Math: Circles

In this unit we will be investigating the measurements of circles and cylinders. With the formulas taught, students will be able to measure the radius, diameter, circumference and area of circles and volume and surface area of cylinders, and investigate their relationships.

Individual Problem

Some examples of student work

Back side of student work, shows work, working backwards with formula of area and circumference.

6.5 Surface Area of a Cylinder

Thursday, January 14 - Monday, January 18
Homework: Homework and practice book p.132-133 #1-4
Textbook Assessment Focus Question p. 260 #6

Goal:

We will be able to calculate the surface area of a cylinder using the given formula:

SA= 2πr² + 2πrh

Students started off the lesson by creating nets of cylinders on graph paper, similar to the diagram on the slide.
We labeled each part of the net to show how we get our formula for surface area.

Surface Area is the sum of 3 areas on a 3-d object.
If we take a cylinder a part, it is two circles and a rectangle.
The sum of the area of two circles is 2πr²The area of a rectangle is length x width, in a circle, height is our length and circumference (2πr) is our width)
giving us the second part of the formula 2πrh

To solve surface area for cylinder above:
SA = 2πr² + 2πrh
= 2 x 3.14 x 3² + 2 x 3.14 x 3 x 5
= 2 x 3.14 x 9 + 3.14 x 3 x 5
= 56.52 + 47.1
= 2662.09 cm ²

Scavenger Hunt:

Students were given clues to lead the to hidden questions around the room. Questions were based on volume and surface area. Congrats TEAMCAP for winning 1st place! Other winning teams were also given table bonus points. 

6.4 Volume of a Cylinder

Tuesday, January 12 - Wednesday, January 13
Homework: Popcorn Activity 

Goal:

We will be able to calculate the volume of a cylinder using the given formula:

V = π r²h (Volume = pi multiplied by the radius squared multiplied by height) OR

V = π r x r x h (Volume = pi multiplied by radius multiplied by radius multiplied by height)

Volume is the amount of space occupied by a solid. That means volume is the amount of space that is inside a cylinder.
We looked back to rectangular prisms to remember that Volume is the base area x height.
So we use our formula to calculate area, then we multiply that by height, giving us the formula: V = π r²h

Refer to the above video for directions on how to solve problems with the given formula.

6.3 Area of a Circle

Friday, January 8 - Monday, January 11
Homework: Practice and Homework Book pgs 128-129 #1-6

Goal:

We will be able to calculate the area of a circle using the given formula:

A = π r² (Area = pi multiplied by the radius squared) or written

A = π r x r (Area = pi multiplied by radius multiplied by radius)

Students were asked to make the note that Area: the number of square units inside the circle. We always write our answer for area in units². In this case, it is cm².

Next we went over the formula for area of a circle.
For missed notes please write the formulas for area:
A= π r² or we can write 
A = π r x r
 We calculated the area of the 15" pizza using the formula both ways. 

Some class problem solving

Some class problem solving

6.2 Circumference

Wednesday, January 6 - Thursday, January 7
Homework: Practice and Homework Book pg. 125 #1-5
and
Math Text Book pg. 245 #6, 7, 8, and 11 A only

Goals: 

We will understand π = 3.14
We will be able to calculate the circumference (distance around the circle) using the given formulas
C = π x d (Circumference = pi multiplied by diameter) or
C = π x 2r (Circumference = pi multiplied by two times the radius)

We measured the distance around circular objects and found their diameter and radius

We divided the distance around the objects by their diameter which averages out to be 3.37. And distance around the objects divided by their radius to find its average to be 6.78.

With this, we can make the conclusion that the Distance Around (also known as circumference) is approximately 3 times the diameter and approximately 6 times the radius!

Circumference Note for Concept Book.

6.1 Investigating Circles - Radius and Diameter

Monday, January 4 - Tuesday January 5
Homework: Practice and Homework Book pg. 123 #1-6

Goal: We will be able to calculate the radius and diameter of circles using the given formulas.
R= D/2 (Radius = Diameter divided by 2)
and
D = 2r (Diameter= Radius multiplied by 2)

Definitions we will be using for the circles unit.

How to calculate radius and diameter using the formulas.

Steps to constructing a circle. Then we did some questions as a class to calculate radius and diameter.

Some practice:

Students were asked to find the center of the logo and radius and diameter of the logo they were given. They were asked to place the logo in the center of the t-shirt. Some measuring or folding of the shirt was required. On the back of the shirts, students were asked to show their work.

More practice:

Students, in their table groups, we given one plate. They were given the problem which asked, "How many plates would you be able to fit over the entire surface of the desk?"
Which meant that they had to find the length/width of the plate (the diameter) and divide that number by the length and width they measured of their desks.
Those two new numbers can be multiplied to find the answer.