Modelling with multiplication and fractions
Model real-world problems involving multiplication, area, fractions, and unit conversion by choosing appropriate representations and interpreting mathematical results in context
What a learner can do afterwards
- Model a tiling/area problem with an array and write the corresponding multiplication
- Represent a recipe-scaling problem as a fraction calculation and interpret the answer in grams
- Use a bar model to set up a unit conversion problem (metres to centimetres)
1 · Read
Some real-life problems need more than one type of maths. You might multiply to find an area, use a fraction to scale a recipe, or convert units like metres to centimetres. The trick is picking the right tool, then checking that your answer makes sense for the real situation.
A cookie recipe uses 200 grams of sugar. Mia wants to make half the recipe. She works out 1/2 × 200 = 100. She needs 100 grams of sugar.
A garden path is 4 metres long. Sam wants to know the length in centimetres, so he draws a bar split into 4 equal metre-sized parts. Each part is 100 centimetres, so he works out 4 × 100 = 400. The path is 400 centimetres long.
When you get a final number, check what it means for the real problem: is it tiles, grams, or centimetres? Matching the number to its units and story tells you the answer makes sense.
Pick arrays for area, fractions for scaling, and bar models for units, then check your answer fits the real problem.
More to read
Area and square feet
Square foot gardening shows how arrays turn into multiplication. A garden bed is split into square feet, with one plant per square. A bed that is 8 squares by 4 squares holds 8 x 4 = 32 squares, so 32 plants. Draw the bed as an array of rows: each row is one group, and the number in each row is the group size. Count one row and count the rows, then multiply. The same array idea works for patios, egg boxes, and classroom desks. Whenever you see neat rows with the same count in each, the array is telling you which multiplication to write.
Tiling and multiplying: two ways to find area
You can find the area of a rectangle in two ways that must agree. First, tile it with unit squares and count: a shape covered by 12 squares has area 12. Second, multiply the side lengths: a 3 by 4 rectangle has area 3 x 4 = 12. Both routes give the same number, and that is the point: the array of tiles IS the multiplication. The same double-check works with fractions later on. A rectangle 2/3 by 3/4 can be tiled with tiny squares to give 1/2, and multiplying 2/3 x 3/4 gives 1/2 too. When two representations agree, you can trust the answer.
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14 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.