Analyzing and Creating Circle Graphs

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Objective

The students will be able to analyze and create venn diagrams and circle graphs

Big Idea

The students will be learning through exploration on how to analyze and create circle graphs and Venn diagrams.

DO NOW

10 minutes

For the DO NOW problem, I’m going to have the students make a list of characteristics of previously learned graphs.  For example, they can list all the elements in a line graph, bar graph, or line plot. (SMP 6) I will be using this for closure at the end when I have them create their Venn diagram. I’m looking for the following:

Line graph – shows change over time, x and y axis, labels, titles, connected lines and dots, can predict, equal intervals, scale starts at zero

Bar graph – shows popularity, x and y axis, labels, titles, separated bars, equal intervals, scale starts at zero, can see the mode

Line Plot – shows frequency, uses a number line and x’s or dots, title, label, can see median and mode

Students can share their responses with a partner to ensure enough information is collected.

Analyzing Circle Graphs and Venn Diagrams

60 minutes

My thoughts for the middle part of the lesson are to have the students answer questions about the graphs and discover the elements on their own.  Then they will use this knowledge to create their own circle graph and venn diagram. So for this lesson, I’m going to reference the slide number and the questions I will ask to get the students to critically and mathematically think of the display shown. (SMP 1, 2, 5, 6)

Slide 4 – Favorite Color (Circle graph with recognizable portions or benchmarks)

  • Ask the students what the circle graph is representing (Favorite color)How do you know (title)
  • How many students were surveyed (100)
  • What can you tell me about the sections of the graph? (1/2 is green, ¼ purple, ¼ orange)  ask for other ways to say this (percentages or decimals)  Add this data to the circle graph as they need this label
  • So, if 100 students were surveyed, how many like green? (50) How many like orange? (25) and How many like purple? (25)
  • What does the total circle represent? (100% or 1 whole)

Slide 5 – Favorite Pet(More sections and only a few benchmarks. Students will need to reason out the other sections)

  • What is this circle graph representing? (Favorite Pets) How do you know (title)
  • How many students were surveyed (100)
  • What can you tell me about the sections of the graph (1/2 dog, ¼ cat, ¼ bird and snake) Ask for Percentages and decimal equivalents.
  • If ¼ is a combination of bird and snake, can we tell how much each portion is worth? (estimate or we would need one of the numbers.)
  • So if bird was 10% of the circle, could you tell me what percentage chose snakes? (15%)
  • How many people chose dog? (50) How many chose cat (25) How many chose bird? (10) and How many chose snake? (15)

Slide 6 – Favorite Pizza topping (Benchmark portions, but with 200 people surveyed)

  • What does this circle graph represent (Favorite pizza toppings) How do you know (title)
  • How many people were surveyed (200).  How does this number relate to the color graph? (double)
  • What can you tell me about the sections of the graph (1/2 cheese, ¼ pepperoni, ¼ sausage)
  • So if 200 people were surveyed, how many chose cheese? (100) How many chose pepperoni (50) and How many chose sausage (50)
  • What do you notice about your answers compared to the color graph (data doubled)

Slide 7

  • What does this circle graph represent? (Amount of sleep)
  • How many people were surveyed? (60) 
  • What can you tell me about the sections of the graph (1/2 sleep 8 – 9 hours, ¼ sleep 10 – 11 hours, and ¼ sleep 6  -7 hours)
  • So if 60 people were surveyed, how many slept 8 – 9 hours? (30). How many slept 10 – 11 hours (15) and How many slept 6 – 7 hours?(15)
  • How can we know for sure our answers are correct?  (add the amount and it should equal 60)

Slide 8 Venn Diagram – 4 sided figures

  • What is the diagram representing (compare/contrast 4 sided figures, 2 sets of parallels and 1 set of parallels
  • How many 4 sided figures have 2 sets of parallels? (5)
  • How many 4 sided figures  have 1 set of parallels (2)
  • How many 4 sided figures can have both (1 quadrilateral)

Slide 9 – Factors of 18 and 24

  • What is the diagram representing (factors of 18 and 24)
  • How many factors does 18 have? (6) What are they? 
  • How many factors does 24 have? (8)What are they?
  • How many factors do they have in common?(4)(What are they?

Slide 10 – Favorite team (cubs and sox)

  • What teams could the people survey choose from (cubs, sox, or both)
  • Who likes the cubs?
  • Who likes the sox?
  • Who can’t decide?
  • How many people were surveyed. 

After the notes, have the students find a partner and work on the around the room or use it with white boards for a more formal assessment.  The around the room is in a power point.  If using for ATR, then print out a slide per page and hang around the room.  If using with white boards, then use as a power point.

Students will be working in pairs to complete 12 problems involving analyzing data in a circle graph and in a Venn Diagram.

  • Have students number a paper from 1 – 12 (Leaving work space for each problem)
  • Remind students to stay with their partner 
  • Only one group/problem.
  • All problems must be discussed  and agreed upon before moving to another problem.
  • Problems are placed around the room for the students to work on.  (I like to put the problems on index cards, construction paper or tag board so that I can use them again )

Closure

10 minutes

The students will be using data to create their own circle graph and venn diagram.  Collect this from them to show evidence of student learning.

Create your own circle graph with the following data.  Out of 100 people surveyed when asked what their favorite season was…

25 chose winter

25 chose fall

50 chose summer 

Create a Venn diagram comparing and contrasting line graphs, line (dot) plots, or bar graphs.  Choose any two.  Use the information from the DO NOW.