How do factor pairs relate to the
dimensions of a rectangle?
What are square numbers?
What are factor pairs?
A factor pair consists of two whole numbers
that are multiplied to get a product.
Ex: All of the factor pairs of 18 are:
1, 18
2, 9
3, 6
Factor Pairs and Rectangles
Factor pairs of a number can be used to make
rectangles with a given area. For example, if you
have 18 tiles that you want to arrange into a
rectangle, you can use the factor pairs listed on
the previous slide to determine the rectangles’
dimensions (the side lengths).
Factor Pairs and Rectangles (cont.)
It is possible to make 3 different rectangles with
18 tiles.
1 by 18
2 by 9
3 by 6
Can you make a square with 18 tiles? Explain.
Square Numbers
A square number is a number that is a result of the
product of a number multiplied by itself. A square
number will have an odd number of factors.
Ex: 9 is a square number because 3 ● 3 = 9.
Since 9 is a square number, you can make a 3 by 3
square using 9 tiles.
What other square numbers can you think of?
Square Numbers (cont.)
The number that is multiplied by itself to
produce a square number is called the square
root of that number. The square root of 9 is 3
because 3 ● 3 = 9. The square root symbol is √.
“The square root of 9” looks like √9.
Square Numbers (cont.)
A shortcut for writing 3 ● 3 is to use an
exponent. 3² or “three squared” may also be
read as “3 to the power of 2” or “3 to the 2nd
power”.
The First 15 Square Numbers
Perfect Square
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
Factors
1 * 1 or 12
2 * 2 or 22
3 * 3 or 32
4 * 4 or 42
5 * 5 or 52
6 * 6 or 62
7 * 7 or 72
8 * 8 or 82
9 * 9 or 92
10 * 10 or 102
11 * 11 or 112
12 * 12 or 12 2
13 * 13 or 132
14 * 14 or 142
15 * 15 or 152
Square Numbers (cont.)
Notice that square numbers run diagonally
through the middle of a multiplication chart!
More Square Numbers
Here is a list of more square numbers:
http://www.maths.com/numbers.square.htm