This handy **Spectrum Math Grade 4 Answer Key Chapter 9 Lesson 9.1 Growing Number Patterns** provides detailed answers for the workbook questions.

## Spectrum Math Grade 4 Chapter 9 Lesson 9.1 Growing Number Patterns Answers Key

**Increasing Pattern**

Think: Each number is added to itself to create the increasing pattern.

16 + 16 = 32

The missing number is 32.

To find o missing number in a growing pattern:

- Find the difference between numbers that are next to each other.
- The differences in the number series will show the pattern.
- Add or subtract to find the missing numbers.

**Decreasing Pattern**

Think: Count by 2s to get the number for the decreasing pattern.

78 – 12 = 66

The missing number is 66.

**Complete each pattern.**

Question 1.

a. 11, 15, 20, 26, 33, ,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is 4. The difference between second and third numbers is 5. We’ve noticed that difference between two consecutive numbers is increasing by one from there onwards. So, last number in the given sequence in the question is 33 and the difference between 33 and the number before it (26) is 7. So, 8 should be added to the last number 33 to get the next number in the sequence. So, the next number in the sequence is 33 + 8 = 41. To get the next number in the sequence 9 should be added to get the next number in the sequence and it will be 41 + 9 = 50.

b. 9, 12, 18, 27, , 54,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is 3. The difference between second and third numbers is 6. We’ve noticed that difference between two consecutive numbers is increasing by three from there onwards. So, last number in the given sequence in the question is 27 and the difference between 27 and the number before it (18) is 9. So, 12 should be added to the last number 27 to get the next number in the sequence. So, the next number in the sequence is 27 + 12 = 39. To get the last number in the sequence 18 should be added to get the next number in the sequence and it will be 54 + 18 = 72.

Question 2.

a. 1, 2, 4, 7, , 16, 22

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is 1. The difference between second and third numbers is 2. We’ve noticed that difference between two consecutive numbers is increasing by one from there onwards. So, last number in the given sequence in the question is 7 and the difference between 7 and the number before it (4) is 3. So, 4 should be added to the last number 7 to get the next number in the sequence. So, the next number in the sequence is 7 + 4 = 11.

b. 16, 28, 52, 100, 196,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is 12. The difference between second and third numbers is 24. We’ve noticed that difference between two consecutive numbers is doubled from there onwards. So, last number in the given sequence in the question is 196 and the difference between 196 and the number before it (100) is 96. Double of 96 is equal to 192. So, 192 should be added to the last number 196 to get the next number in the sequence. So, the next number in the sequence is 196 + 192 = 388.

Question 3.

a. 5, 7, 11, 17, , 35,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is 2. The difference between second and third numbers is 4. We’ve noticed that difference between two consecutive numbers is increasing by two from there onwards. So, last number in the given sequence in the question is 17 and the difference between 17 and the number before it (11) is 6. So, 8 should be added to the last number 17 to get the next number in the sequence. So, the next number in the sequence is 17 + 8 = 25. To get the next number in the sequence 12 should be added to get the next number in the sequence and it will be 35 + 12 =47.

b. 158, 156, 152, 146, , ,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is -2. The difference between second and third numbers is -4. We’ve noticed that difference between two consecutive numbers is decreasing by two from there onwards. So, last number in the given sequence in the question is 146 and the difference between 146 and the number before it (152) is -6. So, -8 should be added to the last number 146 to get the next number in the sequence. So, the next number in the sequence is 146 – 8 = 138. To get the next number in the sequence -10 should be added to get the next number in the sequence and it will be138 – 10 = 128. To get the last number in the sequence -12 should be added to get the next number in the sequence and it will be 128 – 12 = 116.

Question 4.

a. 1128, 1096, 1032, 936,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is -32. The difference between second and third numbers is -64. We’ve noticed that difference between two consecutive numbers is decreasing by thirty – two from there onwards. So, last number in the given sequence in the question is 936 and the difference between 936 and the number before it (1032) is -96. So, -128 should be added to the last number 936 to get the next number in the sequence. So, the next number in the sequence is 936 – 128 = 808.

b. 88, 110, 154, 220, ,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is 22. The difference between second and third numbers is 44. We’ve noticed that difference between two consecutive numbers is increasing by twenty-two from there onwards. So, last number in the given sequence in the question is 220 and the difference between 220 and the number before it (154) is 66. So, 88 should be added to the last number 220 to get the next number in the sequence. So, the next number in the sequence is 220 + 88 = 308. To get the next number in the sequence 110 should be added to get the next number in the sequence and it will be 308 + 110 = 418.

Question 5.

a. 460, 450, 430, , 360,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is -10. The difference between second and third numbers is -20. We’ve noticed that difference between two consecutive numbers is decreasing by ten from there onwards. So, last number in the given sequence in the question is 430 and the difference between 430 and the number before it (450) is -20. So, -23 should be added to the last number 430 to get the next number in the sequence. So, the next number in the sequence is 430 – 30 = 400. To get the next number in the sequence -50 should be added to get the next number in the sequence and it will be 360 – 50 = 310.

b. 923, 915, 904, 890, ,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is -8. The difference between second and third numbers is -11. We’ve noticed that difference between two consecutive numbers is decreasing by three from there onwards. So, last number in the given sequence in the question is 890 and the difference between 890 and the number before it (904) is -14. So, -17 should be added to the last number 890 to get the next number in the sequence. So, the next number in the sequence is 890 – 17 = 873. To get the next number in the sequence -20 should be added to get the next number in the sequence and it will be 873 – 20 = 853.

Question 6.

a. 180, 176, 168, 156, 140,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is -4. The difference between second and third numbers is -8. We’ve noticed that difference between two consecutive numbers is decreasing by four from there onwards. So, last number in the given sequence in the question is 140 and the difference between 140 and the number before it (156) is -16. So, -20 should be added to the last number 140 to get the next number in the sequence. So, the next number in the sequence is 140 – 20 = 120.

b. 64, 74, 86, 100,

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between first two numbers is 10. The difference between second and third numbers is 12. We’ve noticed that difference between two consecutive numbers is increasing by two from there onwards. So, last number in the given sequence in the question is 100 and the difference between 100 and the number before it (86) is 14. So, 16 should be added to the last number 100 to get the next number in the sequence. So, the next number in the sequence is 100 + 16 = 116.

Question 7.

a. , , 65, 80, 100, 125

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between sixth and fifth numbers is 25. The difference between fifth and fourth numbers is 20. The difference between fourth and third numbers is 15. We’ve noticed that difference between two consecutive numbers is decreasing by 5 from the previous difference moving backward. So, the difference between third and second numbers is 15-5=10. So, the second number will be 65-10=55. To get the first number in the sequence, the difference from second number should be 10-5=5. So, the first number will be 55-5=50.

b. , , 54, 96, 152, 222

Answer:

Explanation:

By looking at the given numbers, it’s been noticed that the difference between sixth and fifth numbers is 70. The difference between fifth and fourth numbers is 56. The difference between fourth and third numbers is 42. We’ve noticed that difference between two consecutive numbers is decreasing by 14 from the previous difference moving backward. So, the difference between third and second numbers is 42 – 14 = 28. So, the second number will be 54 – 28 = 26. To get the first number in the sequence, the difference from second number should be 28 – 14 = 14. So, the first number will be 26 – 14 = 12.