Patterns and Input/Output Tables — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. If inputs 1, 2, 3 give outputs 5, 9, 13, what Grade 4 rule fits?
A) Multiply by 4 add 1
B) Multiply by 3 add 2
C) Add 4 each time
D) Multiply by 5 minus 1
1 times 4 plus 1 is 5 and 2 times 4 plus 1 is 9, so the rule is multiply by 4 add 1.
2. Inputs 2, 3, 4 produce outputs 7, 10, 13. The Grade 4 rule is:
A) Multiply by 2 plus 3
B) Multiply by 3 plus 1
C) Add 5 each time
D) Multiply by 4 minus 3
3 times 3 plus 1 is 10 and 4 times 3 plus 1 is 13, so the rule is multiply by 3 plus 1.
3. If inputs 0, 1, 2 give outputs 3, 8, 13 in a Grade 4 table, what is the rule?
A) Multiply by 5 plus 3
B) Multiply by 4 plus 4
C) Add 5 each time
D) Multiply by 3 plus 5
0 times 5 plus 3 is 3 and 1 times 5 plus 3 is 8, so the rule is multiply by 5 plus 3.
4. For Grade 4 inputs 4, 5, 6 with outputs 9, 11, 13, the rule is:
A) Multiply by 2 plus 1
B) Multiply by 3 minus 3
C) Add 5 each time
D) Multiply by 2 minus 1
5 times 2 plus 1 is 11 and 6 times 2 plus 1 is 13, so the rule is multiply by 2 plus 1.
Part B: Fill in the Blank
Write the correct answer on each line.
1. If the Grade 4 rule is multiply by 4 plus 2 and the input is 6, the output is 26.
6 times 4 is 24 and 24 plus 2 is 26, the correct Grade 4 output.
2. Inputs 1, 2, 3 give Grade 4 outputs 4, 7, 10, so the rule is multiply by 3 plus 1.
Adding 1 to 3 times the input gives 4, 7, and 10, matching this Grade 4 pattern.
3. If the Grade 4 rule is multiply by 5 minus 3 and the output is 22, the input was 5.
22 plus 3 is 25 and 25 divided by 5 is 5, so the Grade 4 input was 5.
4. Using the Grade 4 rule add 4 then multiply by 2, input 7 gives output 22.
7 plus 4 is 11 and 11 times 2 is 22, the correct Grade 4 output.
5. If the Grade 4 rule is multiply by 6 plus 1 and the input is 3, the output is 19.
3 times 6 is 18 and 18 plus 1 is 19, the Grade 4 output for this input.