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Chapter 39: Comparing Data Sets and Graphs

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

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

Key Technical Terms

  • Comparing means (The mean is found by adding all values and dividing by the number of values.)
  • Comparing medians (The median is the middle value after data are ordered.)
  • Comparing modes (The mode is the value that appears most often.)
  • Comparing centers of two data sets (Comparing centers of two data sets is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Comparing spread informally (Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Using graphs to compare groups (Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)

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.

39.1 Comparing means

The mean is found by adding all values and dividing by the number of values. 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 the mean of [4, 6, 8, 10].

  1. Add the values to get 28.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 7

Worked Example 2

Problem: Find the mean of [5, 7, 7, 9, 12].

  1. Add the values to get 40.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 8

Worked Example 3

Problem: Find the mean of [3, 5, 8, 8, 11].

  1. Add the values to get 35.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 7

Worked Example 4

Problem: Find the mean of [10, 12, 14, 16].

  1. Add the values to get 52.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 13

Worked Example 5

Problem: Find the mean of [2, 4, 6, 8, 10].

  1. Add the values to get 30.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 6

Worked Example 6

Problem: Find the mean of [1, 5, 5, 6, 13].

  1. Add the values to get 30.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 6

Worked Example 7

Problem: Find the mean of [20, 25, 25, 30].

  1. Add the values to get 100.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 25

Worked Example 8

Problem: Find the mean of [7, 8, 9, 10, 11].

  1. Add the values to get 45.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 9

Worked Example 9

Problem: Find the mean of [3, 3, 4, 5, 9].

  1. Add the values to get 24.
  2. Divide by 5.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 4.8

Worked Example 10

Problem: Find the mean of [12, 15, 18, 21].

  1. Add the values to get 66.
  2. Divide by 4.

Very beginner explanation: The mean shares the total equally among all data values.

Answer: 16.5

Practice Exercise

Create one new Grade 6 problem about Comparing means. 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.

39.2 Comparing medians

The median is the middle value after data are ordered. 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 the median of [4, 6, 8, 10].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 7

Worked Example 2

Problem: Find the median of [5, 7, 7, 9, 12].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 7

Worked Example 3

Problem: Find the median of [3, 5, 8, 8, 11].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 8

Worked Example 4

Problem: Find the median of [10, 12, 14, 16].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 13

Worked Example 5

Problem: Find the median of [2, 4, 6, 8, 10].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 6

Worked Example 6

Problem: Find the median of [1, 5, 5, 6, 13].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 5

Worked Example 7

Problem: Find the median of [20, 25, 25, 30].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 25

Worked Example 8

Problem: Find the median of [7, 8, 9, 10, 11].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 9

Worked Example 9

Problem: Find the median of [3, 3, 4, 5, 9].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 4

Worked Example 10

Problem: Find the median of [12, 15, 18, 21].

  1. Order the data.
  2. Find the middle value or average the two middle values.

Very beginner explanation: The median is based on position after ordering.

Answer: 16.5

Practice Exercise

Create one new Grade 6 problem about Comparing medians. 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.

39.3 Comparing modes

The mode is the value that appears most often. 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 the mode of [4, 6, 8, 10].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 2

Problem: Find the mode of [5, 7, 7, 9, 12].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 7

Worked Example 3

Problem: Find the mode of [3, 5, 8, 8, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 8

Worked Example 4

Problem: Find the mode of [10, 12, 14, 16].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 5

Problem: Find the mode of [2, 4, 6, 8, 10].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 6

Problem: Find the mode of [1, 5, 5, 6, 13].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 5

Worked Example 7

Problem: Find the mode of [20, 25, 25, 30].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 25

Worked Example 8

Problem: Find the mode of [7, 8, 9, 10, 11].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Worked Example 9

Problem: Find the mode of [3, 3, 4, 5, 9].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: 3

Worked Example 10

Problem: Find the mode of [12, 15, 18, 21].

  1. Count how often each value appears.

Very beginner explanation: The mode is the most frequent value.

Answer: No mode

Practice Exercise

Create one new Grade 6 problem about Comparing modes. 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.

39.4 Comparing centers of two data sets

Comparing centers of two data sets is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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 Comparing centers of two data sets. 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.

39.5 Comparing spread informally

Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally to analyze the values 10 and 6. What should be checked first?

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

Very beginner explanation: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally to analyze the values 14 and 9. What should be checked first?

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

Very beginner explanation: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally to analyze the values 3 and 11. What should be checked first?

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

Very beginner explanation: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally to analyze the values 24 and 8. What should be checked first?

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

Very beginner explanation: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally to analyze the values 9 and 3. What should be checked first?

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

Very beginner explanation: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally to analyze the values 29 and 16. What should be checked first?

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

Very beginner explanation: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally to analyze the values 25 and 10. What should be checked first?

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

Very beginner explanation: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally to analyze the values 7 and 16. What should be checked first?

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

Very beginner explanation: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally to analyze the values 20 and 12. What should be checked first?

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

Very beginner explanation: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally to analyze the values 28 and 3. What should be checked first?

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

Very beginner explanation: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 spread informally. 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.

39.6 Using graphs to compare groups

Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups to analyze the values 30 and 15. What should be checked first?

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

Very beginner explanation: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups to analyze the values 13 and 19. What should be checked first?

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

Very beginner explanation: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups to analyze the values 22 and 16. What should be checked first?

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

Very beginner explanation: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups to analyze the values 3 and 9. What should be checked first?

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

Very beginner explanation: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups to analyze the values 28 and 4. What should be checked first?

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

Very beginner explanation: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups to analyze the values 24 and 8. What should be checked first?

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

Very beginner explanation: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups to analyze the values 15 and 7. What should be checked first?

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

Very beginner explanation: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups to analyze the values 3 and 3. What should be checked first?

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

Very beginner explanation: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups to analyze the values 29 and 14. What should be checked first?

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

Very beginner explanation: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups to analyze the values 11 and 9. What should be checked first?

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

Very beginner explanation: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups. 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.

39.7 Reading graph scales

Reading graph scales is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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 Reading graph scales. 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.

39.8 Explaining similarities

Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities to analyze the values 17 and 19. What should be checked first?

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

Very beginner explanation: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities to analyze the values 30 and 9. What should be checked first?

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

Very beginner explanation: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities to analyze the values 9 and 2. What should be checked first?

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

Very beginner explanation: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities to analyze the values 8 and 13. What should be checked first?

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

Very beginner explanation: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities to analyze the values 5 and 19. What should be checked first?

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

Very beginner explanation: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities to analyze the values 5 and 7. What should be checked first?

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

Very beginner explanation: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities to analyze the values 18 and 14. What should be checked first?

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

Very beginner explanation: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities to analyze the values 20 and 9. What should be checked first?

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

Very beginner explanation: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities to analyze the values 5 and 18. What should be checked first?

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

Very beginner explanation: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities to analyze the values 18 and 12. What should be checked first?

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

Very beginner explanation: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining similarities. 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.

39.9 Explaining differences

Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences to analyze the values 13 and 7. What should be checked first?

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

Very beginner explanation: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences to analyze the values 28 and 10. What should be checked first?

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

Very beginner explanation: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences to analyze the values 29 and 5. What should be checked first?

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

Very beginner explanation: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences to analyze the values 3 and 10. What should be checked first?

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

Very beginner explanation: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences to analyze the values 5 and 3. What should be checked first?

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

Very beginner explanation: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences to analyze the values 10 and 17. What should be checked first?

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

Very beginner explanation: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences to analyze the values 6 and 8. What should be checked first?

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

Very beginner explanation: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences to analyze the values 24 and 9. What should be checked first?

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

Very beginner explanation: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences to analyze the values 14 and 18. What should be checked first?

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

Very beginner explanation: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences to analyze the values 28 and 20. What should be checked first?

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

Very beginner explanation: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences. 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.

39.10 Using central tendency to support a conclusion

Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion to analyze the values 25 and 11. What should be checked first?

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

Very beginner explanation: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion to analyze the values 2 and 12. What should be checked first?

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

Very beginner explanation: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion to analyze the values 28 and 7. What should be checked first?

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

Very beginner explanation: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion to analyze the values 5 and 18. What should be checked first?

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

Very beginner explanation: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion to analyze the values 20 and 8. What should be checked first?

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

Very beginner explanation: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion to analyze the values 2 and 8. What should be checked first?

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

Very beginner explanation: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion to analyze the values 30 and 19. What should be checked first?

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

Very beginner explanation: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion to analyze the values 17 and 12. What should be checked first?

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

Very beginner explanation: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion to analyze the values 21 and 18. What should be checked first?

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

Very beginner explanation: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion to analyze the values 23 and 10. What should be checked first?

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

Very beginner explanation: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using central tendency to support a conclusion. 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.

39.11 Choosing evidence from data

Choosing evidence from data is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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.

  1. They are numerical values.
  2. 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 Choosing evidence from 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.

39.12 Real-life comparison problems

Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems to analyze the values 25 and 7. What should be checked first?

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

Very beginner explanation: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems to analyze the values 28 and 9. What should be checked first?

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

Very beginner explanation: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems to analyze the values 20 and 7. What should be checked first?

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

Very beginner explanation: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems to analyze the values 15 and 6. What should be checked first?

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

Very beginner explanation: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems to analyze the values 13 and 11. What should be checked first?

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

Very beginner explanation: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems to analyze the values 2 and 10. What should be checked first?

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

Very beginner explanation: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems to analyze the values 24 and 3. What should be checked first?

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

Very beginner explanation: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems to analyze the values 7 and 12. What should be checked first?

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

Very beginner explanation: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems to analyze the values 28 and 17. What should be checked first?

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

Very beginner explanation: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems to analyze the values 28 and 13. What should be checked first?

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

Very beginner explanation: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems. 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.

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30 Review Questions and Answers

Q1. What is important to understand about Comparing means?

Answer: The mean is found by adding all values and dividing by the number of values.

Q2. What is important to understand about Comparing medians?

Answer: The median is the middle value after data are ordered.

Q3. What is important to understand about Comparing modes?

Answer: The mode is the value that appears most often.

Q4. What is important to understand about Comparing centers of two data sets?

Answer: Comparing centers of two data sets is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Comparing spread informally?

Answer: Comparing spread informally is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Using graphs to compare groups?

Answer: Using graphs to compare groups is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q7. What is important to understand about Reading graph scales?

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

Q8. What is important to understand about Explaining similarities?

Answer: Explaining similarities is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Explaining differences?

Answer: Explaining differences is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q10. What is important to understand about Using central tendency to support a conclusion?

Answer: Using central tendency to support a conclusion is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Choosing evidence from data?

Answer: Choosing evidence from data is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. 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 Real-life comparison problems?

Answer: Real-life comparison problems is a Grade 6 mathematics idea in Comparing Data Sets and Graphs. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. Why should you show your steps?

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

Q14. Why is estimation useful?

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

Q15. Why do units matter?

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

Q16. When should you round?

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

Q17. How can you check an answer?

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

Q18. What should you identify first in a word problem?

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

Q19. What makes a final answer complete?

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

Q20. What should you do if an answer seems unreasonable?

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

Q21. Why are diagrams useful?

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

Q22. Why are tables useful?

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

Q23. Why are graphs useful?

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

Q24. Why should you explain your reasoning?

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

Q25. Why can more than one strategy be correct?

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

Q26. What should you do before using a formula or rule?

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

Q27. How does practice help in mathematics?

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

Q28. 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.

Q29. Why should you compare an exact answer with an estimate?

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

Q30. What does representing mathematics mean?

Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.