## Engage NY Eureka Math 6th Grade Module 4 Lesson 1 Answer Key

### Eureka Math Grade 6 Module 4 Lesson 1 Exercise Answer Key

Exercise 1.
Predict what will happen when a tape diagram has a large number of squares, some squares are removed, and then the same amount of squares are added back on.
Possible answer: When some squares are removed from a tape diagram, and then the same amount of squares are added back on, the tape diagram will end up with the same amount of squares that it started with.

Exercise 2.
Build a tape diagram with 10 squares.
a. Remove six squares. Write an expression to represent the tape diagram.
10 – 6

b. Add six squares onto the tape diagram. Alter the original expression to represent the current tape diagram.
10 – 6 + 6

c. Evaluate the expression.
10

Exercise 3.
Write an equation, using variables, to represent the identities we demonstrated with tape diagrams.
Possible answer: w – x + x = w

Exercise 4.
Using your knowledge of identities, fill In each of the blanks.
a. 4 + 5 – ______ = 4
5

b. 25 – _____ + 10 = 25
10

C. ______ + 16 – 16 = 45
45

d. 56 – 20 + 20 = ______
56

Exercise 5.
Using your knowledge of identities, fill In each of the blanks.
a. a + b – ______ = a
b

b. c – d + d = ______
C

c. e + _______ – f = e
f

d. ________ – h + h = g
g

### Eureka Math Grade 6 Module 4 Lesson 1 Problem Set Answer Key

Question 1.
Fill in each blank.
a. ____ +15 – 15 = 21
21

b. 450 – 230 + 230 = ____
450

c. 1289 – ______ + 856 = 1289
856

Question 2.
Why are the equations w – x + x = w and w + x – x = w called identities?
Possible answer: These equations are called identities because the variables can be replaced with any numbers, and after completing the operations, I returned to the original value.

### Eureka Math Grade 6 Module 4 Lesson 1 Exit Ticket Answer Key

Question 1.
Draw a series of tape diagrams to represent the following number sentences.
a. 3 + 5 – 5 = 3 b. 8 – 2 + 2 = 8 Question 2.
Fill in each blank.
a. 65+ _____ – 15 = 65
15

b. ______ + g – g = k
k

c. a + b – _______ = a
b

d. 367 – 93 + 93 = _________
367

### Eureka Math Grade 6 Module 4 Lesson 1 Opening Exercise Answer Key

a. Draw a tape diagram to represent the following expression: 5 + 4. b. Write an expression for each tape diagram.
i.  ii.  ### Eureka Math Grade 6 Module 4 Lesson 1 Multiplication of Decimals Answer Key

Progression of Exercises

Question 1.
0.5 × 0.5 =
0.25

Question 2.
0.6 × 0.6 =
0.36

Question 3.
0.7 × 0.7 =
0.49

Question 4.
0.5 × 0.6 =
0.3

Question 5.
1.5 × 1.5 =
2.25

Question 6.
2.5 × 2.5 =
6.25

Question 7.
0.25 × 0.25 =
0. 0625

Question 8.
0.1 × 0.1 =