Free printable math problem solving strategies chart
Grades 3–8Understand it, make a plan, carry it out, look back. A routine that works on any problem, at any level, including the ones where no method is obvious. Print it for the wall, or step through the worked examples below.
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Work through one step at a time
Pick a problem and reveal the steps one by one. Answer each stage yourself before uncovering the next.
The four stages are Polya's, first written down in 1945 and still the best description of what solving a problem actually involves: understand, plan, carry out, look back.
Look back is the stage that gets skipped, and it is the one that separates children who catch their own errors from children who need everything marked. It is also where the learning transfers — asking what worked here that might work again is how a method becomes a habit.
Grade 2Maya had 24 stickers. She gave 9 of them to her brother. How many stickers does she have left?
- What do we know?Maya started with 24 stickers. She gave 9 away.
- What is being asked?How many she has left — so the answer will be a number of stickers.
- What is happening?Some of them went away, so the amount goes down. That is subtraction.
- Work it out24 − 9 = 15
- Does it make sense?She started with 24 and gave some away, so the answer should be smaller than 24. It is. Maya has 15 stickers left.
Grade 3There are 6 rows of chairs in the hall. Each row has 8 chairs. How many chairs are there altogether?
- What do we know?There are 6 rows, and every row has the same number: 8 chairs.
- What is being asked?The total number of chairs in the hall.
- What is happening?Equal groups being put together. Six groups of eight, so multiplication — even though the word altogether often means add.
- Work it out6 × 8 = 48
- Does it make sense?Six rows of roughly ten would be about 60, so 48 is in the right area. There are 48 chairs.
Grade 4A library has 53 books to pack. Each box holds 10 books. How many boxes are needed?
- What do we know?There are 53 books, and one box holds 10.
- What is being asked?How many boxes are needed — not how many are full.
- What is happening?A total is being split into equal groups, so division.
- Work it out53 ÷ 10 = 5 remainder 3
- Does it make sense?Five boxes hold only 50, and 3 books would be left over with nowhere to go. So 6 boxes are needed. This is the step people skip: the answer is 6, not 5 remainder 3.
Grade 5A pack of 12 pens costs $9. Sam buys 3 packs and pays with a $30 note. How much change does he get?
- What do we know?One pack costs $9. Sam buys 3 packs. He pays with $30. The 12 pens per pack is not needed.
- What is being asked?The change — so we need the cost first, then the change. Two steps.
- What is happening?Three packs at the same price is multiplication. Then change from $30 is subtraction.
- Work it out3 × $9 = $27, then $30 − $27 = $3
- Does it make sense?$27 is close to $30, so the change should be small. $3 fits. Sam gets $3 change.
One step at a time. Try to answer each question yourself before revealing the next.
How to use this problem solving chart at home
Resist giving the next step. The instinct when a child stalls is to say what to do, and it removes exactly the thing being practised. Ask what do you know instead, and wait longer than feels comfortable.
Have them explain the problem back before starting. Most stuck moments are comprehension rather than method, and they become obvious the moment a child tries to retell the situation.
Praise the plan, not the answer. A sensible approach that produced a wrong answer is worth more than a right answer arrived at by guessing, and saying so out loud changes what a child pays attention to.
The stage everyone skips
Understand, plan and solve get done because they are visibly necessary. Look back gets skipped because the answer is already written down.
Yet it is where most of the value is. Is that answer reasonable? Is it the size I expected? Did I answer the question that was asked, or the calculation I did? Those questions catch the majority of lost marks.
It is also where a method becomes transferable. A child who notices I drew a picture and that made it obvious has gained something for next time; a child who just moves on has gained one answer.
Strategies worth having
Draw it. More problems are solved by a rough sketch than by any other single move, and children reliably underuse it because drawing feels like not doing math.
Try smaller numbers. If the method is unclear with 347 and 289, do it with 4 and 3. The structure shows itself and the real numbers can be put back afterwards.
Work backwards. When a problem gives the end result and asks for the start, going in reverse turns a hard question into an easy one.
Make a table. Anything with two changing quantities becomes much clearer laid out in rows and columns than held in your head.
Where problem solving usually goes wrong
Starting to calculate before finishing the reading.
Choosing an operation by hunting for key words instead of understanding the situation.
Stopping at the first answer, when the question needed a second step.
Skipping the check, which is the cheapest step and the one that catches the most.
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.
- order of operations worksheets — printable practice.
- solving equations worksheets — the next step once this is solid.
- division with remainders worksheets — more practice in the same area.
Everything at this level: Grade 3 math · Grade 4 math · Grade 5 math · Grade 6 math · Grade 7 math · Grade 8 math
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Questions parents ask
What are the four steps of problem solving?
Understand the problem, make a plan, carry out the plan, and look back. They come from the mathematician George Polya and have been the standard description since 1945.
What does understand the problem mean?
Being able to say what you know and what you are being asked, in your own words, without the original sentence in front of you. If a child cannot retell the problem, no amount of arithmetic will help.
What strategies can my child try?
Draw a picture, make a table, work backwards from the answer, try smaller numbers first, look for a pattern, or guess and check systematically. Most stuck moments are solved by drawing it.
What should they do when completely stuck?
Try the same problem with smaller numbers. If the numbers are 347 and 289, do it with 4 and 3 first — the method usually becomes visible, and then the real numbers can go back in.
Why does looking back matter?
Two reasons. It catches errors, because an unreasonable answer announces itself. And it makes the method reusable, because noticing what worked is how a one-off solution turns into a strategy.
What grade is this problem solving chart for?
Grades 3 to 8. The routine does not change with age — only the problems inside it do — which makes it one of the few charts worth keeping up for years.
Is this problem solving 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.