Constructing Circle Graphs
Grade 7 math
Before the Lesson:
The grade sevens will be learning about constructing circle graphs/pie graphs. They have just
finished a unit on percent, so they will be using that knowledge to complete the circle graphs.
They also explored interpreting circle graphs in the first lesson (looking at what a circle is
comprised of, why some sections might be bigger than other sections, what each section
represents and tells the viewer). This topic is important because circle graphs are found in our
everyday lives in the news or on the internet to compare data. Visually representing data is an
important skill. In this lesson the students will be introduced to the topic of constructing circle
graphs and in the next class they will complete an activity involving creating circle graphs. This
activity along with my observations of the students working will allow me to determine if they
understand this topic. If they are able to turn raw data into a circle graph, I will know that they
have an understanding of how to create circle graphs. Technology will be useful in this lesson as
I will use the Smart Board to model working with a protractor and allow the students to come up
and interact with the protractor to make the circle graph. I will also use the white board and dry
erase markers for the students to model percentages of circles. I will also provide circles for them
to practice drawing circle graphs on and protractors to work with on their own if they do not
currently own one.
Materials: Smart Board, Extra Protractors, White Board, Dry Erase Markers, Circle Template
Sheet for each student
Accommodations: The room should be set up so that stronger students are placed beside weaker
math students and so that those who have trouble concentrating are seated at the front of the
room. The notes are given verbally and written on the Smart Board to accommodate different
learners.
Beginning of the Lesson (10 minutes):
Circle graphs can be constructed using a circle with marked increments and percents or by first
calculating degrees/ angles and using a protractor. First, I will ask a student to color in 100% of a
circle. Then I will ask another student to color in 50% of a circle. They will be encouraged to
explain how they knew. The students will become excited because these percentages of a circle
are relatively familiar to them and easy to see. I will ask another volunteer to color in 25% of the
circle and explain. I will ask the students how much of the circle is now colored (75% or color
75%).
Now what if I am not given a percent? What if I am given a fraction? How could I color in 10/20
of the circle?
10/20 = 1/2 = 50% or 10/20 = 50/100 = 50%
Or 5/20 of the circle?
5/20 = 1/4 = 25% or 5/20 = 25/100 = 25%
How much of the circle have I colored all together?
50% + 25% = 75%
How much is left? 25%
6
(Looking at parts of circles as fractions and percents allows the students to see multiple means of
representation)
Middle of the Lesson (Part A) (15 minutes):
After the students have investigated percents and fractions of circles, we will talk about degrees.
How many degrees are in a circle? (If no one responds reference snowboarding/skateboarding
‘360’)
What about if we only color in half (50%). How many degrees is covered by half of the circle?
360/2 = 180 degrees **This is called the central angle
What about one quarter (25%) of the circle? What is the central angle?
360/4 = 90 degrees or 180/2 = 90 degrees
Now that we know how many degrees are covered by 50% and 25%, can you figure out how
many degrees are covered by three quarters or 75% of the circle?
180 + 90 = 270 degrees
Now something a bit harder. What about 10% of the total 360 degrees. What would the central
angle be?
10% of 360 = 36
These percents are not too bad to figure out, but what about if I want to know what percent 12/20
covers?
12/20 = 60/100 = 60%
Thus, we know it is more than half but less than three quarters (between 50% and 75%).
60% = 50% + 10% = 180 + 36 = 216
Is there another way we could figure this out?
12/20 = 60%
60% of the whole circle = 60% of 360 degrees. Now thinking back to your blue sheet on
percents, how do you figure out 60% of something?
60% = 0.60
0.60 x 360 degrees = 216 degrees
Middle of the Lesson (Part B) (20 minutes):
Now we will move on to filling out the chart. First the students will fill out the percent column
on their own to review percents. **Make sure to point out the total at the bottom. I will circulate
to look for misrepresentations of the percents. Once they have completed that, I will have
students give their answers and we will go over it on the board and fill it in.
Next, we will do the first central angle together.
25% of 360 = 0.25 x 360 = 90
I will give them time to fill in the rest of the chart and then go over it as a class.
The question now is how to color in 90 degrees on the circle graph. We need protractors! I will
demonstrate it on the SMART board (they start with 0 each time) and then allow them to fill in
the graph themselves. We will then go over this on the SMART board.
End of the Lesson (2 minutes):
I will review the concept of central angles of circles and how to find the central angle once we
know the percent.