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Chapter 40: Misleading Graphs and Critical Data Literacy

Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.

Grade 7Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
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Chapter Overview

This chapter teaches Misleading Graphs and Critical Data Literacy with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.

Key Technical Terms

  • Sample (a smaller group selected from a population)
  • Bias (an influence that can make results unrepresentative)
  • 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.

40.1 Truncated axes

Truncated axes is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: For y=2x+(1), find y when x=3.

  1. Substitute x=3.
  2. y=2(3)+(1)=7.

Very beginner explanation: Truncated axes is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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

Worked Example 2

Problem: For y=3x+(-2), find y when x=3.

  1. Substitute x=3.
  2. y=3(3)+(-2)=7.

Very beginner explanation: Truncated axes is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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

Worked Example 3

Problem: For y=0.5x+(4), find y when x=3.

  1. Substitute x=3.
  2. y=0.5(3)+(4)=5.5.

Very beginner explanation: Truncated axes is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 5.5

Worked Example 4

Problem: For y=-1x+(5), find y when x=3.

  1. Substitute x=3.
  2. y=-1(3)+(5)=2.

Very beginner explanation: Truncated axes is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 2

Worked Example 5

Problem: For y=4x+(0), find y when x=3.

  1. Substitute x=3.
  2. y=4(3)+(0)=12.

Very beginner explanation: Truncated axes is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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

Worked Example 6

Problem: Explain Truncated axes 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: Truncated axes 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 Truncated axes 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: Truncated axes 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 Truncated axes 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: Truncated axes 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 Truncated axes 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: Truncated axes 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 Truncated axes 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: Truncated axes 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 Truncated axes. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.2 Unequal intervals

Unequal intervals is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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

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

Very beginner explanation: Unequal intervals is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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

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

Very beginner explanation: Unequal intervals is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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

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

Very beginner explanation: Unequal intervals is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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

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

Very beginner explanation: Unequal intervals is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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

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

Very beginner explanation: Unequal intervals is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Unequal intervals 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: Unequal 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 Unequal intervals 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: Unequal 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 Unequal intervals 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: Unequal 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 Unequal intervals 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: Unequal 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 Unequal intervals 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: Unequal 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 Unequal intervals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.3 Distorted pictures

Distorted pictures is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Circle radius 3 cm. Find circumference.

  1. Use C=2πr.
  2. C≈18.85.

Very beginner explanation: Distorted pictures is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 18.85 cm

Worked Example 2

Problem: Circle radius 4 cm. Find circumference.

  1. Use C=2πr.
  2. C≈25.13.

Very beginner explanation: Distorted pictures is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 25.13 cm

Worked Example 3

Problem: Circle radius 5 cm. Find circumference.

  1. Use C=2πr.
  2. C≈31.42.

Very beginner explanation: Distorted pictures is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 31.42 cm

Worked Example 4

Problem: Circle radius 6 cm. Find circumference.

  1. Use C=2πr.
  2. C≈37.70.

Very beginner explanation: Distorted pictures is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 37.70 cm

Worked Example 5

Problem: Circle radius 7 cm. Find circumference.

  1. Use C=2πr.
  2. C≈43.98.

Very beginner explanation: Distorted pictures is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 43.98 cm

Worked Example 6

Problem: Explain Distorted pictures 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: Distorted pictures 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 Distorted pictures 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: Distorted pictures 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 Distorted pictures 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: Distorted pictures 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 Distorted pictures 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: Distorted pictures 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 Distorted pictures 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: Distorted pictures 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 Distorted pictures. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.4 Misleading scales

A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Misleading scales .

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.

  1. Multiply 6 by 2.

Very beginner explanation: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Misleading scales .

Answer: 12 cm

Worked Example 2

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

  1. Multiply 8 by 1.5.

Very beginner explanation: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Misleading scales .

Answer: 12 cm

Worked Example 3

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

  1. Multiply 14 by 0.5.

Very beginner explanation: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Misleading scales .

Answer: 7 cm

Worked Example 4

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

  1. Multiply 5 by 3.

Very beginner explanation: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Misleading scales .

Answer: 15 cm

Worked Example 5

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

  1. Multiply 2.5 by 4.

Very beginner explanation: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Misleading scales .

Answer: 10 cm

Worked Example 6

Problem: Explain Misleading 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: Misleading 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 Misleading 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: Misleading 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 Misleading 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: Misleading 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 Misleading 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: Misleading 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 Misleading 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: Misleading 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 Misleading scales. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.5 Cherry-picked data

Data are observations, measurements, or categories collected to answer questions. This topic focuses on Cherry-picked data .

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

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

Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Cherry-picked data .

Answer: Use a frequency table

Worked Example 2

Problem: Student heights

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

Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Cherry-picked data .

Answer: Measure in centimetres

Worked Example 3

Problem: Number of siblings

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

Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Cherry-picked data .

Answer: Count whole numbers

Worked Example 4

Problem: Survey every 10th student

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

Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Cherry-picked data .

Answer: Check that the list order does not create bias

Worked Example 5

Problem: Survey only basketball team members about school sports

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

Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Cherry-picked data .

Answer: Broaden the sample

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 Cherry-picked data. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.6 Missing labels

Missing labels is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Missing labels: Identify a correct example.

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

Very beginner explanation: Missing labels is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Missing labels: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: Missing labels is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Missing labels: Compare two cases.

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

Very beginner explanation: Missing labels is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Missing labels: Apply the idea in a real situation.

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

Very beginner explanation: Missing labels is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Missing labels: Create and check your own example.

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

Very beginner explanation: Missing labels is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Missing 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: Missing 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 Missing 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: Missing 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 Missing 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: Missing 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 Missing 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: Missing 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 Missing 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: Missing 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 Missing labels. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.7 Missing context

Missing context is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Missing context: Identify a correct example.

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

Very beginner explanation: Missing context is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Missing context: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: Missing context is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Missing context: Compare two cases.

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

Very beginner explanation: Missing context is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Missing context: Apply the idea in a real situation.

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

Very beginner explanation: Missing context is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Missing context: Create and check your own example.

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

Very beginner explanation: Missing context is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Missing context 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: Missing context 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 Missing context 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: Missing context 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 Missing context 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: Missing context 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 Missing context 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: Missing context 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 Missing context 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: Missing context 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 Missing context. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.8 Small samples

A sample is a smaller group selected from a population. This topic focuses on Small samples .

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

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

Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Small samples .

Answer: Use a frequency table

Worked Example 2

Problem: Student heights

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

Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Small samples .

Answer: Measure in centimetres

Worked Example 3

Problem: Number of siblings

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

Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Small samples .

Answer: Count whole numbers

Worked Example 4

Problem: Survey every 10th student

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

Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Small samples .

Answer: Check that the list order does not create bias

Worked Example 5

Problem: Survey only basketball team members about school sports

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

Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Small samples .

Answer: Broaden the sample

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 Small samples. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.9 Biased samples

A sample is a smaller group selected from a population. This topic focuses on Biased samples .

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

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

Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Biased samples .

Answer: Use a frequency table

Worked Example 2

Problem: Student heights

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

Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Biased samples .

Answer: Measure in centimetres

Worked Example 3

Problem: Number of siblings

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

Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Biased samples .

Answer: Count whole numbers

Worked Example 4

Problem: Survey every 10th student

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

Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Biased samples .

Answer: Check that the list order does not create bias

Worked Example 5

Problem: Survey only basketball team members about school sports

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

Very beginner explanation: A sample is a smaller group selected from a population. This topic focuses on Biased samples .

Answer: Broaden the sample

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 Biased samples. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.10 Comparing graph designs

Comparing graph designs is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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.

  1. can exaggerate a small difference
  2. Inspect the axis minimum

Very beginner explanation: Comparing graph designs is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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.

  1. creates unequal visual spacing
  2. Use equal intervals

Very beginner explanation: Comparing graph designs is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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.

  1. can exaggerate area
  2. Use simple bars

Very beginner explanation: Comparing graph designs is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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.

  1. cherry-picks data
  2. Look for the full time range

Very beginner explanation: Comparing graph designs is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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.

  1. weakens trust
  2. Check source and context

Very beginner explanation: Comparing graph designs is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Comparing graph designs 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: Comparing graph designs 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 graph designs 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: Comparing graph designs 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 graph designs 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: Comparing graph designs 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 graph designs 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: Comparing graph designs 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 graph designs 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: Comparing graph designs 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 graph designs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.11 Checking sources

Checking sources is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Checking sources: Identify a correct example.

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

Very beginner explanation: Checking sources is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Checking sources: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: Checking sources is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Checking sources: Compare two cases.

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

Very beginner explanation: Checking sources is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Checking sources: Apply the idea in a real situation.

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

Very beginner explanation: Checking sources is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Checking sources: Create and check your own example.

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

Very beginner explanation: Checking sources is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Checking sources 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: Checking sources 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 Checking sources 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: Checking sources 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 Checking sources 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: Checking sources 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 Checking sources 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: Checking sources 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 Checking sources 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: Checking sources 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 Checking sources. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.12 Evaluating claims

Evaluating claims is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Evaluating claims: Identify a correct example.

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

Very beginner explanation: Evaluating claims is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Evaluating claims: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: Evaluating claims is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Evaluating claims: Compare two cases.

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

Very beginner explanation: Evaluating claims is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Evaluating claims: Apply the idea in a real situation.

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

Very beginner explanation: Evaluating claims is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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: Evaluating claims: Create and check your own example.

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

Very beginner explanation: Evaluating claims is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Evaluating claims 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: Evaluating claims 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 Evaluating claims 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: Evaluating claims 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 Evaluating claims 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: Evaluating claims 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 Evaluating claims 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: Evaluating claims 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 Evaluating claims 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: Evaluating claims 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 Evaluating claims. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.13 Improving misleading graphs

A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Improving misleading graphs .

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.

  1. can exaggerate a small difference
  2. Inspect the axis minimum

Very beginner explanation: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Improving misleading graphs .

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.

  1. creates unequal visual spacing
  2. Use equal intervals

Very beginner explanation: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Improving misleading graphs .

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.

  1. can exaggerate area
  2. Use simple bars

Very beginner explanation: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Improving misleading graphs .

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.

  1. cherry-picks data
  2. Look for the full time range

Very beginner explanation: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Improving misleading graphs .

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

Worked Example 5

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

  1. weakens trust
  2. Check source and context

Very beginner explanation: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Improving misleading graphs .

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

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 Improving misleading graphs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

40.14 Making evidence-based conclusions

Making evidence-based conclusions is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 2^3.

  1. Multiply 2 by itself 3 times.

Very beginner explanation: Making evidence-based conclusions is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 8

Worked Example 2

Problem: Evaluate 3^2.

  1. Multiply 3 by itself 2 times.

Very beginner explanation: Making evidence-based conclusions is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 9

Worked Example 3

Problem: Evaluate 4^2.

  1. Multiply 4 by itself 2 times.

Very beginner explanation: Making evidence-based conclusions is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 16

Worked Example 4

Problem: Evaluate 5^3.

  1. Multiply 5 by itself 3 times.

Very beginner explanation: Making evidence-based conclusions is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 125

Worked Example 5

Problem: Evaluate 10^2.

  1. Multiply 10 by itself 2 times.

Very beginner explanation: Making evidence-based conclusions is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 100

Worked Example 6

Problem: Explain Making evidence-based conclusions 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: Making evidence-based conclusions 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 Making evidence-based conclusions 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: Making evidence-based conclusions 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 Making evidence-based conclusions 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: Making evidence-based conclusions 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 Making evidence-based conclusions 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: Making evidence-based conclusions 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 Making evidence-based conclusions 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: Making evidence-based conclusions 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 Making evidence-based conclusions. 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

  1. Create and solve a new question about Truncated axes . Show your reasoning and check your answer.
  2. Create and solve a new question about Unequal intervals . Show your reasoning and check your answer.
  3. Create and solve a new question about Distorted pictures . Show your reasoning and check your answer.
  4. Create and solve a new question about Misleading scales . Show your reasoning and check your answer.
  5. Create and solve a new question about Cherry-picked data . Show your reasoning and check your answer.
  6. Create and solve a new question about Missing labels . Show your reasoning and check your answer.
  7. Create and solve a new question about Missing context . Show your reasoning and check your answer.
  8. Create and solve a new question about Small samples . Show your reasoning and check your answer.
  9. Create and solve a new question about Biased samples . Show your reasoning and check your answer.
  10. Create and solve a new question about Comparing graph designs . Show your reasoning and check your answer.
  11. Create and solve a new question about Checking sources . Show your reasoning and check your answer.
  12. Create and solve a new question about Evaluating claims . 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%.
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30 Review Questions and Answers

Q1. What is important to remember about Truncated axes?

Answer: Truncated axes is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Unequal intervals?

Answer: Unequal intervals is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Distorted pictures?

Answer: Distorted pictures is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Misleading scales?

Answer: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Misleading scales.

Q5. What is important to remember about Cherry-picked data?

Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Cherry-picked data.

Q6. What is important to remember about Missing labels?

Answer: Missing labels is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Missing context?

Answer: Missing context is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Small samples?

Answer: A sample is a smaller group selected from a population. This topic focuses on Small samples.

Q9. What is important to remember about Biased samples?

Answer: A sample is a smaller group selected from a population. This topic focuses on Biased samples.

Q10. What is important to remember about Comparing graph designs?

Answer: Comparing graph designs is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Checking sources?

Answer: Checking sources is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Evaluating claims?

Answer: Evaluating claims is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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 Improving misleading graphs?

Answer: A misleading graph or claim gives an unfair or distorted impression of the data. This topic focuses on Improving misleading graphs.

Q14. What is important to remember about Making evidence-based conclusions?

Answer: Making evidence-based conclusions is an important Grade 7 idea in Misleading Graphs and Critical Data Literacy. 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.