We included **HMH Into Math Grade 4 Answer Key**** PDF** **Module 10 Lesson 5 Generate and Analyze Number Patterns**Ā to make students experts in learning maths.

## HMH Into Math Grade 4 Module 10 Lesson 5 Answer Key Generate and Analyze Number Patterns

I Can follow a given rule to write numbers in a pattern and identify other features of the pattern that are not stated in the rule.

**Step It Out**

1. Miguel and his family take their dog to the park every 3 days. The calendar shows the first day they went this month. What will be the last day of this month that they go to the park?

A. Mark all of the days on the calendar that Miguel’s family takes their dog to the park.

B. Write the dates in an ordered list.

_____________________

C. Identify the last number in the list. _____________________

D. The last da,y that Miguel’s family will take their dog to the park this month is the ____.

Answer:

The last day of this month that they go to the park = 29 Sunday.

Explanation:

Miguel and his family take their dog to the park every 3 days.

=> All of the days on the calendar that Miguel’s family takes their dog to the park:

First day = 2 Monday.

Next day = 2 + 3 = 5, 8, 11,14,17, 20, 23, 36, 29.

**Turn and Talk** If you did not have a calendar to mark, how could you use the first day and a pattern rule to solve the problem?

Answer:

We can use the first day and a pattern rule to solve the problem by adding 3 to the first day and continue the same.

Explanation:

We can use the first day and a pattern rule to solve the problem by adding 3 to the first day and continue the same.

First day = 2 Monday.

Next day = 2 + 3 = 5, 8, 11,14,17, 20, 23, 36, 29.

**Connect to Vocabulary**

The numbers marked in the calendar form a pattern. A pattern is an ordered set of numbers or objects. Each number or object in the pattern is called a term. A rule tells how to get the next term in the pattern.

**Step It Out
**2. The rule for a pattern is add 5. The first term in the pattern is 7. Write the first 8 terms of the pattern. Then describe other features of the pattern.

A. Use a number line to find the first 8 terms.

B. Describe the pattern using the words odd and even.

___________________________

C. Describe the pattern in the digits in the ones place.

___________________________

Answer:

The pattern:

7,12,17,22,27,32,37,42.

Explanation:

The first term in the pattern is 7.

The rule for a pattern is add 5.

=> 7 + 5 = 12.

=> 12 + 5 = 17.

=> 17 + 5 = 22.

=> 22 + 5 = 27.

=> 27 + 5 = 32.

=> 32 + 5 = 37.

=> 37 + 5 = 42.

=> 42 + 5 = 47.

**Turn and Talk** Why will the numbers in this pattern continue in the way that you described in B or C above?

Answer:

The numbers in this pattern will continue in the way that you described in B or C above because they all same in the process of finding the pattern of the series.

Explanation:

The numbers in this pattern will continue in the way that you described in B or C above because they all same in the process of finding the pattern of the series.

**Check Understanding Math Board
**Use the rule to write the numbers in the pattern. Then describe another feature of the pattern that is not stated in the rule.

Question 1.

Rule: Add 6. First term: 10

10, __, ___, ___, ___, ___, ___, ____

_____________________

Answer:

Pattern:

10,16,22,28,34,40,46,52.

Explanation:

First term: 10

Add 6.

=> 10 + 6 = 16.

=> 16 + 6 = 22.

=> 22 + 6 = 28.

=> 28 + 6 = 34.

=> 34 + 6 = 40.

=> 40 + 6 = 46.

=> 46 + 6 = 52.

Question 2.

Rule: Subtract 4. First term: 55

55, __, ___, ___, ___, ___, ___, ____

_____________________

Answer:

55,59,63,67,71,75,79,83.

Explanation:

First term: 55.

Rule: Subtract 4.

=> 55 + 4 = 59.

=> 59 + 4 = 63.

=> 63 + 4 = 67.

=> 67 + 4 = 71.

=> 71 + 4 = 75.

=> 75 + 4 = 79.

=> 79 + 4 = 83.

**On Your Own
**Question 3.

**Use Structure**Concert promoters give every third person in line a T-shirt. They start with the first person in line. Does the 27th person in line get a T-shirt? Explain.

Answer:

Yes, the 27th person in line gets a T-shirt.

Explanation:

Concert promoters give every third person in line a T-shirt.

=> 0 + 3 = 3.

Multiple of 3: 3,6,9,12,15,18,21,24,27,30.

**Use the rule** to write the numbers in the pattern. Then describe another feature of the pattern.

Question 4.

Rule: Multiply by 2. First term: 2

2, __, ___, ___, ___, ___, ___, ____

_____________________

Answer:

2,4,8,16,32,64,128,256.

Explanation:

First term: 2.

Rule: Multiply by 2.

=> 2 Ć 2 = 4.

=> 4 Ć 2 = 8.

=> 8 Ć 2 = 16.

=> 16 Ć 2 = 32.

=> 32 Ć 2 = 64.

=> 64 Ć 2 = 128.

=> 128 Ć 2 = 256.

Question 5.

Rule: Subtract 10. First term: 113

113, __, ___, ___, ___, ___, ___, ____

_____________________

Answer:

113,103,93,83,73,63,53,43.

Explanation:

First term: 113.

Rule: Subtract 10.

=> 113 – 10 = 103.

=> 103 – 10 = 93.

=> 93 – 10 = 83.

=> 83 – 10 = 73.

=> 73 – 10 = 63.

=> 63 – 10 = 53.

=> 53 – 10 = 43.

Question 6.

Rule: Divide by 2. First term: 896

896, __, ___, ___, ___, ___, ___, ____

_____________________

Answer:

896,448,224,112,56,28,14,7.

Explanation:

First term: 896.

Rule: Divide by 2.

=> 896 Ć· 2 = 448.

=> 448 Ć· 2 = 224.

=> 224 Ć· 2 = 112.

=> 112 Ć· 2 = 56.

=> 56 Ć· 2 = 28.

=> 28 Ć· 2 = 14.

=> 14 Ć· 2 = 7.

Question 7.

**STEM** Paula did an experiment to show how crickets are more active when it is warm outside. The table shows the data Paula collected. She discovered several patterns in her data. Complete the Temperature row using the rule add 5Ā°F. What was the temperature when Paula counted 40 cricket chirps in 15 seconds?

Answer:

Explanation:

Rule add 5Ā°F.

Temperature = 37Ā°F

=> 37Ā°F + 5Ā°F = 42Ā°F

=> 42Ā°F + 5Ā°F = 47Ā°F

=> 47Ā°F + 5Ā°F = 52Ā°F

=> 52Ā°F + 5Ā°F = 57Ā°F

=> 57Ā°F + 5Ā°F = 62Ā°F

=> 62Ā°F + 5Ā°F = 67Ā°F

=> 67Ā°F + 5Ā°F = 72Ā°F

=> 72Ā°F + 5Ā°F = 77Ā°F

**On Your Own
**Question 8.

**Use Structure**Mia wants to save $40 to buy a new game. Her plan is to save $5 the first week and then save $3 each week after that. Show Miaās savings each week until she reaches her goal. How many weeks will it take Mia to save $40?

Answer:

Number of weeks she saves $40 = 5.

Explanation:

Amount of money Mia wants to save to buy a new game = $40.

Amount of money she plans to save for the first week = $5.

Number of days in a week = 7.

=> Amount of money she saves for the first week = Number of days in a week Ć Amount of money she plans to save for the first week

=> 7 Ć $5

=> $35.

Amount of money she plans to save after the first week = $3.

Number of weeks she saves $40 = Amount of money Mia wants to save to buy a new gameĀ Ć· (Amount of money she plans to save for the first week + Amount of money she plans to save after the first week)

= $40 Ć· ($5 + $3)

= $40 Ć· $8

= 5.

Question 9.

**Open Ended** Write a rule for a pattern with a first term of 22. Write the first 10 terms of the pattern.

Rule: _____

First 10 terms: _____

Answer:

22,32,42,52,62,72,82,92,102,112,122.

Explanation:

First term of 22.

Rule Add 10.

=> 22 + 10 = 32.

=> 32 + 10 = 42.

=> 42 + 10 = 52.

=> 52 + 10 = 62.

=> 62 + 10 = 72.

=> 72 + 10 = 82.

=> 82 + 10 = 92.

=> 92 + 10 = 102.

=> 102 + 10 = 112.

=> 112 + 10 = 122.

**Use the rule** to write the numbers in the pattern. Then describe another feature of the pattern.

Question 10.

Rule: Multiply by 3. First term: 7

7, ___, ___, ___, __, ___, ____

_____________________

Answer:

7,21,63,189,567,1701,5103.

Explanation:

First term: 7.

Rule: Multiply by 3.

=> 7 Ć 3 = 21.

=> 21 Ć 3 = 63.

=> 63 Ć 3 = 189.

=> 189 Ć 3 = 567.

=> 567 Ć 3 = 1701.

=> 1701 Ć 3 = 5103.

Question 11.

Rule: Add 10. First term: 52

52, ___, ___, ___, __, ___, ____

_____________________

Answer:

52,62,72,82,92,102,112.

Explanation:

First term: 52.

Rule: Add 10.

=> 52 + 10 = 62.

=> 62 + 10 = 72.

=> 72 + 10 = 82.

=> 82 + 10 = 92.

=> 92 + 10 = 102.

=> 102 + 10 = 112.

=> 112 + 10 = 122.

Question 12.

**Critique Reasoning** Greg says that he has found a way to make a pattern that is only prime numbers. His pattern has a first term of 5 and a rule of add 2. Is Greg correct? Explain how you know.

Answer:

No, Grey is incorrect because first term and second term are prime numbers but later no.

5,7,11,13 are prime numbers but in between 9 is not prime number.

Explanation:

First term in his pattern = 5.

Rule of add 2.

=> 5 + 2 = 7.

=> 7 + 2 = 9.

=> 9 + 2 = 11.

=> 11 + 2 = 13.

=> 13 + 2 = 15.