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Number Patterns Worksheets

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Follow a rule, find the rule, two-step rules, input and output tables, odd and even patterns, and growing shape patterns to draw and count.

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Number patterns

Follow a rule, notice odd and even, use two-step rules, find the rule, and fill in input and output tables.

Shape patterns

Growing patterns of tiles: draw the next figure, fill in the table and say how the pattern grows.

Print at 100% (actual size) for the cleanest tracing lines.

About these number patterns worksheets

A number pattern follows a rule. Start at 5 with the rule add 4 and you get 5, 9, 13, 17, 21 … These pages ask children to use a rule to fill in missing numbers, to find the rule from the numbers, and to use two-step rules such as multiply by 2, then add 1.

Patterns also have features the rule does not mention. With the rule add 5, the numbers take turns being odd and even, because adding an odd number always changes odd to even and back. The odd and even page asks children to notice this and circle what they see, which is exactly what the 4th grade standard asks for.

The input and output tables use the same rules in a table, and the shape pattern pages show figures that grow by the same number of tiles each time. Children draw the next figure, fill in the table and describe how the pattern grows.

Standards

  • CCSS.MATH.CONTENT.4.OA.C.5Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

How to use them

  1. Start with Follow the Rule, then Find the Rule.
  2. Use the odd and even page to talk about why the pattern happens, not just what it is.
  3. Use the input and output tables as a lead-in to functions.
  4. Ask children to describe the shape patterns in words before they fill in the table.

Teaching tips

  • To find a rule, look at how each number changes from the one before.
  • If the numbers grow faster and faster, the rule is probably multiply.
  • Adding an even number keeps odd numbers odd; adding an odd number makes them take turns.
  • For shape patterns, count how many tiles each new figure adds.

Questions teachers and parents ask

What is a number pattern?

A list of numbers made by following a rule, such as start at 3 and add 4: 3, 7, 11, 15 …

How do you find the rule of a pattern?

Look at how each number changes from the one before. If it goes up by the same amount each time, the rule is add that amount; if it doubles, the rule is multiply by 2.

What is an input and output table?

A table where a rule turns each input number into an output number, such as multiply by 3: 4 becomes 12.