Math 7

Unit 4 Circles and Area

Lesson 4.1 Investigating Circles

Focus

The FOCUS section introduces the main concept that will be covered in the lesson.

Measure radius and diameter and discover their relationship.

There isn’t a focus activity for this lesson.

Explore

Explore an idea or problem.
The exploration provides the background for the ideas presented in the lesson.

TEXT Page 130

Read/Work through the  Explore  section on Page 130 in your textbook.

You can do this activity on your own.
Do your best to answer the questions, then watch the Video Tutorial for help or to check your answers.

Watch

Video Tutorial

Connect

Connect summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Pages 130 - 131

Read/Work through the  Connect  section on Pages 130 - 131  in your textbook.

Even if you KNOW you are going to watch the video, READING this section is still important.

Getting the same information in multiple ways can help with understanding.

Demonstrations

The following demonstrations illustrate the ideas of this lesson.

Below is the “formal” definition of a circle.

A circle is a set of points equally far (equidistant)  from a fixed point  (the centre of the circle)

A circle is a set of points

Movie Comments

Okay, let's take this a bit at a time.

Most of us think of a circle as a curved line, not a "set of points".

It turns out that geometrical things like circles, squares, etc.  are all thought of as collections of individual points.

This is not so far fetched however, as the above demonstration hopefully indicates.

In this demonstration, move the slider to increase or decrease the number of points shown.

It starts with 6 points and goes to 1000.

Sort of a circle

A circle is a set of points equally far (equidistant)  from a fixed point  (the centre of the circle)

What if the points are NOT equidistant?

The demonstration below shows what happens if the points are not equidistant.

I've added a bit of "randomness" to each point, so we get something a bit like a circle, but not close enough to qualify.

Movie Comments

The radius of a circle

The radius of a circle is a line that goes from the center of the circle to any point ON the circle.

The plural of radius is radii;  (ray dee eye)
that is, one radius, two or more radii.

Movie Comments

The diameter of a circle

The diameter of a circle is the length of the line through the center of the circle and touching two points on the circle.

Just like with the radius of a circle, sometimes the word diameter is used to refer to the line itself.

The diameter of a circle will always be a length that is TWICE the length of the radius of the same circle.

Chords in a circle

A chord is a line that joins any two points on a circle.

It does NOT have to go through the center of the circle.   (but it can... it just doesn't HAVE to)

A diameter is a "special" chord that does go through the center point of the circle.

It the longest possible chord of any circle.

Movie Comments

Example

The Example will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example

TEXT Page 131

Work through the Example  on Page 131 in your textbook.

Watch

Video Tutorial

Practice Problems

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Assessment Focus a question that gives a good example of the kind of question you would be expected to answer after completing the lesson

Take It Further questions offer enrichment and extension.

Notes

Question 2,    some ideas about drawing a circle without a compass...
LINK

Question 7,    answers will vary.   I couldn’t find a high resolution version of the logo,  so I didn’t think it was helpful to give you the diagram to measure.
In the video I give a few general ideas about the process.

Question 8,    I didn’t do a video for this one.  The idea of finding the center of the circle was discussed in a few places in the lesson.
Here is a sample answer from the book.
Answers may vary. For example:
Fix one end of a measuring tape on the circumference. 
Walk around the circle with the measuring tape at ground level, until you reach the maximum distance across the circle, which is the diameter. 
The centre of the circle is the midpoint of the diameter.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 4", "Question 5"}, {"Question 6", "Question 7", , , }})