Mathematics K–6 · Years 5–6

Area model: multiplying on grid paper

Number and algebra

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

A product such as 23 × 14 is the number of squares in a 23 by 14 rectangle, and splitting the rectangle along tens and ones shows each partial product of the written method.

What you need

A3 sheets of 1 cm grid paper with a grid of at least 36 by 25 squares
coloured pencils and a ruler
base-ten hundreds (10 by 10 flats) and tens
a calculator for checking

How to do it

Outline a rectangle 23 squares long and 14 squares wide on the grid paper.
Split the length into 20 and 3 and the width into 10 and 4 with two lines, making four smaller rectangles. Colour each one.
Find each part: 20 × 10, 20 × 4, 3 × 10 and 3 × 4. Cover the 20 × 10 part with two flats to check it.
Add the four parts to find 23 × 14.
Work 23 × 14 in the vertical written method and match each line to the coloured parts it contains.
Repeat for 36 × 25 on the grid paper, and for 127 × 8 as a sketch not drawn to scale (a rectangle 127 squares long does not fit on the sheet), and check each with a calculator.

What you should see

23 × 14 splits into 200 + 80 + 30 + 12 = 322 squares, and two flats cover the 200 part exactly. In the written method 23 × 4 = 92 is the 80 and 12 parts and 23 × 10 = 230 is the 200 and 30 parts, so 92 + 230 = 322. 36 × 25 gives 600 + 150 + 120 + 30 = 900, and 127 × 8 gives 800 + 160 + 56 = 1016. Each calculator check agrees.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

23 × 14 = 20 × 10 + 3 × 4 = 212, multiplying only tens by tens and ones by ones.
The written method is a different calculation from the area picture.

Safety card

Low riskLearners carry it out

Hazards

none beyond an ordinary classroom

Controls

none needed

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-MR-01 MAO-WM-01
Australian Curriculum v9AC9M5N06

Sources

The pages the author read to write this activity.

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