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 Factors 1 1 * 1 or 12 4 2 * 2 or 22 9 3 * 3 or 32 16 4 * 4 or 42 25 5 * 5 or 52 36 6 * 6 or 62 49 7 * 7 or 72 64 8 * 8 or 82 81 9 * 9 or 92 100 10 * 10 or 102 121 11 * 11 or 112 144 12 * 12 or 12 2 169 13 * 13 or 132 196 14 * 14 or 142 225 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