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Chapter 42: Stacked Bar 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 Stacked Bar Graphs in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Meaning of stacked bar graph (The mean is found by adding all values and dividing by the number of values.)
  • Parts of a whole within bars (Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar Graphs. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Categories (Categories is a Grade 6 mathematics idea in Stacked Bar Graphs. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Legends (Legends is a Grade 6 mathematics idea in Stacked Bar Graphs. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Reading segment values (Reading segment values is a Grade 6 mathematics idea in Stacked Bar Graphs. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Comparing totals (Comparing totals is a Grade 6 mathematics idea in Stacked Bar 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.

42.1 Meaning of stacked bar graph

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 Meaning of stacked bar 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.

42.2 Parts of a whole within bars

Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars 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: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars to analyze the values 20 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: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars to analyze the values 12 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: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars to analyze the values 12 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: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars to analyze the values 24 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: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars to analyze the values 3 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: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars 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: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars to analyze the values 23 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: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars 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: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars 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: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar 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 Parts of a whole within bars. 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.

42.3 Categories

Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories to analyze the values 25 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: Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories to analyze the values 9 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: Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories to analyze the values 7 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: Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories to analyze the values 2 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: Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories to analyze the values 5 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: Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories to analyze the values 5 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: Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories to analyze the values 19 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: Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories to analyze the values 18 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: Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories to analyze the values 14 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: Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories to analyze the values 22 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: Categories is a Grade 6 mathematics idea in Stacked Bar 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 Categories. 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.

42.4 Legends

Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends 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: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends to analyze the values 6 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: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends to analyze the values 5 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: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends to analyze the values 30 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: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends to analyze the values 21 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: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends to analyze the values 15 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: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends to analyze the values 13 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: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends to analyze the values 13 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: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends to analyze the values 26 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: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends to analyze the values 20 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: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Legends. 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.

42.5 Reading segment values

Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values to analyze the values 23 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: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values to analyze the values 4 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: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values to analyze the values 11 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: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values to analyze the values 10 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: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values to analyze the values 30 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: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values to analyze the values 25 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: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values to analyze the values 13 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: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values to analyze the values 29 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: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values to analyze the values 6 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: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values to analyze the values 8 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: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values. 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.

42.6 Comparing totals

Comparing totals is a Grade 6 mathematics idea in Stacked Bar 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 totals to analyze the values 21 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 totals is a Grade 6 mathematics idea in Stacked Bar 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 totals to analyze the values 29 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: Comparing totals is a Grade 6 mathematics idea in Stacked Bar 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 totals to analyze the values 11 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 totals is a Grade 6 mathematics idea in Stacked Bar 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 totals to analyze the values 23 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 totals is a Grade 6 mathematics idea in Stacked Bar 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 totals to analyze the values 13 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: Comparing totals is a Grade 6 mathematics idea in Stacked Bar 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 totals to analyze the values 16 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 totals is a Grade 6 mathematics idea in Stacked Bar 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 totals to analyze the values 27 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: Comparing totals is a Grade 6 mathematics idea in Stacked Bar 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 totals to analyze the values 19 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: Comparing totals is a Grade 6 mathematics idea in Stacked Bar 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 totals 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: Comparing totals is a Grade 6 mathematics idea in Stacked Bar 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 totals 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: Comparing totals is a Grade 6 mathematics idea in Stacked Bar 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 totals. 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.

42.7 Comparing category parts

Comparing category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts to analyze the values 4 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 category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts to analyze the values 24 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 category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts to analyze the values 3 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 category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts to analyze the values 2 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: Comparing category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts to analyze the values 11 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: Comparing category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts to analyze the values 4 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: Comparing category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts to analyze the values 21 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: Comparing category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts to analyze the values 13 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: Comparing category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts to analyze the values 13 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: Comparing category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts to analyze the values 2 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 category parts is a Grade 6 mathematics idea in Stacked Bar 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 category parts. 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.

42.8 Creating stacked bars

A stacked bar graph shows a total and how different parts contribute to that total. 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 stacked bar totals 30 students: 18 chose option A and the rest chose option B. How many chose B?

  1. Start with the total.
  2. Subtract the known segment.

Very beginner explanation: Each stacked segment is part of the full bar total.

Answer: 12 students

Worked Example 2

Problem: A stacked bar totals 30 students: 18 chose option A and the rest chose option B. How many chose B?

  1. Start with the total.
  2. Subtract the known segment.

Very beginner explanation: Each stacked segment is part of the full bar total.

Answer: 12 students

Worked Example 3

Problem: A stacked bar totals 30 students: 18 chose option A and the rest chose option B. How many chose B?

  1. Start with the total.
  2. Subtract the known segment.

Very beginner explanation: Each stacked segment is part of the full bar total.

Answer: 12 students

Worked Example 4

Problem: A stacked bar totals 30 students: 18 chose option A and the rest chose option B. How many chose B?

  1. Start with the total.
  2. Subtract the known segment.

Very beginner explanation: Each stacked segment is part of the full bar total.

Answer: 12 students

Worked Example 5

Problem: A stacked bar totals 30 students: 18 chose option A and the rest chose option B. How many chose B?

  1. Start with the total.
  2. Subtract the known segment.

Very beginner explanation: Each stacked segment is part of the full bar total.

Answer: 12 students

Worked Example 6

Problem: A stacked bar totals 30 students: 18 chose option A and the rest chose option B. How many chose B?

  1. Start with the total.
  2. Subtract the known segment.

Very beginner explanation: Each stacked segment is part of the full bar total.

Answer: 12 students

Worked Example 7

Problem: A stacked bar totals 30 students: 18 chose option A and the rest chose option B. How many chose B?

  1. Start with the total.
  2. Subtract the known segment.

Very beginner explanation: Each stacked segment is part of the full bar total.

Answer: 12 students

Worked Example 8

Problem: A stacked bar totals 30 students: 18 chose option A and the rest chose option B. How many chose B?

  1. Start with the total.
  2. Subtract the known segment.

Very beginner explanation: Each stacked segment is part of the full bar total.

Answer: 12 students

Worked Example 9

Problem: A stacked bar totals 30 students: 18 chose option A and the rest chose option B. How many chose B?

  1. Start with the total.
  2. Subtract the known segment.

Very beginner explanation: Each stacked segment is part of the full bar total.

Answer: 12 students

Worked Example 10

Problem: A stacked bar totals 30 students: 18 chose option A and the rest chose option B. How many chose B?

  1. Start with the total.
  2. Subtract the known segment.

Very beginner explanation: Each stacked segment is part of the full bar total.

Answer: 12 students

Practice Exercise

Create one new Grade 6 problem about Creating stacked bars. 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.

42.9 Choosing a useful scale

Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale 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: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale to analyze the values 5 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: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale to analyze the values 9 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: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale to analyze the values 5 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: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale to analyze the values 29 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: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale to analyze the values 4 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: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale to analyze the values 26 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: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale to analyze the values 25 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: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale to analyze the values 11 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: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale to analyze the values 4 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: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Choosing a useful scale. 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.

42.10 Percent stacked bars introduction

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.

  1. Think of 1% as 1/100.
  2. 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.

  1. Think of 5% as 5/100.
  2. 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.

  1. Think of 10% as 10/100.
  2. 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.

  1. Think of 20% as 20/100.
  2. 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.

  1. Think of 25% as 25/100.
  2. 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.

  1. Think of 50% as 50/100.
  2. 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.

  1. Think of 75% as 75/100.
  2. 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.

  1. Think of 15% as 15/100.
  2. 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.

  1. Think of 30% as 30/100.
  2. 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.

  1. Think of 40% as 40/100.
  2. 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 Percent stacked bars introduction. 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.

42.11 Interpreting changes

Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes to analyze the values 30 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: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes to analyze the values 11 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: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes to analyze the values 12 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: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes 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: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes to analyze the values 21 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: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes to analyze the values 13 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: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes to analyze the values 3 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: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes to analyze the values 19 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: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes to analyze the values 17 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: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes to analyze the values 4 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: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 Interpreting changes. 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.

42.12 Real-life stacked-bar data

Real-life stacked-bar data is a Grade 6 mathematics idea in Stacked Bar 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 Real-life stacked-bar 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.

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30 Review Questions and Answers

Q1. What is important to understand about Meaning of stacked bar graph?

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

Q2. What is important to understand about Parts of a whole within bars?

Answer: Parts of a whole within bars is a Grade 6 mathematics idea in Stacked Bar Graphs. 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 Categories?

Answer: Categories is a Grade 6 mathematics idea in Stacked Bar Graphs. 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 Legends?

Answer: Legends is a Grade 6 mathematics idea in Stacked Bar 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 Reading segment values?

Answer: Reading segment values is a Grade 6 mathematics idea in Stacked Bar 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 Comparing totals?

Answer: Comparing totals is a Grade 6 mathematics idea in Stacked Bar 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 Comparing category parts?

Answer: Comparing category parts is a Grade 6 mathematics idea in Stacked Bar 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 Creating stacked bars?

Answer: A stacked bar graph shows a total and how different parts contribute to that total.

Q9. What is important to understand about Choosing a useful scale?

Answer: Choosing a useful scale is a Grade 6 mathematics idea in Stacked Bar 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 Percent stacked bars introduction?

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

Q11. What is important to understand about Interpreting changes?

Answer: Interpreting changes is a Grade 6 mathematics idea in Stacked Bar 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 stacked-bar data?

Answer: Real-life stacked-bar data is a Grade 6 mathematics idea in Stacked Bar 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.