072e. Pie Charts and Divided Bar Graphs

Learning Intentions

• To understand that pie charts and divided bar graphs are used to represent proportions of a total
• Draw and Interpret a pie chart
• draw and interpret a divided bar Draw

Pre-requisite Summary

• Understand that a proportion compares a part to a whole
• Know that fractions, decimals and percentages can represent proportions
• Be able to Solve a fraction or percentage of a total
• Understand that a full circle represents a whole, or
• Know that a full angle around a point is
• Be able to label categories and frequencies clearly
• Understand that equal totals are important when comparing proportions in divided bar graphs
• Be able to Use a ruler and protractor accurately when constructing graphs

Worked Examples

Worked Example 1

a) Explain why pie charts and divided bar graphs are useful for showing proportions of a total.

b) State what the whole represents in a pie chart.

c) State what the whole represents in a divided bar graph.

Worked Example 2

A class survey gives:

• Sport:
• Music:
• Art: a) Draw a pie chart. b) Label each sector. c) State which category has the greatest proportion.

Worked Example 3

A group of students travel to school by:

• bus:
• car:
• walk: a) Convert each category to a proportion of the total. b) Draw a divided bar graph. c) Interpret the graph.

Worked Example 4

A pie chart shows the proportions of favourite fruits:

• apples:
• bananas:
• oranges: a) Convert each fraction to an angle. b) Draw the pie chart. c) Explain how the sector sizes show the proportions.

Worked Example 5

A divided bar graph shows the proportions of water use in a house:

• bathroom:
• kitchen:
• garden: a) Draw the divided bar graph. b) Label each section. c) State which section is the smallest.

Worked Example 6

A pie chart or divided bar graph is given.

a) Read the largest category.

b) Read the smallest category.

c) Estimate a proportion for one category.

Problems

Problem 1

a) Explain why pie charts and divided bar graphs are useful for showing proportions of a total.

b) State what the whole represents in a pie chart.

c) State what the whole represents in a divided bar graph.

Problem 2

A class survey gives:

• Reading:
• Gaming:
• Drawing: a) Draw a pie chart. b) Label each sector. c) State which category has the greatest proportion.

Problem 3

A group of students Choose lunch options:

• sandwich:
• pasta:
• sushi:
• salad: a) Convert each category to a proportion of the total. b) Draw a divided bar graph. c) Interpret the graph.

Problem 4

A pie chart shows the proportions of pets owned:

• dogs:
• cats:
• fish: a) Convert each fraction to an angle. b) Draw the pie chart. c) Explain how the sector sizes show the proportions.

Problem 5

A divided bar graph shows the proportions of time spent after school:

• homework:
• sport:
• screen time: a) Draw the divided bar graph. b) Label each section. c) State which section is the largest.

Problem 6

A pie chart or divided bar graph is given.

a) Read the largest category.

b) Read the smallest category.

c) Estimate a proportion for one category.

Exercises

Understanding and Fluency

Exercise 1.

State whether each graph type shows proportions of a whole:

a) pie chart

b) divided bar graph

c) line graph

Exercise 2.

For each graph, state what represents the whole:

a) the full circle in a pie chart

b) the full bar in a divided bar graph

c) one sector in a pie chart

Exercise 3.

Convert each percentage to an angle for a pie chart:

a)

b)

c)

Exercise 4.

Convert each percentage to an angle for a pie chart:

a)

b)

c)

Exercise 5.

Draw a pie chart for:

a) red

b) blue

c) green

Exercise 6.

Draw a pie chart for:

a) football

b) basketball

c) tennis

Exercise 7.

Draw a divided bar graph for:

a) apples

b) bananas

c) oranges

Exercise 8.

Draw a divided bar graph for:

a) walking

b) bus

c) car

Exercise 9.

Interpret the graph by stating:

a) the largest category

b) the smallest category

c) one category that is about one-quarter of the total

Exercise 10.

Interpret the graph by estimating:

a) a category that is about half the total

b) two categories that together make about

c) the difference in proportion between the largest and smallest categories

Reasoning

Exercise 11.

Explain why a pie chart is suitable for showing parts of a whole.

Exercise 12.

A student draws a pie chart but the sector angles add to . Explain the mistake.

Exercise 13.

Explain why the full bar in a divided bar graph must represent the same total each time.

Exercise 14.

A student says the tallest section in a divided bar graph means the largest proportion. Explain why this is incorrect.

Exercise 15.

Explain why larger sectors in a pie chart represent larger proportions.

Exercise 16.

A student labels a pie chart but does not include a title. Explain why this makes interpretation harder.

Problem-solving

Exercise 17.

A survey of favourite pets gives: dogs , cats , fish , birds .

a) Find the total.

b) Draw a divided bar graph.

c) State which pet is chosen by the greatest proportion.

Exercise 18.

A class of students chooses transport to school:

bus , car , walk , bike .

a) Convert each category to a fraction or percentage of the total.

b) Draw a pie chart.

c) Interpret the chart.

Exercise 19.

A daily time-use survey gives: sleep h, school h, homework h, leisure h.

a) Express each part as a proportion of h.

b) Draw a divided bar graph.

c) State which two categories are equal.

Exercise 20.

A pie chart shows spending in a week:

food ,

travel ,

entertainment ,

savings .

a) Draw the pie chart.

b) State the angle for food.

c) Identify the two equal categories.

Exercise 21.

A sports club survey gives: soccer , netball , swimming , tennis .

a) Draw a divided bar graph.

b) State the most popular sport.

c) Estimate how much more popular soccer is than tennis.

Exercise 22.

A pie chart is used to show favourite fruits in a class: apples , bananas , grapes , oranges .

a) Draw the chart.

b) State the angle for bananas.

c) Explain why apples take the largest sector.

Potential Misunderstandings

• Students may think pie charts and divided bar graphs show frequencies directly rather than proportions of a total
• Students may forget that the whole pie chart must add to
• Students may forget that the full divided bar must represent the entire total, or
• Students may convert percentages to angles incorrectly
• Students may draw sectors that do not match the calculated proportions
• Students may compare the height of sections in a divided bar graph instead of the length of each section
• Students may label categories unclearly or forget to include a title
• Students may think the largest category in a pie chart must always be more than half, which is not true