Grade 7 Math Chapter 38: Bar Graphs, Line Graphs, and Histograms

Chapter Overview

This chapter teaches Bar Graphs, Line Graphs, and Histograms with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.

Key Technical Terms

Circle Graph (a graph using sectors of a circle to show parts of a whole)
Estimate (a close approximation used to check whether an answer is reasonable)
Solution (a value or result that satisfies the problem)
Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
Reasonableness (whether an answer makes sense in the context of the problem)

How to Learn This Chapter

Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

38.1 Bar graphs

Bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate this graph issue: Axis starts at 95 instead of 0.

can exaggerate a small difference
Inspect the axis minimum

Very beginner explanation: Bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 2

Problem: Evaluate this graph issue: Intervals change from 1 to 10.

creates unequal visual spacing
Use equal intervals

Very beginner explanation: Bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 3

Problem: Evaluate this graph issue: 3D pictures are scaled in height and width.

can exaggerate area
Use simple bars

Very beginner explanation: Bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 4

Problem: Evaluate this graph issue: Only two favourable years are shown.

cherry-picks data
Look for the full time range

Very beginner explanation: Bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 5

Problem: Evaluate this graph issue: Graph has no source.

weakens trust
Check source and context

Very beginner explanation: Bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 6

Problem: Classify the data [4, 6, 8].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 7

Problem: Classify the data [5, 9, 10, 12].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 8

Problem: Classify the data [3, 7, 7, 11].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 9

Problem: Classify the data [20, 25, 30].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 10

Problem: Classify the data [6, 8, 9, 12, 15].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Practice Exercise

Create one new question about Bar graphs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.2 Double bar graphs

Double bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate this graph issue: Axis starts at 95 instead of 0.

can exaggerate a small difference
Inspect the axis minimum

Very beginner explanation: Double bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 2

Problem: Evaluate this graph issue: Intervals change from 1 to 10.

creates unequal visual spacing
Use equal intervals

Very beginner explanation: Double bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 3

Problem: Evaluate this graph issue: 3D pictures are scaled in height and width.

can exaggerate area
Use simple bars

Very beginner explanation: Double bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 4

Problem: Evaluate this graph issue: Only two favourable years are shown.

cherry-picks data
Look for the full time range

Very beginner explanation: Double bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 5

Problem: Evaluate this graph issue: Graph has no source.

weakens trust
Check source and context

Very beginner explanation: Double bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 6

Problem: Classify the data [4, 6, 8].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 7

Problem: Classify the data [5, 9, 10, 12].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 8

Problem: Classify the data [3, 7, 7, 11].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 9

Problem: Classify the data [20, 25, 30].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 10

Problem: Classify the data [6, 8, 9, 12, 15].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Practice Exercise

Create one new question about Double bar graphs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.3 Line graphs

Line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate this graph issue: Axis starts at 95 instead of 0.

can exaggerate a small difference
Inspect the axis minimum

Very beginner explanation: Line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 2

Problem: Evaluate this graph issue: Intervals change from 1 to 10.

creates unequal visual spacing
Use equal intervals

Very beginner explanation: Line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 3

Problem: Evaluate this graph issue: 3D pictures are scaled in height and width.

can exaggerate area
Use simple bars

Very beginner explanation: Line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 4

Problem: Evaluate this graph issue: Only two favourable years are shown.

cherry-picks data
Look for the full time range

Very beginner explanation: Line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 5

Problem: Evaluate this graph issue: Graph has no source.

weakens trust
Check source and context

Very beginner explanation: Line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 6

Problem: Classify the data [4, 6, 8].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 7

Problem: Classify the data [5, 9, 10, 12].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 8

Problem: Classify the data [3, 7, 7, 11].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 9

Problem: Classify the data [20, 25, 30].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 10

Problem: Classify the data [6, 8, 9, 12, 15].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Practice Exercise

Create one new question about Line graphs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.4 Broken-line graphs

Broken-line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate this graph issue: Axis starts at 95 instead of 0.

can exaggerate a small difference
Inspect the axis minimum

Very beginner explanation: Broken-line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 2

Problem: Evaluate this graph issue: Intervals change from 1 to 10.

creates unequal visual spacing
Use equal intervals

Very beginner explanation: Broken-line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 3

Problem: Evaluate this graph issue: 3D pictures are scaled in height and width.

can exaggerate area
Use simple bars

Very beginner explanation: Broken-line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 4

Problem: Evaluate this graph issue: Only two favourable years are shown.

cherry-picks data
Look for the full time range

Very beginner explanation: Broken-line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 5

Problem: Evaluate this graph issue: Graph has no source.

weakens trust
Check source and context

Very beginner explanation: Broken-line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 6

Problem: Classify the data [4, 6, 8].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 7

Problem: Classify the data [5, 9, 10, 12].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 8

Problem: Classify the data [3, 7, 7, 11].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 9

Problem: Classify the data [20, 25, 30].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 10

Problem: Classify the data [6, 8, 9, 12, 15].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Practice Exercise

Create one new question about Broken-line graphs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.5 Histograms

Histograms is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate this graph issue: Axis starts at 95 instead of 0.

can exaggerate a small difference
Inspect the axis minimum

Very beginner explanation: Histograms is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 2

Problem: Evaluate this graph issue: Intervals change from 1 to 10.

creates unequal visual spacing
Use equal intervals

Very beginner explanation: Histograms is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 3

Problem: Evaluate this graph issue: 3D pictures are scaled in height and width.

can exaggerate area
Use simple bars

Very beginner explanation: Histograms is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 4

Problem: Evaluate this graph issue: Only two favourable years are shown.

cherry-picks data
Look for the full time range

Very beginner explanation: Histograms is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 5

Problem: Evaluate this graph issue: Graph has no source.

weakens trust
Check source and context

Very beginner explanation: Histograms is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 6

Problem: Classify the data [4, 6, 8].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 7

Problem: Classify the data [5, 9, 10, 12].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 8

Problem: Classify the data [3, 7, 7, 11].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 9

Problem: Classify the data [20, 25, 30].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 10

Problem: Classify the data [6, 8, 9, 12, 15].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Practice Exercise

Create one new question about Histograms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.6 Graph titles

Graph titles is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Graph titles: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Graph titles is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Graph titles: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Graph titles is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Graph titles: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Graph titles is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Graph titles: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Graph titles is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Graph titles: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Graph titles is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Explain Graph titles in one simple sentence.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Graph titles becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Graph titles and explain why.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Graph titles becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Graph titles using a table, diagram, number line, graph, or equation.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Graph titles becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Graph titles problem, how can you check the answer?

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Graph titles becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Graph titles could be useful.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Graph titles becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Graph titles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.7 Axis labels

Axis labels is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate this graph issue: Axis starts at 95 instead of 0.

can exaggerate a small difference
Inspect the axis minimum

Very beginner explanation: Axis labels is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 2

Problem: Evaluate this graph issue: Intervals change from 1 to 10.

creates unequal visual spacing
Use equal intervals

Very beginner explanation: Axis labels is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 3

Problem: Evaluate this graph issue: 3D pictures are scaled in height and width.

can exaggerate area
Use simple bars

Very beginner explanation: Axis labels is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 4

Problem: Evaluate this graph issue: Only two favourable years are shown.

cherry-picks data
Look for the full time range

Very beginner explanation: Axis labels is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 5

Problem: Evaluate this graph issue: Graph has no source.

weakens trust
Check source and context

Very beginner explanation: Axis labels is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: The display may be misleading; revise it for fair comparison.

Worked Example 6

Problem: Explain Axis labels in one simple sentence.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Axis labels becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Axis labels and explain why.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Axis labels becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Axis labels using a table, diagram, number line, graph, or equation.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Axis labels becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Axis labels problem, how can you check the answer?

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Axis labels becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Axis labels could be useful.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Axis labels becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Axis labels. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.8 Scales

Scales is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Scale factor 2; original side 6 cm. Find image side.

Multiply 6 by 2.

Very beginner explanation: Scales is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 12 cm

Worked Example 2

Problem: Scale factor 1.5; original side 8 cm. Find image side.

Multiply 8 by 1.5.

Very beginner explanation: Scales is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 12 cm

Worked Example 3

Problem: Scale factor 0.5; original side 14 cm. Find image side.

Multiply 14 by 0.5.

Very beginner explanation: Scales is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 7 cm

Worked Example 4

Problem: Scale factor 3; original side 5 cm. Find image side.

Multiply 5 by 3.

Very beginner explanation: Scales is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 15 cm

Worked Example 5

Problem: Scale factor 4; original side 2.5 cm. Find image side.

Multiply 2.5 by 4.

Very beginner explanation: Scales is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 10 cm

Worked Example 6

Problem: Explain Scales in one simple sentence.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Scales becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Scales and explain why.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Scales becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Scales using a table, diagram, number line, graph, or equation.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Scales becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Scales problem, how can you check the answer?

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Scales becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Scales could be useful.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Scales becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Scales. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.9 Intervals

Intervals is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Favourite school subject

Classify it as categorical/qualitative data.
Choose an appropriate collection/organization method.

Very beginner explanation: Intervals is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Use a frequency table

Worked Example 2

Problem: Student heights

Classify it as quantitative continuous data.
Choose an appropriate collection/organization method.

Very beginner explanation: Intervals is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Measure in centimetres

Worked Example 3

Problem: Number of siblings

Classify it as quantitative discrete data.
Choose an appropriate collection/organization method.

Very beginner explanation: Intervals is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Count whole numbers

Worked Example 4

Problem: Survey every 10th student

Classify it as systematic sample.
Choose an appropriate collection/organization method.

Very beginner explanation: Intervals is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Check that the list order does not create bias

Worked Example 5

Problem: Survey only basketball team members about school sports

Classify it as biased sample.
Choose an appropriate collection/organization method.

Very beginner explanation: Intervals is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: Broaden the sample

Worked Example 6

Problem: Explain Intervals in one simple sentence.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Intervals becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Intervals and explain why.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Intervals becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Intervals using a table, diagram, number line, graph, or equation.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Intervals becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Intervals problem, how can you check the answer?

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Intervals becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Intervals could be useful.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Intervals becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Intervals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.10 Reading graphs

Reading graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Reading graphs: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Reading graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Reading graphs: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Reading graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Reading graphs: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Reading graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Reading graphs: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Reading graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Reading graphs: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Reading graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Explain Reading graphs in one simple sentence.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Reading graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Reading graphs and explain why.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Reading graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Reading graphs using a table, diagram, number line, graph, or equation.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Reading graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Reading graphs problem, how can you check the answer?

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Reading graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Reading graphs could be useful.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Reading graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Reading graphs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.11 Comparing graphs

Comparing graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Comparing graphs: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Comparing graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Comparing graphs: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Comparing graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Comparing graphs: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Comparing graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Comparing graphs: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Comparing graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Comparing graphs: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Comparing graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Explain Comparing graphs in one simple sentence.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Comparing graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Comparing graphs and explain why.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Comparing graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Comparing graphs using a table, diagram, number line, graph, or equation.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Comparing graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Comparing graphs problem, how can you check the answer?

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Comparing graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Comparing graphs could be useful.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Comparing graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Comparing graphs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.12 Choosing an appropriate graph

Choosing an appropriate graph is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Choosing an appropriate graph: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Choosing an appropriate graph is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Choosing an appropriate graph: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Choosing an appropriate graph is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Choosing an appropriate graph: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Choosing an appropriate graph is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Choosing an appropriate graph: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Choosing an appropriate graph is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Choosing an appropriate graph: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Choosing an appropriate graph is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Explain Choosing an appropriate graph in one simple sentence.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Choosing an appropriate graph becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Choosing an appropriate graph and explain why.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Choosing an appropriate graph becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Choosing an appropriate graph using a table, diagram, number line, graph, or equation.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Choosing an appropriate graph becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Choosing an appropriate graph problem, how can you check the answer?

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Choosing an appropriate graph becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Choosing an appropriate graph could be useful.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Choosing an appropriate graph becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Choosing an appropriate graph. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.13 Creating graphs

Creating graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Creating graphs: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Creating graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Creating graphs: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Creating graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Creating graphs: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Creating graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Creating graphs: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Creating graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Creating graphs: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Creating graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Explain Creating graphs in one simple sentence.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Creating graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Creating graphs and explain why.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Creating graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Creating graphs using a table, diagram, number line, graph, or equation.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Creating graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Creating graphs problem, how can you check the answer?

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Creating graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Creating graphs could be useful.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Creating graphs becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Creating graphs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

38.14 Interpreting trends

Interpreting trends is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Interpreting trends: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Interpreting trends is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Interpreting trends: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Interpreting trends is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Interpreting trends: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Interpreting trends is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Interpreting trends: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Interpreting trends is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Interpreting trends: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Interpreting trends is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Explain Interpreting trends in one simple sentence.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Interpreting trends becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Interpreting trends and explain why.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Interpreting trends becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Interpreting trends using a table, diagram, number line, graph, or equation.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Interpreting trends becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Interpreting trends problem, how can you check the answer?

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Interpreting trends becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Interpreting trends could be useful.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Interpreting trends becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Interpreting trends. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

Chapter Notes, Practice, and Common Mistakes

Chapter Notes

Read the complete question before choosing an operation, formula, graph, or model.
Write technical words together with their meaning until you are comfortable using them.
Show all important steps so another student can follow your reasoning.
Keep units, labels, signs, axes, variables, and mathematical symbols clear.
Estimate before or after calculating when an estimate can help check reasonableness.
For real-life problems, explain what the final number means in the situation.

Extra Practice

Create and solve a new question about Bar graphs . Show your reasoning and check your answer.
Create and solve a new question about Double bar graphs . Show your reasoning and check your answer.
Create and solve a new question about Line graphs . Show your reasoning and check your answer.
Create and solve a new question about Broken-line graphs . Show your reasoning and check your answer.
Create and solve a new question about Histograms . Show your reasoning and check your answer.
Create and solve a new question about Graph titles . Show your reasoning and check your answer.
Create and solve a new question about Axis labels . Show your reasoning and check your answer.
Create and solve a new question about Scales . Show your reasoning and check your answer.
Create and solve a new question about Intervals . Show your reasoning and check your answer.
Create and solve a new question about Reading graphs . Show your reasoning and check your answer.
Create and solve a new question about Comparing graphs . Show your reasoning and check your answer.
Create and solve a new question about Choosing an appropriate graph . Show your reasoning and check your answer.

Common Mistakes

Using a biased or unrepresentative sample.
Reading graph scales incorrectly.
Treating a misleading graph as trustworthy without checking the axes.
Assuming dependent events are independent.
Using percentages in a circle graph that do not total 100%.

30 Review Questions and Answers

Q1. What is important to remember about Bar graphs?

Answer: Bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q2. What is important to remember about Double bar graphs?

Answer: Double bar graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q3. What is important to remember about Line graphs?

Answer: Line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q4. What is important to remember about Broken-line graphs?

Answer: Broken-line graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q5. What is important to remember about Histograms?

Answer: Histograms is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q6. What is important to remember about Graph titles?

Answer: Graph titles is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q7. What is important to remember about Axis labels?

Answer: Axis labels is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q8. What is important to remember about Scales?

Answer: Scales is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q9. What is important to remember about Intervals?

Answer: Intervals is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q10. What is important to remember about Reading graphs?

Answer: Reading graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q11. What is important to remember about Comparing graphs?

Answer: Comparing graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q12. What is important to remember about Choosing an appropriate graph?

Answer: Choosing an appropriate graph is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q13. What is important to remember about Creating graphs?

Answer: Creating graphs is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q14. What is important to remember about Interpreting trends?

Answer: Interpreting trends is an important Grade 7 idea in Bar Graphs, Line Graphs, and Histograms. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q15. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q16. Why is estimation useful?

Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.

Q17. Why do units matter?

Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.

Q18. When should you round?

Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.

Q19. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.

Q20. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the relationship connecting them.

Q21. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q22. What should you do if an answer seems unreasonable?

Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.

Q23. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.

Q24. Why are tables useful?

Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.

Q25. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer you obtained.

Q26. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.

Q27. How should you study this chapter?

Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.

Q28. When is a calculator useful?

Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.

Q29. Why compare more than one strategy?

Answer: Different strategies can make a problem easier and provide a way to verify the result.

Q30. What is a mathematical model?

Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.