Free printable mental math strategies chart
Grades 1–5Six ways to work something out in your head instead of writing it down, with the steps for each and when to reach for it. Print it for the wall, or run the strategies below on fresh numbers as many times as you like.
Tap the chart to open it at full size
Watch each strategy work
Pick a strategy and it demonstrates itself on real numbers, broken into the steps you would actually think. Press for new numbers and it does it again with different ones.
That repetition is the point. A strategy explained once looks like a trick; the same strategy applied to five different pairs looks like a method. Children need to see it work several times before they will risk it on their own homework.
Notice that the steps change while the shape stays identical. Make ten always splits the second number, compensation always overshoots and comes back, counting up always stops at the next ten first. The numbers are incidental.
Make tenAdding single digits that cross ten
8 + 8
- 8 needs 2 more to reach 10
- Split the 8 into 2 and 6
- 8 + 2 = 10, then 10 + 6 = 16
- Answer
- 16
- Use it when
- Adding single digits that cross ten
Press for new numbers a few times. The steps change, the method does not.
How to use this mental math chart at home
Ask how they did it, not just what they got. The answer to 8 + 7 tells you nothing; how they reached 15 tells you everything. A child counting on fingers and a child using make ten have arrived at the same place by very different routes.
Introduce one strategy at a time and stay with it for a week. Six methods offered at once produces a child who uses none of them, because choosing between six is harder than the arithmetic was.
Then let them keep their own. Children often invent a method that is not on this chart and works perfectly well. That is a good sign, not a problem to correct — mental math is about noticing structure, and noticing your own is better than borrowing someone else's.
Mental math is not the same as being quick
Speed is a side effect, not the goal, and framing it as speed does real damage. A child under time pressure abandons thinking and falls back on counting, which is the opposite of what these strategies are for.
What the strategies actually teach is that numbers have structure. 47 + 19 is easier than it looks because 19 is nearly 20. 16 × 5 is easier because 5 is half of 10. Seeing that is a mathematical skill in its own right, and it carries into algebra later.
It also builds number sense that catches errors. A child who knows 47 + 19 is about 66 will notice immediately if a written method produces 56 or 156.
Choosing the right strategy
Each of these suits a particular shape of problem. Make ten is for crossing a tens boundary with small numbers. Near doubles is for numbers one or two apart. Compensation is for anything ending in 8 or 9.
Counting up is for subtraction where the numbers are close together — 62 − 58 is trivial counted up and awkward taken away. Splitting by place value is the general-purpose one that works on almost any two-digit addition.
The skill being built is the choosing, not the executing. That is why the widget above shows when to use each strategy alongside the steps, and why it is worth asking a child which method they would pick before they start.
Where mental math usually goes wrong
Forgetting the adjustment in compensation. Rounding 19 up to 20, adding, and then not taking the extra 1 back off. This is the single most common slip.
Splitting the wrong number. In make ten, the number being split is the second one, chosen to top the first up to ten.
Trying to hold too much in your head. If a strategy needs three intermediate numbers remembered at once, it is not helping. Writing one of them down is allowed.
Using a mental method on numbers that do not suit it. 47 + 38 does not want compensation. Part of the skill is recognizing when to reach for a pencil instead.
After the chart goes up
A chart explains the idea but gives a child nothing to do. These do the rest.
- number sense at Mathify Kids — every topic in this area, sorted by grade.
- number bonds worksheets — printable practice.
- addition facts worksheets — the next step once this is solid.
- multiplication facts worksheets — more practice in the same area.
Everything at this level: Grade 1 math · Grade 2 math · Grade 3 math · Grade 4 math · Grade 5 math
Charts that pair with this one
Charts that work well printed alongside this one.
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Addition chart
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Subtraction chart
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Multiplication chart
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Estimation and Rounding chart
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Place Value chart
Last reviewed
Questions parents ask
What is mental math?
Working something out in your head using the structure of the numbers, rather than following the written column method. It is not about being fast — it is about noticing that 47 + 19 is easier if you treat the 19 as 20 minus 1.
What is the make ten strategy?
Splitting a number so you can reach a round ten first. For 8 + 7, take 2 from the 7 to make 8 into 10, then add the remaining 5 to get 15. Ten is easy to add to, so getting there first makes the rest simple. It depends on knowing the number bonds to ten by heart.
What is compensation in math?
Rounding a number to something easier, calculating, then adjusting. 47 + 19 becomes 47 + 20 = 67, then take back the extra 1 to get 66. It works for subtraction too, and it is the strategy adults use most often without noticing.
Why count up to subtract?
Because for numbers that are close together it is far easier than taking away. For 62 − 58, count from 58 to 60, which is 2, then 60 to 62, which is another 2, so the answer is 4. Every jump lands on a round number, which is what makes it possible in your head.
Should my child still learn the written methods?
Yes. Mental strategies and written methods do different jobs — mental for numbers that are friendly, written for numbers that are not. A child with both chooses; a child with only one method uses it on everything, including the problems it suits worst.
What grade is this mental math chart for?
Grades 1 to 5. Make ten and near doubles usually arrive in Grade 1 or 2, splitting and compensation in Grade 3, and doubling and halving alongside multiplication in Grade 4.
Is this mental math chart free to print?
Yes. Open it full size and print as many copies as you need for home or a classroom, with no account and no watermark. Reselling it or re-hosting the file elsewhere is not allowed — link to this page instead.