Worksheet: Two-Step Input–Output Patterns

In this worksheet, we will practice finding the missing number and identifying patterns in input–output tables using two-step rules.

Q1:

The rule for the given pattern is multiply by 4, then add 1.

What are the next two numbers?

  • A 212, 849
  • B 213, 853
  • C 212, 848
  • D211, 843
  • E 213, 852

Q2:

The rule for this input-output table is multiply by 6.

The input numbers follow the pattern add 1.

What number is ?

The output numbers will also follow a pattern. Describe this pattern.

  • Amultiply by 6
  • Badd 6
  • Cadd 7

We can use the numbers in the table to calculate in two ways. What are they?

  • A and
  • B and
  • C and

Q3:

The rule for this input-output table is multiply by 4.

Jacob has shown that the pattern for the input numbers is subtract 3.

Describe the pattern that the output numbers will follow.

  • A subtract 3
  • B subtract 12
  • C multiply by 4

Q4:

The rule for this input-output table is divide by 4.

The input numbers follow the pattern add 4.

What number is 𝑥 ?

The output numbers will also follow a pattern. What is it?

  • AAdd 1
  • BAdd 2
  • CMultiply by 2

Using the numbers in the table, find two ways to calculate 𝑦 .

  • A 2 0 ÷ 4 and 4 + 1
  • B 2 0 × 4 and 4 + 2
  • C 2 0 + 4 and 3 + 2

Q5:

Michael followed addition and subtraction rules to make a group of addition sentences.

What do you notice about the sums?

  • AThey are all the same.
  • BThe sums are different and have no pattern.
  • CThe sums follow a pattern of adding 1.

Fill in the Blank: In an addition expression, if I add a number to one addend and the other addend, the sum stays the same.

  • Asubtract it from
  • Badd it to

Q6:

Complete the rule for the pattern: Multiply by , then add 2. 1 , 5 , 1 7 , 5 3 , 1 6 1 .

  • A 2
  • B 3
  • C6
  • D 5
  • E 4

Q7:

Complete the rule for the pattern: Divide by , then add 3. 3 8 , 2 2 , 1 4 , 1 0 , 8 .

  • A6
  • B 2
  • C 3
  • D 5
  • E 4

Q8:

The rule for the given pattern is multiply by 2, then add 7.

What is the next number in 4 , 1 5 , 3 7 , ?

  • A 67
  • B 74
  • C 81
  • D 261
  • E95

Q9:

The rule for this input-output table is divide by 6.

Benjamin has shown that the pattern for the input numbers is add 12.

Describe the pattern that the output numbers will follow.

  • A multiply by 6
  • B divide by 6
  • C add 2

Q10:

The rule for this input-output table is divide by 3.

Jacob has shown that the pattern for the input numbers is subtract 9.

Describe the pattern that the output numbers will follow.

  • A subtracting 3
  • B multiplying by 3
  • C adding 3

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