Patterns and Number Sequences — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
The next number in 9, 18, 27, 36 is 44.
Corrected: The next number in 9, 18, 27, 36 is 45.
The pattern jumps by 9 each time: 9, 18, 27, 36. Adding 9 to 36 gives 45, not 44, so the corrected next number is 45.
2. Fix the sentence:
The rule for the pattern 30, 25, 20, 15 is add 5.
Corrected: The rule for the pattern 30, 25, 20, 15 is subtract 5.
The numbers are getting smaller (30 down to 15), which means the rule has to subtract, not add. Each step drops by exactly 5, so the correct rule is subtract 5.
3. Fix the sentence:
In the pattern 7, 14, 21, 28, the next number is 34.
Corrected: In the pattern 7, 14, 21, 28, the next number is 35.
This is the 7-times-table, so each number grows by 7. After 28 you add 7 more to reach 35, not 34.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The pattern 8, 16, 24, 32 follows the rule add 8.
Subtract any pair of side-by-side numbers to find the rule: 16 minus 8 is 8, and 24 minus 16 is also 8. The same gap appears every time, so the rule is add 8.
2. What comes next in 11, 22, 33, 44, 55?
These are the multiples of 11 in order, so each step adds 11. Adding 11 to 44 gives 55 as the next number in the sequence.
3. In the repeating pattern sun, moon, star, sun, moon, the next shape is star.
The pattern repeats in a sun-moon-star group, and the second group has only reached sun and moon. Star is the missing shape that finishes the second group.
4. An input-output table uses the rule add 6. If the input is 14, the output is 20.
Apply the rule by adding 6 to the input number 14. Since 14 plus 6 equals 20, the output that comes out of the table is 20.
Part C: True or False?
Read each statement. Circle True or False.
1. The pattern 12, 15, 18, 21 follows the rule add 3.
True False
Check the gaps: 15 minus 12 is 3, 18 minus 15 is 3, and 21 minus 18 is 3. The same gap of 3 appears every time, so the rule is add 3.
2. The next number after 50, 40, 30, 20 is 15.
True False
The numbers drop by 10 each step, so the rule is subtract 10. Subtracting 10 from 20 lands on 10, not 15.
3. A shrinking pattern gets smaller each time.
True False
The word "shrinking" describes something getting smaller, which matches a pattern that subtracts at every step. A growing pattern would do the opposite by adding.