Free printable number patterns chart
Grades 1–5Skip counting, counting back, doubling, growing gaps and rules that take turns — how to spot each one and work out what comes next. Print it for the wall, or find the rule in as many fresh patterns as you like below.
Tap the chart to open it at full size
Find the rule, then check
Pick a pattern type and a new sequence appears with the next term missing. Work it out before pressing show — that gap between guessing and checking is where the learning happens.
Start by looking at the gaps rather than the numbers. For most patterns, subtracting each term from the next gives you the rule immediately, and a child who does that first has a method rather than an instinct.
The growing gaps and taking turns patterns are the ones that break that habit usefully. When the gaps are not equal, look at the gaps between the gaps. When nothing works between neighbors, compare every second number instead.
- The rule
- Work it out, then press show
- What comes next
- —
Look at the gap between each pair of numbers first. That is where almost every rule hides.
How to use this number patterns chart at home
Ask for the rule, not the next number. A child can often guess what comes next without being able to say why, and the saying why is the whole point. If they can describe the rule, the next number follows for free.
Write the gaps underneath. Physically writing 3, 3, 3 or 1, 2, 3 between the terms turns a vague look-at-it task into something concrete. It is the single most useful habit in this topic and almost nobody teaches it explicitly.
Then run patterns backwards. Given 12, 15, 18, 21, what came before the 12? Working in reverse tests whether the rule is really understood or just being followed forwards.
Patterns are where algebra starts
Describing a rule in words — start at 4 and add 3 each time — is the first step toward writing it with letters. By Grade 7 that same pattern becomes an expression, and children who spent time describing rules find that transition much gentler.
It also builds the habit of looking for structure rather than calculating. A child who sees 3, 6, 9, 12 and thinks three times table has noticed something; a child who works out each gap by subtracting has done arithmetic. Both get the answer, only one is doing pattern work.
This is why the widget above asks for the rule before it asks for the number. Getting the next term right by counting on is not evidence the pattern was understood.
Adding patterns and multiplying patterns
The two look identical at the start and separate quickly. 2, 4 could be add two or double. 2, 4, 6 settles it one way; 2, 4, 8 settles it the other.
That is a useful lesson beyond patterns: two examples are never enough to be sure of a rule. Children happily commit to a rule after two terms and then have to unpick it, and pointing out why is worth doing once explicitly.
The giveaway is the gaps. Equal gaps mean adding. Gaps that grow in proportion to the numbers mean multiplying — and if the numbers roughly double each time, the rule almost certainly involves doubling.
Where number patterns usually go wrong
Deciding the rule from two terms. Always check it against a third and a fourth before committing.
Giving a rule without a starting point. Add 3 describes infinitely many patterns; start at 4 and add 3 describes one.
Missing a multiplying pattern. Trying to find a fixed gap in 3, 9, 27, 81 and concluding there is no rule.
Only looking at neighbors. In alternating patterns nothing consistent appears between neighboring terms, and every second term has to be compared instead.
After the chart goes up
A chart explains the idea but gives a child nothing to do. These do the rest.
- number sense at Mathify Kids — every topic in this area, sorted by grade.
- skip counting worksheets — printable practice.
- even and odd numbers worksheets — the next step once this is solid.
- comparing numbers worksheets — more practice in the same area.
Everything at this level: Grade 1 math · Grade 2 math · Grade 3 math · Grade 4 math · Grade 5 math
Charts that pair with this one
Charts that work well printed alongside this one.
Browse all 45 math charts
Last reviewed
Questions parents ask
How do you find the rule in a number pattern?
Work out the gap between each pair of neighboring terms. If the gap is the same every time, that gap is the rule. If it is not, check whether each term is being multiplied instead, or whether the gaps themselves follow a pattern.
What is a growing pattern?
One where the gap changes as you go. In 3, 4, 6, 9, 13 the gaps are 1, 2, 3 and 4 — the numbers do not grow by a fixed amount, but the gaps do. Looking at the gaps between the gaps is the technique, and it is a genuinely new idea when children first meet it.
What is the difference between a pattern that adds and one that multiplies?
An adding pattern grows by the same amount each step, so the gaps are equal. A multiplying pattern grows by the same factor, so the gaps get bigger and bigger. 2, 4, 6, 8 adds two; 2, 4, 8, 16 doubles. The first two terms look identical, which is why you always check three or more.
How do you describe a rule properly?
Say what you do to get from one term to the next, including the starting number. Start at 4 and add 3 each time is a complete rule; add 3 on its own is not, because it does not say where to begin.
What if a pattern has two rules?
Some patterns alternate — add 3, then add 8, then add 3 again. If nothing consistent shows up between neighboring terms, compare every second term instead. That usually makes the two rules visible straight away.
What grade is this number patterns chart for?
Grades 1 to 5. Skip counting patterns arrive first, doubling and multiplying around Grade 3, and growing or alternating patterns by Grades 4 and 5. Patterns lead directly into sequences and then into algebra.
Is this number patterns chart free to print?
Yes. Open it full size and print as many copies as you need for home or a classroom, with no account and no watermark. Reselling it or re-hosting the file elsewhere is not allowed — link to this page instead.