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?

  • A211, 843
  • B212, 849
  • C213, 853
  • D212, 848
  • E213, 852

Q2:

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

The input numbers follow the pattern add 1.

What number is 𝑥?

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

  • AAdd 7
  • BMultiply by 6
  • CAdd 6

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

  • A11×6 and 60+6
  • B11×6 and 60×6
  • C11×7 and 60+7

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.

  • Amultiply by 4
  • Bsubtract 12
  • Csubtract 3

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?

  • AMultiply by 2
  • BAdd 1
  • CAdd 2

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

  • A20×4 and 4+2
  • B20+4 and 3+2
  • C20÷4 and 4+1

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 follow a pattern of adding 1.
  • CThe sums are different and have no pattern.

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.

  • Aadd it to
  • Bsubtract it from

Q6:

Complete the rule for the pattern: Multiply by, then add 2. 1,5,17,53,161.

  • A2
  • B4
  • C5
  • D6
  • E3

Q7:

Complete the rule for the pattern: Divide by, then add 3. 38,22,14,10,8.

  • A5
  • B4
  • C2
  • D6
  • E3

Q8:

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

What is the next number in 4,15,37,?

  • A74
  • B81
  • C67
  • D261
  • 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.

  • Amultiply by 6
  • Bdivide by 6
  • Cadd 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.

  • Asubtracting 3
  • Bmultiplying by 3
  • Cadding 3

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