Primary 1 to 6

Singapore primary maths, worked out.

Every step, and why it works, for the parent sitting beside the child.

Your child is stuck on a word problem. See the model, working and reasoning one step at a time — then practise another question built on the same pattern.

See the pattern. Then practise it.

See the working Build a worksheet

A worked solution, start to finish. Open it →

✓ Every solution is checked before it goes up. See what is checked

Free today

Problem of the day One problem, worked out, free all day A different one every morning at the same address. Ask your child to try it on paper first, then go through the working together. Open today’s problem →

What is here

Four ways in, depending on tonight

See one worked out, print a sheet for tonight, look up the pattern behind a question your child keeps getting wrong, or take the whole list by topic.

Behind each problem are more questions like it, with different numbers. The ▶ beside one opens its drawing.

1015 Questions, every one worked out Every step, with the reason for it written beside it. Browse them by pattern, or print a sheet for tonight and watch any question your child got wrong. See the problems → Build a worksheet →

33 Patterns and skills The 19 patterns behind most Primary 5 and 6 word problems, and the skills the younger years are built on. See the patterns → 10 Topics covered Every solution by topic, easiest first, and what is still missing. The revision list →

A worked solution

What a solution shows you

You can usually get the answer. Saying why, so your child can do the next one without you, is the hard part. Every solution here gives you the picture that makes the step obvious and the sentence to say out loud. Below is one, in four pieces.

The question at the top of a worked solution. — **The question** In full, at the top, so your child can point at the sentence a step came from.

A bar model divided into four parts, three labelled chocolate and one almond. — **Bars, drawn to scale** The amounts as lengths. What is equal looks equal, and what is left over is a piece you can put a finger on.

A gold-boxed note: make every fraction count the same whole. — **The key step** The step that does the work, written out as one sentence. That sentence is what your child takes to the next question.

The final answer, boxed in red: Mrs Hoon sold 960 cookies. — **The answer** A full sentence, in the words of the question, so it is clear what the number counts.

See the working, step by step. Open this solution →

Worksheets

Make a worksheet

Choose how many questions you want from each topic, choose how hard, and press print. Your child gets a clean sheet with room to work; you get the full working on separate pages, so you are not solving it again at nine o’clock at night.

Pick the topics. By subject — fractions, ratio, speed — or by the problem pattern you want drilled.
Pick the level. Standard, challenging, very challenging, or a mix of all three.
Print it. The questions on one sheet, the working on the pages after, and the whole sheet saved in the link so you can print the same one again.

Build a worksheet Or browse by topic

Enough in every topic for a term of sheets.

Name: Date: 8 questions

Question 1

Ali had 3 times as many marbles as Ben. After Ali gave 24 marbles to Ben, the two boys had the same number. How many did Ali have at first?

Question 2

A tank was three-quarters full. After 18 litres were drawn off it was half full. How much does the tank hold?

✓ Working printed on the pages after, for you

Problem patterns

Name the pattern and the question stops being a surprise

A word problem looks new every time and hardly ever is. Most Primary 5 and 6 questions are built on one of 19 patterns: which amount stayed the same, which one changed, what one unit is worth.

You will start spotting the pattern in the homework before your child does.

Units and parts 125 worked solutions

Large numbers and operation order illustrated in pencil.

Large numbers and operation order 104 worked solutions

Decimals and percentages illustrated in pencil.

Decimals and percentages 102 worked solutions

Seeing it move 47 worked solutions $P5 fraction foundations illustrated in pencil.$ P5 fraction foundations 38 worked solutions

Angle and shape properties illustrated in pencil.

Angle and shape properties 31 worked solutions

All 33 patterns and skills, with how to spot each one and the mistake children make →

Sent in by readers

Send me the one you are stuck on

Type it out or photograph the page — either is enough. Every submission is read by hand. I cannot work out all of them, but the ones that teach something are published here in full, for everybody to use.

Overlapping shapes — find A : B : C The shading is where two shapes overlap, so one area has two names — the shaded 1/6 of A is the shaded 1/5 of B plus the shaded 1/3 of C, and that single equation is what links three shapes that otherwise share nothing. Solved → Grid drawing: equal-area triangle without overlap Compare grid movements: equal or proportional right-and-up/down movements show parallel lines, which can prove both a trapezium and equal triangle heights. Solved → Rectangle ACEG — the shaded triangles Both shaded triangles have their base on the same line BF and X is its midpoint, so the two bases are equal (10 cm each) and the two heights are AB and BC — which add to the whole side AC. Where B sits on AC never matters. Solved →

All 18 sent in by readers →

What to send

The question, and the answer if you have it. If you were taught a particular method and want that one followed, say so — otherwise it is worked out from scratch.

Send in a problem

The 33 problem patterns

All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.

A PDF, and a note when new solutions go up.