Chapter 39: Circle Graphs
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Circle Graphs with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Percent (a ratio out of 100)
- Circle Graph (a graph using sectors of a circle to show parts of a whole)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
39.1 Meaning of circle graph
A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Meaning of circle graph .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: A category is 10% of a circle graph. Find its sector angle.
- Angle = 10% × 360°.
- 0.1×360=36°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Meaning of circle graph .
Answer: 36°
Worked Example 2
Problem: A category is 20% of a circle graph. Find its sector angle.
- Angle = 20% × 360°.
- 0.2×360=72°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Meaning of circle graph .
Answer: 72°
Worked Example 3
Problem: A category is 25% of a circle graph. Find its sector angle.
- Angle = 25% × 360°.
- 0.25×360=90°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Meaning of circle graph .
Answer: 90°
Worked Example 4
Problem: A category is 30% of a circle graph. Find its sector angle.
- Angle = 30% × 360°.
- 0.3×360=108°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Meaning of circle graph .
Answer: 108°
Worked Example 5
Problem: A category is 40% of a circle graph. Find its sector angle.
- Angle = 40% × 360°.
- 0.4×360=144°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Meaning of circle graph .
Answer: 144°
Worked Example 6
Problem: Find the mean of [4, 6, 8].
- Add the values: 18.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 6
Worked Example 7
Problem: Find the mean of [5, 9, 10, 12].
- Add the values: 36.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 9
Worked Example 8
Problem: Find the mean of [3, 7, 7, 11].
- Add the values: 28.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 7
Worked Example 9
Problem: Find the mean of [20, 25, 30].
- Add the values: 75.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 25
Worked Example 10
Problem: Find the mean of [6, 8, 9, 12, 15].
- Add the values: 50.
- Divide by 5.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 10
Practice Exercise
Create one new question about Meaning of circle graph. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.2 Whole circle as 100%
Whole circle as 100% is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Circle radius 3 cm. Find circumference.
- Use C=2πr.
- C≈18.85.
Very beginner explanation: Whole circle as 100% is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 18.85 cm
Worked Example 2
Problem: Circle radius 4 cm. Find circumference.
- Use C=2πr.
- C≈25.13.
Very beginner explanation: Whole circle as 100% is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 25.13 cm
Worked Example 3
Problem: Circle radius 5 cm. Find circumference.
- Use C=2πr.
- C≈31.42.
Very beginner explanation: Whole circle as 100% is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 31.42 cm
Worked Example 4
Problem: Circle radius 6 cm. Find circumference.
- Use C=2πr.
- C≈37.70.
Very beginner explanation: Whole circle as 100% is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 37.70 cm
Worked Example 5
Problem: Circle radius 7 cm. Find circumference.
- Use C=2πr.
- C≈43.98.
Very beginner explanation: Whole circle as 100% is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 43.98 cm
Worked Example 6
Problem: Explain Whole circle as 100% in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Whole circle as 100% becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Whole circle as 100% and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Whole circle as 100% becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Whole circle as 100% using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Whole circle as 100% becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Whole circle as 100% problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Whole circle as 100% becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Whole circle as 100% could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Whole circle as 100% becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Whole circle as 100%. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.3 Whole circle as 360 degrees
Whole circle as 360 degrees is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Circle radius 3 cm. Find circumference.
- Use C=2πr.
- C≈18.85.
Very beginner explanation: Whole circle as 360 degrees is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 18.85 cm
Worked Example 2
Problem: Circle radius 4 cm. Find circumference.
- Use C=2πr.
- C≈25.13.
Very beginner explanation: Whole circle as 360 degrees is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 25.13 cm
Worked Example 3
Problem: Circle radius 5 cm. Find circumference.
- Use C=2πr.
- C≈31.42.
Very beginner explanation: Whole circle as 360 degrees is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 31.42 cm
Worked Example 4
Problem: Circle radius 6 cm. Find circumference.
- Use C=2πr.
- C≈37.70.
Very beginner explanation: Whole circle as 360 degrees is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 37.70 cm
Worked Example 5
Problem: Circle radius 7 cm. Find circumference.
- Use C=2πr.
- C≈43.98.
Very beginner explanation: Whole circle as 360 degrees is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 43.98 cm
Worked Example 6
Problem: Explain Whole circle as 360 degrees in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Whole circle as 360 degrees becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Whole circle as 360 degrees and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Whole circle as 360 degrees becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Whole circle as 360 degrees using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Whole circle as 360 degrees becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Whole circle as 360 degrees problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Whole circle as 360 degrees becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Whole circle as 360 degrees could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Whole circle as 360 degrees becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Whole circle as 360 degrees. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.4 Converting percent to sector angle
Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting percent to sector angle .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of 80.
- 10% = 0.1.
- 0.1×80=8.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting percent to sector angle .
Answer: 8
Worked Example 2
Problem: Find 25% of 60.
- 25% = 0.25.
- 0.25×60=15.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting percent to sector angle .
Answer: 15
Worked Example 3
Problem: Find 15% of 120.
- 15% = 0.15.
- 0.15×120=18.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting percent to sector angle .
Answer: 18
Worked Example 4
Problem: Find 5% of 250.
- 5% = 0.05.
- 0.05×250=12.5.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting percent to sector angle .
Answer: 12.5
Worked Example 5
Problem: Find 13% of 75.
- 13% = 0.13.
- 0.13×75=9.75.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting percent to sector angle .
Answer: 9.75
Worked Example 6
Problem: Find 10% of 90.
- 10% = 0.1.
- 0.1 × 90 = 9.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 9
Worked Example 7
Problem: Find 25% of 64.
- 25% = 0.25.
- 0.25 × 64 = 16.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 16
Worked Example 8
Problem: Find 15% of 140.
- 15% = 0.15.
- 0.15 × 140 = 21.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 21
Worked Example 9
Problem: Find 5% of 260.
- 5% = 0.05.
- 0.05 × 260 = 13.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 13
Worked Example 10
Problem: Find 20% of 75.
- 20% = 0.2.
- 0.2 × 75 = 15.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 15
Practice Exercise
Create one new question about Converting percent to sector angle. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.5 Converting sector angle to percent
Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting sector angle to percent .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of 80.
- 10% = 0.1.
- 0.1×80=8.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting sector angle to percent .
Answer: 8
Worked Example 2
Problem: Find 25% of 60.
- 25% = 0.25.
- 0.25×60=15.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting sector angle to percent .
Answer: 15
Worked Example 3
Problem: Find 15% of 120.
- 15% = 0.15.
- 0.15×120=18.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting sector angle to percent .
Answer: 18
Worked Example 4
Problem: Find 5% of 250.
- 5% = 0.05.
- 0.05×250=12.5.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting sector angle to percent .
Answer: 12.5
Worked Example 5
Problem: Find 13% of 75.
- 13% = 0.13.
- 0.13×75=9.75.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting sector angle to percent .
Answer: 9.75
Worked Example 6
Problem: Find 10% of 90.
- 10% = 0.1.
- 0.1 × 90 = 9.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 9
Worked Example 7
Problem: Find 25% of 64.
- 25% = 0.25.
- 0.25 × 64 = 16.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 16
Worked Example 8
Problem: Find 15% of 140.
- 15% = 0.15.
- 0.15 × 140 = 21.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 21
Worked Example 9
Problem: Find 5% of 260.
- 5% = 0.05.
- 0.05 × 260 = 13.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 13
Worked Example 10
Problem: Find 20% of 75.
- 20% = 0.2.
- 0.2 × 75 = 15.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 15
Practice Exercise
Create one new question about Converting sector angle to percent. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.6 Creating circle graphs from percentages
Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Creating circle graphs from percentages .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of 80.
- 10% = 0.1.
- 0.1×80=8.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Creating circle graphs from percentages .
Answer: 8
Worked Example 2
Problem: Find 25% of 60.
- 25% = 0.25.
- 0.25×60=15.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Creating circle graphs from percentages .
Answer: 15
Worked Example 3
Problem: Find 15% of 120.
- 15% = 0.15.
- 0.15×120=18.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Creating circle graphs from percentages .
Answer: 18
Worked Example 4
Problem: Find 5% of 250.
- 5% = 0.05.
- 0.05×250=12.5.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Creating circle graphs from percentages .
Answer: 12.5
Worked Example 5
Problem: Find 13% of 75.
- 13% = 0.13.
- 0.13×75=9.75.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Creating circle graphs from percentages .
Answer: 9.75
Worked Example 6
Problem: Find 10% of 90.
- 10% = 0.1.
- 0.1 × 90 = 9.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 9
Worked Example 7
Problem: Find 25% of 64.
- 25% = 0.25.
- 0.25 × 64 = 16.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 16
Worked Example 8
Problem: Find 15% of 140.
- 15% = 0.15.
- 0.15 × 140 = 21.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 21
Worked Example 9
Problem: Find 5% of 260.
- 5% = 0.05.
- 0.05 × 260 = 13.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 13
Worked Example 10
Problem: Find 20% of 75.
- 20% = 0.2.
- 0.2 × 75 = 15.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 15
Practice Exercise
Create one new question about Creating circle graphs from percentages. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.7 Creating circle graphs from frequencies
A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Creating circle graphs from frequencies .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: A category is 10% of a circle graph. Find its sector angle.
- Angle = 10% × 360°.
- 0.1×360=36°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Creating circle graphs from frequencies .
Answer: 36°
Worked Example 2
Problem: A category is 20% of a circle graph. Find its sector angle.
- Angle = 20% × 360°.
- 0.2×360=72°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Creating circle graphs from frequencies .
Answer: 72°
Worked Example 3
Problem: A category is 25% of a circle graph. Find its sector angle.
- Angle = 25% × 360°.
- 0.25×360=90°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Creating circle graphs from frequencies .
Answer: 90°
Worked Example 4
Problem: A category is 30% of a circle graph. Find its sector angle.
- Angle = 30% × 360°.
- 0.3×360=108°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Creating circle graphs from frequencies .
Answer: 108°
Worked Example 5
Problem: A category is 40% of a circle graph. Find its sector angle.
- Angle = 40% × 360°.
- 0.4×360=144°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Creating circle graphs from frequencies .
Answer: 144°
Worked Example 6
Problem: A category is 10% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.1 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 36°
Worked Example 7
Problem: A category is 20% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.2 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 72°
Worked Example 8
Problem: A category is 25% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.25 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 90°
Worked Example 9
Problem: A category is 30% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.3 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 108°
Worked Example 10
Problem: A category is 40% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.4 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 144°
Practice Exercise
Create one new question about Creating circle graphs from frequencies. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.8 Reading circle graphs
A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Reading circle graphs .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: A category is 10% of a circle graph. Find its sector angle.
- Angle = 10% × 360°.
- 0.1×360=36°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Reading circle graphs .
Answer: 36°
Worked Example 2
Problem: A category is 20% of a circle graph. Find its sector angle.
- Angle = 20% × 360°.
- 0.2×360=72°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Reading circle graphs .
Answer: 72°
Worked Example 3
Problem: A category is 25% of a circle graph. Find its sector angle.
- Angle = 25% × 360°.
- 0.25×360=90°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Reading circle graphs .
Answer: 90°
Worked Example 4
Problem: A category is 30% of a circle graph. Find its sector angle.
- Angle = 30% × 360°.
- 0.3×360=108°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Reading circle graphs .
Answer: 108°
Worked Example 5
Problem: A category is 40% of a circle graph. Find its sector angle.
- Angle = 40% × 360°.
- 0.4×360=144°.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Reading circle graphs .
Answer: 144°
Worked Example 6
Problem: A category is 10% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.1 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 36°
Worked Example 7
Problem: A category is 20% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.2 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 72°
Worked Example 8
Problem: A category is 25% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.25 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 90°
Worked Example 9
Problem: A category is 30% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.3 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 108°
Worked Example 10
Problem: A category is 40% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.4 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 144°
Practice Exercise
Create one new question about Reading circle graphs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.9 Comparing categories
Comparing categories is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Comparing categories: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Comparing categories is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Comparing categories: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Comparing categories is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Comparing categories: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Comparing categories is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Comparing categories: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Comparing categories is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Comparing categories: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Comparing categories is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Comparing categories in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Comparing categories becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Comparing categories and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Comparing categories becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Comparing categories using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Comparing categories becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Comparing categories problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Comparing categories becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Comparing categories could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Comparing categories becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Comparing categories. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.10 Missing-sector problems
Missing-sector problems is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: A category is 10% of a circle graph. Find its sector angle.
- Angle = 10% × 360°.
- 0.1×360=36°.
Very beginner explanation: Missing-sector problems is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 36°
Worked Example 2
Problem: A category is 20% of a circle graph. Find its sector angle.
- Angle = 20% × 360°.
- 0.2×360=72°.
Very beginner explanation: Missing-sector problems is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 72°
Worked Example 3
Problem: A category is 25% of a circle graph. Find its sector angle.
- Angle = 25% × 360°.
- 0.25×360=90°.
Very beginner explanation: Missing-sector problems is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 90°
Worked Example 4
Problem: A category is 30% of a circle graph. Find its sector angle.
- Angle = 30% × 360°.
- 0.3×360=108°.
Very beginner explanation: Missing-sector problems is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 108°
Worked Example 5
Problem: A category is 40% of a circle graph. Find its sector angle.
- Angle = 40% × 360°.
- 0.4×360=144°.
Very beginner explanation: Missing-sector problems is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 144°
Worked Example 6
Problem: Explain Missing-sector problems in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Missing-sector problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Missing-sector problems and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Missing-sector problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Missing-sector problems using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Missing-sector problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Missing-sector problems problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Missing-sector problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Missing-sector problems could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Missing-sector problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Missing-sector problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.11 Circle graphs in surveys
A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in surveys .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in surveys .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in surveys .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in surveys .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in surveys .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in surveys .
Answer: Broaden the sample
Worked Example 6
Problem: A category is 10% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.1 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 36°
Worked Example 7
Problem: A category is 20% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.2 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 72°
Worked Example 8
Problem: A category is 25% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.25 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 90°
Worked Example 9
Problem: A category is 30% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.3 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 108°
Worked Example 10
Problem: A category is 40% of a circle graph. Find the sector angle.
- A full circle is 360°.
- Multiply 0.4 × 360°.
Very beginner explanation: A circle graph represents 100% with 360°, so 1% corresponds to 3.6°.
Answer: 144°
Practice Exercise
Create one new question about Circle graphs in surveys. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.12 Circle graphs in budgets
A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in budgets .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Paint a room
- Model wall area and paint coverage
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in budgets .
Answer: Estimate litres and cost
Worked Example 2
Problem: Tile a floor
- Model floor area and tile area
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in budgets .
Answer: Estimate tile count plus waste
Worked Example 3
Problem: Plan a school event
- Model attendance and cost per person
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in budgets .
Answer: Estimate total cost
Worked Example 4
Problem: Compare transportation
- Model fixed and per-kilometre costs
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in budgets .
Answer: Find a break-even distance
Worked Example 5
Problem: Plan monthly savings
- Model starting savings plus monthly deposits
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in budgets .
Answer: Predict when a goal is reached
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Circle graphs in budgets. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
39.13 Checking totals
Checking totals is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Checking totals: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Checking totals is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Checking totals: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Checking totals is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Checking totals: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Checking totals is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Checking totals: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Checking totals is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Checking totals: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Checking totals is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Checking totals in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Checking totals becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Checking totals and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Checking totals becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Checking totals using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Checking totals becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Checking totals problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Checking totals becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Checking totals could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Checking totals becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Checking totals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Meaning of circle graph . Show your reasoning and check your answer.
- Create and solve a new question about Whole circle as 100% . Show your reasoning and check your answer.
- Create and solve a new question about Whole circle as 360 degrees . Show your reasoning and check your answer.
- Create and solve a new question about Converting percent to sector angle . Show your reasoning and check your answer.
- Create and solve a new question about Converting sector angle to percent . Show your reasoning and check your answer.
- Create and solve a new question about Creating circle graphs from percentages . Show your reasoning and check your answer.
- Create and solve a new question about Creating circle graphs from frequencies . Show your reasoning and check your answer.
- Create and solve a new question about Reading circle graphs . Show your reasoning and check your answer.
- Create and solve a new question about Comparing categories . Show your reasoning and check your answer.
- Create and solve a new question about Missing-sector problems . Show your reasoning and check your answer.
- Create and solve a new question about Circle graphs in surveys . Show your reasoning and check your answer.
- Create and solve a new question about Circle graphs in budgets . Show your reasoning and check your answer.
Common Mistakes
- Using a biased or unrepresentative sample.
- Reading graph scales incorrectly.
- Treating a misleading graph as trustworthy without checking the axes.
- Assuming dependent events are independent.
- Using percentages in a circle graph that do not total 100%.
30 Review Questions and Answers
Q1. What is important to remember about Meaning of circle graph?
Answer: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Meaning of circle graph.
Q2. What is important to remember about Whole circle as 100%?
Answer: Whole circle as 100% is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q3. What is important to remember about Whole circle as 360 degrees?
Answer: Whole circle as 360 degrees is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q4. What is important to remember about Converting percent to sector angle?
Answer: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting percent to sector angle.
Q5. What is important to remember about Converting sector angle to percent?
Answer: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Converting sector angle to percent.
Q6. What is important to remember about Creating circle graphs from percentages?
Answer: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Creating circle graphs from percentages.
Q7. What is important to remember about Creating circle graphs from frequencies?
Answer: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Creating circle graphs from frequencies.
Q8. What is important to remember about Reading circle graphs?
Answer: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Reading circle graphs.
Q9. What is important to remember about Comparing categories?
Answer: Comparing categories is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Missing-sector problems?
Answer: Missing-sector problems is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q11. What is important to remember about Circle graphs in surveys?
Answer: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in surveys.
Q12. What is important to remember about Circle graphs in budgets?
Answer: A circle graph divides a circle into sectors to show parts of a whole. This topic focuses on Circle graphs in budgets.
Q13. What is important to remember about Checking totals?
Answer: Checking totals is an important Grade 7 idea in Circle Graphs. Identify what is known, what must be found, choose an appropriate strategy, 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 final answer is reasonable before accepting it.
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 of a calculation 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 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, check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q26. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q27. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q28. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q29. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q30. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.