Chapter 50: Data Displays and Critical Data Literacy
Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.
What this chapter covers
This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.
50.1 Frequency tables
Frequency tables is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- Find the common difference: 3.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 2
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- Find the common difference: 4.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 3
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- Find the common difference: -2.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 4
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- Find the common difference: 0.5.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 5
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- Find the common difference: -2.5.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 7, 13, 19, ... for two more terms.
- Find the common difference: 6.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 25, 31
Worked Example 7
Problem: Continue the pattern -3, 2, 7, ... for two more terms.
- Find the common difference: 5.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 12, 17
Worked Example 8
Problem: Continue the pattern 0.5, 1.75, 3, ... for two more terms.
- Find the common difference: 1.25.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 4.25, 5.5
Worked Example 9
Problem: Continue the pattern 12, 9, 6, ... for two more terms.
- Find the common difference: -3.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 3, 0
Worked Example 10
Problem: Continue the pattern 100, 110, 120, ... for two more terms.
- Find the common difference: 10.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 130, 140
Practice exercise
Create one new Grade 8 problem involving Frequency tables. Show the important steps, include units when needed, and explain how you checked the answer.
50.2 Relative-frequency tables
Relative-frequency tables is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- Find the common difference: 3.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 2
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- Find the common difference: 4.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 3
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- Find the common difference: -2.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 4
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- Find the common difference: 0.5.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 5
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- Find the common difference: -2.5.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 7, 13, 19, ... for two more terms.
- Find the common difference: 6.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 25, 31
Worked Example 7
Problem: Continue the pattern -3, 2, 7, ... for two more terms.
- Find the common difference: 5.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 12, 17
Worked Example 8
Problem: Continue the pattern 0.5, 1.75, 3, ... for two more terms.
- Find the common difference: 1.25.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 4.25, 5.5
Worked Example 9
Problem: Continue the pattern 12, 9, 6, ... for two more terms.
- Find the common difference: -3.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 3, 0
Worked Example 10
Problem: Continue the pattern 100, 110, 120, ... for two more terms.
- Find the common difference: 10.
- Add the same difference each time.
Very beginner explanation: An arithmetic pattern changes by the same amount from one term to the next.
Answer: 130, 140
Practice exercise
Create one new Grade 8 problem involving Relative-frequency tables. Show the important steps, include units when needed, and explain how you checked the answer.
50.3 Bar graphs
Bar graphs is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify this data set: [4, 6, 8].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 2
Problem: Classify this data set: [5, 9, 10, 12].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 3
Problem: Classify this data set: [3, 7, 7, 11].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 4
Problem: Classify this data set: [20, 25, 30].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 5
Problem: Classify this data set: [6, 8, 9, 12, 15].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 6
Problem: Classify this data set: [2, 4, 4, 5, 20].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 7
Problem: Classify this data set: [10, 11, 12, 13, 14].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 8
Problem: Classify this data set: [1, 3, 5, 7, 9].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 9
Problem: Classify this data set: [8, 8, 8, 9, 10].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 10
Problem: Classify this data set: [15, 18, 21, 24, 27].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Practice exercise
Create one new Grade 8 problem involving Bar graphs. Show the important steps, include units when needed, and explain how you checked the answer.
50.4 Line graphs
Line graphs is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find the supplementary angle to 35°.
- Supplementary angles total 180°.
- 180° - 35° = 145°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 145°
Worked Example 2
Problem: Find the supplementary angle to 48°.
- Supplementary angles total 180°.
- 180° - 48° = 132°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 132°
Worked Example 3
Problem: Find the supplementary angle to 67°.
- Supplementary angles total 180°.
- 180° - 67° = 113°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 113°
Worked Example 4
Problem: Find the supplementary angle to 72°.
- Supplementary angles total 180°.
- 180° - 72° = 108°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 108°
Worked Example 5
Problem: Find the supplementary angle to 110°.
- Supplementary angles total 180°.
- 180° - 110° = 70°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 70°
Worked Example 6
Problem: Find the supplementary angle to 25°.
- Supplementary angles total 180°.
- 180° - 25° = 155°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 155°
Worked Example 7
Problem: Find the supplementary angle to 58°.
- Supplementary angles total 180°.
- 180° - 58° = 122°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 122°
Worked Example 8
Problem: Find the supplementary angle to 83°.
- Supplementary angles total 180°.
- 180° - 83° = 97°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 97°
Worked Example 9
Problem: Find the supplementary angle to 95°.
- Supplementary angles total 180°.
- 180° - 95° = 85°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 85°
Worked Example 10
Problem: Find the supplementary angle to 120°.
- Supplementary angles total 180°.
- 180° - 120° = 60°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 60°
Practice exercise
Create one new Grade 8 problem involving Line graphs. Show the important steps, include units when needed, and explain how you checked the answer.
50.5 Histograms
Histograms is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 50 cm
Worked Example 2
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 120 cm
Worked Example 3
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 275 cm
Worked Example 4
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 360 cm
Worked Example 5
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 405 cm
Worked Example 6
Problem: Convert 5.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 5.5 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 550 cm
Worked Example 7
Problem: Convert 7.25 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 7.25 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 725 cm
Worked Example 8
Problem: Convert 8.8 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 8.8 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 880 cm
Worked Example 9
Problem: Convert 10.1 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 10.1 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 1,010 cm
Worked Example 10
Problem: Convert 12.45 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 12.45 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 1,245 cm
Practice exercise
Create one new Grade 8 problem involving Histograms. Show the important steps, include units when needed, and explain how you checked the answer.
50.6 Circle graphs review
Circle graphs review is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify this data set: [4, 6, 8].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 2
Problem: Classify this data set: [5, 9, 10, 12].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 3
Problem: Classify this data set: [3, 7, 7, 11].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 4
Problem: Classify this data set: [20, 25, 30].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 5
Problem: Classify this data set: [6, 8, 9, 12, 15].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 6
Problem: Classify this data set: [2, 4, 4, 5, 20].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 7
Problem: Classify this data set: [10, 11, 12, 13, 14].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 8
Problem: Classify this data set: [1, 3, 5, 7, 9].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 9
Problem: Classify this data set: [8, 8, 8, 9, 10].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 10
Problem: Classify this data set: [15, 18, 21, 24, 27].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Practice exercise
Create one new Grade 8 problem involving Circle graphs review. Show the important steps, include units when needed, and explain how you checked the answer.
50.7 Infographics
Infographics is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify this data set: [4, 6, 8].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 2
Problem: Classify this data set: [5, 9, 10, 12].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 3
Problem: Classify this data set: [3, 7, 7, 11].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 4
Problem: Classify this data set: [20, 25, 30].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 5
Problem: Classify this data set: [6, 8, 9, 12, 15].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 6
Problem: Classify this data set: [2, 4, 4, 5, 20].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 7
Problem: Classify this data set: [10, 11, 12, 13, 14].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 8
Problem: Classify this data set: [1, 3, 5, 7, 9].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 9
Problem: Classify this data set: [8, 8, 8, 9, 10].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 10
Problem: Classify this data set: [15, 18, 21, 24, 27].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Practice exercise
Create one new Grade 8 problem involving Infographics. Show the important steps, include units when needed, and explain how you checked the answer.
50.8 Choosing an appropriate display
Choosing an appropriate display is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Choosing an appropriate display: Explain Choosing an appropriate display in one simple sentence.
- Look at the words in “Choosing an appropriate display”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Choosing an appropriate display is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Choosing an appropriate display: A student says, “I can use Choosing an appropriate display without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Choosing an appropriate display: What is the first step when solving a problem about Choosing an appropriate display?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Choosing an appropriate display: After solving a Choosing an appropriate display problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Choosing an appropriate display: Give one way Choosing an appropriate display could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Choosing an appropriate display can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Choosing an appropriate display: Which representation could help explain Choosing an appropriate display: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Choosing an appropriate display: A student gets an answer for Choosing an appropriate display but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Choosing an appropriate display: Why can estimation help before a detailed Choosing an appropriate display calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Choosing an appropriate display: How can you test whether your rule for Choosing an appropriate display works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Choosing an appropriate display: How would you teach Choosing an appropriate display to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Choosing an appropriate display. Show the important steps, include units when needed, and explain how you checked the answer.
50.9 Reading graph scales
Reading graph scales is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify this data set: [4, 6, 8].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 2
Problem: Classify this data set: [5, 9, 10, 12].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 3
Problem: Classify this data set: [3, 7, 7, 11].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 4
Problem: Classify this data set: [20, 25, 30].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 5
Problem: Classify this data set: [6, 8, 9, 12, 15].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 6
Problem: Classify this data set: [2, 4, 4, 5, 20].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 7
Problem: Classify this data set: [10, 11, 12, 13, 14].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 8
Problem: Classify this data set: [1, 3, 5, 7, 9].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 9
Problem: Classify this data set: [8, 8, 8, 9, 10].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 10
Problem: Classify this data set: [15, 18, 21, 24, 27].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Practice exercise
Create one new Grade 8 problem involving Reading graph scales. Show the important steps, include units when needed, and explain how you checked the answer.
50.10 Comparing data displays
Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Comparing data displays.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify this data set: [4, 6, 8].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 2
Problem: Classify this data set: [5, 9, 10, 12].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 3
Problem: Classify this data set: [3, 7, 7, 11].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 4
Problem: Classify this data set: [20, 25, 30].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 5
Problem: Classify this data set: [6, 8, 9, 12, 15].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 6
Problem: Classify this data set: [2, 4, 4, 5, 20].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 7
Problem: Classify this data set: [10, 11, 12, 13, 14].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 8
Problem: Classify this data set: [1, 3, 5, 7, 9].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 9
Problem: Classify this data set: [8, 8, 8, 9, 10].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 10
Problem: Classify this data set: [15, 18, 21, 24, 27].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Practice exercise
Create one new Grade 8 problem involving Comparing data displays. Show the important steps, include units when needed, and explain how you checked the answer.
50.11 Misleading graphs
Misleading graphs is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify this data set: [4, 6, 8].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 2
Problem: Classify this data set: [5, 9, 10, 12].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 3
Problem: Classify this data set: [3, 7, 7, 11].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 4
Problem: Classify this data set: [20, 25, 30].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 5
Problem: Classify this data set: [6, 8, 9, 12, 15].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 6
Problem: Classify this data set: [2, 4, 4, 5, 20].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 7
Problem: Classify this data set: [10, 11, 12, 13, 14].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 8
Problem: Classify this data set: [1, 3, 5, 7, 9].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 9
Problem: Classify this data set: [8, 8, 8, 9, 10].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 10
Problem: Classify this data set: [15, 18, 21, 24, 27].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Practice exercise
Create one new Grade 8 problem involving Misleading graphs. Show the important steps, include units when needed, and explain how you checked the answer.
50.12 Checking data sources
Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Checking data sources.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Classify this data set: [4, 6, 8].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 2
Problem: Classify this data set: [5, 9, 10, 12].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 3
Problem: Classify this data set: [3, 7, 7, 11].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 4
Problem: Classify this data set: [20, 25, 30].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 5
Problem: Classify this data set: [6, 8, 9, 12, 15].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 6
Problem: Classify this data set: [2, 4, 4, 5, 20].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 7
Problem: Classify this data set: [10, 11, 12, 13, 14].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 8
Problem: Classify this data set: [1, 3, 5, 7, 9].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 9
Problem: Classify this data set: [8, 8, 8, 9, 10].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Worked Example 10
Problem: Classify this data set: [15, 18, 21, 24, 27].
- The values are numerical.
- Ask whether they are counts or measurements.
Very beginner explanation: Quantitative data are numbers that represent counts or measurements.
Answer: Quantitative data
Practice exercise
Create one new Grade 8 problem involving Checking data sources. Show the important steps, include units when needed, and explain how you checked the answer.
50.13 Making evidence-based conclusions
Making evidence-based conclusions is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Making evidence-based conclusions: Explain Making evidence-based conclusions in one simple sentence.
- Look at the words in “Making evidence-based conclusions”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Making evidence-based conclusions is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Making evidence-based conclusions: A student says, “I can use Making evidence-based conclusions without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Making evidence-based conclusions: What is the first step when solving a problem about Making evidence-based conclusions?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Making evidence-based conclusions: After solving a Making evidence-based conclusions problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Making evidence-based conclusions: Give one way Making evidence-based conclusions could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Making evidence-based conclusions can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Making evidence-based conclusions: Which representation could help explain Making evidence-based conclusions: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Making evidence-based conclusions: A student gets an answer for Making evidence-based conclusions but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Making evidence-based conclusions: Why can estimation help before a detailed Making evidence-based conclusions calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Making evidence-based conclusions: How can you test whether your rule for Making evidence-based conclusions works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Making evidence-based conclusions: How would you teach Making evidence-based conclusions to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Making evidence-based conclusions. Show the important steps, include units when needed, and explain how you checked the answer.
Chapter 50 Review Questions and Answers
Q1. What is important to remember about Frequency tables?
Answer: Frequency tables is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q2. What is important to remember about Relative-frequency tables?
Answer: Relative-frequency tables is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q3. What is important to remember about Bar graphs?
Answer: Bar graphs is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q4. What is important to remember about Line graphs?
Answer: Line graphs is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q5. What is important to remember about Histograms?
Answer: Histograms is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Circle graphs review?
Answer: Circle graphs review is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q7. What is important to remember about Infographics?
Answer: Infographics is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Choosing an appropriate display?
Answer: Choosing an appropriate display is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q9. What is important to remember about Reading graph scales?
Answer: Reading graph scales is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Comparing data displays?
Answer: Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Comparing data displays.
Q11. What is important to remember about Misleading graphs?
Answer: Misleading graphs is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q12. What is important to remember about Checking data sources?
Answer: Data are observations, measurements, or categories collected to answer questions. In this section, the focus is Checking data sources.
Q13. What is important to remember about Making evidence-based conclusions?
Answer: Making evidence-based conclusions is an important Grade 8 concept in Data Displays and Critical Data Literacy. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a calculated answer is reasonable.
Q16. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the mathematical relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question and check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, rates, relationships, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer was obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.
Q26. When is a calculator useful?
Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.
Q27. Why compare more than one strategy?
Answer: Different strategies may make a problem easier and provide a way to verify the result.
Q28. What is mathematical communication?
Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.
Q29. What is mathematical modelling?
Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.
Q30. Why should assumptions be stated?
Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.