Grade 6 Math Chapter 44: Misleading Graphs and Critical Data Literacy

Chapter Overview

This chapter teaches Misleading Graphs and Critical Data Literacy in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

Truncated axes (Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Unequal intervals (Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Oversized pictures (Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Missing labels (Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Missing context (Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Small samples (A sample is a smaller group selected from a population.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

44.1 Truncated axes

Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Truncated axes to analyze the values 2 and 12. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Truncated axes to analyze the values 15 and 10. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Truncated axes to analyze the values 20 and 16. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Truncated axes to analyze the values 8 and 2. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Truncated axes to analyze the values 21 and 18. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Truncated axes to analyze the values 8 and 2. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Truncated axes to analyze the values 13 and 5. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Truncated axes to analyze the values 5 and 13. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Truncated axes to analyze the values 25 and 8. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Truncated axes to analyze the values 11 and 4. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Truncated axes. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

44.2 Unequal intervals

Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Unequal intervals to analyze the values 17 and 11. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Unequal intervals to analyze the values 15 and 11. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Unequal intervals to analyze the values 16 and 15. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Unequal intervals to analyze the values 26 and 15. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Unequal intervals to analyze the values 19 and 10. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Unequal intervals to analyze the values 27 and 3. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Unequal intervals to analyze the values 6 and 12. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Unequal intervals to analyze the values 5 and 18. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Unequal intervals to analyze the values 10 and 20. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Unequal intervals to analyze the values 23 and 13. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Unequal intervals. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

44.3 Oversized pictures

Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Oversized pictures to analyze the values 12 and 11. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Oversized pictures to analyze the values 25 and 5. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Oversized pictures to analyze the values 5 and 12. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Oversized pictures to analyze the values 3 and 4. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Oversized pictures to analyze the values 4 and 16. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Oversized pictures to analyze the values 25 and 20. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Oversized pictures to analyze the values 10 and 16. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Oversized pictures to analyze the values 26 and 5. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Oversized pictures to analyze the values 12 and 17. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Oversized pictures to analyze the values 20 and 10. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Oversized pictures. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

44.4 Missing labels

Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Missing labels to analyze the values 15 and 6. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Missing labels to analyze the values 23 and 15. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Missing labels to analyze the values 2 and 6. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Missing labels to analyze the values 19 and 14. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Missing labels to analyze the values 3 and 7. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Missing labels to analyze the values 18 and 11. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Missing labels to analyze the values 18 and 16. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Missing labels to analyze the values 16 and 14. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Missing labels to analyze the values 5 and 10. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Missing labels to analyze the values 4 and 13. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Missing labels. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

44.5 Missing context

Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Missing context to analyze the values 28 and 13. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Missing context to analyze the values 2 and 14. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Missing context to analyze the values 21 and 4. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Missing context to analyze the values 10 and 5. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Missing context to analyze the values 2 and 7. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Missing context to analyze the values 2 and 4. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Missing context to analyze the values 8 and 4. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Missing context to analyze the values 25 and 18. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Missing context to analyze the values 6 and 13. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Missing context to analyze the values 17 and 4. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Missing context. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

44.6 Small samples

A sample is a smaller group selected from a population. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Small samples. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

44.7 Biased samples

A sample is a smaller group selected from a population. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

The population is the full group of interest.
The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Biased samples. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

44.8 Cherry-picking data

Cherry-picking data is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify the data values [4, 6, 8, 10] as quantitative or qualitative.

They are numerical values.
Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 2

Problem: Classify the data values [5, 7, 7, 9, 12] as quantitative or qualitative.

They are numerical values.
Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 3

Problem: Classify the data values [3, 5, 8, 8, 11] as quantitative or qualitative.

They are numerical values.
Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 4

Problem: Classify the data values [10, 12, 14, 16] as quantitative or qualitative.

They are numerical values.
Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 5

Problem: Classify the data values [2, 4, 6, 8, 10] as quantitative or qualitative.

They are numerical values.
Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 6

Problem: Classify the data values [1, 5, 5, 6, 13] as quantitative or qualitative.

They are numerical values.
Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 7

Problem: Classify the data values [20, 25, 25, 30] as quantitative or qualitative.

They are numerical values.
Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 8

Problem: Classify the data values [7, 8, 9, 10, 11] as quantitative or qualitative.

They are numerical values.
Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 9

Problem: Classify the data values [3, 3, 4, 5, 9] as quantitative or qualitative.

They are numerical values.
Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 10

Problem: Classify the data values [12, 15, 18, 21] as quantitative or qualitative.

They are numerical values.
Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Practice Exercise

Create one new Grade 6 problem about Cherry-picking data. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

44.9 Misleading percentages

Percent means 'per hundred' and compares a quantity with 100 equal parts. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find 1% of 80.

Think of 1% as 1/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 0.8

Worked Example 2

Problem: Find 5% of 120.

Think of 5% as 5/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6

Worked Example 3

Problem: Find 10% of 64.

Think of 10% as 10/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6.4

Worked Example 4

Problem: Find 20% of 250.

Think of 20% as 20/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 50

Worked Example 5

Problem: Find 25% of 96.

Think of 25% as 25/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 24

Worked Example 6

Problem: Find 50% of 40.

Think of 50% as 50/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 20

Worked Example 7

Problem: Find 75% of 200.

Think of 75% as 75/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 150

Worked Example 8

Problem: Find 15% of 60.

Think of 15% as 15/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 9

Worked Example 9

Problem: Find 30% of 150.

Think of 30% as 30/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 45

Worked Example 10

Problem: Find 40% of 90.

Think of 40% as 40/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 36

Practice Exercise

Create one new Grade 6 problem about Misleading percentages. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.

44.10 Comparing graph designs

Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Comparing graph designs to analyze the values 20 and 4. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Comparing graph designs to analyze the values 2 and 10. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Comparing graph designs to analyze the values 9 and 5. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Comparing graph designs to analyze the values 21 and 16. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Comparing graph designs to analyze the values 8 and 2. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Comparing graph designs to analyze the values 22 and 19. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Comparing graph designs to analyze the values 3 and 10. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Comparing graph designs to analyze the values 10 and 18. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Comparing graph designs to analyze the values 19 and 5. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Comparing graph designs to analyze the values 5 and 11. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Comparing graph designs. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is ignoring the scale, labels, units, or the type of data shown.

44.11 Checking sources

Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Checking sources to analyze the values 11 and 7. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Checking sources to analyze the values 24 and 15. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Checking sources to analyze the values 8 and 7. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Checking sources to analyze the values 4 and 11. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Checking sources to analyze the values 28 and 4. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Checking sources to analyze the values 15 and 9. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Checking sources to analyze the values 3 and 4. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Checking sources to analyze the values 24 and 6. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Checking sources to analyze the values 19 and 17. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Checking sources to analyze the values 29 and 10. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Checking sources. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

44.12 Improving a misleading graph

Improving a misleading graph is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A bar graph starts its vertical axis at 95 instead of 0, making small differences look huge. What should you notice?

Check the axis starting value.
Compare the visual difference with the numerical difference.

Very beginner explanation: Graph design can change how strongly differences appear.

Answer: The truncated axis may exaggerate the differences.

Worked Example 2

Problem: A bar graph starts its vertical axis at 95 instead of 0, making small differences look huge. What should you notice?

Check the axis starting value.
Compare the visual difference with the numerical difference.

Very beginner explanation: Graph design can change how strongly differences appear.

Answer: The truncated axis may exaggerate the differences.

Worked Example 3

Problem: A bar graph starts its vertical axis at 95 instead of 0, making small differences look huge. What should you notice?

Check the axis starting value.
Compare the visual difference with the numerical difference.

Very beginner explanation: Graph design can change how strongly differences appear.

Answer: The truncated axis may exaggerate the differences.

Worked Example 4

Problem: A bar graph starts its vertical axis at 95 instead of 0, making small differences look huge. What should you notice?

Check the axis starting value.
Compare the visual difference with the numerical difference.

Very beginner explanation: Graph design can change how strongly differences appear.

Answer: The truncated axis may exaggerate the differences.

Worked Example 5

Problem: A bar graph starts its vertical axis at 95 instead of 0, making small differences look huge. What should you notice?

Check the axis starting value.
Compare the visual difference with the numerical difference.

Very beginner explanation: Graph design can change how strongly differences appear.

Answer: The truncated axis may exaggerate the differences.

Worked Example 6

Problem: A bar graph starts its vertical axis at 95 instead of 0, making small differences look huge. What should you notice?

Check the axis starting value.
Compare the visual difference with the numerical difference.

Very beginner explanation: Graph design can change how strongly differences appear.

Answer: The truncated axis may exaggerate the differences.

Worked Example 7

Problem: A bar graph starts its vertical axis at 95 instead of 0, making small differences look huge. What should you notice?

Check the axis starting value.
Compare the visual difference with the numerical difference.

Very beginner explanation: Graph design can change how strongly differences appear.

Answer: The truncated axis may exaggerate the differences.

Worked Example 8

Problem: A bar graph starts its vertical axis at 95 instead of 0, making small differences look huge. What should you notice?

Check the axis starting value.
Compare the visual difference with the numerical difference.

Very beginner explanation: Graph design can change how strongly differences appear.

Answer: The truncated axis may exaggerate the differences.

Worked Example 9

Problem: A bar graph starts its vertical axis at 95 instead of 0, making small differences look huge. What should you notice?

Check the axis starting value.
Compare the visual difference with the numerical difference.

Very beginner explanation: Graph design can change how strongly differences appear.

Answer: The truncated axis may exaggerate the differences.

Worked Example 10

Problem: A bar graph starts its vertical axis at 95 instead of 0, making small differences look huge. What should you notice?

Check the axis starting value.
Compare the visual difference with the numerical difference.

Very beginner explanation: Graph design can change how strongly differences appear.

Answer: The truncated axis may exaggerate the differences.

Practice Exercise

Create one new Grade 6 problem about Improving a misleading graph. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is ignoring the scale, labels, units, or the type of data shown.

44.13 Making evidence-based conclusions

Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Making evidence-based conclusions to analyze the values 5 and 19. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Making evidence-based conclusions to analyze the values 3 and 2. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Making evidence-based conclusions to analyze the values 17 and 15. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Making evidence-based conclusions to analyze the values 5 and 11. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Making evidence-based conclusions to analyze the values 3 and 6. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Making evidence-based conclusions to analyze the values 8 and 5. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Making evidence-based conclusions to analyze the values 18 and 12. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Making evidence-based conclusions to analyze the values 10 and 4. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Making evidence-based conclusions to analyze the values 23 and 5. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Making evidence-based conclusions to analyze the values 8 and 13. What should be checked first?

Identify what each value represents.
Choose the rule, representation, or comparison that matches the topic.
Show the reasoning before accepting the result.

Very beginner explanation: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Making evidence-based conclusions. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

30 Review Questions and Answers

Q1. What is important to understand about Truncated axes?

Answer: Truncated axes is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q2. What is important to understand about Unequal intervals?

Answer: Unequal intervals is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q3. What is important to understand about Oversized pictures?

Answer: Oversized pictures is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q4. What is important to understand about Missing labels?

Answer: Missing labels is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q5. What is important to understand about Missing context?

Answer: Missing context is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q6. What is important to understand about Small samples?

Answer: A sample is a smaller group selected from a population.

Q7. What is important to understand about Biased samples?

Answer: A sample is a smaller group selected from a population.

Q8. What is important to understand about Cherry-picking data?

Answer: Cherry-picking data is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q9. What is important to understand about Misleading percentages?

Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.

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

Answer: Comparing graph designs is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q11. What is important to understand about Checking sources?

Answer: Checking sources is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q12. What is important to understand about Improving a misleading graph?

Answer: Improving a misleading graph is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. What is important to understand about Making evidence-based conclusions?

Answer: Making evidence-based conclusions is a Grade 6 mathematics idea in Misleading Graphs and Critical Data Literacy. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q14. Why should you show your steps?

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

Q15. Why is estimation useful?

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

Q16. Why do units matter?

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

Q17. When should you round?

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

Q18. How can you check an answer?

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

Q19. What should you identify first in a word problem?

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

Q20. What makes a final answer complete?

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

Q21. What should you do if an answer seems unreasonable?

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

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships that are harder to see in words alone.

Q23. Why are tables useful?

Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.

Q24. Why are graphs useful?

Answer: Graphs make relationships, changes, trends, and comparisons visible.

Q25. Why should you explain your reasoning?

Answer: An explanation shows why a method works instead of only giving a final number.

Q26. Why can more than one strategy be correct?

Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.

Q27. What should you do before using a formula or rule?

Answer: Check what each quantity means and whether the rule matches the situation.

Q28. How does practice help in mathematics?

Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.

Q29. What is a good way to learn from a mistake?

Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.

Q30. Why should you compare an exact answer with an estimate?

Answer: The estimate gives a quick reasonableness check for the exact calculation.