Breaking Numbers into Two Parts
A 30-minute Kindergarten lesson on decomposing numbers to 10, where the discovery is that there is more than one right answer and the child gets to find them all.
Breaking Numbers into Two Parts is a free 30-minute Kindergarten maths lesson plan for Common Core standard K.OA.A.3 — break numbers up to 10 into two parts in different ways. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.
- Grade:
- Kindergarten
- Length:
- 30 minutes
- Standard:
- K.OA.A.3
Kindergarten · Operations & Algebraic Thinking
K.OA.A.3
Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation.
Objective
Students will be able to split a number up to 10 into two parts in more than one way and record each split.
Students are successful when they can
- Finds at least three different splits of the same number.
- Records a split as a drawing and as an equation.
- Says that all the splits still make the same total.
What you need
- Two-colour counters, 10 per child
- A paper plate or a divided tray for each child
- Recording strips with blanks: 7 = ___ + ___
- The printable practice sheet linked at the end of this plan
The lesson
Warm-up — shake and spill
5 min- Each child shakes five two-colour counters in cupped hands and spills them.
- Count the reds and the yellows. Everyone had five; almost nobody had the same split.
- Collect four different results on the board without comment yet.
Teach — the same number, split many ways
8 min- Take seven counters and split them 6 and 1 on a divided tray.
- Write 7 = 6 + 1. Then move one counter across and write 7 = 5 + 2.
- Keep going: 4 and 3, then 3 and 4. Ask whether the last two are the same split. They are not — the trays look different.
- Ask whether any counters were added or removed. None were, and that is why every line still starts with 7.
- Include 7 = 7 + 0 deliberately, so zero appears as a legitimate part.
“There is not one right way to break seven. There are eight of them, and your job is to find as many as you can.”
Guided practice — find them all
8 min- Pairs take a number — 5, 6, 7 or 8 — and find every split they can, recording each on a strip.
- Prompt the pairs who are hunting randomly to move one counter at a time across the tray. The system finds them all; random guessing finds most.
- Ask each pair how they know they have finished.
Independent practice
6 min- Children complete a break-apart page for a single number.
- Repeated splits — 4 and 2 written twice — mean the search is unsystematic, which is the thing to teach next, not the arithmetic.
Close
3 min- Hold six counters, show four, and hide the rest. Ask how many are hidden.
- That question is the whole point of decomposition, and it is where tomorrow's lesson starts.
What goes wrong, and why
Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.
Thinks 7 = 4 + 3 means 4 + 3 has been asked and 7 is the answer.
Why: The equals sign has always had the answer on its right. Written this way round it reads backwards, so the child reverses it to make sense.
Fix: Write it both ways for the same split and read both aloud as 'is the same as'. Equals means balance, and the earlier that is true the less has to be unlearned in Grade 3.
Finds two or three splits and says there are no more.
Why: Searching randomly runs out of new ideas long before it runs out of splits, and there is no reason yet to believe an organised search exists.
Fix: Move one counter across at a time, starting from all-on-one-side. The list comes out in order, and the child can see when it has ended.
Rejects 8 + 0 as a way to break 8.
Why: Breaking has been understood as requiring two real piles, and an empty pile does not look like a part.
Fix: Ask how many are on the empty side. Zero is the answer to a real question, and including it is what makes the list complete rather than nearly complete.
If they are not there yet
- Start with 5, where the whole set can be seen without counting and a wrong split is noticed by the child rather than the adult.
- Use a divided tray so the two parts stay physically separate and do not need to be held apart mentally.
If they finish early
- Find every split of 10 and put them in order. The pattern in the two columns is worth a conversation.
- Ask how many splits a number has, and whether the answer is predictable from the number.
- Hide one part and ask for it, which turns decomposition into subtraction.
Exit ticket
Show two different ways to break 6 into two parts. Write both.
What to look for: Two genuinely different splits, recorded as equations. The same split written twice with the parts swapped is worth accepting today and questioning tomorrow — the trays really do look different.
Printable practice for K.OA.A.3
Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.
- Break Apart 5Fill in the missing part.
- Break Apart 6 and 7Fill in the missing part.
Questions about Breaking Numbers into Two Parts
How long does the Breaking Numbers into Two Parts lesson take?
30 minutes, split across 5 timed sections: warm-up 5 min, teach 8 min, guided practice 8 min, independent practice 6 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.
Which standard does Breaking Numbers into Two Parts teach?
CCSS.MATH.CONTENT.K.OA.A.3 — K.OA.A.3, Operations & Algebraic Thinking for Kindergarten: “Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation.” In plain terms, break numbers up to 10 into two parts in different ways.
What do I need to teach this lesson?
Two-colour counters, 10 per child, a paper plate or a divided tray for each child, recording strips with blanks: 7 = ___ + ___ and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.
What mistakes should I expect in this lesson?
Three, each a reasoning error rather than carelessness: thinks 7 = 4 + 3 means 4 + 3 has been asked and 7 is the answer; finds two or three splits and says there are no more and rejects 8 + 0 as a way to break 8. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.
How do I know whether the lesson worked?
The exit ticket asks: “Show two different ways to break 6 into two parts. Write both.” Two genuinely different splits, recorded as equations. The same split written twice with the parts swapped is worth accepting today and questioning tomorrow — the trays really do look different. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.
Is there a worksheet to go with Breaking Numbers into Two Parts?
Yes — 2 printable K.OA.A.3 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.
Is Breaking Numbers into Two Parts free to use?
Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.
Last reviewed 2026-09-05. Aligned to K.OA.A.3 of the Common Core State Standards for mathematics.