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3.02 Groups and arrays


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Do you remember how multiplication can be thought of as  repeated addition  ?


Example 1

Answer the following:


Write this addition as a multiplication:\,\, 10+10+10+10+10+10+10+10

Worked Solution
Create a strategy

We can rewrite the addition as a multiplication using: \text{Number of groups}\times\text{Amount in each group}

Apply the idea

We have 8 groups of 10. We can rewrite this as multiplication: 10+10+10+10+10+10+10+10=8\times 10


Find the value of 8 \times 10.

Worked Solution
Create a strategy

Use skip counting or a multiplication table.

Apply the idea

By skip counting by 10 eight times, we have10, \,20, \,30, \,40, \,60, \,70, \,80

So, 8 \times 10=80.

Idea summary

If we are adding groups of the same size, we can also write it as a multiplication:

\text{Number of groups}\times\text{Amount in each group}

Arrays as products

In this video we see how rows and columns (called an array), can be used to solve multiplication.

Loading video...


Example 2

Which of these number sentences describe the array?

There may be more than one correct answer.

The image shows an array with 8 columns and 2 rows.
8 \times 2 =16
16 \times 2 = 8
2 \times 8 =16
Worked Solution
Create a strategy

If we multiply the number of rows by the number of columns, we find the total number of squares.

Apply the idea
\displaystyle \text{Rows}\displaystyle =\displaystyle 2Count the number of rows
\displaystyle \text{Columns}\displaystyle =\displaystyle 8Count the number of columns
\displaystyle 8 \times 2\displaystyle =\displaystyle 16Multiply the columns by the rows
\displaystyle 2 \times 8\displaystyle =\displaystyle 16Multiply the rows by the columns

The number sentences which describe the array are options A and C.

Idea summary

We get the same answer whichever way we look at our array.

An image showing an array with 2 columns and 4 rows. Ask your teacher for more infromation.



uses mental and informal written strategies for multiplication and division

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