One of the most useful mental math strategies in addition is making ten. This strategy involves breaking apart one of the numbers (called an addend) so that you can first make ten, and then add what's left over. Since ten is such an easy number to work with, this strategy makes addition faster and simpler.
When we "break" an addend, we're splitting it into two smaller parts that are easier to work with. We choose these parts strategically to help us make ten first.
Example: 8 + 5 - We can break the 5 into 2 + 3 - Now we have: 8 + 2 + 3 - First, make ten: 8 + 2 = 10 - Then add the rest: 10 + 3 = 13 - So 8 + 5 = 13
Making ten works because: - Ten is a friendly number: It's easy to add to ten in your head - We use place value: Making ten uses our understanding that 10 + any single digit is a teen number - It's faster than counting: Once you make ten, the rest is automatic - It builds number sense: You learn to see numbers flexibly, as parts that can be rearranged
Let's break down the process of using this powerful strategy.
Look at your two addends and find which one is closer to ten: - 8 + 5: The 8 is closer to ten (it only needs 2 more) - 6 + 7: The 7 is closer to ten (it only needs 3 more) - 9 + 4: The 9 is closest to ten (it only needs 1 more)
Usually, we'll work with the larger number and "complete" it to make ten.
Ask yourself: "What do I need to add to get to ten?" - For 8: 8 + ? = 10 → Need 2 (because 8 + 2 = 10) - For 7: 7 + ? = 10 → Need 3 (because 7 + 3 = 10) - For 9: 9 + ? = 10 → Need 1 (because 9 + 1 = 10)
This is where knowing your partners of ten becomes essential!
Now split the other addend into: - The amount needed to make ten - The leftover amount
Example: 7 + 5 - We want to make 7 into 10 - 7 needs 3 to make 10 - Break 5 into 3 + 2 - Now we have: 7 + 3 + 2
Add the part that makes ten: - 7 + 3 = 10
Add what's left to ten: - 10 + 2 = 12
Complete solution: 7 + 5 = 7 + 3 + 2 = 10 + 2 = 12
Let's work through several examples to see how this strategy applies to different problems.
Step 1: Which is closer to ten? 8 is closer (needs 2)
Step 2: What makes 8 into 10? 2 (because 8 + 2 = 10)
Step 3: Break 6 into 2 + 4 - 6 = 2 + 4
Step 4: Make ten first - 8 + 2 = 10
Step 5: Add the leftover - 10 + 4 = 14
Answer: 8 + 6 = 14
Step 1: Which is closer to ten? 9 is very close (needs only 1)
Step 2: What makes 9 into 10? 1 (because 9 + 1 = 10)
Step 3: Break 5 into 1 + 4 - 5 = 1 + 4
Step 4: Make ten first - 9 + 1 = 10
Step 5: Add the leftover - 10 + 4 = 14
Answer: 9 + 5 = 14
Step 1: Which is closer to ten? 7 is closer (needs 3)
Step 2: What makes 7 into 10? 3 (because 7 + 3 = 10)
Step 3: Break 6 into 3 + 3 - 6 = 3 + 3
Step 4: Make ten first - 7 + 3 = 10
Step 5: Add the leftover - 10 + 3 = 13
Answer: 6 + 7 = 13
Step 1: Which is closer to ten? 9 is closest (needs only 1)
Step 2: What makes 9 into 10? 1 (because 9 + 1 = 10)
Step 3: Break 8 into 1 + 7 - 8 = 1 + 7
Step 4: Make ten first - 9 + 1 = 10
Step 5: Add the leftover - 10 + 7 = 17
Answer: 9 + 8 = 17
Seeing this strategy visually helps understanding and memory.
For 8 + 5:
[====8====][++][+++]
|---------|--|---|
0 8 10 13
For 8 + 5: - Draw a ten frame with 8 filled - 2 empty spaces remain (this is what we need from 5) - Fill those 2 spaces (now we have 10) - 3 from the 5 are left over - Result: 10 + 3 = 13
For 8 + 5:
5
/ \
2 3
This strategy is most useful for specific types of problems:
7 + 6, 8 + 5, 9 + 7, etc.
When one number is close to 10
8 + anything, 9 + anything
Mental math situations
For 3 + 4, you probably already know it's 7
When both numbers are far from 10
For 3 + 4, making ten doesn't help much
When you already know the fact
To use this strategy effectively, you must know partners of ten automatically: - 1 + 9 = 10 - 2 + 8 = 10 - 3 + 7 = 10 - 4 + 6 = 10 - 5 + 5 = 10 - 6 + 4 = 10 - 7 + 3 = 10 - 8 + 2 = 10 - 9 + 1 = 10
If you have to think hard about these, practice them first! They're the key that unlocks this strategy.
This strategy is designed for mental math. Here's how to practice thinking through it:
For 7 + 6: - Say: "Seven needs three to make ten" - Think: "I'll take 3 from the 6" - Say: "Seven plus three is ten" - Think: "I have 3 left over from the 6" - Say: "Ten plus three is thirteen"
For 9 + 4: - Picture the 9 - Picture taking 1 from the 4 to complete the 9 - See 10 + 3 in your mind - Answer: 13
For 8 + 5: - Hold up 8 fingers - Need 2 more for 10 (fold down 2 fingers from one hand) - Those 2 come from the 5 - 5 - 2 = 3 left over - Answer: 10 + 3 = 13
This strategy helps in everyday situations:
"I'm buying items for $8 and $6" - "Eight plus two makes ten, that's four more left" - "So eight plus six is fourteen dollars"
"I scored 9 points, then 7 points" - "Nine plus one makes ten, six more left" - "So that's sixteen points total"
"I have 7 baseball cards, found 8 more" - "Seven plus three makes ten, five more left" - "So I have fifteen cards now"
"Worked 9 minutes, then 6 more minutes" - "Nine plus one makes ten, five more left" - "So that's fifteen minutes total"
Materials: Index cards
Create: - Cards with addition problems (8 + 5) - Practice breaking the addend to make ten - Write the steps on the back
Challenge: Can you do it without looking at the back?
Materials: Ten frame and counters (or drawings)
Activity: 1. Fill a ten frame with a number like 8 2. Get counters for the second addend (like 5) 3. Fill the ten frame completely (using 2 of the 5) 4. Count the leftover counters (3 remaining) 5. Say: "10 + 3 = 13, so 8 + 5 = 13"
Materials: Number line from 0-20
Activity: 1. Start at the first addend (like 7) 2. Jump to 10 (jump of 3) 3. Jump the rest (jump of 4 for 7 + 7) 4. Where you land is your answer!
Materials: Timer, problem list
Challenge: - 10 problems using make-ten strategy - Time how long it takes - Try to beat your time tomorrow!
Activity: - Throughout your day, find addition situations - Practice using make-ten strategy mentally - "Mom gave me 8 crackers, dad gave me 5" - Think: "8 + 2 = 10, 3 left over, so 13 crackers!"
Fluency means using this strategy automatically without thinking hard about each step.
Week 1: Focus on adding to 9 - 9 + 2, 9 + 3, 9 + 4, etc. - These are easiest because you only need 1 to make ten
Week 2: Add problems with 8 - 8 + 3, 8 + 4, 8 + 5, etc. - Need 2 to make ten
Week 3: Add problems with 7 - 7 + 4, 7 + 5, 7 + 6, etc. - Need 3 to make ten
Week 4: Add problems with 6 - 6 + 5, 6 + 6, 6 + 7, etc. - Need 4 to make ten
Week 5: Mix all types - Random problems from 6 + 5 through 9 + 9
Morning (3 minutes): - 5 problems using make-ten - Say the steps out loud
Midday (3 minutes): - 5 problems done silently in your head - Write just the answer
Evening (2 minutes): - Review any problems that were tricky - Practice those specific combinations
Solution: Break the smaller addend or the one that's not as close to ten. This gives you the pieces you need to complete the larger number to make ten.
Solution: Write down just the breaking step at first: - 8 + 5 - 8 + (2 + 3) - Then solve mentally from there
Solution: At first, it is longer! But with practice, you'll do it faster than counting. Be patient—speed comes with practice.
Solution: Stop and practice those first! You can't efficiently use this strategy without instant recall of partners of ten. Use flashcards, games, or songs to build that foundation.
This strategy is the mental version of what we do when we regroup in written addition: - Both involve making a new ten - The written algorithm and mental strategy use the same concept
Making ten reinforces place value: - Once you have ten ones, you have one ten - Adding to ten creates teen numbers (one ten plus ones)
Making ten helps with subtraction too: - If 8 + 5 = 13, then 13 - 5 = 8 and 13 - 8 = 5 - Understanding addition helps with related subtraction
Breaking numbers prepares you for algebraic manipulation: - Seeing that 5 = 2 + 3 is like seeing that x = a + b - You're learning that numbers can be represented flexibly
You've mastered this strategy when you can: - ✓ Quickly identify partners of ten - ✓ Determine how much more any number needs to reach ten - ✓ Break an addend appropriately - ✓ Solve problems like 8 + 5 mentally in under 5 seconds - ✓ Explain the strategy to someone else - ✓ Choose when this strategy is most helpful
This strategy prepares you for:
Breaking an addend to make ten is a powerful mental math strategy that makes addition faster and develops number sense. By learning to see numbers flexibly and use ten as a friendly benchmark, you're building mathematical thinking that will serve you well beyond simple addition. Practice this strategy regularly, especially with numbers close to ten, and soon you'll find yourself using it naturally without even thinking about the steps. Remember, every expert mental math calculator started right where you are, and with practice, you'll develop the same speed and confidence!
One of the most useful mental math strategies in addition is making ten. This strategy involves breaking apart one of the numbers (called an addend) so that you can first make ten, and then add what's left over. Since ten is such an easy number to work with, this strategy makes addition faster and simpler.
When we "break" an addend, we're splitting it into two smaller parts that are easier to work with. We choose these parts strategically to help us make ten first.
Example: 8 + 5 - We can break the 5 into 2 + 3 - Now we have: 8 + 2 + 3 - First, make ten: 8 + 2 = 10 - Then add the rest: 10 + 3 = 13 - So 8 + 5 = 13
Making ten works because: - Ten is a friendly number: It's easy to add to ten in your head - We use place value: Making ten uses our understanding that 10 + any single digit is a teen number - It's faster than counting: Once you make ten, the rest is automatic - It builds number sense: You learn to see numbers flexibly, as parts that can be rearranged
Let's break down the process of using this powerful strategy.
Look at your two addends and find which one is closer to ten: - 8 + 5: The 8 is closer to ten (it only needs 2 more) - 6 + 7: The 7 is closer to ten (it only needs 3 more) - 9 + 4: The 9 is closest to ten (it only needs 1 more)
Usually, we'll work with the larger number and "complete" it to make ten.
Ask yourself: "What do I need to add to get to ten?" - For 8: 8 + ? = 10 → Need 2 (because 8 + 2 = 10) - For 7: 7 + ? = 10 → Need 3 (because 7 + 3 = 10) - For 9: 9 + ? = 10 → Need 1 (because 9 + 1 = 10)
This is where knowing your partners of ten becomes essential!
Now split the other addend into: - The amount needed to make ten - The leftover amount
Example: 7 + 5 - We want to make 7 into 10 - 7 needs 3 to make 10 - Break 5 into 3 + 2 - Now we have: 7 + 3 + 2
Add the part that makes ten: - 7 + 3 = 10
Add what's left to ten: - 10 + 2 = 12
Complete solution: 7 + 5 = 7 + 3 + 2 = 10 + 2 = 12
Let's work through several examples to see how this strategy applies to different problems.
Step 1: Which is closer to ten? 8 is closer (needs 2)
Step 2: What makes 8 into 10? 2 (because 8 + 2 = 10)
Step 3: Break 6 into 2 + 4 - 6 = 2 + 4
Step 4: Make ten first - 8 + 2 = 10
Step 5: Add the leftover - 10 + 4 = 14
Answer: 8 + 6 = 14
Step 1: Which is closer to ten? 9 is very close (needs only 1)
Step 2: What makes 9 into 10? 1 (because 9 + 1 = 10)
Step 3: Break 5 into 1 + 4 - 5 = 1 + 4
Step 4: Make ten first - 9 + 1 = 10
Step 5: Add the leftover - 10 + 4 = 14
Answer: 9 + 5 = 14
Step 1: Which is closer to ten? 7 is closer (needs 3)
Step 2: What makes 7 into 10? 3 (because 7 + 3 = 10)
Step 3: Break 6 into 3 + 3 - 6 = 3 + 3
Step 4: Make ten first - 7 + 3 = 10
Step 5: Add the leftover - 10 + 3 = 13
Answer: 6 + 7 = 13
Step 1: Which is closer to ten? 9 is closest (needs only 1)
Step 2: What makes 9 into 10? 1 (because 9 + 1 = 10)
Step 3: Break 8 into 1 + 7 - 8 = 1 + 7
Step 4: Make ten first - 9 + 1 = 10
Step 5: Add the leftover - 10 + 7 = 17
Answer: 9 + 8 = 17
Seeing this strategy visually helps understanding and memory.
For 8 + 5:
[====8====][++][+++]
|---------|--|---|
0 8 10 13
For 8 + 5: - Draw a ten frame with 8 filled - 2 empty spaces remain (this is what we need from 5) - Fill those 2 spaces (now we have 10) - 3 from the 5 are left over - Result: 10 + 3 = 13
For 8 + 5:
5
/ \
2 3
This strategy is most useful for specific types of problems:
7 + 6, 8 + 5, 9 + 7, etc.
When one number is close to 10
8 + anything, 9 + anything
Mental math situations
For 3 + 4, you probably already know it's 7
When both numbers are far from 10
For 3 + 4, making ten doesn't help much
When you already know the fact
To use this strategy effectively, you must know partners of ten automatically: - 1 + 9 = 10 - 2 + 8 = 10 - 3 + 7 = 10 - 4 + 6 = 10 - 5 + 5 = 10 - 6 + 4 = 10 - 7 + 3 = 10 - 8 + 2 = 10 - 9 + 1 = 10
If you have to think hard about these, practice them first! They're the key that unlocks this strategy.
This strategy is designed for mental math. Here's how to practice thinking through it:
For 7 + 6: - Say: "Seven needs three to make ten" - Think: "I'll take 3 from the 6" - Say: "Seven plus three is ten" - Think: "I have 3 left over from the 6" - Say: "Ten plus three is thirteen"
For 9 + 4: - Picture the 9 - Picture taking 1 from the 4 to complete the 9 - See 10 + 3 in your mind - Answer: 13
For 8 + 5: - Hold up 8 fingers - Need 2 more for 10 (fold down 2 fingers from one hand) - Those 2 come from the 5 - 5 - 2 = 3 left over - Answer: 10 + 3 = 13
This strategy helps in everyday situations:
"I'm buying items for $8 and $6" - "Eight plus two makes ten, that's four more left" - "So eight plus six is fourteen dollars"
"I scored 9 points, then 7 points" - "Nine plus one makes ten, six more left" - "So that's sixteen points total"
"I have 7 baseball cards, found 8 more" - "Seven plus three makes ten, five more left" - "So I have fifteen cards now"
"Worked 9 minutes, then 6 more minutes" - "Nine plus one makes ten, five more left" - "So that's fifteen minutes total"
Materials: Index cards
Create: - Cards with addition problems (8 + 5) - Practice breaking the addend to make ten - Write the steps on the back
Challenge: Can you do it without looking at the back?
Materials: Ten frame and counters (or drawings)
Activity: 1. Fill a ten frame with a number like 8 2. Get counters for the second addend (like 5) 3. Fill the ten frame completely (using 2 of the 5) 4. Count the leftover counters (3 remaining) 5. Say: "10 + 3 = 13, so 8 + 5 = 13"
Materials: Number line from 0-20
Activity: 1. Start at the first addend (like 7) 2. Jump to 10 (jump of 3) 3. Jump the rest (jump of 4 for 7 + 7) 4. Where you land is your answer!
Materials: Timer, problem list
Challenge: - 10 problems using make-ten strategy - Time how long it takes - Try to beat your time tomorrow!
Activity: - Throughout your day, find addition situations - Practice using make-ten strategy mentally - "Mom gave me 8 crackers, dad gave me 5" - Think: "8 + 2 = 10, 3 left over, so 13 crackers!"
Fluency means using this strategy automatically without thinking hard about each step.
Week 1: Focus on adding to 9 - 9 + 2, 9 + 3, 9 + 4, etc. - These are easiest because you only need 1 to make ten
Week 2: Add problems with 8 - 8 + 3, 8 + 4, 8 + 5, etc. - Need 2 to make ten
Week 3: Add problems with 7 - 7 + 4, 7 + 5, 7 + 6, etc. - Need 3 to make ten
Week 4: Add problems with 6 - 6 + 5, 6 + 6, 6 + 7, etc. - Need 4 to make ten
Week 5: Mix all types - Random problems from 6 + 5 through 9 + 9
Morning (3 minutes): - 5 problems using make-ten - Say the steps out loud
Midday (3 minutes): - 5 problems done silently in your head - Write just the answer
Evening (2 minutes): - Review any problems that were tricky - Practice those specific combinations
Solution: Break the smaller addend or the one that's not as close to ten. This gives you the pieces you need to complete the larger number to make ten.
Solution: Write down just the breaking step at first: - 8 + 5 - 8 + (2 + 3) - Then solve mentally from there
Solution: At first, it is longer! But with practice, you'll do it faster than counting. Be patient—speed comes with practice.
Solution: Stop and practice those first! You can't efficiently use this strategy without instant recall of partners of ten. Use flashcards, games, or songs to build that foundation.
This strategy is the mental version of what we do when we regroup in written addition: - Both involve making a new ten - The written algorithm and mental strategy use the same concept
Making ten reinforces place value: - Once you have ten ones, you have one ten - Adding to ten creates teen numbers (one ten plus ones)
Making ten helps with subtraction too: - If 8 + 5 = 13, then 13 - 5 = 8 and 13 - 8 = 5 - Understanding addition helps with related subtraction
Breaking numbers prepares you for algebraic manipulation: - Seeing that 5 = 2 + 3 is like seeing that x = a + b - You're learning that numbers can be represented flexibly
You've mastered this strategy when you can: - ✓ Quickly identify partners of ten - ✓ Determine how much more any number needs to reach ten - ✓ Break an addend appropriately - ✓ Solve problems like 8 + 5 mentally in under 5 seconds - ✓ Explain the strategy to someone else - ✓ Choose when this strategy is most helpful
This strategy prepares you for:
Breaking an addend to make ten is a powerful mental math strategy that makes addition faster and develops number sense. By learning to see numbers flexibly and use ten as a friendly benchmark, you're building mathematical thinking that will serve you well beyond simple addition. Practice this strategy regularly, especially with numbers close to ten, and soon you'll find yourself using it naturally without even thinking about the steps. Remember, every expert mental math calculator started right where you are, and with practice, you'll develop the same speed and confidence!