Unit 1.1  perfect squares and the area model
what do we need to know?
 Area: defined as the "space" inside a shape
 Area of triangle: (base x height)/2
 Area of a rectangle: base x height
 Area of a square: base x height
 Perimeter: Addition of all the sides
 Area of triangle: (base x height)/2
 Area of a rectangle: base x height
 Area of a square: base x height
 Perimeter: Addition of all the sides
Class notes




more information
what is a square number?
To square a number, you multiply it by itself. For example:
Here is a chart with the square numbers up to 30. With practice, you'll be able to memorize at least the first 12 square numbers, which will result very useful. Take a look:
why are these numbers called square numbers?
Let's recall that a square has 4 sides of equal length. Let's use one of the examples above:
This square has a side length of 4 units. Because the side length is the same, it means that the base and the height of a square are the same. As you may recall, to calculate the area of a square we multiply its base time its area:
Area = Base x Height
= 4 x 4 = 16
Area = Base x Height
= 4 x 4 = 16
In other words, square numbers are called "SQUARE NUMBERS" because they model the area of a square. When you multiply a number times itself, you are essentially calculating the area of a square with a side length equal to that number.
Be aware that, from now on, square numbers could be referred to as PERFECT SQUARES.
Be aware that, from now on, square numbers could be referred to as PERFECT SQUARES.
As you can see in the picture above, a perfect square represents the area of a square. For example, a square of area equal to 4 has to have a side length of 2, because Base (2) x Height (2) = 4. When given an area, then, you must find the number that multiplied by itself gives you that area. This is where the concept of a SQUARE ROOT comes in, which we will learn next lesson.
examples of numbers that are not perfect squares
6, 8, 12, and 20
6 can make rectangles 1×6 and 2×3 BUT never a square.
8 can make rectangles 1×8 and 2×4 BUT never a square.
12 can make rectangles 1×12, 2×6, and 3×4 BUT never a square.
20 can make rectangles 1×20, 2×10, and 4×5 BUT never a square.
A square number, or perfect square, is the result of squaring a number. Notice how we are dealing with whole numbers (this is going to be important next lesson).
6 can make rectangles 1×6 and 2×3 BUT never a square.
8 can make rectangles 1×8 and 2×4 BUT never a square.
12 can make rectangles 1×12, 2×6, and 3×4 BUT never a square.
20 can make rectangles 1×20, 2×10, and 4×5 BUT never a square.
A square number, or perfect square, is the result of squaring a number. Notice how we are dealing with whole numbers (this is going to be important next lesson).
how to determine the perimeter if only the area is known
Recall that:
Perimeter = addition of all sides
So, to find the perimeter, we need to figure out the side length. For a square, this is easier since all side lengths are equal.
If you know the area of a square, you can figure out the side length by finding the number that multiplies itself to give the area.
The following square has an area of 144 units square.
Perimeter = addition of all sides
So, to find the perimeter, we need to figure out the side length. For a square, this is easier since all side lengths are equal.
If you know the area of a square, you can figure out the side length by finding the number that multiplies itself to give the area.
The following square has an area of 144 units square.
Since it is a square, we know that all side lengths are equal. We also know that Area = Base x Height, where the base and the height are identical.
Therefore, we are looking for a number that multiplied by itself gives you 144. If you look at the table, you'll see that 12 squared is 144. That is: 12 x 12 = 144 Thus, the side length must be 12. To find the perimeter, we must add all side lengths: Perimeter = 12 + 12 + 12 +12 = 48 units = 12 x 4 = 48 units. 
how to determine the area if the perimeter is known
Since we are dealing with squares, you can think about it this way:
Because the perimeter of a square is the sum of 4 equal side lengths, then:
Side length of a square = Perimeter / 4
Once we know the side length, we can calculate the area:
Area = side length x side length = side length squared
Because the perimeter of a square is the sum of 4 equal side lengths, then:
Side length of a square = Perimeter / 4
Once we know the side length, we can calculate the area:
Area = side length x side length = side length squared
THINGS TO REMEMBER
NOTICE THE UNITS (THEY ARE IMPORTANT):
Units that are squared describe AREAS.
Units that are neither squared nor tripled describe PERIMETERS.
And look at this cool fact:
Units that are squared describe AREAS.
Units that are neither squared nor tripled describe PERIMETERS.
And look at this cool fact:
The PERFECT SQUARE numbers form the down middle diagonal on the multiplication table!
videos that may help
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Worksheets









review  workbook
math_8__unit_1.1.pdf  
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