Grade 1 · Operations · MAT-01-OPS-007
Add Within 20
Add within 20 using make-10, doubles, near-doubles, counting on, and decomposition.
Learning objectives
What you should be able to do
- Add within 20 using make-10, doubles, near-doubles, counting on, and decomposition.
- Choose an efficient strategy based on the addends.
- Explain teen-number sums as one ten plus some ones.
Prerequisite check
Make sure the foundation is ready.
Checks bridge-to-ten strategy.
Checks fact relationships.
Learn
Build the idea from meaning, not memorization.
Addition within 20 is built from familiar structures
Sums greater than ten are easier when connected to ten, doubles, or known facts. Instead of treating each problem as new, choose a structure that fits the addends.
Make ten for near-ten addends
For 9+6, move 1 from the 6 to the 9: 9+1+5=10+5=15. The total stays the same because the 6 was decomposed into 1 and 5.
Doubles and near-doubles reduce work
For 7+7, use the known double 14. For 7+8, use 7+7=14 and add one more to get 15.
A teen sum has place-value structure
When 8+6=14, the result is one ten and four ones. Ten-frame models help show why crossing ten does not create an entirely new kind of 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.
- make ten
- double
- near double
- compare strategies
Worked examples
Twenty different ways to see the concept work.
9+2
11Make ten: 9+1+1.
9+5
14Make ten: 10+4.
9+8
17Make ten: 10+7.
8+3
118+2+1.
8+6
148+2+4.
8+8
16Double eight.
7+4
117+3+1.
7+7
14Double seven.
7+8
15Near-double: 7+7+1.
6+6
12Double six.
6+7
13Near-double: 6+6+1.
5+9
14Reorder to 9+5, then make ten.
4+8
12Reorder to 8+4, then 8+2+2.
3+9
129+1+2.
2+9
119+1+1.
10+7
17Ten plus seven ones.
11+4
15Count on four from eleven.
12+3
15Three more than twelve.
Explain 8+7 two ways.
15Make ten: 8+2+5; or near-double: 7+7+1.
Why can 6+8 be solved as 8+6?
Commutative propertyThe addend order can change without changing the sum.
Practice
Guided practice with hints
01Solve 9+7.
Hint: Make ten first.
Answer: 16
02Solve 8+5.
Hint: Use 8+2+3.
Answer: 13
03Solve 7+7.
Hint: Recognize a double.
Answer: 14
04Solve 6+7.
Hint: Use a near-double.
Answer: 13
05Solve 5+9.
Hint: Reorder to put 9 first.
Answer: 14
06Explain 14 as tens and ones.
Hint: Think place value.
Answer: 1 ten and 4 ones.
Practice
Independent practice
019+4
Answer: 13
028+7
Answer: 15
037+6
Answer: 13
046+5
Answer: 11
055+8
Answer: 13
064+9
Answer: 13
0710+8
Answer: 18
0813+4
Answer: 17
Common mistakes
Learn to catch the error, not just the answer.
Write the full decomposition before recombining.
Scan for doubles and near-doubles before counting one by one.
Represent the sum as one ten plus remaining ones.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Combine small game scores that produce totals within 20.
- Find totals of two small groups of classroom objects without recounting from 1.
Challenge problems
Solve 9+9 two ways.
18; double nine, or 9+1+8.
Which is more efficient for 8+8: make-ten or doubles?
Usually doubles, because 8+8=16 is a known double.
Why does 7+8 equal 15 if 7+7=14?
The second addend is one greater, so the sum is one greater.
Find two different addition expressions equal to 17.
Examples: 9+8 and 10+7.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Strategy Sprint: Add 20
Choose a strategy and solve sums within 20.
Practice
Mastery check
019+6
Answer: 15
028+5
Answer: 13
037+8
Answer: 15
046+6
Answer: 12
055+9
Answer: 14
0610+7
Answer: 17
07Name a strategy for 8+7.
Answer: Make ten or near-double.
08Explain 15 as place value.
Answer: 1 ten and 5 ones.
Terminology
Words to know
- sum
- The result of addition.
- strategy
- A chosen method for solving a problem.
- near-double
- An addition fact one away from a double.
- decompose
- Split a number into parts without changing its 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 within 20, word problems, and equations with unknowns.