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Chapter 43: Choosing and Creating Graphs

Learn Grade 5 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.

Grade 5Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
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Chapter Overview

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

Key Technical Terms

  • Bar graphs (a Grade 5 idea used in this chapter)
  • Double bar graphs (a Grade 5 idea used in this chapter)
  • Stacked-bar graphs (a Grade 5 idea used in this chapter)
  • Line graphs (a Grade 5 idea used in this chapter)
  • Choosing the best graph (a Grade 5 idea used in this chapter)
  • Graph titles (a Grade 5 idea used in this chapter)
  • Axis labels (a Grade 5 idea used in this chapter)
  • Using appropriate scales (a Grade 5 idea used in this chapter)
  • Citing a data source (a Grade 5 idea used in this chapter)
  • Explaining why a graph type fits the data (a Grade 5 idea used in this chapter)

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.

43.1 Bar graphs

Bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Bar graphs?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Worked Example 2

Problem: What should you identify first before solving a problem about Bar graphs?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Bar graphs.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Bar graphs problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Bar graphs.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Bar graphs can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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.

43.2 Double bar graphs

Double bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Double bar graphs?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Double bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Double bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Worked Example 2

Problem: What should you identify first before solving a problem about Double bar graphs?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Double bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Double bar graphs.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Double bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Double bar graphs problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Double bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Double bar graphs.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Double bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Double bar graphs can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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.

43.3 Stacked-bar graphs

Stacked-bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Stacked-bar graphs?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Stacked-bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Stacked-bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Worked Example 2

Problem: What should you identify first before solving a problem about Stacked-bar graphs?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Stacked-bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Stacked-bar graphs.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Stacked-bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Stacked-bar graphs problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Stacked-bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Stacked-bar graphs.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Stacked-bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Stacked-bar graphs can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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 Stacked-bar graphs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

43.4 Line graphs

Line graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Line graphs?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Line graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Line graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Worked Example 2

Problem: What should you identify first before solving a problem about Line graphs?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Line graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Line graphs.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Line graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Line graphs problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Line graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Line graphs.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Line graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Line graphs can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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.

43.5 Choosing the best graph

Choosing the best graph helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Choosing the best graph?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Choosing the best graph helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Choosing the best graph helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Worked Example 2

Problem: What should you identify first before solving a problem about Choosing the best graph?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Choosing the best graph helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Choosing the best graph.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Choosing the best graph helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Choosing the best graph problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Choosing the best graph helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Choosing the best graph.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Choosing the best graph helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Choosing the best graph can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Choosing the best graph in one simple sentence.

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

Very beginner explanation: Choosing the best 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 the best graph and explain why.

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

Very beginner explanation: Choosing the best 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 the best graph using a table, diagram, number line, graph, or equation.

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

Very beginner explanation: Choosing the best 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 the best graph problem, how can you check the answer?

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

Very beginner explanation: Choosing the best 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 the best graph could be useful.

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

Very beginner explanation: Choosing the best 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 the best graph. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

43.6 Graph titles

Graph titles helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Graph titles?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Graph titles helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Graph titles helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Worked Example 2

Problem: What should you identify first before solving a problem about Graph titles?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Graph titles helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Graph titles.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Graph titles helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Graph titles problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Graph titles helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Graph titles.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Graph titles helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Graph titles can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Graph titles in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. 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.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. 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.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. 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?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. 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.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. 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.

43.7 Axis labels

Axis labels is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Axis labels?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Axis labels is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: Axis labels is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Worked Example 2

Problem: What should you identify first before solving a problem about Axis labels?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Axis labels is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Axis labels.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Axis labels is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Axis labels problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Axis labels is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Axis labels.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Axis labels is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: Axis labels can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Axis labels in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. 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.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. 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.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. 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?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. 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.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. 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.

43.8 Using appropriate scales

Using appropriate scales is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Using appropriate scales?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Using appropriate scales is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: Using appropriate scales is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Worked Example 2

Problem: What should you identify first before solving a problem about Using appropriate scales?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Using appropriate scales is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Using appropriate scales.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Using appropriate scales is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Using appropriate scales problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Using appropriate scales is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Using appropriate scales.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Using appropriate scales is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: Using appropriate scales can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Using appropriate scales in one simple sentence.

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

Very beginner explanation: Using appropriate 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 Using appropriate scales and explain why.

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

Very beginner explanation: Using appropriate 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 Using appropriate scales using a table, diagram, number line, graph, or equation.

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

Very beginner explanation: Using appropriate 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 Using appropriate scales problem, how can you check the answer?

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

Very beginner explanation: Using appropriate 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 Using appropriate scales could be useful.

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

Very beginner explanation: Using appropriate 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 Using appropriate scales. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

43.9 Citing a data source

Citing a data source helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Citing a data source?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Citing a data source helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Citing a data source helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Worked Example 2

Problem: What should you identify first before solving a problem about Citing a data source?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Citing a data source helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Citing a data source.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Citing a data source helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Citing a data source problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Citing a data source helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Citing a data source.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Citing a data source helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Citing a data source can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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 Citing a data source. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

43.10 Explaining why a graph type fits the data

Explaining why a graph type fits the data helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Explaining why a graph type fits the data?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Explaining why a graph type fits the data helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Explaining why a graph type fits the data helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Worked Example 2

Problem: What should you identify first before solving a problem about Explaining why a graph type fits the data?

  1. Read the complete problem.
  2. Mark the information that is given.
  3. Identify exactly what the question asks you to find.

Very beginner explanation: Explaining why a graph type fits the data helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Explaining why a graph type fits the data.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Explaining why a graph type fits the data helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Explaining why a graph type fits the data problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Explaining why a graph type fits the data helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Explaining why a graph type fits the data.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Explaining why a graph type fits the data helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Explaining why a graph type fits the data can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

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

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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].

  1. These values are numerical.
  2. 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 Explaining why a graph type fits the data. 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 question before calculating.
  • Represent the mathematics with a model, table, graph, diagram, number line, or equation when useful.
  • Show the reasoning and check the final answer with a second method when possible.

Extra Practice

  1. Create and solve one original problem about Bar graphs.
  2. Create and solve one original problem about Double bar graphs.
  3. Create and solve one original problem about Stacked-bar graphs.
  4. Create and solve one original problem about Line graphs.
  5. Create and solve one original problem about Choosing the best graph.
  6. Create and solve one original problem about Graph titles.

Common Mistakes

  • Skipping the meaning and trying to memorize a rule only.
  • Using the wrong operation because the question was not read completely.
  • Ignoring units, labels, place values, or the context of the problem.
  • Not estimating or checking whether the final answer is reasonable.
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30 Review Questions and Answers

Q1. What is the key idea in Bar graphs?

Answer: Bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Q2. What is the key idea in Double bar graphs?

Answer: Double bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Q3. What is the key idea in Stacked-bar graphs?

Answer: Stacked-bar graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Q4. What is the key idea in Line graphs?

Answer: Line graphs helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Q5. What is the key idea in Choosing the best graph?

Answer: Choosing the best graph helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Q6. What is the key idea in Graph titles?

Answer: Graph titles helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Q7. What is the key idea in Axis labels?

Answer: Axis labels is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Q8. What is the key idea in Using appropriate scales?

Answer: Using appropriate scales is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Q9. What is the key idea in Citing a data source?

Answer: Citing a data source helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Q10. What is the key idea in Explaining why a graph type fits the data?

Answer: Explaining why a graph type fits the data helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Q11. Why should you estimate before or after a calculation?

Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.

Q12. Why are labels and units important?

Answer: They show what a number represents and help prevent mixing unlike quantities.

Q13. How can a diagram help solve a problem?

Answer: A diagram makes quantities and relationships visible before calculation.

Q14. How can inverse operations check an answer?

Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.

Q15. Why should you show steps?

Answer: Showing steps makes reasoning clear and helps find where an error happened.

Q16. What should you do after making a mistake?

Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.

Q17. How can a number line support reasoning?

Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.

Q18. When is a table useful?

Answer: A table organizes related values so patterns and comparisons are easier to see.

Q19. When is a graph useful?

Answer: A graph makes trends, comparisons, locations, or data patterns visible.

Q20. How do you decide which operation to use?

Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.

Q21. Why should you check place value?

Answer: A digit or decimal has a different value depending on its position.

Q22. What makes an answer reasonable?

Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.

Q23. How can you explain mathematical reasoning clearly?

Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.

Q24. Why can more than one strategy be correct?

Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.

Q25. How should you approach a difficult Grade 5 problem?

Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.

Q26. How can you practise Choosing and Creating Graphs effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q27. How can you practise Choosing and Creating Graphs effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q28. How can you practise Choosing and Creating Graphs effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q29. How can you practise Choosing and Creating Graphs effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.

Q30. How can you practise Choosing and Creating Graphs effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.