Transcript 1.1 Square Numbers and Area Models

Chapter 1: Square Roots
and the Pythagorean
Theorem
1.1 Square Numbers and
Area Models
Activating Prior Knowledge
Refresh area: the amount of surface a
shape covers. It is measured in square
units.
 Area of a rectangle:
A=bxh
 Area of a triangle:
A=bxh
2
Complete “Check” #1 a) – d) on your own.
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Refresher…
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Reminder: What is the difference
between rectangles and squares?
Is every square a rectangle?
Yes!
Is every rectangle a square?
No!
Investigate, pg. 6
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Draw as many rectangles as you can of
the following areas: (on grid paper)
• 4 square units
• 6 square units
• 8 square units
• 9 square units
• 10 square units
• 12 square units
• 16 square units
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For how many areas above were you
able to make a square?
• 4, 9, and 16 square units
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What is the side length of each square
you made?
• 4 square units: side length = 2
• 9 square units: side length = 3
• 16 square units: side length = 4
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How is the side length of a square
related to its area?
• **The side length of a square
multiplied by itself equals the area. **
5 units
5 units
side length = 5 units
area = 5 x 5 = 25 units2
Connect, pg. 7
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When we multiply a number by itself, we
square the number.
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eg: the square of 4 is 4 x 4 = 16
We write, 4 x 4 = 42
So, 42 = 4 x 4 = 16
We say four squared is sixteen.
16 is a square number or perfect square
One way to model a square number is to draw
a square whose area is equal to the square
number.
Example 1, pg. 7
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To show that 49 is a square number, use a
diagram, symbols, and words.
Draw a square with area 49 square units. The
side length of the square is 7 units.
Then, 49 = 7 x 7 = 72
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We say: Forty-nine is seven squared.
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7 units
7 units
side length = 7 units
area = 7 x 7 = 49 units2
On your own…
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Using a diagram, show that 14 is not a
square number.
On your own…
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Show that 14 is not a square number.
1
2
14
7
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Can you make a square with 14 square
units?
• No, just two rectangles.
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Try example 2 on pg. 7
Consecutive Squares
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Consecutive squares: squares of consecutive
numbers.
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Eg. 12 = 1, 22 = 4, 32 = 9, are the first 3 consecutive
squares.
Are there any squares between consecutive
numbers?
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No, square are always products of whole numbers and
consecutive squares are the squares of consecutive
numbers.
Hint: Think of a number line.
Common Misconceptions
52 does not equal 5 x 2 = 10
 52 is five multiplied by itself: 5 x 5 = 25
 Likewise, if you see 53, it is not
5 x 3 = 15, rather, it is 5 x 5 x 5 = 125
What does 59 look like?
5x5x5x5x5x5x5x5x5
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On a sheet of loose leaf,
complete the following…
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Put your name, date, and assignment
title at the top (1.1: Square Numbers and
Area Models).
#4 on pg. 8 in textbook
Extra Practice Sheet 1 #1 – 6
Due date: next class, Friday, Sept. 17