Kindergarten · Operations · MAT-K-OPS-002
Decompose Numbers to 5
Break a whole number from 1–5 into two parts in more than one way.
Learning objectives
What you should be able to do
- Break a whole number from 1–5 into two parts in more than one way.
- Record decompositions with objects, number bonds, and equations.
- Explain that changing the parts does not change the whole when no objects are added or removed.
Prerequisite check
Make sure the foundation is ready.
Checks understanding that parts can form a whole.
Checks the total before splitting it.
Learn
Build the idea from meaning, not memorization.
Decomposing reverses the viewpoint
When composing, we start with parts and join them. When decomposing, we start with the whole and separate it into parts. A group of five can be split into two and three, one and four, or other valid pairs.
The whole is conserved
If five counters are separated into two groups, there are still five counters altogether. Splitting changes organization, not quantity.
A number bond shows the structure
A number bond places the whole in one position and connects it to its parts. For 5 split into 2 and 3, the bond means the same thing as 5 = 2 + 3.
Finding all decompositions builds flexibility
A strong learner can see several ways to split a number instead of relying on a single memorized pair. This flexibility supports subtraction, missing-addend problems, and making ten.
Interactive math lab
Change it. See what stays true.
Ten-Frame Lab
Fill the frame from left to right and connect the visible amount to the numeral.
5 filled; 5 empty; 10 spaces altogether.
- split whole
- drag between parts
- find missing part
- list all splits
Worked examples
Twenty different ways to see the concept work.
Split 2 into two parts.
1 and 1The two parts still total two.
Split 3 as one and the rest.
1 and 2Removing one from the group leaves two.
Split 3 another way.
0 and 3A zero part is allowed.
Split 4 equally.
2 and 2Both parts contain two.
Split 4 into 1 and another part.
1 and 3Three objects remain.
Split 5 into 2 and another part.
2 and 3Three remain after two are separated.
Split 5 into 4 and another part.
4 and 1One remains.
Split 5 with an empty part.
5 and 0The empty part contributes zero.
Write 4 split into 1 and 3 as an equation.
4 = 1 + 3The parts reconstruct the whole.
Write 5 split into 2 and 3.
5 = 2 + 3Two and three together equal five.
A whole of 3 is split into 2 and ?.
1One object remains.
A whole of 4 is split into 3 and ?.
1Three plus one returns four.
A whole of 5 is split into 1 and ?.
4One plus four returns five.
A whole of 5 is split into 0 and ?.
5Zero leaves the entire whole in the other part.
Two groups after splitting 4 are 2 and 2. Check the whole.
2 + 2 = 4Recomposing verifies the split.
Two groups after splitting 5 are 3 and 2. Check the whole.
3 + 2 = 5No objects were lost.
Move one object from the 1-part to the 4-part of five.
0 and 5The parts change while the whole remains five.
Move one object from a 2-and-3 split of five.
1 and 4 or 3 and 2 depending directionMoving an object changes the parts but not the whole.
Can 5 decompose into 2 and 2?
NoThose parts total four, not five.
Explain why splitting 5 does not make fewer objects.
All five objects remain present; only their grouping changes.Decomposition reorganizes the whole.
Practice
Guided practice with hints
01Split 3 into two groups.
Hint: Move one object away first.
Answer: 1 and 2 is one answer.
02Complete 4 = 1 + __.
Hint: What remains after one of four is separated?
Answer: 3
03Complete 5 = 3 + __.
Hint: Recompose to check.
Answer: 2
04Which split is valid for 4: 2+2 or 2+3?
Hint: Add the parts.
Answer: 2+2
05Show two different splits of 5.
Hint: Move one counter between groups.
Answer: Examples: 1+4 and 2+3.
06Why does the total stay 5?
Hint: Count all objects across both groups.
Answer: No object was added or removed.
Practice
Independent practice
01Complete 3=1+__.
Answer: 2
02Complete 4=2+__.
Answer: 2
03Complete 5=4+__.
Answer: 1
04Complete 5=0+__.
Answer: 5
05Give a split of 4 that uses 1.
Answer: 1 and 3
06Give a split of 5 that uses 2.
Answer: 2 and 3
07Is 5=2+2 correct?
Answer: No
08Name two different ways to decompose 5.
Answer: Examples: 1+4 and 2+3.
Common mistakes
Learn to catch the error, not just the answer.
Keep both part groups visible and count all objects to verify the whole.
Always check by joining the parts mentally or physically.
Generate multiple pairs and verify each by recomposing.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Separate five classroom objects into two baskets in several different ways.
- Share four counters into two groups and record every distinct split.
Challenge problems
List all unordered decompositions of 4.
0+4, 1+3, 2+2
How does moving one counter from one part to the other affect the whole?
The parts change by one in opposite directions; the whole stays fixed.
Why is 3+2 a check for the decomposition 5→3 and 2?
Recombining the parts produces the original whole five.
Explain the difference between composing and decomposing.
Composing joins parts into a whole; decomposing separates a whole into parts.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Split It
Divide a target whole into two valid parts and find more than one solution.
Practice
Mastery check
01What does decompose mean?
Answer: Break a whole into parts.
02Decompose 3 into two parts.
Answer: Examples: 1+2, 0+3.
03Complete 4=1+__.
Answer: 3
04Complete 5=2+__.
Answer: 3
05Give two different decompositions of 5.
Answer: Examples: 1+4 and 2+3.
06How do you verify a decomposition?
Answer: Join or add the parts and check that they equal the original whole.
07Can one part be zero?
Answer: Yes.
08Why does the whole stay the same when split?
Answer: No objects are added or removed.
Terminology
Words to know
- decompose
- Separate a whole into smaller parts.
- number bond
- A diagram showing how parts connect to a whole.
- recompose
- Join separated parts again to check the whole.
- missing part
- An unknown part needed with a known part to make the whole.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Kindergarten Operations & Algebraic Thinking
Standards progression for composing, decomposing, adding, and subtracting within 10.