Kindergarten · Operations · MAT-K-OPS-001
Compose Numbers to 5
Build each whole number from 1–5 using two smaller parts.
Learning objectives
What you should be able to do
- Build each whole number from 1–5 using two smaller parts.
- Represent a part-part-whole relationship with objects, drawings, and an equation.
- Explain that the parts can change while the whole stays fixed.
Prerequisite check
Make sure the foundation is ready.
Checks cardinality within 5.
Checks representation of the whole and parts.
Learn
Build the idea from meaning, not memorization.
A whole can be made from parts
Composing means joining smaller quantities to make a whole. Three can be made from one and two, because one object joined with two objects makes three objects altogether.
The same whole can have different part pairs
Five can be made as 0 and 5, 1 and 4, 2 and 3, 3 and 2, 4 and 1, or 5 and 0. The arrangement of the parts changes, but the whole remains five.
Pictures and equations tell the same story
Two red counters and one blue counter can be drawn as ●● + ●, and recorded as 2 + 1 = 3. The objects, drawing, spoken sentence, and equation are different representations of the same relationship.
Part-whole thinking prepares for arithmetic
Seeing a number as parts helps with addition, subtraction, making ten, place value, fractions, and later algebra. The goal is flexible number sense, not memorizing only one way to make a number.
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 by color
- join parts
- find missing part
- show multiple compositions
Worked examples
Twenty different ways to see the concept work.
Make 2 from two parts.
1 + 1 = 2One and one compose two.
Make 3 using 1 and another part.
1 + 2 = 3Two completes the whole three.
Make 3 a different way.
2 + 1 = 3The order changes, but the whole remains three.
Make 4 with equal parts.
2 + 2 = 4Two groups of two make four.
Make 4 with one part equal to 1.
1 + 3 = 4One and three combine to four.
Make 5 with 2 and another part.
2 + 3 = 5Three is the missing part.
Make 5 with 4 and another part.
4 + 1 = 5One completes five.
Use zero as a part of 5.
0 + 5 = 5Adding no objects leaves five.
Compose 3 from a red group of 2 and blue group of 1.
2 + 1 = 3Color changes representation, not the total.
Compose 4 from 3 apples and 1 banana.
3 + 1 = 4Different object types can still form one counted whole.
Two parts are 1 and 1. What is the whole?
2Join the parts and count both.
Two parts are 2 and 2. What is the whole?
4Four objects are present altogether.
Two parts are 3 and 2. What is the whole?
5Three joined with two makes five.
Which pair makes 4: 1+2 or 1+3?
1 + 3One plus three contains four objects.
Which pair makes 5: 2+2 or 2+3?
2 + 3Two plus three makes five.
A whole of 5 has one part 1. Find another possible part.
4One and four compose five.
A whole of 4 has one part 0. Find the other part.
4Zero contributes no objects.
Rearrange the two parts 2 and 3. Does the whole change?
No; the whole is still 5.All five objects remain in the combined set.
Show 5 with fingers on two hands.
For example 2 and 3The fingers form two parts of one whole.
Explain why 1+4 and 2+3 can both describe 5.
Both pairs contain five objects altogether.A whole can be composed in multiple ways.
Practice
Guided practice with hints
01Build 3 using two groups.
Hint: Try one object in one group.
Answer: 1 and 2, or 2 and 1, or 0 and 3.
02Complete 2 + __ = 5.
Hint: Count on from two until five.
Answer: 3
03Complete 1 + __ = 4.
Hint: How many more objects are needed?
Answer: 3
04Which pair makes 5: 3 and 2 or 3 and 1?
Hint: Join each pair and count.
Answer: 3 and 2
05Use two colors to make 4.
Hint: Split four counters into two color groups.
Answer: Any valid split totaling 4.
06Does switching 1 and 4 change the whole 5?
Hint: Count all objects after switching.
Answer: No
Practice
Independent practice
01Complete 1 + __ = 2.
Answer: 1
02Complete 1 + __ = 3.
Answer: 2
03Complete 2 + __ = 4.
Answer: 2
04Complete 2 + __ = 5.
Answer: 3
05Which pair makes 4: 3+1 or 3+2?
Answer: 3+1
06What whole is made by 1 and 3?
Answer: 4
07What whole is made by 0 and 5?
Answer: 5
08Name two different pairs that make 5.
Answer: Examples: 1+4 and 2+3.
Common mistakes
Learn to catch the error, not just the answer.
Join or mentally combine both parts before naming the whole.
A whole can be split into unequal parts, such as 1 and 4 making 5.
Zero is a valid part that contributes no objects, such as 0+5=5.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Split five snack pieces between two plates in several ways and record each pair.
- Use two colors of blocks to build the same total in multiple combinations.
Challenge problems
List all unordered part pairs for 5.
0+5, 1+4, 2+3
Why do 2+3 and 3+2 make the same whole?
They contain the same five objects, only grouped in a different order.
Can a whole of 4 have one part larger than 4?
No, not when both parts are nonnegative quantities that combine to exactly 4.
Explain how composing numbers helps with later addition.
Addition is the process of combining parts to determine a whole.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Build the Whole
Choose two parts that exactly build a target number from 1–5.
Practice
Mastery check
01What does compose mean?
Answer: Join parts to make a whole.
02Make 3 with two parts.
Answer: Examples: 1+2, 2+1, 0+3.
03Make 4 with two equal parts.
Answer: 2+2
04Complete 2+__=5.
Answer: 3
05Give two different ways to make 5.
Answer: Examples: 1+4 and 2+3.
06Does 4+1 make the same whole as 1+4?
Answer: Yes; both make 5.
07Can zero be a part? Give an example.
Answer: Yes; 0+5=5.
08Explain part and whole.
Answer: Parts are smaller quantities joined together; the whole is their combined total.
Terminology
Words to know
- compose
- Join parts to make a whole.
- part
- A quantity that contributes to a larger whole.
- whole
- The complete quantity made from all parts.
- equation
- A mathematical statement showing two expressions have the same value.
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.