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 5, 10, 15, 20 is 22.
Corrected: The next number in 5, 10, 15, 20 is 25.
Counting by 5s gives 5, 10, 15, 20, 25. The rule adds 5 each time, so the number after 20 is 25, not 22.
2. Fix the sentence:
The rule for the pattern 2, 4, 6, 8 is add 3.
Corrected: The rule for the pattern 2, 4, 6, 8 is add 2.
Look at the jumps: 2 to 4 is 2, 4 to 6 is 2, and 6 to 8 is 2. Each step grows by 2, so the rule is add 2.
3. Fix the sentence:
The pattern 3, 6, 9, 12 continues with 14.
Corrected: The pattern 3, 6, 9, 12 continues with 15.
The numbers 3, 6, 9, 12 are skip-counts of 3. Adding 3 to 12 gives 15, which is the next number in the pattern.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In the pattern A, B, C, A, B, C, the next letter is A.
The pattern repeats the group A, B, C over and over. After C comes the start of the group again, so the next letter is A.
2. The pattern 10, 20, 30, 40 follows the rule add 10.
Each number jumps from 10 to 20 to 30 to 40, and every jump is 10. So the rule is add 10.
3. What comes next in 4, 8, 12, 16, 20?
Counting by 4s makes 4, 8, 12, 16, 20. Adding 4 to 16 lands on 20.
4. An input-output table uses the rule add 5. If the input is 7, the output is 12.
The rule says add 5 to whatever goes in. Putting 7 in and adding 5 gives 7 + 5 = 12 as the output.
Part C: True or False?
Read each statement. Circle True or False.
1. The pattern 1, 3, 5, 7, 9 follows the rule add 2.
True False
True. The numbers 1, 3, 5, 7, 9 each grow by 2: 1+2=3, 3+2=5, 5+2=7, 7+2=9.
2. In the pattern 10, 20, 30, 40, the next number is 45.
True False
False. The pattern jumps by 10 each time, so after 40 comes 50, not 45.
3. A repeating pattern like red, blue, red, blue uses the same group over and over.
True False
True. A repeating pattern works by using the same group, like red and blue, again and again in the same order.