Real-World Mathematical Modelling · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Modelling real problems with ratio, volume, and scale

Mathematics · Mathematical Thinking · ages 10-11
Name ______________________   Date ____________

  1. Lemonade needs 2 lemon wedges per glass. A double number line shows 2, 4, 6, 8, 10 wedges for 1 to 5 glasses. How many wedges for 6 glasses?

    • 12 wedges
    • 8 wedges
    • 11 wedges
    • 14 wedges

  2. Which tool helps you compare two amounts that grow together, like cups of flour and number of cookies?

    • A double number line
    • A single bar showing only one amount
    • A pie chart of percentages

  3. A measurement answer should always be rounded to the nearest whole number, no matter what it measures.

    Circle one:   True   False

  4. Which formula finds the volume of a box shape?

    • length x width
    • length x width x height
    • length + width + height

  5. A box is 4 cm long, 3 cm wide and 2 cm tall. What is its volume in cubic centimetres?

    Answer: ______________

  6. Juice concentrate and water mix in the ratio 1:4. How many cups of water go with 3 cups of concentrate?

    Answer: ______________

  7. Flour and sugar are in the ratio 3:2. A bar model shows the 3 flour parts hold 15 cups. How many cups of sugar are needed?

    • 10 cups
    • 15 cups
    • 6 cups
    • 25 cups

  8. A minibus holds 8 children. 30 children need transport. How many minibuses are needed?

    • 4 minibuses
    • 3 minibuses
    • 3.75 minibuses
    • 5 minibuses

  9. Maria's tank holds 6000 cm cubed of water. She says this equals 6000 litres. What mistake did she make?

    • She multiplied instead of dividing the side lengths
    • She used the wrong formula for volume
    • She forgot 1000 cm cubed equals 1 litre, so it's really 6 litres

  10. A shop mixes paint in a ratio of 3 parts blue to 4 parts yellow. To make 35 litres of mixed paint altogether, how many litres of blue paint are needed?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Modelling real problems with ratio, volume, and scale W1-mt_yqZiX6vS7D-s1

  1. 12 wedges · 6 glasses need 6 lots of 2 wedges, and 6 x 2 = 12 wedges.
  2. A double number line · A double number line lines up two amounts that grow together, like cookies and eggs, so you can see the ratio at every step.
  3. False · The right rounding depends on what you're measuring. Money often rounds to the nearest cent, while a room's length might round to the nearest centimetre.
  4. length x width x height · Volume of a box comes from multiplying all three dimensions: length, width, and height.
  5. 24 · 4 x 3 x 2 = 24 cubic centimetres.
  6. 12 · 3 cups of concentrate need 3 lots of 4 cups of water: 3 x 4 = 12.
  7. 10 cups · One part is 15 / 3 = 5 cups, and sugar needs 2 parts: 2 x 5 = 10 cups.
  8. 4 minibuses · 3 full minibuses carry 24 children, leaving 6 who need a fourth bus, so round up to 4.
  9. She forgot 1000 cm cubed equals 1 litre, so it's really 6 litres · Since 1000 cm cubed equals 1 litre, 6000 cm cubed is 6 litres, not 6000 litres.
  10. 15 · There are 7 total parts (3 + 4). 35 divided by 7 = 5 litres per part, so blue paint is 3 x 5 = 15 litres.
Worksheet · LightMySky