can see that after counting back 4 tens we will land at 39 from 79. Now we have to count back 7 ones from 39. Finally, we land on 32 which is the subtraction value.

Question 11.

84 – 6 = ________

Answer:

84 – 6 = 78

Explanation:

06 comprises of 0 tens and 6 ones. So, we need to start at 84 and count back 0 tens and 6 ones.

In the above image we can see that after counting back 0 tens we will land at 84 from 84. Now we have to count back 6 ones from 84. Finally, we land on 78 which is the subtraction value.

**Algebra** Write the digit that makes each equation true.

Question 12.

73 – ☐2 = 41

5☐ – 32 = 26

Answer:

73 – **3**2 = 41

5**8** – 32 = 26

Explanation:

In the first equation the digit that make the equation true is 3. Subtract tens part. Subtract three from seven then the difference is 4. Subtract ones. Subtract two from three then the difference is 1. The equation is 73 – 32 = 41.

In the second equation the digit that makes the equation true is 8. Subtract tens part. Subtract three from five then the difference is 2. Subtract ones. Subtract two from eight then the difference is 6. The equation is 58 – 32 = 26.

Question 13.

46 – ☐1 = 15

78 – 36 = ☐2

Answer:

46 – **3**1 = 15

78 – 36 = **4**2

Explanation:

In the first equation the digit that make the equation true is 3. Subtract tens part. Subtract three from four then the difference is 1. Subtract ones. Subtract one from six then the difference is 5. The equation is 46 – 31 = 15.

In the second equation the digit that makes the equation true is 4. Subtract tens part. Subtract three from seven then the difference is 4. Subtract ones. Subtract six from eight then the difference is 2. The equation is 78 – 36 = 42.

Question 14.

53 – ☐2 = 31

99 – ☐3 = 16

Answer:

53 – **2**2 = 31

99 – **8**3 = 16

Explanation:

In the first equation the digit that make the equation true is 2. Subtract tens part. Subtract two from five then the difference is 3. Subtract ones. Subtract two from three then the difference is 1. The equation is 53 – 22 = 31.

In the second equation the digit that makes the equation true is 8. Subtract tens part. Subtract eight from nine then the difference is 1. Subtract ones. Subtract three from nine then the difference is 6. The equation is 99 – 83 = 16.

**Problem Solving**

Use Tools Use the hundred chart to solve the problems below.

Question 15.

Darren’s puzzle has 98 pieces. Darren fits 55 pieces together. How many more pieces does Darren still need to fit to complete the puzzle?

________ ______ = ________ pieces

Answer:

Darren still need to fit 43 more pieces to complete the puzzle.

Explanation :

Darren’s puzzle has 98 pieces. Darren fits 55 pieces together. So subtract 55 pieces from 98 pieces.

55 comprises of 5 tens and 5 ones. So, we need to start at 98 and count back 5 tens and 5 ones.

In the above image we can see that after counting back 5 tens we will land at 48 from 98. Now we have to count back 5 ones from 48. Finally, we land on 43 which is the subtraction value. Darren still need to fit 43 more pieces to complete the puzzle.

Question 16.

A test has 86 questions. Glenda needs to answer 23 more questions to finish the test. How many test questions has Glenda answered already?

______ questions

Answer:

86 – 23 = **63**

Glenda answered 63 questions already.

Explanation:

A test has 86 questions. Glenda needs to answer 23 more questions to finish the test. So subtract 23 questions from 83 questions.

23 comprises of 2 tens and 3 ones. So, we need to start at 86 and count back 2 tens and 3 ones.

In the above image we can see that after counting back 2 tens we will land at 66 from 86. Now we have to count back 3 ones from 66. Finally, we land on 63 which is the subtraction value. Glenda answered 63 questions already.

Question 17.

**Higher Order Thinking** Chris wants to subtract 76 – 42. Write the steps he can take to subtract 42 from 76 on the hundred chart.

Answer:

Start at 76 move up 7 times and move to the left 2 times. Then the difference is 34.

76 – 42 = **34**

Explanation:

42 comprises of 4 tens and 2 ones. So, we need to start at 76 and count back 4 tens and 2 ones.

After counting back 4 tens we will land at 36 from 76. Now we have to count back 2 ones from 36. Finally, we land on 34 which is the subtraction value.

Question 18.

**Assessment Practice** which has a difference of 26? Choose all that apply.

☐ 56 – 30

☐ 69 – 43

☐ 75 – 49

☐ 92 – 76

Answer:

56 – 30 = 26

69 – 43 = 26

75 – 49 = 26

92 – 76 = 16

First 3 equations have the difference of 26.

Explanation:

Subtract 30 from 56 then the difference is 26.

Subtract 43 from 69 then the difference is 26.

Subtract 49 from 75 then the difference is 26.

Subtract 76 from 92 then the difference is 16.

### Lesson 5.2 Count Back to Subtract on an Open Number Line

**Solve & Share**

Jeremy had 56 bug stickers. He gave 24 stickers to Eric. How many bug stickers does Jeremy have left? Use the open number line below to show your work.

I can … use an open number line to subtract tens and ones.

Answer:

Jeremy have 32 bug stickers left.

Explanation:

Jeremy had 56 bug stickers. He gave 24 stickers to Eric. Here we used an open number line. First place 56 on the line. Here subtracting number 24 is 2 tens and 4 ones. So, count back 2 tens from 56. The numbers are 46, 36. Then count back 4 ones from 36. The numbers are 35, 34, 33, 32. Subtract 24 stickers from 56 stickers then the difference is 32.Jeremy have 32 bug stickers.

Visual Learning Bridge

Convince Me! How can the open number line help you keep track as you count back?

I am able to see my progress.

**Guided Practice**

Use an open number line to find each difference.

Question 1.

28 – 24 = ___________

Answer:

28 – 24 = **4**

Explanation:

In the above image we used a open number line to find the difference. First place 28 on the line. The subtracting number 24 is 2 tens and 4 ones. So, count back 2 tens from 28. The numbers are 18, 8. Then count back 4 ones from 8. The number is 4. By subtracting 24 from 28 the difference is 4.

Question 2.

50 – 35 = ___________

Answer:

50 – 35 = **15**

Explanation:

In the above image we used a open number line to find the difference. First place 50 on the line. The subtracting number 35 is 3 tens and 5ones. So, count back 3 tens from 50. The numbers are 40, 30, 20. Then count back 5 ones from 20. The number is 5. By subtracting 35 from 50 the difference is 15.

**Independent Practice**

Use an open number line to find each difference.

Question 3.

45 – 13 = ___________

Answer:

45 – 13 = **32**

Explanation:

In the above image we used a open number line to find the difference. First place 45 on the line. The subtracting number 13 is 1 ten and 3 ones. So, count back 1 ten from 45. The number is 35. Then count back 3 ones from 35. The number is 32. By subtracting 13 from 45 the difference is 32.

Question 4.

63 – 22 = ___________

Answer:

63 – 22 = **41**

Explanation:

In the above image we used a open number line to find the difference. First place 63 on the line. The subtracting number 22 is 2 tens and 2 ones. So, count back 2 tens from 63. The numbers are 53,43. Then count back 2 ones from 43. The number is 41. By subtracting 22 from 63 the difference is 41.

Question 5.

78 – 46 = ___________

Answer:

78 – 46 = **32**

Explanation:

In the above image we used a open number line to find the difference. First place 78 on the line. The subtracting number 46 is 4 tens and 6 ones. So, count back 4 tens from 78. The numbers are 68, 58, 48, 38. Then count back 6 ones from 38. The number is 32. By subtracting 46 from 78 the difference is 32.

Question 6.

92 – 37 = ___________

Answer:

92 – 37 = **55**

Explanation:

In the above image we used a open number line to find the difference. First place 92 on the line. The subtracting number 37 is 3 tens and 7 ones. So, count back 3 tens from 92. The numbers are 82, 72, 62. Then count back 7 ones from 62. The number is 55. By subtracting 37 from 92 the difference is 55.

Question 7.

80 – 44 = ?

Break apart the number you are subtracting into tens and ones.

Answer:

80 – 44 = **36 **

44 is 4 tens and 4 ones.

Explanation:

In the above image we used a open number line to find the difference. First place 80 on the line. The subtracting number 44 is 4 tens and 4 ones. So, count back 4 tens from 80. The numbers are 70, 60, 50, 40. Then count back 4 ones from 40. The number is 36. By subtracting 44 from 80 the difference is 36.

Question 8.

**Number Sense** How many tens and ones will you count back to solve this problem: 56 – 38 = ? Solve the problem.

___________ tens ___________ ones

_______ – _______ = ________

Answer:

**3** tens and **8** ones

56 – 38 = **18**

Explanation:

In the above image we used a open number line to find the difference. First place 56 on the line. The subtracting number 38 is 3 tens and 8 ones. So, count back 3 tens from 56. The numbers are 46, 36, 26. Then count back 8 ones from 26. The number is 18. By subtracting 38 from 56 the difference is 18.

**Problem Solving**

Use an open number line to solve each problem.

Question 9.

Use Tools There are 47 raffle tickets to sell for the fair. Ms. Brown’s class sells 23 raffle tickets. How many raffle tickets are left to sell?

________ raffle tickets

Answer:

24 raffle tickets are left to sell.

Explanation:

There are 47 raffle tickets to sell for the fair. Ms. Brown’s class sells 23 raffle tickets. Here the subtracting number is 23. In the above image we used a open number line to find the difference. First place 47 on the line. The subtracting number 23 is 2 tens and 3 ones. So, count back 2 tens from 47. The numbers are 37, 27. Then count back 3 ones from 27. The number is 24. By subtracting 23 from 47 the difference is 24. There are 24 raffle tickets left to sell.

Question 10.

Use Tools Ethan counts 78 carrots. He sells 35 carrots at the farmers market. How many carrots does Ethan have left?

_________ carrots

Answer:

Ethan have 43 carrots left.

Explanation:

Ethan counts 78 carrots. He sells 35 carrots at the farmers market. Here the subtracting number is 35. In the above image we used a open number line to find the difference. First place 78 on the line. The subtracting number 35 is 3 tens and 5 ones. So, count back 3 tens from 78. The numbers are 68, 58, 48. Then count back 5 ones from 48. The number is 43. By subtracting 35 carrots from 78 carrots the difference is 43 carrots. Ethan have 43 carrots left.

Question 11.

**Higher Order Thinking** Show two different ways to find 63 – 25 using the open number lines.

Answer:

63 – 25 = **38**

Explanation:

In the above image we used a open number lines to find the difference.

The first open number line.

First place 63 on the line. The subtracting number 25 is 2 tens and 5 ones. So, count back 2 tens from 63. The numbers are 53,43. Then count back 5 ones from 43. The number is 38. By subtracting 25 from 63 the difference is 38.

The second open number line.

First place 63 on the line. The subtracting number 25 is 2 tens and 5 ones. So, count back 2 tens from 63. The number is 43. Then count back 3 ones from 43. The number is 40. After that count back 2 ones from 40. The number is 38. By subtracting 25 from 63 the difference is 38.

Question 12.

**Assessment Practice** Jen solved a subtraction problem using the open number line shown. Write the equation that her work below shows.

Answer:

Explanation:

In the above image we can observe a open number line to find the difference. First place 56 on the line. The subtracting number 22 is 2 tens and 2 ones. So, count back 2 tens from 56. The numbers are 46, 36. Then count back 2 ones from 36. The number is 24. By subtracting 22 from 56 the difference is 34. The equation for the above open number line is 56 – 22 = 34.

### Lesson 5.3 Add Up to Subtract Using an Open Number Line

**Solve & Share**

There are 50 children at the park. 28 are boys and the rest are girls. How many girls are at the park? Use the open number line to solve. Show your work.

I can … add up to subtract using an open number line.

Answer:

There are 22 girls at the park.

Explanation:

There are 50 children at the park. 28 are boys and the rest are girls. In the above image we used a open number line to find the difference. First place 50 on the line. The subtracting number 28 is 2 tens and 8 ones. So, count back 2 tens from 50. The numbers are 40, 30. Then count back 5 ones from 30. The number is 25. Again count back 3 ones from 25. The number is 22. By subtracting 28 from 50 the difference is 22. There are 22 girls at the park.

The equation for the above open number line is 50 – 28 = 22.

Visual Learning Bridge

Convince Me! How can you add up to find 42 – 17?

Answer:

42 – 17 = **25**

Explanation:

In the above image we used a open number line. We can add up from 17 to subtract. First place 17 on the number line. Add 3 to get to 20. Then add 10, and 10 again to get to 40. Then add 2 to land on 42. Add the tens and ones. By adding 3,10, 10, and 2 the sum is 25. Subtracting 17 from 42 the difference is 25. We can check by adding 17 with 25 then the sum is 42.

**Guided Practice**

Add up to find each difference. Use an open number line.

Question 1.

Answer:

45 – 27 = 18

3 + 10 + 5 = 18

Explanation:

In the above image we used a open number line. We can add up from 27 to subtract. First place 27 on the number line. Add 3 to get to 30. Then add 10 to get to 40. Then add 5 to land on 45. Add the tens and ones. By adding 3,10, and 5 the sum is 18. Subtracting 27 from 45 the difference is 18. We can check by adding 27 with 18 then the sum is 45.

Question 2.

66 – 39 = ________

Answer:

66 – 39 = **27**

Explanation:

In the above image we used a open number line. We can add up from 39 to subtract. First place 39 on the number line. Add 1 to get to 40. Then add 10, and 10 again to get to 60. Then add 6 to land on 66. Add the tens and ones. By adding 1,10, 10, and 6 the sum is 27. Subtracting 39 from 66 the difference is 27. We can check by adding 39 with 27 then the sum is 66.

**Independent Practice**

Add up to find each difference. Use an open number line.

Question 3.

41 – 19 = ________

Answer:

41 – 19 = **22**

Explanation:

In the above image we used a open number line. We can add up from 19 to subtract. First place 19 on the number line. Add 1 to get to 20. Then add 10, and 10 again to get to 40. Then add 1 to land on 41. Add the tens and ones. By adding 1,10, 10, and 1 the sum is 22. Subtracting 19 from 41 the difference is 22. We can check by adding 19 with 22 then the sum is 41.

Question 4.

63 – 34 = ________

Answer:

63 – 34 = **29**

Explanation:

In the above image we used a open number line. We can add up from 34 to subtract. First place 34 on the number line. Add 6 to get to 40. Then add 10, and 10 again to get to 60. Then add 3 to land on 63. Add the tens and ones. By adding 6,10, 10, and 3 the sum is 29. Subtracting 34 from 63 the difference is 29. We can check by adding 34 with 29 then the sum is 63.

Question 5.

83 – 58 = ________

Answer:

83 – 58 = **25**

Explanation:

In the above image we used a open number line. We can add up from 58 to subtract. First place 58 on the number line. Add 2 to get to 60. Then add 10, and 10 again to get to 80. Then add 3 to land on 83. Add the tens and ones. By adding 2,10, 10, and 3 the sum is 25. Subtracting 58 from 83 the difference is 25. We can check by adding 58 with 25 then the sum is 83.

Question 6.

74 – 46 = ________

Answer:

74 – 46 = **28**

Explanation:

In the above image we used a open number line. We can add up from 46 to subtract. First place 46 on the number line. Add 4 to get to 50. Then add 10, and 10 again to get to 70. Then add 4 to land on 74. Add the tens and ones. By adding 4,10, 10, and 4 the sum is 28. Subtracting 46 from 74 the difference is 28. We can check by adding 46 with 28 then the sum is 74.

Question 7.

72 – 34 =________

Don’t forget to find the sum of the tens and the ones you added up. That is the difference.

Answer:

72 – 34 = **38**

Explanation:

In the above image we used a open number line. We can add up from 34 to subtract. First place 34 on the number line. Add 6 to get to 40. Then add 10, 10 and 10 again to get to 70. Then add 2 to land on 72. Add the tens and ones. By adding 6,10, 10, 10 and 2 the sum is 38. Subtracting 34 from 72 the difference is 38. We can check by adding 34 with 38 then the sum is 72.

Question 8.

enVision® STEM Rob had 34 snowballs. Some melted and now he has 18 snowballs. How many snowballs melted?

Answer:

16 snowballs melted.

Explanation:

Rob had 34 snowballs. Some melted and now he has 18 snowballs. In the above image we used a open number line. We can add up from 18 to subtract. First place 18 on the number line. Add 2 to get to 20. Then add 10 to get to 30. Then add 4 to land on 34. Add the tens and ones. By adding 2,10 and 4 the sum is 16. Subtracting 18 from 34 the difference is 16. We can check by adding 18 with 16 then the sum is 34. Total 16 snowballs melted.

**Problem Solving**

Add up to solve each problem. Use an open number line. Write the equations.

Question 9.

Be Precise Dino has 41 crayons. He gives 23 crayons to Bridget, and 7 crayons to Dan. How many crayons does Dino have left? Solve using two steps.

Answer:

Dino left with 11 crayons.

Explanation:

Dino has 41 crayons. He gives 23 crayons to Bridget, and 7 crayons to Dan.

**Step 1:**

In the above image we used a open number line. We can add up from 23 to subtract. First place 23 on the number line. Add 7 to get to 30. Then add 10 to get to 40. Then add 1 to land on 41. Add the tens and ones. By adding 7,10 and 1 the sum is 18. Subtracting 23 from 41 the difference is 18. Dino left with 18 crayons.

**Step 2:**

In the above image we used a open number line. We can add up from 7 to subtract. First place 7 on the number line. Add 3 to get to 10. Then add 8 to land on 18. Add the tens and ones. By adding 3, and 8 the sum is 11. Subtracting 7 from 18 the difference is 11. Now Dino left with 11 crayons.

Question 10.

**Higher Order Thinking** Show two different ways to add up to find 72 – 35.

1. ______ – _______ = _______

Answer:

72 – 35 = **37**

72 – 35 =** 37**

Explanation:

**Step 1:**

In the above image we used a open number line. We can add up from 35 to subtract. First place 35 on the number line. Add 5 to get to 40. Then add 10, 10, and 10 to get to 70. Then add 2 to land on 72. Add the tens and ones. By adding 5,10,10, 10 and 2 the sum is 37. Subtracting 35 from 72 the difference is 37. We can check by adding 35 with 37 then the sum is 72.

**Step 2:**

In the above image we used a open number line. We can add up from 35 to subtract. First place 35 on the number line. Add 5 to get to 40. Then add 30 to get to 70. Then add 2 to land on 72. Add the tens and ones. By adding 5, 30 and 2 the sum is 37. Subtracting 35 from 72 the difference is 37. We can check by adding 35 with 37 then the sum is 72.

Question 11.

**Assessment Practice** Find 46 – 25. Show your work on the open number line and then write an equation.

Answer:

Explanation:

In the above image we used a open number line. We can add up from 25 to subtract. First place 25 on the number line. Add 5 to get to 30. Then add 10 to get to 40. Then add 6 to land on 46. Add the tens and ones. By adding 5,10 and 6 the sum is 21. Subtracting 25 from 46 the difference is 21. We can check by adding 25 with 21 then the sum is 46.

### Lesson 5.4 Break Apart Numbers to Subtract

**Solve & Share**

Use any strategy to find 42 – 7. Use pictures, words, or numbers to explain.

I can … break apart I-digit numbers to help me subtract mentally.

Answer:

Explanation:

In the above image we can observe 42 – 7 equation. There are 4 tens and 2 ones in 42. So break apart the number that we are subtracting 7 into 2 + 5. First subtract 2 from 42 then the difference is 40. Then subtract 5 from the difference 40 then the result is 35. By subtracting 7 from 42 the difference is 35.

Visual Learning Bridge

Convince Me! Look at the problem above. Why wasn’t the 6 broken apart into 1 + 5 to find 33 – 6?

Answer:

Here we doesn’t use the 6 broken apart into 1 + 5 to find 33 – 6. Because we want the ones digit of “3” from the first number to match our break apart number.

**Guided Practice**

Subtract. Break apart the number you are subtracting. Show your work.

Question 1.

Answer:

43 – 3 = 40

40 – 6 = **34**

Explanation:

In the above image we can observe the subtracting number 9. Break apart 9 into 3 and 6. Start at 43 draw a circle for 40. First subtract 3 from 43 then the difference is 40. Draw a circle to 40. Then subtract 6 from the difference 40 then the result is 34. By subtracting 9 from 43 the difference is 34.

Question 2.

Answer:

24 – 4 = 20

20 – 2 = **18**

Explanation:

In the above image we can observe the subtracting number 6. Break apart 6 into 4 and 2. Start at 24 draw a circle for 24. First subtract 4 from 24 then the difference is 20. Draw a circle to 20. Then subtract 2 from the difference 20 then the result is 18. By subtracting 6 from 24 the difference is 18.

**Independent Practice**

Subtract. Break apart the number you are subtracting. Show your work. Use a hundred chart if needed.

Question 3.

Answer:

35 – 5 = 30

30 – 3 = **27**

Explanation:

In the above image we can observe the subtracting number 8. Break apart 8 into 5 and 3. First subtract 5 from 35 then the difference is 30. Then subtract 3 from the difference 30 then the result is 27. By subtracting 8 from 35 the difference is 27.

Question 4.

Answer:

41 – 1 = 40

40 – 4 = **36**

Explanation:

In the above image we can observe the subtracting number 5. Break apart 5 into 1 and 4. First subtract 1 from 41 then the difference is 40. Then subtract 4 from the difference 40 then the result is 36. By subtracting 5 from 41 the difference is 36.

Question 5.

Answer:

82 – 2 = 80

80 – 5 = **75**

Explanation:

In the above image we can observe the subtracting number 7. Break apart 7 into 2 and 5. First subtract 2 from 82 then the difference is 80. Then subtract 5 from the difference 80 then the result is 75. By subtracting 7 from 82 the difference is 75.

Question 6.

Answer:

53 – 3 = 50

50 – 4 = **46**

Explanation:

In the above image we can observe the subtracting number 7. Break apart 7 into 3 and 4. First subtract 3 from 53 then the difference is 50. Then subtract 4 from the difference 50 then the result is 46. By subtracting 7 from 53 the difference is 46.

Question 7.

Answer:

97 – 7 = 90

90 – 1 = 89

Explanation:

In the above image we can observe the subtracting number 8. Break apart 8 into 7 and 1. First subtract 7 from 97 then the difference is 90. Then subtract 1 from the difference 90 then the result is 89. By subtracting 8 from 97 the difference is 89.

Question 8.

Answer:

64 – 4 = 60

60 – 5 = **55**

Explanation:

In the above image we can observe the subtracting number 9. Break apart 9 into 4 and 5. First subtract 4 from 64 then the difference is 60. Then subtract 5 from the difference 60 then the result is 55. By subtracting 9 from 64 the difference is 55.

Question 9.

86 – 8 = _______

Answer:

86 – 6 = 80

80 – 2 = **78**

Explanation:

In the above image we can observe the subtracting number 8. Break apart 8 into 6 and 2. First subtract 6 from 86 then the difference is 80. Then subtract 2 from the difference 80 then the result is 78. By subtracting 8 from 86 the difference is 78.

Question 10.

________ = 32 – 9

Answer:

32 – 2 = 30

30 – 7 = 23

Explanation:

In the above image we can observe the subtracting number 9. Break apart 9 into 2 and 7. First subtract 2 from 32 then the difference is 30. Then subtract 7 from the difference 30 then the result is 23. By subtracting 9 from 32 the difference is 23.

Question 11.

93 – 6 = _______

Answer:

93 – 3 = 90

90 – 3 = **87**

Explanation:

In the above image we can observe the subtracting number 6. Break apart 6 into 3 and 3. First subtract 3 from 93 then the difference is 90. Then subtract 3 from the difference 90 then the result is 87. By subtracting 6 from 93 the difference is 87.

Question 12.

**Algebra** One number makes both equations true.

Find the missing number.

The missing number is ________

Answer:

The missing number is **8.**

Explanation:

In the above image we can observe two mathematical operations with two missing numbers. Add 48 with 8 then the sum is 56. Next subtract 8 from 56 then the difference is 48. The number that makes the both equation true is 8.

**Problem Solving**

Solve each problem. Show your work.

Question 13.

Explain Karen has 7 pencils. Karen’s teacher has 45 pencils. How many fewer pencils does Karen have than her teacher? Explain how you solved the problem.

Answer:

45 – 5 = 40

40 – 2 = **38**

Karen have 38 fewer pencils than her teacher.

Explanation:

Karen has 7 pencils. Karen’s teacher has 45 pencils. In the above image we can observe the subtracting number 7. Break apart 7 into 5 and 2. First subtract 5 from 45 then the difference is 40. Then subtract 2 from the difference 40 then the result is 38. By subtracting 7 from 45 the difference is 38. Karen have 38 fewer pencils than her teacher.

Question 14.

Higher Order Thinking Write a story problem about 63 – 8. Then solve.

63 – 8 = ________

Answer:

There are 63 stickers. I gave away 8 stickers. How many stickers are left ?

63 – 3 = 60

60 – 5 = **55
**55 stickers are left.

Explanation:

There are 63 stickers. I gave away 8 stickers. In the above image we can observe the subtracting number 8. Break apart 8 into 3 and 5. First subtract 3 from 63 then the difference is 60. Then subtract 5 from the difference 60 then the result is 55. By subtracting 8 from 63 the difference is 55. 55 stickers are left.

Question 15.

Duane has 24 seashells. He gives 9 shells to his cousin Rob. How many seashells does Duane have now?

A. 16

B. 15

C. 14

D. 13

Answer:

Option B is correct.

Explanation:

In the above image we can observe the subtracting number 9. Break apart 9 into 4 and 5. First subtract 4 from 24 then the difference is 20. Then subtract 5 from the difference 20 then the result is 15. By subtracting 9 from 24 the difference is 15. So option B is correct.

Question 16.

**Assessment Practice** Find 86 – 7. Show your work.

86 – 7 = __________

Answer:

86 – 6 = 80

80 – 1 = **79**

Explanation:

In the above image we can observe the subtracting number 7. Break apart 7 into 6 and 1. First subtract 6 from 86 then the difference is 80. Then subtract 1from the difference 80 then the result is 79. By subtracting 7 from 86 the difference is 79.

### Lesson 5.5 Subtract Using Compensation

**Solve & Share**

Yuri wants to use mental math to find 86 – 29. Show how Yuri could find the difference. Explain how she could use mental math.

I can … make numbers that are easier to subtract, then use mental math to find the difference.

Answer:

Explanation:

In the above image we can observe that the subtracting number 29. Break apart 29 into 20 and 9. First Subtract 20 from 86 then the difference is 66. After that break apart 9 into 6 and 3. Subtract 6 from the difference 66 then the result is 60. Then subtract 3 from 60 the difference is 57. By subtracting 29 from 86 the difference is 57.

Visual Learning Bridge

Convince Me! Marc says to find 61 – 13, it’s easier to subtract 10 instead of 13. He says if you subtract 3 from 13 to get 10, you must subtract 3 more from your answer. Do you agree? Explain.

Answer:

Yes

61 – 10 = 51

51 – 3 = **48**

Explanation:

I agree with Marc. It’s easier to subtract 10 instead of 13. Marc says if we subtract 3 from 13 to get 10, We must subtract 3 more from your answer. Subtract 10 from 61 then the difference is 51. Subtract 3 from 51 then the difference is 48.

**Guided Practice**

Use compensation to make numbers that are easier to subtract. Then solve. Show your work.

Question 1.

Question 2.

Answer:

Explanation:

In the above image we can observe an equation 76 – 27 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by adding the same amount. Then subtract using mental math. Add 3 to the addends 76 and 27. Then the equation is 79 – 30 = ?. Subtract 30 from 79 then the difference is 49.

Question 3.

Answer:

Explanation:

In the above image we can observe an equation 52 – 15 = ?. Here we are using compensation method to make numbers that are easier to subtract. Add 5 to 15. Then the equation is 52 – 20 = ?. Then subtract using mental math. Subtract 20 from 52 then the difference is 32. Then add 5 to the answer 32. After adding 5 to the number 32 the sum is 37. By subtracting 15 from 52 the difference is 37.

Question 4.

Answer:

Explanation:

In the above image we can observe an equation 93 – 39 = ?. Here we are using compensation method to make numbers that are easier to subtract. Add 1 to 39. Then the equation is 93 – 40 = ?. Then subtract using mental math. Subtract 40 from 93 then the difference is 53. Then add 1 to the answer 53. After adding 1 to the number 53 the sum is 54. By subtracting 39 from 93 the difference is 54.

**Independent Practice**

Use compensation to make numbers that are easier to subtract. Then solve. Show your work.

Question 5.

73 – 9 = ________

Answer:

Explanation:

In the above image we can observe an equation 73 – 9 = ?. Here we are using compensation method to make numbers that are easier to subtract. Add 1 to 9. Then the equation is 73 – 10 = ?. Then subtract using mental math. Subtract 10 from 73 then the difference is 63. Then add 1 to the answer 63. After adding 1 to the number 63 the sum is 64. By subtracting 9 from 73 the difference is 64.

Question 6.

35 – 16 = ________

Answer:

Explanation:

In the above image we can observe an equation 35 – 16 = ?. Here we are using compensation method to make numbers that are easier to subtract. Add 4 to 16. Then the equation is 35 – 20 = ?. Then subtract using mental math. Subtract 20 from 35 then the difference is 15. Then add 4 to the answer 15. After adding 4 to the number 15 the sum is 19. By subtracting 16 from 35 the difference is 19.

Question 7.

43 – 28 = ________

Answer:

Explanation:

In the above image we can observe an equation 43 – 28 = ?. Here we are using compensation method to make numbers that are easier to subtract. Add 2 to 28. Then the equation is 43 – 30 = ?. Then subtract using mental math. Subtract 30 from 43 then the difference is 13. Then add 2 to the answer 13. After adding 2 to the number 13 the sum is 15. By subtracting 28 from 43 the difference is 15.

Question 8.

51 – 27 = ________

Answer:

Explanation:

In the above image we can observe an equation 51 – 27= ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by adding the same amount. Then subtract using mental math. Add 3 to the addends 51 and 27. Then the equation is 54 – 30 = ?. Subtract 30 from 54 then the difference is 24.

Question 9.

74 – 35 = ________

Answer:

Explanation:

In the above image we can observe an equation 74 – 35 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by adding the same amount. Then subtract using mental math. Add 5 to the addends 74 and 35. Then the equation is 79 – 40 = ?. Subtract 40 from 79 then the difference is 39.

Question 10.

99 – 21 = ________

Answer:

Explanation:

In the above image we can observe an equation 99 – 21 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by subtracting the same amount. Then subtract using mental math. Subtract 1 from both numbers 99 and 21. Then the equation is 98 – 20 = ?. Subtract 20 from 98 then the difference is 78.

Question 11.

**Higher Order Thinking** Yoshi says that to find 91 – 32, he can subtract 2 from both numbers. Then he can subtract using mental math. He says the answer is 59. Do you agree? Explain.

Answer:

Explanation:

Yes I agree with Yoshi. In the above image we can observe an equation 91 – 32 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by subtracting the same amount. Then subtract using mental math. Subtract 2 from both numbers 91 and 32. Then the equation is 89 – 30 = ?. Subtract 30 from 89 then the difference is 59.

**Problem Solving**

Solve each problem. Show your thinking.

Question 12.

Make Sense There were some buttons in a jar. Mrs. Kim puts 19 more buttons in the same jar. Now there are 45 buttons in the jar. How many buttons were in the jar to begin with?

_________ buttons

Answer:

There are 26 buttons in the jar to begin.

Explanation:

There were some buttons in a jar. Mrs. Kim puts 19 more buttons in the same jar. Now there are 45 buttons in the jar. In the above image we can observe an equation 45 – 19 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by adding the same amount. Then subtract using mental math. Add 1 to the addends 45 and 19. Then the equation is 46 – 20 = ?. Subtract 20 from 46 then the difference is 26. There are 26 buttons in the jar to begin.

Question 13.

Romi has 42 cards. Lisa has 75 cards. How many more cards does Lisa have than Romi?

Think about more cards what you are trying to find.

__________ more cards

Answer:

Lisa have 33 more cards than Romi.

Explanation:

Romi has 42 cards. Lisa has 75 cards. In the above image we can observe an equation 75 – 42 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by subtracting the same amount. Then subtract using mental math. Subtract 2 from both numbers 75 and 42. Then the equation is 73 – 40 = ?. Subtract 40 from 73 then the difference is 33. Lisa have 33 more cards than Romi.

Question 14.

**Higher Order Thinking** Greg found 72 – 24. First he subtracted 20 because he thinks it is easier. Use words and numbers to explain how Greg could have found the difference.

Answer:

Explanation:

In the above image we can observe a equation 72 – 24. Subtract 20 from both the numbers then the equation is 52 – 4. Break apart 4 into 2 and 2. First subtract 2 from 52 then the difference is 50. Then subtract 2 from the difference 50 the result is 48.

Question 15.

**Assessment Practice** Use the numbers on the cards. Write the missing numbers to solve the problem.

Answer:

Explanation:

In the above image we can observe an equation 53 – 28 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by adding the same amount. Then subtract using mental math. Add 2 to the addends 53 and 28. Then the equation is 55 – 30 = ?. Subtract 30 from 55 then the difference is 25. The missing number is 25.

### Lesson 5.6 Practice Subtracting Using Strategies

**Solve & Share**

Randy got 42 craft sticks for a project. He used 19 sticks. How many sticks are left? Choose any strategy. Solve. Show and explain your work.

I can … choose a strategy to help me subtract two-digit numbers.

_______ sticks

Answer:

23 sticks are left.

Explanation:

Randy got 42 craft sticks for a project. He used 19 sticks. In the above image we can observe an equation 42 – 19 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by adding the same amount. Then subtract using mental math. Add 1 to the addends 42 and 19. Then the equation is 43 – 20 = ?. Subtract 20 from 43 then the difference is 23. 23 sticks are left.

Visual Learning Bridge

Convince Me! In Another Way above, why was 3 added to 37 and then added to 25?

Answer:

In Compensation method we have to add the number on both sides. Here we are adding 3 to 37. Subtract 40 from 65 the difference is 25. Add 3 to the difference 25 then the sum is 28.

**Guided Practice**

Find each difference. Use any strategy. Show your work.

Question 1.

46 – 18 = ________

2 + 10 + 10 + 6 = 28

46 – 18 = **28**

Explanation:

In the above image we used a open number line. We can add up from 18 to subtract. First place 18 on the number line. Add 2 to get to 20. Then add 10, and 10 to get to 40. Then add 6 to land on 46. Add the tens and ones. By adding 2, 10, 10 and 6 the sum is 28. Subtracting 18 from 46 the difference is 28. We can check by adding 18 with 28 then the sum is 46.

Question 2.

83 – 46 = _______

Answer:

Explanation:

In the above image we used a open number line. We can add up from 46 to subtract. First place 46 on the number line. Add 4 to get to 50. Then add 10, 10, and 10 to get to 80. Then add 3 to land on 83. Add the tens and ones. By adding 4,10,10, 10 and 3 the sum is 37. Subtracting 46 from 83 the difference is 37. We can check by adding 46 with 37 then the sum is 83.

**Independent Practice**

Find each difference. Use any strategy. Show your work.

Question 3.

62 – 21 = _______

Answer:

Explanation:

In the above image we can observe an equation 62 – 21 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by subtracting the same amount. Then subtract using mental math. Subtract 1 from both numbers 62 and 21. Then the equation is 61 – 20 = ?. Subtract 20 from 61 then the difference is 41.

Question 4.

33 – 6 = _______

Answer:

Explanation:

In the above image we used a open number line. We can add up from 6 to subtract. First place 6 on the number line. Add 4 to get to 10. Then add 10, and 10 to get to 30. Then add 3 to land on 33. Add the tens and ones. By adding 4, 10, 10 and 3 the sum is 27. Subtracting 6 from 33 the difference is 27. We can check by adding 6 with 27 then the sum is 33.

Question 5.

94 – 45 = _______

Answer:

Explanation:

In the above image we can observe an equation 94 – 45 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by adding the same amount. Then subtract using mental math. Add 5 to the addends 94 and 45. Then the equation is 99 – 50 = ?. Subtract 50 from 99 then the difference is 49.

Question 6.

55 – 18 = _______

Answer:

Explanation:

In the above image we used a open number line. We can add up from 18 to subtract. First place 18 on the number line. Add 2 to get to 20. Then add 10, 10, and 10 to get to 50. Then add 5 to land on 55. Add the tens and ones. By adding 2, 10, 10, 10 and 5 the sum is 37. Subtracting 18 from 55 the difference is 37. We can check by adding 18 with 37 then the sum is 55.

Question 7.

44 – 7 = _______

Answer:

Explanation:

In the above image we can observe an equation 44 – 7 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by adding the same amount. Then subtract using mental math. Add 3 to the addends 44 and 7. Then the equation is 47 – 10 = ?. Subtract 10 from 47 then the difference is 17.

Question 8.

80 – 61 = _______

Answer:

Explanation:

In the above image we used a open number line. We can add up from 61 to subtract. First place 61 on the number line. Add 9 to get to 70. Then add 10 to land on 80. Add the tens and ones. By adding 9 and 10 the sum is 19. Subtracting 61 from 80 the difference is 19. We can check by adding 61 with 19 then the sum is 80.

Question 9.

77 – 9 = _______

Answer:

Explanation:

In the above image we can observe an equation 77 – 9 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by adding the same amount. Then subtract using mental math. Add 1 to the addends 77 and 9. Then the equation is 78 – 10 = ?. Subtract 10 from 78 then the difference is 68.

Question 10.

100 – 55 = _______

Answer:

Explanation:

In the above image we can observe an equation 100 – 55 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both numbers by subtracting the same amount. Then subtract using mental math. Subtract 5 from both numbers 100 and 55. Then the equation is 95 – 50 = ?. Subtract 50 from 95 then the difference is 45.

Question 11.

72 – 48 = _______

Answer:

Explanation:

In the above image we used a open number line. We can add up from 48 to subtract. First place 48 on the number line. Add 2 to get to 50. Then add 10, and 10 to get to 70. Then add 2 to land on 72. Add the tens and ones. By adding 2, 10, 10, and 2 the sum is 24. Subtracting 48 from 72 the difference is 24. We can check by adding 48 with 24 then the sum is 72.

**Number Sense** Write the digit that makes each equation true.

Question 12.

5☐ – 6 = 47

Answer:

5**3** – 6 = 47

Explanation:

In the above equation the digit that make the equation true is 3. Subtract six from 53 then the difference is 47. The equation is 53 – 6 = 47.

Question 13.

☐4 – 28 = 56

Answer:

**8**4 – 28 = 56

Explanation:

In the above equation the digit that make the equation true is 8. Subtract 28 from 84 then the difference is 56. The equation is 84 – 28 = 56.

Question 14.

61 – 1☐ = 46

Answer:

61 – 1**5** = 46

Explanation:

In the above equation the digit that make the equation true is 5. Subtract 15 from 61 then the difference is 46. The equation is 61 – 15 = 46.

**Problem Solving**

Use any strategy to solve each problem.

Question 15.

Luis has 31 stickers. Martin has 12 fewer stickers than Luis. Kaley has 45 stickers. How many stickers do Martin and Luis have in all? Do they have more or fewer stickers than Kaley? Explain.

_________ stickers

Circle:

more

fewer

Answer:

Luis and Martin have 43 stickers in all and Kaley have 45 stickers.

Luis and Martin have 2 fewer stickers than Kaley.

Explanation:

Luis has 31 stickers. Martin has 12 fewer stickers than Luis. Kaley has 45 stickers. First add 31 stickers and 12 stickers then the sum is 43 stickers in all. Luis and Martin have 2 fewer stickers than Kaley.

Question 16.

Kyle made 44 clay beads on Monday. On Tuesday, he made 8 fewer beads than he made on Monday. On Wednesday, he made 10 fewer beads than on Tuesday. How many beads did Kyle make on Wednesday?

_______ beads

Answer:

Kyle made 44 clay beads on Monday.

44 – 8 = **36**

Kyle made 36 beads on Tuesday.

36 – 10 = **26**

Kyle made 26 beads on Wednesday.

Explanation:

Kyle made 44 clay beads on Monday. On Tuesday, he made 8 fewer beads than he made on Monday. Subtract 8 beads from 44 beads then the difference is 36. Kyle made 36 beads on Tuesday. On Wednesday, he made 10 fewer beads than on Tuesday. Subtract 10 beads from 36 beads then the difference is 26. Kyle made 26 beads on Wednesday.

Question 17.

**Assessment Practice** Find the difference. 63 – 18 = ________

Explain how you solved the problem.

Answer:

2 + 10 + 10 + 10 + 10 + 3 = 45

63 – 18 = 45

Explanation:

In the above image we used a open number line. We can add up from 18 to subtract. First place 18 on the number line. Add 2 to get to 20. Then add 10, 10, 10 and 10 to get to 60. Then add 3 to land on 63. Add the tens and ones. By adding 2, 10, 10, 10, 10, and 3 the sum is 45. Subtracting 18 from 63 the difference is 45. We can check by adding 18 with 45 then the sum is 63.

### Lesson 5.7 Solve One-Step and Two-Step Problems

**Solve & Share**

Some frogs were sitting on a pond. 16 more frogs joined them. Now there are 49 frogs on the pond. How many frogs were on the pond at first? Show how you know.

I can … solve one- and two-step problems using addition or subtraction.

Answer:

33 frogs are there on the pond at first.

Explanation:

Some frogs were sitting on a pond. 16 more frogs joined them. Now there are 49 frogs on the pond. Subtract 16 frogs from 49 frogs. First break apart 16 into 10 and 6. Subtract 10 from 49 then the difference is 39. Next subtract the 6 frogs from 39 frogs then the difference is 33 frogs. At first 33 frogs are there on the pond.

Visual Learning Bridge

Convince Me! Cory scored some points. Then he scored 8 more points. He scored 14 points in all. How many points did Cory score at first? How can you solve the problem?

Answer:

Cory scored 6 points.

Explanation:

Cory scored some points. Then he scored 8 more points. He scored 14 points in all. Subtract 8 points from 14 points then the difference is 6. Cory scored 6 points.

**Guided Practice**

Complete both equations to solve the problem. Use the bar diagram to help you.

Question 1.

Some people got on the bus at the first stop. 9 more people got on the bus at the second stop. There are 21 people on the bus now. How many people got on the bus at the first stop?

Answer:

At the first stop 12 people got on the bus.

Explanation:

Some people got on the bus at the first stop. 9 more people got on the bus at the second stop. There are 21 people on the bus now. Subtract 9 people from 21 people then the difference is 12 people. At the first stop 12 people got on the bus.

**Independent Practice**

Solve each problem. Show your work.

Question 2.

There are 24 peas on Kim’s plate. Kim eats 15 peas. Then Kim’s mother puts 8 more peas on her plate. How many peas are on Kim’s plate now?

__________ peas

Answer:

There are 17 peas on Kim’s plate.

Explanation:

There are 24 peas on Kim’s plate. Kim eats 15 peas. Subtract 15 peas from 24 peas then the difference is 9 peas. Then Kim’s mother puts 8 more peas on her plate. Add 9 peas with 8 more peas then the sum is 17 peas. There are 17 peas on Kim’s plate.

Question 3.

Sue took out 5 books from the library on Monday. She took out 6 books from the library on Tuesday. Then she returned 3 books on Wednesday. How many books does Sue have on Thursday?

________ books

Answer:

5 + 6 = 11

11 – 3 = 8

Sue have 8 books on Thursday.

Explanation:

Sue took out 5 books from the library on Monday. She took out 6 books from the library on Tuesday. Add the books on Monday and Tuesday. Add 5 books with 6 books then the sum is 11 books. Now Sue have 11 books. Then she returned 3 books on Wednesday. Subtract 3 books from 11 books then the difference is 8 books. Sue have 8 books on Thursday.

Question 4.

**Higher Order Thinking** Mr. Wing’s class collected some cans to recycle on Tuesday. They collected 18 more cans : on Wednesday. The class collected 44 cans in all. How many cans did the class collect on Tuesday?

Answer:

The class collect 26 can on Tuesday.

Explanation:

Mr. Wing’s class collected some cans to recycle on Tuesday. They collected 18 more cans on Wednesday. The class collected 44 cans in all. Subtract 18 cans from 44 cans then the difference is 26 cans. The class collect 26 can on Tuesday.

**Problem Solving**

Write equations to solve the problems.

Question 5.

Make Sense Elaine put 13 photos in the album. Ken put some more photos in the album. There are 32 photos in the album in all. How many photos did Ken add?

_________ photos

Answer:

Ken add 19 more photos in the album.

Explanation:

Elaine put 13 photos in the album. Ken put some more photos in the album. There are 32 photos in the album in all. Subtract 13 photos from 32 photos then the difference is 19 photos. Ken add 19 more photos in the album.

Question 6.

Make Sense Kris sees some students in the library. Then 10 more students enter the library. Now Kris sees 20 students. How many students were in the library to start?

_________ students

Answer:

There are 10 students in the library to start.

Explanation:

Kris sees some students in the library. Then 10 more students enter the library. Now Kris sees 20 students. Subtract 10 students from 20 students then the difference is 10. There are 10 students in the library to start.

Question 7.

**Higher Order Thinking** There are 15 vocabulary words in Week I. There are 8 more vocabulary words in Week 2 than in Week I. How many words are there in both weeks?

Step 1: _______ + ________

Step 2: _______ + _________

_________ words

Answer:

Step 1: **15 + 8 = 23**

Step 2: **23 + 15 = 38**

**38** words are there in both weeks.

Explanation:

There are 15 vocabulary words in Week I. There are 8 more vocabulary words in Week 2 than in Week I.

**Step 1:**

Add 15 words with 8 words then the sum is 23 words. In Week 2 there are 23 vocabulary words.

**Step 2:**

Add 15 words with 23 words then the sum is 38 words. 38 words are there in both weeks.

Question 8.

**Assessment Practice** Blake puts 8 marbles in the bag. Cole puts 9 marbles in the bag. Then Blake takes out 7 marbles from the bag. How many marbles are in the bag now? Solve. Show your work.

_________ marbles

Answer:

Step 1: **8 + 9 = 17**

Step 2: **17 – 7 = 10**

Now there are 10 marbles in the bag.

Explanation:

Blake puts 8 marbles in the bag. Cole puts 9 marbles in the bag. Then Blake takes out 7 marbles from the bag.

**Step 1:**

Add 8 marbles with 9 marbles then the sum is 17 marbles. Total number of marbles are 17.

**Step 2:**

Subtract 7 marbles from 17 marbles then the difference is 10 marbles. Now there are 10 marbles in the bag.

### Lesson 5.8 Problem Solving

**Critique Reasoning**

**Solve & Share**

Bill collects and sells seashells. He has 45 shells, finds 29 shells, and sells 20 shells. How many seashells does Bill have now?

Tara says you have to subtract 45 – 29 and then add 20 to solve the problem. Do you agree with Tara’s thinking? Circle your answer. Use pictures, words, or equations to explain.

I can … critique the thinking of others by using what I know about addition and subtraction.

Answer:

Bill have 54 seashells.

Explanation:

Bill collects and sells seashells. He has 45 shells, finds 29 shells, and sells 20 shells. First break apart 45 into 40 and 5 after that break 29 into 20 and 9. Add 40 with 20 then the sum is 60. Then add 5 with 9 then the sum is 14. Add these two numbers 60 and 14 then the sum is 74. Subtract 20 shells from 74 shells then the difference is 54 shells. Bill have 54 seashells. So Don’t agree with Tara’s thinking. So draw a circle for Do Not Agree.

Thinking Habits

What questions can I ask to understand other people’s thinking?

Are there mistakes in other people’s thinking?

Visual Learning Bridge

Convince Me! What question would you ask Kelly to help her check her reasoning?

Answer:

I could ask her for the total number of people swimming.

**Guided Practice**

Circle your answer. Use pictures, words, or equations to explain your reasoning.

Question 1.

51 people were on a train. 33 people left the train. How many people are on the train now?

Ryan says 18 people. He broke apart 33 into 30 and 3. Then he subtracted each number. Does Ryan’s reasoning make sense?

Answer:

Now there are 18 people on the train.

Explanation:

51 people were on a train. 33 people left the train. Ryan says 18 people. He broke apart 33 into 30 and 3. Then he subtracted each number. I am agree with Ryan’s reasoning. First break apart 33 into 30 and 3. Subtract 30 from 51 then the difference is 21. Then subtract 3 from 21 then the difference is 18. There are 18 people on the train. So draw a circle for agree.

**Independent Practice**

Circle your answer. Use pictures, words, or equations to explain your reasoning.

Question 2.

Jill put 53 buttons in a box. Marci put 17 buttons in another box.

Jarod says Marci has 33 fewer buttons than Jill. He thinks 53 – 20 is easier to subtract than 53 – 17. He subtracts 53 – 20 and gets 33.

Do you agree or not agree with Jarod’s thinking?

Answer:

Explanation:

Jill put 53 buttons in a box. Marci put 17 buttons in another box.

Jarod says Marci has 33 fewer buttons than Jill. He thinks 53 – 20 is easier to subtract than 53 – 17. He subtracts 53 – 20 and gets 33. I am agree with Jarod’s thinking because he forgot to add 3 to his answer.

First add 3 to 17 then the equation is 53 – 20 = ?. Subtract 20 from 53 then the difference is 33. Then add 3 to the 33 then the sum is 36. So draw a circle for Do Not Agree.

Question 3.

Rob has 68 more puzzle pieces than Gina. Rob has 90 puzzle pieces.

Carol says Gina has 22 puzzle pieces. Carol says she found 90 – 68 using an open number line. She added up 2 and 20 more from 68 and got 90.

Does Carol’s reasoning make sense?

Answer:

Explanation:

Rob has 68 more puzzle pieces than Gina. Rob has 90 puzzle pieces.

Carol says Gina has 22 puzzle pieces. Carol says she found 90 – 68 using an open number line. She added up 2 and 20 more from 68 and got 90. Carol’s reasoning is correct. So draw a circle for Agree.

In the above image we used a open number line. We can add up from 68 to subtract. First place 68 on the number line. Add 2 to get to 70. Then add 10 to get to 80. Then add 10 to land on 90. Add the tens and ones. By adding 2, 10, and 10 the sum is 22. Subtracting 68 from 90 the difference is 22.

**Problem Solving**

**Performance Task**

Reading Books Ricky read the first 3 chapters of a book. Chapter 1 has 11 pages. Chapter 2 has 7 pages. Chapter 3 has 9 pages.

Sally read 46 pages of her book. How many more pages did Sally read than Ricky?

Question 4.

Make Sense What steps do you need to take to solve the problem?

Answer:

First I need to know how many pages Ricky read.

Question 5.

Look for a Pattern Is there a shortcut to find how many pages Ricky read? Explain.

Answer:

11 + 7 + 9 = ?

11 + 9 = 20

20 + 7 =** 27
**Ricky read 27 pages.

Explanation:

Ricky read the first 3 chapters of a book. Chapter 1 has 11 pages. Chapter 2 has 7 pages. Chapter 3 has 9 pages. Add 11 pages with 7 pages and 9 pages then we get the total number of pages. First add 11 pages with 9 pages then the sum is 20 pages. Add 9 pages with 20 pages then the sum is 27 pages. Ricky read 27 pages.

Question 6.

Explain Sally drew this open number line. Sally says she read 21 more pages than Ricky. Do you agree? Explain.

Answer:

Explanation:

Sally read 46 pages of her book. Ricky read 27 pages. Sally says she read 21 more pages than Ricky. I am not agree with Sally answer. Subtract 27 pages from 46 pages then the difference is 19 pages.

### Topic 5 Fluency Practice Activity

**Find & Match**

Find a partner. Point to a clue. Read the clue.

Look below the clues to find a match. Write the clue letter in the box next to the match.

Find a match for every clue.

I can … add and subtract within 20.

Clues

A. Every difference is 10.

B. Every sum is 11.

C. Every sum and difference is 6.

D. Exactly three sums are the same.

E. Exactly three differences are the same.

F. Every sum is the same as 9 + 4.

G. Every difference is odd.

H. Exactly three sums are even.

Answer:

Explanation:

In the above image we can observe the list below.

A. Every difference is 10.

10 – 0 = 10

20 – 10 = 10

14 – 4 = 10

19 – 9 = 10

B. Every sum is 11.

5 + 6 = 11

4 + 7 = 11

9 + 2 = 11

3 + 8 = 11

C. Every sum and difference is 6.

14 – 8 = 6

3 + 3 = 6

15 – 9 = 6

0 + 6 = 6

D. Exactly three sums are the same.

8 + 6 = 14

7 + 8 = 15

9 + 6 = 15

10 + 5 = 15

E. Exactly three differences are the same.

12 – 5 = 7

17 – 8 = 9

14 – 7 = 7

16 – 9 = 7

F. Every sum is the same as 9 + 4.

7 + 6 = 13

3 + 10 = 13

8 + 5 = 13

4 + 9 = 13

G. Every difference is odd.

15 – 8 = 7

18 – 9 = 9

12 – 7 = 5

13 – 6 = 7

H. Exactly three sums are even.

6 + 6 = 12

2 + 8 = 10

7 + 4 = 11

5 + 7 = 12

### Topic 5 Vocabulary Review

Understand Vocabulary

Word List

- break apart
- compatible numbers
- compensation
- difference
- mental math
- ones
- open number line
- tens

Choose a term from the Word List to complete each sentence.

Question 1.

You can count back or add up to subtract on an ___________

Answer:

You can count back or add up to subtract on an **open number line**.

Question 2.

To find 42 – 7, you can ________ into 2 + 5.

Answer:

To find 42 – 7, you can **break apart** **7** into 2 + 5.

Question 3.

The answer to a subtraction problem is called the __________

Answer:

The answer to a subtraction problem is called the **difference**.

Question 4.

There are 6 ________ in the number 36.

Answer:

There are 6 **ones** in the number 36.

Question 5.

In 43, there are _______ tens.

Answer:

In 43, there are **4** tens.

Question 6.

In 76, there are _______ tens and ________ ones.

Answer:

In 76, there are **7** tens and** 6** ones.

Question 7.

Break apart 8 to find 65 – 8.

Answer:

Break a part 8 into 5 + 3 to find 65 – 8.

65 – 5 = 60

60 – 3 = **57**

**Use Vocabulary in Writing**

Question 8.

Use words to tell how to find 54 – 19. Use terms from the Word List.

Answer:

54 – 19

+1 +1

55 – 20 = 35

Explanation:

I can use compensation to add 1 to both numbers. I can use mental math to subtract 55 – 20 = 35.

### Topic 5 Reteaching

**Set A**

You can use a hundred chart to help you subtract. Find 65 – 31.

Start at 31. Move right 4 ones to 35. Then move down 3 tens to 65. 3 tens and 4 ones is 34.

Use a hundred chart to solve the problems.

Question 1.

67 – 42 = _______

Answer:

Explanation:

In the above we can observe a hundred chart. Start at 42. Move right 5 ones to 47. Then move down 2 tens to 67. 2 tens and 5 ones is 25. By Subtracting 42 from 67 the difference is 25.

Question 2.

70 – 33 = ________

Answer:

Explanation:

In the above we can observe a hundred chart. Start at 33. Move right 7 ones to 40. Then move down 3 tens to 70. 3 tens and 7 ones is 37. By Subtracting 33 from 70 the difference is 37.

Question 3.

58 – 42 = _______

Answer:

Explanation:

In the above we can observe a hundred chart. Start at 42. Move right 6 ones to 48. Then move down 1 ten to 58. 1 ten and 6 ones is 16. Subtracting 42 from 58 the difference is 16.

Question 4.

63 – 38 = ________

Answer:

Explanation:

In the above we can observe a hundred chart. Start at 38. Move right 5 ones to 43. Then move down 2 tens to 63. 2 tens and 5 ones is 25. Subtracting 38 from 63 the difference is 25.

**Set B**

You can use an open number line to find 57 – 24.

Place 57 on the number line. 24 is 2 tens and 4 ones. So, you can count back by 10 two times. Then count back 4.

Use an open number line to find each difference.

Question 5.

38 – 13 = _________

Answer:

38 – 13 = **25**

Explanation:

In the above image we can observe a open number line. Place 38 on the number line. 13 is 1 ten and 3 ones. So, you can count back by 10 one times. Then count back 3. Then we land on 25. By subtracting 38 – 13 = 25.

Question 6.

93 – 36 = _______

Answer:

93 – 36 = **57**

Explanation:

In the above image we can observe a open number line. Place 93 on the number line. 36 is 3 ten and 6 ones. So, you can count back by 10 three times. Then count back 6. Then we land on 57. By subtracting 93 – 36 = 57.

**Set C**

Find 62 – 37.

Place 37 on the line. Then add up to 62. You can add 3 to get to 40. Then add two 10s to get to 60. Then add 2 to get to 62. Add the jumps of tens and ones: 3+ 10 + 10 + 2 = 25.

Add up on an open number line to find each difference.

Question 7.

75 – 47 = ________

Answer:

75 – 47 = **28**

Explanation:

In the above image we used a open number line. We can add up from 47 to subtract. First place 47 on the number line. Add 3 to get to 50. Then add 10, and 10 to get to 70. Then add 5 to land on 75. Add the tens and ones. By adding 3, 10, 10, and 5 the sum is 28. Subtracting 47 from 75 the difference is 28. We can check by adding 47 with 28 then the sum is 75.

Question 8.

52 – 29 = _________

Answer:

52 -29 =** 23**

Explanation:

In the above image we used a open number line. We can add up from 29 to subtract. First place 29 on the number line. Add 1 to get to 30. Then add 10, and 10 to get to 50. Then add 2 to land on 52. Add the tens and ones. By adding 1, 10, 10, and 2 the sum is 23. Subtracting 29 from 52 the difference is 23. We can check by adding 29 with 23 then the sum is 52.

**Set D**

Break apart 7 to find 54 – 7.

Subtract. Break apart the number you are subtracting. Show your work.

Question 9.

52 – 6 = _______

Answer:

52 – 6 = **46**

Explanation:

In the above image we can observe the subtracting number 6. Break apart 6 into 2 and 4. First subtract 2 from 52 then the difference is 50. Then subtract 4 from the difference 50 then the result is 46. By subtracting 6 from 52 the difference is 46.

Question 10.

45 – 9 = _________

Answer:

45 – 9 = **36**

Explanation:

In the above image we can observe the subtracting number 9. Break apart 9 into 5 and 4. First subtract 5 from 45 then the difference is 40. Then subtract 4 from the difference 40 then the result is 36. By subtracting 9 from 45 the difference is 36.

**Set E**

74 – 27 = ?

Use compensation to solve.

Use compensation to subtract.

Question 11.

42 – 18 = _______

Answer:

42 – 18

+2

42 – **20** = **22**

+2

42 – 20 = **24
**42 – 18 =

**24**

Explanation:

In the above image we can observe an equation 42 – 18 = ?. Here we are using compensation method to make numbers that are easier to subtract. Add 2 to 18. Then the equation is 42 – 20 = ?. Then subtract using mental math. Subtract 20 from 42 then the difference is 22. Then add 2 to the answer 22. After adding 2 to the number 22 the sum is 24. By subtracting 18 from 42 the difference is 24.

Question 12.

84 – 37 = _______

Answer:

84 – 37

+3

84 – **40** = **44**

+3

84 – 40 =** 47**

84 – 37 = **47**

Explanation:

In the above image we can observe an equation 84 – 37 = ?. Here we are using compensation method to make numbers that are easier to subtract. Add 3 to 37. Then the equation is 84 – 40 = ?. Then subtract using mental math. Subtract 40 from 84 then the difference is 44. Then add 3 to the answer 44. After adding 3 to the number 44 the sum is 47. By subtracting 37 from 84 the difference is 47.

**Set F**

You can use different strategies and tools to subtract.

For example, you can:

Use any strategy to solve the problem. Show your work.

Question 13.

Lily has a puzzle with 8 fewer pieces than Jake has. Jake has 45 pieces. How many pieces does Lily have?

________ pieces

Answer:

45 – 8 = ?

45 – 8

+2

45 – 10 = **35**

+2

45 – 10 = **37**

45 – 8 =** 37
**

Lily have 37 pieces.

Explanation:

Lily has a puzzle with 8 fewer pieces than Jake has. Jake has 45 pieces. In the above image we can observe an equation 45 – 8 = ?. Here we are using compensation method to make numbers that are easier to subtract. Add 2 to 8. Then the equation is 45 -10 = ?. Then subtract using mental math. Subtract 10 from 45 then the difference is 35. Then add 2 to the answer 35. After adding 2 to the number 35 the sum is 37. By subtracting 8 from 45 the difference is 37. Lily have 37 pieces.

**Set G**

Use the bar diagram and write two equations to model and solve the problem.

Mason read 34 pages in two days. He read 8 pages on Day 1. How many pages did he read on Day 2?

Answer:

Manson read 26 pages on Day 2.

Explanation:

Mason read 34 pages in two days. He read 8 pages on Day 1. Subtract 8 pages from 34 pages then the difference is 26. Manson read 26 pages on Day 2.

Add or subtract to solve the problem. Show your work.

Question 14.

Gene bakes 60 muffins in one day. He bakes 24 of the muffins before lunch. How many muffins does he bake after lunch?

________ muffins

Answer:

Gene bakes 36 muffins after lunch.

Explanation:

Gene bakes 60 muffins in one day. He bakes 24 of the muffins before lunch as we can observe in the above image. Subtract 24 muffins from 60 muffins then the difference is 36 muffins. Gene bakes 36 muffins after lunch.

**Set H**

**Thinking Habits**

Critique Reasoning

What questions can I ask to understand other people’s thinking?

Are there mistakes in other people’s thinking?

Do you agree or disagree? Explain.

Question 15.

Ken has 29 more stamps than Jamie. Ken has 52 stamps. Lisa says Jamie has 23 stamps.

Lisa added up from 29, then 20 more from 30, and 2 more to get to 52. Does Lisa’s reasoning make sense?

Answer:

I agree with Lisa’s reasoning.

Explanation:

Ken has 29 more stamps than Jamie. Ken has 52 stamps. Lisa says Jamie has 23 stamps. Lisa added up from 29, then 20 more from 30, and 2 more to get to 52. I agree with Lisa’s reasoning.

In the above image we used a open number line. We can add up from 29 to subtract. First place 29 on the number line. Add 1 to get to 30. Then add 10, and 10 to get to 50. Then add 2 to land on 52. Add the tens and ones. By adding 1, 10, 10, and 2 the sum is 23. Subtracting 29 from 52 the difference is 23. Jamie has 23 stamps.

### Topic 5 Assessment Practice

Question 1.

A store has 68 candles. Then they sell 29 of the candles. 6 candles are returned. How many candles do they have now?

A. 39

B. 33

C. 45

D. 97

Answer:

68 – 29 = **39**

39 + 6 = **45**

Now they have 45 candles. So option C is correct.

Explanation:

A store has 68 candles. Then they sell 29 of the candles. 6 candles are returned. Subtract 29 candles from 68 candles then the difference is 39. Add 39 candles with 6 candles then the sum is 45. They have 45 candles. So option C is correct.

Question 2.

Claire thinks this number line models 48 + 30 = 78. She thinks 3 tens have been added to 48. Is she correct? Choose the correct explanation.

A. No. The number line shows starting at 48 and counting back 3 tens.

B. Yes. The number line shows starting at 48 and counting on 3 tens.

C. No. The number line shows starting at 38 and counting back 3 tens.

D. No. The number line shows starting at 48 and counting back 4 tens.

Answer:

Claire is not correct. So option A is correct answer.

Question 3.

Tony has 66 rocks. He gives 23 rocks to Chris.

How many rocks does Tony have now? Write an equation to show your work and solve.

Answer:

Now Tony have 43 rocks.

Explanation:

Tony has 66 rocks. He gives 23 rocks to Chris. In the above we can observe a hundred chart. Start at 23. Move right 3 ones to 26. Then move down 4 tens to 66. 4 tens and 3 ones is 43. By Subtracting 23 from 66 the difference is 43. Tony have 43 rocks.

Question 4.

Which is the difference of 34 – 7?

A. 26

B. 27

C. 28

D. 29

Answer:

34 – 7 = 27

Option B is correct.

Question 5.

Keena has 64 balloons. 28 of the balloons are red. 14 balloons are green. The rest of the balloons are purple. How many of the balloons are purple?

A. 22

B. 36

C. 42

D. 50

Answer:

28 + 14 + ? = 64

42 + ? = 64

64 – 42 = 22

There are 22 purple balloons. Option A is correct.

Explanation:

Keena has 64 balloons. 28 of the balloons are red. 14 balloons are green. The rest of the balloons are purple. First add 28 red balloons with 14 green balloons then the sum is 42 balloons. Subtract 42 balloons from 64 balloons then the difference is 22. There are 22 purple balloons.

Question 6.

Joe has 43 stickers. Then he gives away 9 stickers. Which equations can be used to find how many stickers Joe has left?

A. 43 + 7 = 50 and 50 + 2 = 52

B. 43 + 10 = 53 and 53 – 1 = 52

C. 43 – 3 = 40 and 40 + 6 = 46

D. 43 – 10 = 33 and 33 + 1 = 34

Answer:

43 – 9

+1

43 – 10 = 33

+1

43 – 10 = 34

Option D is correct.

Explanation:

In the above image we can observe an equation 43 – 9 = ?. Here we are using compensation method to make numbers that are easier to subtract. Add 1 to 9. Then the equation is 43 – 10 = ?. Then subtract using mental math. Subtract 10 from 43 then the difference is 33. Then add 1 to the answer 33. After adding 1 to the number 33 the sum is 34. By subtracting 9 from 43 the difference is 34.

Question 7.

Subtract. Break apart the number you are subtracting. Show your work.

73 – 6 = ?

73 – 6 = _________

Answer:

Break 6 into 3 and 3

73 – 3 = 70

70 – 3 = **67**

73 – 6 = **67**

Explanation:

Break apart 6 into 3 and 3. Subtract 3 from 73 then the difference is 70. After that subtract 3 from 70 the difference is 67. By subtracting 6 from 73 the difference is 67.

Question 8.

A. Write the equation that the number line shows.

Answer:

82 – 50 = 32

Explanation:

In the below image we can observe open number line. Place 82 on the number line. Then count back 10 three times then we land on 52. Count back 2 ones we land on 50. Add the numbers 2, 10, 10, 10 is equal to 32. By subtracting 50 from 82 the difference is 32.

B. Then, explain what the jumps are showing.

Answer:

In the above image we can observe the jumps. The jumps are 10, 10, 10, 2.

Question 9.

The number line below shows adding up to subtract to find 68 – 36. What is the difference? Explain how you know.

Answer:

68 – 36 = 32

Explanation:

In the above image we used a open number line. We can add up from 36 to subtract. First place 36 on the number line. Add 10, 10 and 10 to get to 66. Then add 2 to land on 68. Add the tens and ones. By adding 10, 10, 10, and 2 the sum is 32. Subtracting 36 from 68 the difference is 32.

Question 10.

Use the open number line to find the difference.

80 – 42 = ?

80 – 42 = ________

Answer:

80 – 42 = 38

Explanation:

In the above image we used a open number line to find the difference. First place 80 on the line. The subtracting number 42 is 4 tens and 2 ones. So, count back 4 tens from 80. The numbers are 70, 60, 50, 40. Then count back 2 ones from 40. The number is 38. By subtracting 42 from 80 the difference is 38.

Question 11.

A. 33 ants are on a leaf. 15 ants leave. How many ants are left? Jay adds 2 to 33 to make an easier problem, 35 – 15. He says 20 ants are left. Circle whether you agree or do not agree.

Agree

Do Not Agree

Answer:

33 – 15 = 18

18 ants are left.

I am not agree with Jay thinking.

B. Explain why you agree or do not agree with Jay’s strategy.

Answer:

33 ants are on a leaf. 15 ants leave. Jay adds 2 to 33 to make an easier problem, 35 – 15. He says 20 ants are left. The equation is 33 – 15 = ?. Here we are using compensation method to make numbers that are easier to subtract. Subtract 2 from 15. Then the equation is 33 – 13 = ?. Then subtract using mental math. Subtract 13 from 33 then the difference is 20. Then subtract 2 from the answer 20. After subtracting 2 from the number 20 the difference is 18. By subtracting 15 from 33 the difference is 18.

Question 12.

Use the open number lines. Show two different ways to find 74 – 28. Show your work.

One Way

74 – 28 = ________

Another Way

74 – 28 = _________

Answer:

One way

74 – 28 = 46

Explanation:

In the above image we used a open number line to find the difference. First place 74 on the line. The subtracting number 28 is 2 tens and 8 ones. So, count back 2 tens from 74. The numbers are 64, 54. Then count back 8 ones from 54. The number is 46. By subtracting 28 from 74 the difference is 46.

Another way

74 – 28 = 46

In the above image we used a open number line to find the difference. First place 74 on the line. The subtracting number 28 is 2 tens and 8 ones. So, count back 2 tens from 74. The number is 54. Then count back 8 ones from 54. The number is 46. By subtracting 28 from 74 the difference is 46.

Question 13.

Use the numbers on the cards. Write the missing numbers to solve the problem. What strategy did you use to solve the problem? Explain.

Answer:

The missing numbers are 3, 75, 40, 35.

Explanation:

In the above image we can observe an equation 72 – 37 = ?. Here we are using compensation method to make numbers that are easier to subtract. Change both addends by adding the same amount. Then subtract using mental math. Add 3 to the addends 72 and 37. Then the equation is 75 – 40 = ?. Subtract 40 from 75 then the difference is 35.

Question 14.

5 black cows are at the ranch. 9 brown cows join them. Then 6 cows leave the ranch. How many cows are still at the ranch? Solve. Show your work.

Step 1

Step 2

Answer

________ cows

Answer:

Step 1: 5 + 9 = 14

Step 2: 14 – 6 = 8

8 cows are still at the ranch.

Explanation:

5 black cows are at the ranch. 9 brown cows join them. Then 6 cows leave the ranch. First add black cows with 9 brown cows then the sum is 14 cows. Subtract 6 cows from 14 cows the difference is 8. 8 cows are still at the ranch.

### Topic 5 Performance Task

**Beautiful Boats**

Chen’s family goes to the lake for a vacation. They count the boats that they see.

Question 1.

How many more motorboats does Chen see than sailboats?

Use the open number line to solve.

________ more motorboats

Answer:

36 – 12 = 24

Chen see 24 motorboats than sailboats.

Explanation:

Chen’s family goes to the lake for a vacation. They see 12 sailboats, 28 rowboats, 36 motorboats. In the above image we used a open number line to find the difference. First place 36 on the line. The subtracting number 12 is 1 ten and 2 ones. So, count back 1 ten from 36. The number is 26. Then count back 2 ones from 26. The number is 24. By subtracting 12 from 36 the difference is 24. Chen see 24 motorboats than sailboats.

Question 2.

Maria’s family saw 57 rowboats on their vacation. How many more rowboats did they see than Chen’s family?

Use compensation to solve. Explain how you found your answer.

__________ more rowboats

Answer:

Maria’s family saw 29 more rowboats than Chen’s family.

Explanation:

In the above image we can observe an equation 57 – 28= ?. Here we are using compensation method to make numbers that are easier to subtract. Add 2 to 28. Then the equation is 57 – 30 = ?. Then subtract using mental math. Subtract 30 from 57 then the difference is 27. Then add 2 to the answer 29. After adding 2 to the number 27 the sum is 29. By subtracting 28 from 57 the difference is 29. Maria’s family saw 29 more rowboats than Chen’s family.

Question 3.

Chen’s sisters have toy boats. They have 21 yellow boats. They have 9 fewer red boats than yellow boats. How many boats do they have in all?

Choose any strategy. Show your work.

________ boats

Answer:

21 – 9 = 12

They have 12 red boats.

21 + 12 = 33

They have 33 boats in all.

Explanation:

Chen’s sisters have toy boats. They have 21 yellow boats. They have 9 fewer red boats than yellow boats. First subtract 9 boats from 21 boats then the difference is 12 boats. They have 12 red boats. Add 21 yellow boats with 12 red boats then the sum is 33 boats. They have 33 boats in all.

Question 4.

Julie’s family saw 94 boats on their vacation. How many more boats did they see than Chen’s family?

Part A

What do you need to do to solve the problem?

Answer:

We need how many boats does Chen’s family see on their vacation.

Part B

How many boats did Chen see? Show your work. Then explain how you found your answer.

________ boats

Answer:

12 sailboats + 28 Rowboats + 36 Motorboats = 76 boats

Chen’s family saw 76 boats on their vacation.

Explanation:

Add 12 sailboats with 28 Rowboats and 36 Motorboats then the sum is 76 boats. Chen’s family saw 76 boats on their vacation.

Part C

Julie said that her family saw 18 more boats than Chen’s family. She broke apart 76 into 70 + 4 + 2. Then she subtracted each number from 94. Does Julie’s reasoning make sense? Explain.

Answer:

Break 76 into 70 + 4 + 2

94 – 70 = 24

24 – 4 = 20

20 – 2 = 18

Yes Julie’s reasoning is correct. Julie family saw 18 more boats than Chen’s family.

Explanation:

Julie said that her family saw 18 more boats than Chen’s family. She broke apart 76 into 70 + 4 + 2. Then she subtracted each number from 94. Yes Julie’s reasoning is correct. First subtract 70 from 94 then the difference is 24. Subtract 4 rom 24 the difference is 20. Subtract 2 from 20 then the difference is 18. Julie family saw 18 more boats than Chen’s family.