This handy Spectrum Math Grade 4 Answer Key Chapter 9 Posttest provides detailed answers for the workbook questions.

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Complete the number patterns.

Question 1.
25, 24, 23, 25, , 25, 24, 23, 25, , Explanation:
As it is said that it is a number pattern, so the question follows the pattern 25, 24, 23, and so on. As the number of the pattern ended in the question is 25, the next numbers would be 24, and 23 again.

b. 256, 257, 256, 258, , 256, 257, 256, 258, , Explanation:
As it is said that it is a number pattern, so the question follows the pattern 256, 257, 256, 258 and so on. As the number of the pattern ended in the question is 258, the next numbers would be 256 and 259. The alternate number in the pattern is increasing by 1 as we can observe in the given pattern.

Question 2.
a. 66, 55, 44, , 66, 55, 44, , Explanation:
By looking at the given numbers, it’s been noticed that the difference between two consecutive numbers is 11. So, the last number in the given sequence in the question is 44 and so the required next number in the sequence is 44 -11 = 33. The last number in the sequence is 33 – 11 = 22.

b. 570, 551, 531, 510, , 465, ,  Explanation:
By looking at the given numbers, it’s been noticed that the difference between first two numbers is -19. The difference between second and third numbers is -20. We’ve noticed that difference between two consecutive numbers is decreasing by one from there onwards. So, last number in the given sequence in the question is 510 and the difference between 510 and the number before it (531) is -21. So, -22 should be added to the last number 510 to get the next number in the sequence. So, the next number in the sequence is 510 – 22 = 488. To get the next number in the sequence -24 should be added to get the next number in the sequence and it will be 465 – 24 = 441. To get the last number in the sequence -25 should be added to get the next number in the sequence and it will be 441 – 25 = 416.

Question 3.
a. 14, 28, 44, 62, ,  Explanation:
By looking at the given numbers, it’s been noticed that the difference between first two numbers is 14. The difference between second and third numbers is 16. 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 62 and the difference between 62 and the number before it (44) is 18. So, 20 should be added to the last number 62 to get the next number in the sequence. So, the next number in the sequence is 62 + 20 = 82. To get the next number in the sequence 22 should be added to get the next number in the sequence and it will be 82 + 22 = 104.

b. , 26, , 42, 53, 66, 81 Explanation:
By looking at the given numbers, it’s been noticed that the difference between seventh and sixth numbers is 15. The difference between sixth and fifth numbers is 13. The difference between fifth and fourth numbers is 11. We’ve noticed that difference between two consecutive numbers is decreasing by 2 from the previous difference moving backward. So, the difference between fourth and third numbers should be 11-2=9. So, the third number will be 42-9=33. Similarly, the difference between the third and second numbers is 33-26=7. So, to get the first number in the sequence, the difference from second number will be 7-2=5.  So, the first number will be 26-5=21.

Draw the objects that complete the pattern.

Question 4.
a.  Explanation:
Drawn the objects which completes the given pattern as you can observe in the above image.

b.  Explanation:
Drawn the objects which completes the given pattern as you can observe in the above image.

Question 5.  