What is this skill?
A number pattern is a list of numbers that follows a rule. Fourth graders generate a pattern from a rule, such as “start at 16 and add 11,” and work out the rule from a list, such as 7, 18, 29, 40, which adds 11 each time. They also notice features the rule does not state, like whether the numbers alternate between odd and even.
The common rules are adding or subtracting the same number, and sometimes multiplying (3, 6, 12, 24 doubles each time). To find a rule, a child looks at the differences between neighbors. If they are all the same, the rule is addition of that amount. If the gaps keep growing, the pattern may be multiplying. Children then use the rule to find the next terms, and explain in words how they know the pattern will continue. Number patterns also appear on a hundreds chart, where counting by 3s or 7s paints a visible shape.
Why it matters
Patterns are the roots of algebra. Spotting a rule, stating it and using it to predict what comes next is the same thinking a student later uses with variables and functions. It also supports skip counting, multiplication and division facts, which are patterns too.
Pattern work also builds careful looking. Children learn to test a guess against every term, not only the first two, and to state a rule in words. That habit of checking and explaining is useful far beyond math.
Common mistakes
- Looking only at the first two numbers. A rule has to fit every step, so test it across the whole list.
- Finding the difference between the wrong neighbors or making a small arithmetic slip, giving a rule that is off by one.
- Mixing up adding and multiplying, such as seeing 6, 12, 24 and saying “add 6.”
- Writing the last number again as the next term, or starting from the wrong number.
- Stating the rule as “it goes up” instead of giving the exact amount.
How to help at home
- Make up patterns for each other. One person writes the first four terms and the other finds the rule and the next number.
- Look for patterns in everyday numbers: house numbers on one side of the street, steps in a staircase, a savings plan.
- Ask “How do you know?” and have your child test the rule on each pair of neighbors.
- Use a hundreds chart and color a pattern, like every 7th number, to see it on the grid.
- Try a growing pattern with objects, like toothpick shapes, and write the count for each step.
Worked examples
These are real questions from the Tutorsaurus number patterns and rules practice, with the answers worked out.
Example 1
What is the rule? 16, 21, 26, 31, …
Choices: Subtract 5, Multiply by 5, Add 6, Add 5
Answer: Add 5. Each number is 5 more than the one before: the rule is add 5.
Example 2
What is the rule? 7, 18, 29, 40, …
Choices: Add 11, Add 10, Add 12, Multiply by 11
Answer: Add 11. Each number is 11 more than the one before: the rule is add 11.
Example 3
What comes next? 16, 27, 38, 49, …
Answer: 60. The rule is "add 11". 49 + 11 = 60.