Grade 1 · Operations · MAT-01-OPS-006
Make 10 to Add
Decompose an addend to complete a ten, then add the remaining part.
Learning objectives
What you should be able to do
- Decompose an addend to complete a ten, then add the remaining part.
- Use ten-frames and equations to explain make-10 strategies for sums within 20.
- Choose make-10 when one addend is close to 10.
Prerequisite check
Make sure the foundation is ready.
Checks Kindergarten make-10 fluency.
Checks splitting and associative reasoning.
Learn
Build the idea from meaning, not memorization.
Ten is a useful benchmark for mental addition
When one addend is near ten, split the other addend so part of it completes ten. Then add the leftover part to ten.
Example: 8+5
Eight needs two to make ten. Split five into two and three: 8+5 = 8+2+3 = 10+3 = 13. The total stays the same because five was decomposed, not changed.
Ten-frames make the strategy visible
Fill the empty spaces in the first ten-frame using counters from the second addend. Any counters left over show the ones beyond ten.
Make-10 is a choice, not a requirement
For some facts another strategy may be easier. Good fluency includes choosing a method that is accurate and efficient.
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.
- decompose second addend
- fill first ten
- move leftovers
- write equivalent equations
Worked examples
Twenty different ways to see the concept work.
9+2
9+1+1=11Nine needs one to make ten.
9+3
9+1+2=12Split three into one and two.
9+4
9+1+3=13Make ten, then add three.
9+5
9+1+4=14Make ten first.
8+3
8+2+1=11Eight needs two.
8+4
8+2+2=12Split four into two and two.
8+5
8+2+3=13Ten plus three.
8+6
8+2+4=14Use two to complete ten.
7+4
7+3+1=11Seven needs three.
7+5
7+3+2=12Make ten then two.
7+6
7+3+3=13Split six into three and three.
6+5
6+4+1=11Six needs four.
6+6
6+4+2=12Split one six into four and two.
5+7
7+3+2=12Use commutative property, then make ten.
4+9
9+1+3=13Reorder and complete ten.
3+8
8+2+1=11Reorder then make ten.
Why does splitting 5 into 2+3 preserve 8+5?
2+3 still equals 5The addend value is unchanged.
Ten-frame for 9+4: fill how many holes first?
1One space completes ten.
Ten-frame for 7+5: move how many to first frame?
3Three spaces are empty.
When is make-10 especially useful?
When an addend is near 10Only a small part is needed to complete the benchmark.
Practice
Guided practice with hints
01Solve 9+4.
Hint: Nine needs one; split four.
Answer: 13
02Solve 8+5.
Hint: Eight needs two.
Answer: 13
03Solve 7+6.
Hint: Seven needs three.
Answer: 13
04Solve 6+5.
Hint: Six needs four.
Answer: 11
05Solve 5+8 efficiently.
Hint: Reorder to 8+5.
Answer: 13
06Why is 10+3 easier than 8+5?
Hint: Ten is a familiar place-value benchmark.
Answer: 13 is seen as ten and three.
Practice
Independent practice
019+6
Answer: 15
028+7
Answer: 15
037+4
Answer: 11
046+6
Answer: 12
054+8
Answer: 12
063+9
Answer: 12
07What does 8 need to make 10?
Answer: 2
08What does 7 need to make 10?
Answer: 3
Common mistakes
Learn to catch the error, not just the answer.
Show the full decomposition, such as 5=2+3.
Add the leftover ones after the ten is complete.
Choose strategically; doubles may be better for 6+6, for example.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Mentally combine small quantities that cross from single digits into teen totals.
- Use ten-frame structures to reason about game scores or object collections beyond 10.
Challenge problems
Use make-10 for 9+8.
9+1+7=17
Use make-10 for 8+8.
8+2+6=16, though doubles is also efficient.
Why does make-10 connect to place value?
Teen numbers are one ten plus leftover ones.
Compare strategies for 6+6.
Make-10 gives 6+4+2=12; doubles directly gives 12. Doubles may be more efficient.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Bridge to Ten
Move the right number of counters to complete ten, then add leftovers.
Practice
Mastery check
019+3
Answer: 12
028+4
Answer: 12
037+5
Answer: 12
046+5
Answer: 11
05Explain 8+5 using make-10.
Answer: 8+2+3=10+3=13
06What does 9 need to make ten?
Answer: 1
07Why does decomposition not change total?
Answer: The split parts still equal the original addend.
08When is make-10 useful?
Answer: When an addend is close to ten and the sum crosses ten.
Terminology
Words to know
- make-10 strategy
- Complete a group of ten, then add any leftover part.
- decompose
- Split a number into parts without changing its total value.
- benchmark
- A familiar reference number used for efficient reasoning.
- equivalent expression
- A different expression with the same value.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 1 Operations & Algebraic Thinking
Grade 1 addition/subtraction fluency, properties, and strategy progression.