Number Chains
Updated October 2026 · 6 free printables
Number chain worksheets for 1st to 3rd grade: start with the colored number, follow the arrows (+2, -1, +5 and later x2 or ÷2) and write each new number in the next circle. Caterpillar chains repeat one rule along the body, and number loops bring you back to the start number if every step is right.
For older kids there are mystery chains where the rule is hidden and has to be found from the numbers, and backward chains where only the last number is given, so kids have to work back with the opposite operation. Each PDF comes with an answer key.
All 6 Number Chains, One by One
Here is a closer look at every page in this collection: what it practices, which grade it fits and a tip for each one.
-
1. Number Chains: Add and Take Away Within 20
A free printable number chains: add and take away within 20 worksheet with an answer key. Start with the colored number. Follow the arrows and write each new number in the next circle. It matches first grade goals, roughly ages 6 to 7. Use small objects like buttons or cereal to check tricky problems.
-
2. Caterpillar Number Chains
A free printable caterpillar number chains worksheet with an answer key. The number on the head is the start. Use the rule on the leaf to fill in every body part. It matches first grade goals, roughly ages 6 to 7. Say the row out loud to hear the pattern.
-
3. Number Loops That Come Back to the Start
A free printable number loops that come back to the start worksheet with an answer key. Start at START and go around the loop. If you do every step right, you land on the start number again. Second graders usually finish it in 10 to 15 minutes. Have your child say each fact out loud while writing the answer.
-
4. Mystery Rule Chains: Find the Rule
A free printable mystery rule chains: find the rule worksheet with an answer key. Each chain uses the same rule on every arrow. Find the rule, write it in the boxes and fill in the missing numbers. It fits second grade, around ages 7 to 8.
-
5. Number Chains With Times and Divide
A free printable number chains with times and divide worksheet with an answer key. Follow the arrows: add, subtract, multiply and divide. Write each answer in the next circle. It is aimed at third grade, around ages 8 to 9. Skip-count out loud to check any fact you are not sure about.
-
6. Backward Number Chains: Find the Start
A free printable backward number chains: find the start worksheet with an answer key. Only the last number is given. Work backward with the opposite operation to fill every circle. Third graders can use it for practice, review or a quick check before a test.
Tips for number chains
- Point at each arrow as you go and say the step out loud: 'twelve, plus three, fifteen'.
- Write small helper numbers next to the circle when a step crosses ten, then erase them.
- When a chain has x and ÷, slow down and check that each answer looks reasonable before moving on.
Fun math facts
- A rule that adds the same number every time makes an arithmetic sequence, the kind of pattern taught in later grades.
- Doubling 1 just ten times already gives 1,024, which is why x2 chains grow so fast.
- Working backward with opposite operations is how algebra problems like x + 7 = 15 are solved.
Fun ways to use your printables
- Play a car game: one person says a start number and a rule, and everyone counts along out loud.
- Make a paper chain with one number on each link and hang it up as a counting garland.
- Let your child write a mystery chain for you, then switch and see who finds the rule faster.
How to print
Click Download PDF and print at 100% on US Letter or A4 paper. Page 1 is the worksheet and page 2 is the answer key, so choose “page 1” in the print dialog if you only want the practice page. Every worksheet is free for home, homeschool and classroom use, so print as many copies as you need.
Frequently asked questions
What is a number chain in math?
A row of circles joined by arrows. Each arrow shows an operation, and you apply it to the number before it to get the next number. It is a fun way to do a string of mental math.
How do I find the rule in a mystery chain?
Look at the first two numbers and ask what happened: did the number get bigger or smaller, and by how much? Then test the same rule on the next pair before filling the empty circles.
How do you work a number chain backward?
Start at the last number and undo each step with the opposite operation: adding becomes subtracting and multiplying becomes dividing. When you reach the start, check by going forward again.
Why do the number loops come back to the start?
The steps cancel each other out: the numbers added in the loop are exactly as many as the numbers taken away. If a child does not land on the start number, there is a mistake somewhere in the loop.