Addition Strategies
Counting On
What is counting on?
Counting on is a fast way to add two numbers. Instead of counting both numbers from 1, you start with the bigger number and count up the smaller number. This saves time and helps you add quickly!
How to count on:
- Step 1: Look at both numbers. Find the bigger number.
- Step 2: Say the bigger number in your head.
- Step 3: Count up using the smaller number.
- Step 4: The last number you say is the answer!
Example: 5 + 3
- Start at 5 (the bigger number)
- Count up 3 more: 6, 7, 8
- Answer is 8
When to use counting on:
- When adding a small number to a bigger number
- When adding numbers up to 20
- When you want to add quickly in your head
| Addition | Start at | Count up | Answer |
|---|---|---|---|
| 7 + 2 | 7 | 8, 9 | 9 |
| 9 + 4 | 9 | 10, 11, 12, 13 | 13 |
| 12 + 3 | 12 | 13, 14, 15 | 15 |
| 8 + 5 | 8 | 9, 10, 11, 12, 13 | 13 |
Use counting on to add 6 + 3.
- Find the bigger number: 6 is bigger than 3
- Start at 6
- Count up 3 numbers: 7 (1st), 8 (2nd), 9 (3rd)
- The last number is 9
Answer: 9
Mia has 8 crayons. Her mom gives her 5 more. How many crayons does Mia have now? Use counting on.
- Mia starts with 8 crayons
- She gets 5 more crayons
- Start at 8 (the bigger number)
- Count up 5 numbers: 9, 10, 11, 12, 13
- 8 + 5 = 13 crayons
Answer: 13 crayons
Tom counted on to add 7 + 6 and got 14. Is he correct? If not, find the right answer.
- Start at the bigger number: 7
- Count up 6 numbers:
- 8 (1st)
- 9 (2nd)
- 10 (3rd)
- 11 (4th)
- 12 (5th)
- 13 (6th)
- The last number is 13, not 14
- Tom made a mistake. The correct answer is 13
Answer: No, Tom is wrong. The correct answer is 13.
Key Points
- Counting on starts with the bigger number and counts up
- Always find the larger number first to save time
- Use your fingers or a number line to help count on
- Count on means you don't start from 1 — you start from the bigger number
- This strategy works best when one number is small
- Counting on is faster than counting everything from 1
Making Ten and Doubles Facts
What is making ten?
Making ten is a strategy where you break apart a number to make a group of 10 first, then add what's left. It's easier to add numbers when one of them is 10!
How to make ten:
- Step 1: Look at the two numbers
- Step 2: See how many more you need to make the first number into 10
- Step 3: Take that many from the second number
- Step 4: Now you have 10 + the remaining number
Example: 8 + 5
- 8 needs 2 more to make 10
- Take 2 from 5 (leaving 3)
- Now: 10 + 3 = 13
What are doubles facts?
Doubles facts are addition problems where you add a number to itself. These are super easy to remember!
Doubles facts to memorize:
| Double | Answer | Easy to Remember Because... |
|---|---|---|
| 1 + 1 | 2 | One and one is two |
| 2 + 2 | 4 | Two pairs of shoes = 4 shoes |
| 3 + 3 | 6 | Two hands of 3 fingers each |
| 4 + 4 | 8 | Two squares of 4 |
| 5 + 5 | 10 | Two hands! |
| 6 + 6 | 12 | Two groups of 6 |
| 7 + 7 | 14 | Two weeks (7 days each) |
| 8 + 8 | 16 | Two octopus legs? No, 8+8=16 |
| 9 + 9 | 18 | Two nines make eighteen |
| 10 + 10 | 20 | Two tens make twenty |
Use the making ten strategy to add 9 + 6.
- 9 needs 1 more to make 10
- Take 1 from 6 (6 - 1 = 5)
- Now we have 10 + 5
- 10 + 5 = 15
Answer: 15
Remember your doubles facts. What is 7 + 7?
- This is a doubles fact (same number added to itself)
- 7 + 7 = 14
- We know this because 7 + 7 = 14
Answer: 14
Sam knows that 5 + 5 = 10. How can he use this to find 5 + 6?
- 5 + 5 = 10 (doubles fact)
- 5 + 6 is just 1 more than 5 + 5
- Because 6 is 1 more than 5
- So 5 + 6 = 10 + 1 = 11
- Check with counting on: 5 + 6 → start at 6, count 5 → 7,8,9,10,11 ✓
Answer: 11
Key Points
- Making ten makes addition easier by creating a group of 10 first
- Doubles facts are number pairs where both numbers are the same
- Memorize doubles facts up to 10 + 10 for quick addition
- Making ten works best when one number is close to 10
- You can use a ten frame to visualize making ten
- Knowing doubles helps you solve near doubles (like 5+6)
Near Doubles and Mental Addition
What are near doubles?
Near doubles are addition problems where the two numbers are almost the same — they differ by 1 or 2. You can use a doubles fact you already know and then add or subtract a little.
How to use near doubles:
- Step 1: Find the smaller number
- Step 2: Use the doubles fact for that number
- Step 3: Add the difference
Examples of near doubles:
| Near Double | Doubles Fact | Adjustment | Answer |
|---|---|---|---|
| 5 + 6 | 5 + 5 = 10 | +1 | 11 |
| 7 + 8 | 7 + 7 = 14 | +1 | 15 |
| 9 + 8 | 8 + 8 = 16 | +1 | 17 |
| 4 + 6 | 5 + 5 = 10 | -? Wait, better: 4+4=8, then +2 | 10 |
What is mental addition?
Mental addition means adding numbers in your head without using paper, fingers, or a calculator. Using strategies like counting on, making ten, doubles, and near doubles helps you add mentally!
Mental addition strategies summary:
| Strategy | When to Use | Example |
|---|---|---|
| Counting on | Small number + bigger number | 12 + 3 = 15 |
| Making ten | One number close to 10 | 8 + 5 = 13 |
| Doubles | Same numbers | 6 + 6 = 12 |
| Near doubles | Numbers differ by 1 or 2 | 7 + 8 = 15 |
Use the near doubles strategy to add 8 + 9.
- 8 and 9 are near doubles (they differ by 1)
- Find the doubles fact for the smaller number: 8 + 8 = 16
- 9 is 1 more than 8, so add 1 to the doubles fact
- 16 + 1 = 17
- Check: 8 + 9 = 17
Answer: 17
Add these mentally using the best strategy: 7 + 5.
- Choose the best strategy: Making ten works well here
- 7 needs 3 more to make 10
- Take 3 from 5 (5 - 3 = 2)
- Now: 10 + 2 = 12
- Check with counting on: Start at 7, count 5 → 8,9,10,11,12 ✓
Answer: 12
Emma used the near doubles strategy for 4 + 6 and got 11. Is she correct? Explain and give the correct answer.
- 4 and 6 differ by 2 (not 1)
- Let's check: 4 + 6
- Near doubles strategy: Use 5 + 5 = 10 (double of 5)
- 4 is 1 less than 5, 6 is 1 more than 5
- So 4 + 6 = 10 (they balance!)
- Emma's answer of 11 is wrong
- Correct answer: 4 + 6 = 10
- Verification: Counting on from 6 → 7,8,9,10 ✓
Answer: No, Emma is wrong. The correct answer is 10.
Key Points
- Near doubles use a doubles fact and adjust by 1 or 2
- Mental addition means adding without writing or using tools
- Choose the best strategy for each problem
- For near doubles that differ by 2, the numbers balance around the middle
- Practice all strategies to become a fast mental math whiz
- The more you practice, the easier mental addition becomes!