How to Teach Mental Math Strategies for Addition and Subtraction

A child who reaches for paper to solve 8 + 7, or counts on their fingers for 15 - 9, has not developed mental math fluency. This is not about speed — it is about having strategies that make computation efficient.

Mental math strategies are specific, teachable techniques. They are not natural talent. Here are the ones that matter most.

Why mental math matters

Mental math is not a party trick. It is:

• Faster: Mental strategies are more efficient than written algorithms for most everyday calculations
• A sign of number sense: A child who can mentally compute has deep understanding of how numbers work
• Essential for estimation: You cannot estimate if you cannot compute mentally
• The foundation for algebra: Algebraic manipulation is essentially mental math with variables

Key Insight: Children who count on their fingers are not slow — they are missing strategies. Give them the strategies, and the speed follows naturally.

Strategy 1: Make a ten

This is the single most important mental math strategy. It depends on knowing bonds of 10.

8 + 5: Think "8 needs 2 more to make 10. Take 2 from the 5. That leaves 3. So 10 + 3 = 13."

7 + 6: Think "7 needs 3 to make 10. Take 3 from the 6. That leaves 3. So 10 + 3 = 13."

9 + 4: Think "9 + 1 = 10. Take 1 from the 4, leaves 3. So 10 + 3 = 13."

Notice that 9 + anything is the easiest make-a-ten: just move 1 from the other number.

To teach this, use a ten frame:

Show 8 counters. "How many empty spaces? 2. So if we are adding 5, we fill those 2 spaces first (that is making 10), and we have 3 left over. 10 + 3 = 13."

Strategy 2: Doubles and near-doubles

The doubles facts (2+2, 3+3, 4+4, 5+5, 6+6, 7+7, 8+8) are easy to memorize because they have a rhythm and pattern.

Once doubles are known, near-doubles become easy:

• 6 + 7: "That is almost 6 + 6 = 12, plus 1 more = 13."
• 8 + 7: "That is almost 8 + 8 = 16, minus 1 = 15."
• 5 + 6: "That is 5 + 5 = 10, plus 1 = 11."

Teach doubles first as memorized facts. Then show that any near-double is just one away from a known fact.

Strategy 3: Compensation

Adjust one number to make the problem easier, then compensate:

Addition:

• 29 + 14: "29 is almost 30. 30 + 14 = 44. But I added 1 too many, so 44 - 1 = 43."
• 47 + 25: "47 + 25. Round 47 to 50. 50 + 25 = 75. I added 3 too many, so 75 - 3 = 72."

Subtraction:

• 52 - 19: "19 is almost 20. 52 - 20 = 32. But I subtracted 1 too many, so 32 + 1 = 33."
• 83 - 47: "83 - 50 = 33. I subtracted 3 too many, so 33 + 3 = 36."

This strategy requires understanding that if you change the problem, you must adjust the answer. It develops flexible thinking about numbers.

Strategy 4: Breaking apart (partial sums)

Split numbers into place-value components and add separately:

• 34 + 23: "30 + 20 = 50. 4 + 3 = 7. So 50 + 7 = 57."
• 65 + 27: "60 + 20 = 80. 5 + 7 = 12. So 80 + 12 = 92."

For subtraction:

• 75 - 32: "70 - 30 = 40. 5 - 2 = 3. So 40 + 3 = 43."

This strategy works well for problems that do not require regrouping. When regrouping is needed, make-a-ten or compensation may be easier.

Strategy 5: Counting up for subtraction

Instead of subtracting, count up from the smaller number:

• 82 - 75: "From 75 to 80 is 5. From 80 to 82 is 2. So 5 + 2 = 7."
• 63 - 48: "From 48 to 50 is 2. From 50 to 63 is 13. So 2 + 13 = 15."

This is particularly powerful when the numbers are close together.

Key Insight: There is no single "best" strategy. Flexible mental math means choosing the strategy that fits the specific problem. 9 + 6 calls for make-a-ten. 7 + 8 calls for doubles. 99 + 34 calls for compensation. Teach multiple strategies and let your child develop judgment about which to use when.

How to practice

• Daily quick drills: 5-10 mental math problems per day, discussing strategies after each one. "How did you think about that?"
• "What is your strategy?": After every mental computation, ask how they did it. Naming strategies reinforces them.
• Strategy of the week: Focus on one strategy for a week. "This week, try to use make-a-ten whenever you can."
• Real-world math: "We have 23 minutes until dinner. We need to leave in 15 minutes for soccer. Is there enough time?" Let them compute mentally.

Signs your child needs strategy instruction

• They count on fingers for everything: They have no alternatives to counting.
• They get the right answer but it takes 10+ seconds for basic facts: Correct but slow means they are counting internally. Strategies will speed this up naturally.
• They can only do math on paper: They have learned procedures but not number relationships.
• They know facts in isolation but cannot apply them: They memorized 8 + 7 = 15 but cannot figure out 18 + 7 or 28 + 7. Strategies generalize; memorized facts do not.

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Mental math is not about being a human calculator. It is about understanding numbers well enough to work with them flexibly. Each strategy above gives your child a new way to see number relationships. Together, they transform math from something your child does with paper into something they do with their mind.

If you want a system that builds these strategies progressively — starting with the ones your child is ready for and adapting as they develop fluency — that is how Lumastery works.