Mathematics K–6 · Years 3–4

Arrays and area: multiplication facts to 10 by 10

Number and algebra

Practical, model not builtLow risk

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The idea

A multiplication fact is the number of squares in a rectangle of rows and columns, so a hard fact can be split into two easy rectangles and added.

What you need

100 square tiles or a 10 by 10 array card with a sliding L-shaped mask
1 cm grid paper and coloured pencils
a sheet of card to cover part of an array

How to do it

Lay tiles as 6 rows of 7. Count the tiles by rows (7, 14, 21 and so on) and write 6 times 7 = 42.
Cover the last column with the card so 6 rows of 5 show plus a hidden strip. Say 6 times 5 = 30, then uncover and add the 6 rows of 2 to reach 42.
Turn the array a quarter turn to show 7 rows of 6 and count again.
A partner builds a tile array and covers it with the card so only the top row and the left column show. Work out the total from the visible edges, then uncover and count to check.
On the grid paper colour a 9 by 8 rectangle, split it into 9 by 5 and 9 by 3 with a line, and write the two facts that add to 72.

What you should see

6 rows of 7 hold 42 tiles, found by counting by sevens or as 30 plus 12 after splitting. The quarter turn shows 7 rows of 6 with the same 42 tiles. A partly covered array with 4 tiles showing along the top and 6 down the side has 24 tiles, confirmed by uncovering. The 9 by 8 rectangle splits into 45 plus 27, which is 72, and splitting off 5 columns the same way works for any fact with a 6, 7, 8 or 9 in it.

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.

6 times 7 and 7 times 6 are different facts with different answers.
Multiplication always makes a number bigger by adding the two numbers.

Safety card

Low riskLearners carry it out

Hazards

none beyond ordinary classroom materials

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 AuthorityMA2-MR-01 MAO-WM-01
Australian Curriculum v9AC9M3N04AC9M3A03AC9M4A02

Sources

The pages the author read to write this activity.

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