Grade 1 · Operations · MAT-01-OPS-001
Addition Facts Within 10
Add two numbers with sums within 10 using objects, number relationships, and mental strategies.
Learning objectives
What you should be able to do
- Add two numbers with sums within 10 using objects, number relationships, and mental strategies.
- Use counting on, doubles, and near-doubles to solve addition facts efficiently.
- Explain why multiple strategies can produce the same correct sum.
Prerequisite check
Make sure the foundation is ready.
Checks conceptual meaning of addition.
Checks flexible number sense.
Learn
Build the idea from meaning, not memorization.
Fluency means accurate, flexible, and increasingly efficient
Knowing addition facts is more than answering quickly. A fluent learner can choose a sensible strategy, explain it, and recognize relationships among facts.
Counting on reduces unnecessary work
For 6+2, keep 6 in mind and count 7,8 rather than recounting six objects from 1. Counting on is especially useful when one addend is small.
Doubles and near-doubles build families of facts
Knowing 4+4=8 helps with 4+5 because 4+5 is one more than the double 4+4. Related facts reduce memorization.
Order can change without changing the sum
Three plus five and five plus three both total eight. Grade 1 learners begin to use this commutative structure intentionally even before formal terminology is emphasized.
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.
- count on
- double match
- near double
- make ten
Worked examples
Twenty different ways to see the concept work.
1+1
2One and one make two.
2+1
3Count on one from two.
3+2
5Count on 4,5.
4+1
5Adding one makes one more.
5+2
7Count on 6,7.
6+3
9Count on 7,8,9.
7+2
9Two more than seven is nine.
8+1
9One more than eight is nine.
9+1
10One more completes ten.
5+5
10This is a double.
4+4
8Double four is eight.
3+3
6Double three is six.
2+2
4Double two is four.
4+5
9Use double 4+4=8, then one more.
3+4
7Use double 3+3=6, then one more.
2+5
7Switch mentally to 5+2 and count on two.
1+7
8One more than seven is eight.
0+6
6Adding zero leaves the amount unchanged.
6+4
10Six and four are complements to ten.
Explain why 2+6 and 6+2 match.
Both combine the same two quantitiesChanging order does not change how many objects are in the whole.
Practice
Guided practice with hints
01Solve 5+2.
Hint: Keep 5 and count on two.
Answer: 7
02Solve 4+4.
Hint: Recognize a double.
Answer: 8
03Solve 4+5.
Hint: Use 4+4 first.
Answer: 9
04Solve 1+8.
Hint: One more than eight.
Answer: 9
05Solve 6+4.
Hint: Think make ten.
Answer: 10
06Solve 2+7 efficiently.
Hint: Start from the larger addend.
Answer: 9
Practice
Independent practice
012+3
Answer: 5
024+2
Answer: 6
033+5
Answer: 8
046+2
Answer: 8
055+4
Answer: 9
067+3
Answer: 10
070+9
Answer: 9
084+5
Answer: 9
Common mistakes
Learn to catch the error, not just the answer.
Use counting on, doubles, or known combinations when appropriate.
In 6+2, start at six, then the two hops are seven and eight.
Connect doubles, near-doubles, make-ten pairs, and reversed addends.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Combine small groups of coins, blocks, or game points with totals to 10.
- Use addition facts to track how many items are present after small increases.
Challenge problems
If 4+4=8, find 4+5 without recounting.
9
Which is easier to count on for 2+7: start at 2 or 7? Why?
Start at 7 because only two forward counts are needed.
Find two different addition facts that equal 10.
Examples: 6+4 and 7+3.
Explain a strategy for 3+6.
Use 6+3 and count on 7,8,9, or another valid strategy.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Fact Path: Add
Solve addition facts by choosing a strategy before selecting the sum.
Practice
Mastery check
013+2
Answer: 5
024+4
Answer: 8
034+5
Answer: 9
046+3
Answer: 9
057+3
Answer: 10
060+8
Answer: 8
07Name one efficient strategy for 2+6.
Answer: Start at 6 and count on two.
08Why can 3+5 and 5+3 have same sum?
Answer: They combine the same quantities in a different order.
Terminology
Words to know
- addition fact
- A basic addition equation used frequently.
- double
- An addition fact with two equal addends.
- near-double
- A fact one away from a known double.
- fluency
- Accurate, flexible, and increasingly efficient use of facts and strategies.
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.