Math 8Square Roots

and the Pythagorean

TheoremStudent Notes Booklet

Name: ___________________________________

Class: ________________

Investigate:

You will need a partner and 20 square tiles.

Make as many different rectangles as you can with each area. Then draw your rectangles on the grid paper provided.

4 square units 6 square units 8 square units 9 square units

12 square units 16 square units 20 square units

For how many were you able to make squares?

What is the side length of each square you made?

How is the side length related to the area?

Find 2 areas greater than 20 that make a square.

How do you know you could make a square for these areas?

When we multiply a number by itself, we call it a ____________________________

Example: Show that 49 is a square number.

Example: Find the perimeter of the picture:

Homework Questions:

Pg 8: 4, 5, 7, 10, 11, 14, 16,

Extension Questions:

19, 20, 21

A=169 cm2

Investigate:

6 84 3 4

2 3 2 5 2 7 21 1 1 1 1 1 1 11 2 3 4 5 6 7 8 9 10 1

112 13 14 1

516 17 18 1

920 21 22 2

324 25 26 2

728 29 30

Complete the factors for 9-30.

Which numbers only have 2 factors?

Which numbers have an even number of factors?

Which numbers have an odd number of factors?

Which numbers are square numbers? How do you know?

Example:

Find the square of each number:

a) 5 b) 15

Find the square root of 64.

Draw a square with an area of 64 on the grid paper.

Homework Questions:

Pg 15: 6, 7, 10, 11 ac, 13 aceg, 17, 18, 19

Extension Questions:

20, 21, 22

Investigate:

Do the investigation on page 17.

How many squares did you draw?

Describe any patterns in your measurements.

How did you find the area and side length in each?

Example:

Homework Questions:

Pg 20: 3, 4, 5, 7, 9, 10

Extension Questions:

11, 12, 14

S

R

Q

P

Investigate:

Place each square root on the number line to show approximate value.

√2√5√11√18√24

Check your estimates with a partner and then using your calculator.

Example:

Which whole number is √96 closer to? How do you know?

Homework Questions:

Pg 25: 4, 5, 6, 8, 9, 11, 14, 16, 23

Extension Questions:

18, 20, 21

Discover a relationship among the side lengths of a right triangle.

Who is this Pythagorean guy? Who is this Pythagorean guy? Pythagoras was born on the island of Samos, and may have travelled widely in his youth, visiting Egypt and other places seeking knowledge. Around 530 BC, he moved to Croton, a Greek colony in southern Italy. He is often revered as a great mathematician, mystic and scientist, and he is best known for the Pythagorean theorem which bears his name.

Label the sides. Hypotenuse, Leg A, Leg B

Pythagoras noticed a connection between the hypotenuse and the 2 other legs.

This relationship is called: _____________________________________

Example:

Find the length of the hypotenuse.

Example:

Find the length of leg A.

Homework Questions:

Pg 34: 3, 5, 6, 7, 9, 10,

Extension Questions:

12, 13, 15, 16, 17

4 cm4 cm

5 cm

10 cm

Investigate:

Draw an obtuse, a right angle, and an acute triangle.

Draw squares on each side. Find area of all squares.

Does the Pythagorean Theorem work for all? Why or why not?

Example:

Is this a right triangle? How do you know?

Homework Questions:

Pg 43: 3, 4, 5, 6 aceg, 7bdf, 9, 12,

Extension Questions:

11, 13, 15, 17

Investigate:

A doorway is 2.0 m high and 1.0 m wide.

A square piece of plywood has a side length of 2.2 m.

Can the plywood fit through the door?

How do you know? Show your work.

Example:

Find the length of the hypotenuse.

Homework Questions:

Pg 49: 2, 3, 4, 5, 6, 8, 9, 11, 15, 16

Extension Questions:

14, 17, 19, 20, 22

Unit Test Date: _______________________________________________

Complete pages 54-59 for review.

h 33cm

56cm