Sunday, January 22, 2012

Pythagorean Relationship Scavenger Hunt

Welcome to the next Unit in Math.  Pythagoras.  This is an introductory scavenger hunt that will introduce you to what you will be learning.  
This assignment is to be done quietly.  You will receive inclass deductions if you are too loud or off task.

A) Set up Instructions
  • Fold a piece of in to quarters (hamburger hotdog folds)
  • Put your name and room number in the upper left quadrant.
  • Put Pythagoras Scavenger hunt in the upper right quadrant.


B) Upper Left Quadrant
  1. Define a Right Triangle (text book).  Explain what the legs and hypotenuse are.


C) Upper and lower Right Quadrants
  1. Define the Pythagorean Relationship. (textbook)
  2. Use the grid paper provide to draw a right triangle with sides that measure 3cm, 4cm and 5 cm.  Label the legs side a and b.  Label the hypotenuse side c. Cut this triangle off of the grid paper and relabel the side lengths if you have cut them out.
  3. Create 3 squares on your grid paper.  
  • One square has an area of 9 squares
  • One square has an area of 16 squares
  • One square has an area of 25 squares
  • Lightly colour each one a different colour

Using glue stick can you use the three squares and the right triangle to explain the Pythagorean relationship. a2 + b2 = c2

D) Lower Left Quadrant

Use the following numbers and shapes to explain the Pythagorean Relationship.
Draw a right Triangle
Attach 3 squares to each of the sides of the right triangle.
Now place the following labels and numbers into the diagram (it does not need to be to scale)

side a, side b, side c, hypotenuse,
a2, b2, c2
8 cm, 10 cm, 6 cm
100 cm2, 36 cm2, 64 cm2

Due Tuesday during class. We will correct it in class


Wednesday, January 11, 2012

Some more Squaring Work

Here are a few questions.  Try them out and see if they improve your test score on Thursday's quiz.
Feel free to leave answers as a comment! :)

1. Use prime factorization to show whether 120 and 196 are perfect squares?

2. What is the area of  a square picture with a side length of 22cm?

3. Challenge yourself to memorize the perfect square numbers from 1 to 225.  Can you repeat them from lowest to highest and then back down to lowest in under 1 minute? Bonus mark on the quiz if you can do this!

4. Determine which of the following numbers are perfect squares: 10, 100, 1000, 10 000, 100 000.
a) State the square root of each perfect square.
b)How do you know that the others are not perfect squares?
c)Create a quick method for determining mentally if the numbers are perfect squares.
d)Use this method to determine if 1 000 000 000 is a perfect square.

5. Determine the square root of 6400, 640 000, 64 000 000.
a) Describe a quick method for determining mentally the square root each number above.
b) Explain why this method does not work for evaluating the square root of 640.
What is the square toot of 640 000 000 000. How did you find your answer.

Tuesday, January 10, 2012