Primary 3 More Word Problems Study Guide

Primary 3 word problems in five short steps: two-step problems and groups, bar models for two and three quantities, guess and check, before-and-after changes, and working backwards, with something to try at each step and worked examples to finish.

Start here

How do you solve P3 word problems?

Draw the story first, then find what one unit is worth.

Read one sentence at a time and draw what it says. Each person gets a bar. When one amount is "3 times as many" as another, its bar is 3 equal units. Mark the total with a brace and the unknown with a "?". The drawing then shows which step to do first.

The same habit runs through the whole chapter:

  • two-step problems: find one thing at a time, in the right order;
  • bar models: set the difference aside so every bar is made of equal units;
  • guess and check: try, check the total, then improve the try;
  • before and after: see what changed and what stayed the same;
  • working backwards: undo the wrong step, or cross out what two totals share.
1

Step 1

Two-step word problems and equal groups

Find one thing at a time. Ask what the question needs first and write that step on its own line. When things come in groups, count the groups first, then answer what the question asked.

A stall gives 1 free badge for every 2 badges bought. Lina gets 18 badges, all from full offers. How many badges does she pay for?

18 badges

paid for free

    Try it

    A shop gives 1 free pen for every 4 pens bought. Ali gets 25 pens, all from full offers. How many pens does he pay for?

    Two steps and groups: practise 11 questions → ▶ Watch the lesson: Groups, gaps and offers Groups, gaps and offers: practise 11 questions →
    2

    Step 2

    Bar models for two and three quantities

    Make every bar out of equal units. "Times as many" tells you how many units a bar has. "More than" adds a piece, the difference, shown in orange. Set that piece aside, and the total shares out equally.

      Try it

      Lina and Raj have 48 cards altogether. Lina has 2 times as many cards as Raj. How many cards does Raj have?

      ▶ Watch 2 lessons: Two quantities Two quantities: practise 12 questions → ▶ Watch the lesson: Three quantities Three quantities: practise 11 questions →
      3

      Step 3

      Guess and check

      Try, check, then improve the try. Keep the number of things the same in every try. Work out the total, compare it with the total you need, and let the gap tell you which way to change the next try.

      Mr Tan has 9 bags of marbles. Each small bag has 3 marbles. Each large bag has 5 marbles. There are 37 marbles altogether. How many large bags are there?

      Tap a bag to swap small and large

      TryLarge bagsSmall bagsMarblesCheck

      Each try you check is written here.

      Try it

      Ms Tan has 7 boxes of crayons. Each small box holds 4 crayons and each big box holds 6 crayons. There are 34 crayons in all. How many big boxes are there?

      ▶ Watch the lesson: Guess and check Guess and check: practise 12 questions →
      4

      Step 4

      Before and after word problems

      See what changed and what stayed the same. When one person gives to another, the gap closes from both ends. When one amount stays the same, it is 1 unit before and after. When two amounts start equal, only the changes make the difference.

      Rani has 30 shells and Kai has 18 shells. How many shells must Rani give Kai so that they have the same number?

      Drag the slider: Rani gives Kai some shells

      Try it

      Ken has 40 stamps and Zul has 26 stamps. How many stamps must Ken give Zul so that they have the same number?

      ▶ Watch the lesson: Transfer and difference Transfer and difference: practise 12 questions → ▶ Watch the lesson: One quantity unchanged One quantity unchanged: practise 11 questions → ▶ Watch the lesson: Equal at first Equal at first: practise 11 questions →
      5

      Step 5

      Comparing two totals and undoing a wrong step

      Cross out what is the same, or go back the way you came. When two shopping trips share the same items, cross them out: the extra items make the extra cost. When someone did the wrong calculation, undo it first to find the number, then do the right one.

        Try it

        Ali was asked to divide a number by 2. Instead, he multiplied it by 2 and got 36. What is the correct answer?

        ▶ Watch the lesson: Equal groups in two totals Equal groups in two totals: practise 8 questions → ▶ Watch the lesson: Undo the wrong operation Undo the wrong operation: practise 12 questions →

        Primary 3 word problems, worked step by stepTry each question first. Then show a hint, or the working one line at a time.

        Two stepsBasic

        A baker bakes 4 trays of 15 buns. She packs the buns into bags of 6. How many bags can she fill?

        The bags need the number of buns, so find the buns first. Only then put them into bags.
        1. First, the buns: 15 × 4 = 60.
        2. Then the bags: 60 ÷ 6 = 10.
        Answer: 10 bags
        Two quantitiesBasic

        Aisyah and Jun Hao have 75 stickers altogether. Aisyah has 13 more stickers than Jun Hao. How many stickers does Aisyah have?

        Draw Jun Hao's bar as 1 unit. Aisyah's bar is 1 unit and 13 more. Set the 13 aside, and what is left makes 2 equal units.
        1. Set the difference aside: 2 units = 75 − 13 = 62.
        2. 1 unit = 62 ÷ 2 = 31. This is Jun Hao's bar.
        3. Aisyah's bar is 1 unit and 13 more: 31 + 13 = 44.
        4. Check: 44 + 31 = 75, the total in the question.
        Answer: 44 stickers
        Three quantitiesIntermediate

        Farhan, Mei Ling and Raju have 95 marbles altogether. Mei Ling has 3 times as many marbles as Farhan. Raju has 11 more marbles than Mei Ling. How many marbles does Raju have?

        Farhan is 1 unit. Draw Mei Ling with the same unit, then Raju as long as Mei Ling and 11 more. Set Raju's 11 aside before sharing.
        1. Count the units: 1 unit + 3 units + 3 units = 7 units.
        2. Set the 11 aside: 7 units = 95 − 11 = 84.
        3. 1 unit = 84 ÷ 7 = 12.
        4. Mei Ling: 3 × 12 = 36. Raju: 36 + 11 = 47.
        Answer: 47 marbles
        One quantity unchangedIntermediate

        Jia Hui had 5 times as many beads as Nadia. Jia Hui used 36 beads. Then she had 2 times as many beads as Nadia. Nadia's beads did not change. How many beads did Jia Hui have at first?

        Nadia's beads stay the same, so Nadia is 1 unit before and after. Jia Hui is 5 units before and 2 units after.
        1. The units Jia Hui used: 5 units − 2 units = 3 units, so 3 units = 36.
        2. 1 unit = 36 ÷ 3 = 12.
        3. Jia Hui at first: 5 × 12 = 60.
        4. Check: 60 − 36 = 24, and 24 is 2 times Nadia's 12.
        Answer: 60 beads
        Equal at firstChallenge

        Wei Ming and Hana had the same number of stamps at first. Wei Ming bought 15 more stamps and Hana gave away 9 stamps. Then Wei Ming had 4 times as many stamps as Hana. How many stamps did each of them have at first?

        Draw two equal bars. Wei Ming's grows by 15 and Hana's loses 9 from the end. They started equal, so the difference now comes only from the two changes.
        1. Difference now: 15 + 9 = 24.
        2. Wei Ming is 4 units and Hana is 1 unit: 4 units − 1 unit = 3 units, so 3 units = 24.
        3. 1 unit = 24 ÷ 3 = 8. This is Hana now.
        4. Add back what Hana gave away: 8 + 9 = 17.
        Answer: 17 stamps each
        6

        Step 6

        Check yourself

        Five quick questions, one from each step. Answers are not saved; they show where to practise next.

        1. Markers are placed every 4 m along a straight 28 m path, with a marker at each end. How many markers are there?

        2. Wei Jie and Arif have 50 marbles altogether. Wei Jie has 8 more marbles than Arif. How many marbles does Arif have?

        3. There are 7 stools and chairs. Each stool has 3 legs and each chair has 4 legs. There are 25 legs altogether. How many chairs are there?

        4. Siew Lan had 4 times as many beads as Hakim. She gave away 15 beads. Then she had the same number of beads as Hakim. How many beads does Hakim have?

        5. 3 pens and 2 rulers cost $13. 5 pens and 2 rulers cost $19. How much does one pen cost?

        0/5
        Answer all five to see where to practise next.
        For parents

        How to use this guide. Sit with your child for the bar models in Step 2. Before each tap, ask "What does this sentence tell us to draw?" Drawing one sentence at a time is the whole skill, and saying it aloud helps it stick. Each step takes two or three minutes; the whole guide about fifteen.

        If your child jumps straight to a sum, ask for the drawing first. In the worked examples, let your child try, then reveal the working one line at a time and ask what the next line should be.

        More study guides

        Before this: Multiplication and DivisionNext: Bar GraphsPrimary 3 Numbers up to 10 000 study guidePrimary 3 Addition and Subtraction Within 10 000 study guidePrimary 3 Money study guide
        Lessons and practice

        P3 More Word Problems lessons and practice

        11 lesson videos and 122 questions across ten subtopics, from Basic to Challenge, each with a worked solution.

        Watch and practise →