Kindergarten · Operations · MAT-K-OPS-008
Make 10
Find the number that combines with any number 0–10 to make 10.
Learning objectives
What you should be able to do
- Find the number that combines with any number 0–10 to make 10.
- Use a ten-frame and equations to represent complements to ten.
- Recall and explain common make-10 pairs as a foundation for mental arithmetic.
Prerequisite check
Make sure the foundation is ready.
Checks whole-and-missing-part reasoning.
Checks visual readiness for complements to ten.
Learn
Build the idea from meaning, not memorization.
Ten is a powerful benchmark
A ten-frame has exactly ten spaces. If six are filled, four are empty. Without recounting all ten spaces, the picture shows 6 + 4 = 10.
Complements are partners that complete ten
The complement to 7 is 3 because 7+3=10. The complement to 3 is 7 for the same reason. Knowing these pairs makes later addition and subtraction much faster.
Make-10 pairs form a pattern
As one part grows by one, the other part shrinks by one: 0+10, 1+9, 2+8, 3+7, 4+6, 5+5. The whole stays ten.
Making ten becomes a mental strategy
Later, a problem such as 8+5 can be reorganized by giving 2 of the 5 to the 8, creating 10+3. Kindergarten make-10 work lays the conceptual foundation for that strategy.
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.
- fill to ten
- name complement
- match pairs
- move between parts
Worked examples
Twenty different ways to see the concept work.
0 + __ = 10
10All ten are needed when starting at zero.
1 + __ = 10
9Nine more complete ten.
2 + __ = 10
8Two filled spaces leave eight empty.
3 + __ = 10
7Three and seven are complements.
4 + __ = 10
6Four plus six makes ten.
5 + __ = 10
5Five and five are equal halves of ten.
6 + __ = 10
4Six filled spaces leave four.
7 + __ = 10
3Seven plus three completes ten.
8 + __ = 10
2Two more are needed.
9 + __ = 10
1One more makes ten.
10 + __ = 10
0Ten is already complete.
A ten-frame has 6 counters. How many empty spaces?
4Ten total spaces minus six filled leaves four.
A frame has 8 filled. How many more counters to fill it?
28+2=10.
Which pair makes 10: 3+6 or 3+7?
3+7Three and seven total ten.
Which pair makes 10: 5+5 or 5+4?
5+5Five plus five equals ten.
If 4's complement is 6, what is 6's complement?
4The same pair works in reverse order.
Move one counter from the 3-part to the 7-part.
2 and 8The parts change by one but still total ten.
Complete 10−7=__.
3Subtraction finds the complement.
Explain 9+1 using a ten-frame.
Nine filled cells plus the one empty cell makes a full frame.The visual shows the complement immediately.
Why are make-10 pairs useful?
They turn ten into a familiar benchmark for later mental addition and subtraction.Knowing complements reduces counting and supports place value.
Practice
Guided practice with hints
01A frame has 7 filled. How many empty?
Hint: There are ten spaces total.
Answer: 3
02Complete 4+__=10.
Hint: Count empty spaces after four.
Answer: 6
03Complete 8+__=10.
Hint: How many spaces remain?
Answer: 2
04Which is the complement to 5?
Hint: What plus five equals ten?
Answer: 5
05Use subtraction to find the complement to 6.
Hint: Calculate 10−6.
Answer: 4
06Explain why 3+7 and 7+3 both make 10.
Hint: They use the same two parts.
Answer: The order changes, not the whole.
Practice
Independent practice
011+__=10
Answer: 9
022+__=10
Answer: 8
034+__=10
Answer: 6
046+__=10
Answer: 4
058+__=10
Answer: 2
069+__=10
Answer: 1
0710−3
Answer: 7
08What is the complement to 5?
Answer: 5
Common mistakes
Learn to catch the error, not just the answer.
Identify the known filled part, then count the unfilled spaces needed to complete ten.
3+7 and 7+3 use the same quantities and both make ten.
If ten is already complete, zero more are needed.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Fill a ten-frame from a partially filled state and state how many counters were needed.
- Group ten classroom objects into two color groups and name both part quantities.
Challenge problems
List all unordered make-10 pairs.
0+10,1+9,2+8,3+7,4+6,5+5
If one part changes from 4 to 5 while the whole stays 10, what happens to the other part?
It changes from 6 to 5.
Why is the complement of 8 equal to 2?
Because exactly two more are needed to reach the benchmark ten.
How might make-10 help with 9+4 later?
Use 1 of the 4 to make 10, leaving 3, so 10+3=13.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Make-10 Match
Match each number card to its complement so every pair totals ten.
Practice
Mastery check
01Complement to 2?
Answer: 8
02Complement to 4?
Answer: 6
03Complement to 5?
Answer: 5
04Complement to 7?
Answer: 3
05Complement to 9?
Answer: 1
06Complete 10−6.
Answer: 4
07What does complement to ten mean?
Answer: The amount needed with a given part to total ten.
08Explain the pattern in make-10 pairs.
Answer: When one part increases by one, the other decreases by one so the whole remains ten.
Terminology
Words to know
- benchmark
- A familiar reference number used to reason efficiently; here, ten.
- complement to ten
- The quantity needed with another quantity to make ten.
- ten-frame
- A 2-by-5 arrangement of ten spaces used to visualize numbers around ten.
- pair
- Two quantities considered together.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Kindergarten Operations & Algebraic Thinking
Standards progression for addition/subtraction stories, unknowns, and making ten.