Multiplication and Division

Lesson

In the same way arrays and the area of rectangles can help with multiplication, they are really useful for division also. This video shows you how to use arrays and rectangles to solve division problems, when dividing two-digit numbers by one-digit numbers.

Let's use an area model to find the answer to $45\div3$45÷3.

We set up the area model using a rectangle like this.

$3$3 Total area: $45$45 Now if we don't know what $45\div3$45÷3 is straight away, we start with something we do know, like groups of $10$10.

Fill in the area used so far if we take out $10$10 groups of $3$3.

$10$10 $3$3 $\editable{}$ Total area: $45$45 How much area is remaining?

$10$10 $3$3 $30$30 $\editable{}$ Total area: $45$45 What is the width of the second rectangle?

$10$10 $\editable{}$ $3$3 $30$30 $15$15 Total area: $45$45 Using the area model above, what is $45\div3$45÷3?

We can divide $68$68 by $4$4 by drawing $68$68 dots in $4$4 rows.

To work this out we can count groups of $4$4 until we reach $68$68.

But that could take a long time if we go $1$1 group of $4$4 at a time, so let's count up in larger groups.

If we first count $10$10 groups of $4$4, how many dots will we have used?

$\editable{}$ dots $4$4 rows $68$68 dots How many dots are remaining when we take away the first $40$40?

$40$40 dots $\editable{}$ dots $4$4 rows $68$68 dots How many columns of $4$4 dots will we have in the group of $28$28?

Here is the complete array.

$10$10 columns $7$7 columns $40$40 dots $28$28 dots $4$4 rows Total: $68$68 dots Using this, what is $68\div4$68÷4?

We want to find $36\div6$36÷6.

Fill in the widths of the rectangles on the area model.

$\editable{}$ $\editable{}$ $6$6 $30$30 $6$6 Total area: $36$36 Using the area model above, what is $36\div6$36÷6?

Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality