We included **HMH Into Math Grade 5 Answer Key PDF** **Module 19 Lesson 4 Generate and Identify Numerical Patterns **to make students experts in learning maths.

## HMH Into Math Grade 5 Module 19 Lesson 4 Answer Key Generate and Identify Numerical Patterns

I Can use two rules to generate numerical patterns, write ordered pairs using corresponding terms, and identify a relationship between them.

**Step It Out**

Question 1.

Antonia and Connor are playing a patterns game. Each draws a card and finds the first five numbers in the pattern. Then they try to find a relationship between the corresponding numbers in both patterns.

A. Complete the table.

Answer:

B. Write the first five ordered pairs with the x-coordinate representing the numbers in Antonia’s pattern and the y-coordinate representing the corresponding numbers in Connor’s pattern.

Answer:

C. Does there appear to be a relationship between Antonia’s numbers and Connor’s numbers? If so, describe the relationship.

Answer:

The difference between Antonia’s number and Connor’s number is 1

2 – 1 = 1

4 – 3 = 1

8 – 7 = 1

**Turn and Talk** How can you use Antonia’s pattern to find the seventh number in Connor’s pattern?

Answer:

subtract 1 from the Antonia’s 7th number

Antonia’s 6th number is 64

Antonia’s 7th number is 128

Question 2.

Nora and Pavel are playing a game. The game cards show either “Move forward 3.” or “Move forward 6.” Just by chance, Nora draws “Move forward 3.” on her first three turns. Pavel draws “Move forward 6.” on his first three turns.

A. At what number on the game board is Nora after her first turn? Her second turn? Her third turn?

Answer:

3, 6 , 9 just multiplying with 3.

B. At what number on the game board is Pavel after his first turn? His second turn? His third turn?

Answer:

6, 12 , 18 Just multiplying with 6.

C. Using Nora’s locations as the x-coordinates and Pavel’s locations as the y-coordinates, write the ordered pairs after each turn.

Answer:

(3, 6) (6, 12) (9 , 18) there the order pairs made from Nora’s locations and Pavel’s locations

D. Does there appear to be a relationship between Pavel’s location and Nora’s location? Explain.

Answer:

yes, there is a relation ship between Pavel’s location and Nora’s location

3 x 2 = 6

6 x 2 = 12

9 x 2= 18

multiple of 2.

**Turn and Talk** What is another way to describe the relationship between Pavel’s location and Nora’s location?

Answer:

3 + 3 = 6

6 + 6 = 12

9 + 9 = 18

adding same number to the Nora’s location gives the Pavel’s location

**Check Understanding**

Question 1.

Erin and Joshua are writing number patterns.

Erin: Start at 1; rule: “Add 1, then multiply by 3.”

Joshua: Start at \(\frac{1}{2}\) rule: “Add \(\frac{1}{2}\), then multiply by 2.”

Use the numbers in Erin’s pattern for the x-coordinates and the numbers in Joshua’s pattern for the y-coordinates. Write the first five ordered pairs.

Answer:0

Erin’s pattern for the x-coordinates are 1, 3, 12, 39, 120

Joshua’s pattern for the y-coordinates are 2, 6, 14, 30, 62

ordered pairs are (1, 2), (3 , 6), (12, 14), (39, 30), (120, 62)

Question 2.

Kona and Isabella do pushups each week. On the first day, Kona does 3 pushups and follows the rule “Add 3” for the number of pushups on the following days. Isabella does 1 pushup and follows the rule “Add 1” for the number of pushups on the following days. They follow their patterns for 5 days.

How many pushups does Kona do on each day?

Answer:

Kona does 3 pushups and follows the rule “Add 3”

3, 6, 9, 12, 15

Isabella does 1 pushup and follows the rule “Add 1”

1, 2, 3, 4, 5

How many pushups does Isabella do on each day?

Answer:

only one pushup that Isabella do on each day.

Write the ordered pairs for the corresponding numbers of pushups, using Isabella’s numbers for the x-coordinates and Kona’s numbers for the y-coordinates.

Answer:

Isabella’s numbers for the x-coordinates and Kona’s numbers for the y-coordinates.

(3, 1), (6, 2), (9, 3), (12, 4), (15, 5)

Does there appear to be a relationship between the number of pushups Kona does and the number of pushups Isabella does? If so, describe the relationship.

Answer:

The quotient of 3 and 1 is 3

The quotient of 6 and 2 is 3 as on.

**On Your Own**

Question 3.

Zach and Eliza are writing number patterns. Zach starts with 1 and uses the rule “Multiply by 2, then add 1.” Eliza starts with 2 and uses the rule “Add 1, then multiply by 2.”

Write the first five ordered pairs with the x-coordinate representing the numbers in Zach’s pattern and the y-coordinate representing the corresponding numbers in Eliza’s pattern.

Answer:

Zach starts with 1 and uses the rule “Multiply by 2, then add 1.”

1, 3, 7, 15, 31

Eliza starts with 2 and uses the rule “Add 1, then multiply by 2.”

2, 6, 14, 30, 62

What appears to be the relationship between Zach’s numbers and Eliza’s numbers?

Answer:

The relation ship between the numbers is adding the same number

1 + 1 = 2

3 + 3 = 6

7 + 7 = 14

Question 4.

**Reason** Quentin’s hair grows \(\frac{3}{2}\) centimeters every month and Maurice’s hair grows 1 centimeter every month. On haircut day, the length of Maurice’s hair and Quentin’s hair is 2 centimeters. The boys do not get another haircut for 4 months.

Complete the table to show the length in centimeters of each boy’s hair.

Find the difference in the lengths of the boys’ hair each month.

Answer:

Does there appear to be a relationship in the monthly differences? If so, what is the relationship?

Answer:

No, there is no relationship between the length of Maurice’s hair and Quentin’s hair.