Chapter 20: Scale Factors, Scale Drawings, and Similarity
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Scale Factors, Scale Drawings, and Similarity with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Factor (a number that divides another number exactly)
- Mathematical Model (a mathematical representation of a real situation)
- 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.
20.1 Scale
Scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Scale factor 2; original side 6 cm. Find image side.
- Multiply 6 by 2.
Very beginner explanation: Scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12 cm
Worked Example 2
Problem: Scale factor 1.5; original side 8 cm. Find image side.
- Multiply 8 by 1.5.
Very beginner explanation: Scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12 cm
Worked Example 3
Problem: Scale factor 0.5; original side 14 cm. Find image side.
- Multiply 14 by 0.5.
Very beginner explanation: Scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7 cm
Worked Example 4
Problem: Scale factor 3; original side 5 cm. Find image side.
- Multiply 5 by 3.
Very beginner explanation: Scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 15 cm
Worked Example 5
Problem: Scale factor 4; original side 2.5 cm. Find image side.
- Multiply 2.5 by 4.
Very beginner explanation: Scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 10 cm
Worked Example 6
Problem: Explain Scale 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: Scale 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 Scale 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: Scale 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 Scale 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: Scale 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 Scale 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: Scale 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 Scale 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: Scale 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 Scale. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.2 Scale factor
A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Scale factor .
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: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Scale factor .
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Scale factor .
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Scale factor .
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Scale factor .
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Scale factor .
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 6
Problem: List all positive factors of 18.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 7
Problem: List all positive factors of 24.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 8
Problem: List all positive factors of 30.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Worked Example 9
Problem: List all positive factors of 42.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 7, 14, 21, 42
Worked Example 10
Problem: List all positive factors of 60.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Practice Exercise
Create one new question about Scale factor. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.3 Enlargement
Enlargement is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Enlargement: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Enlargement is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Enlargement: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Enlargement is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Enlargement: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Enlargement is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Enlargement: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Enlargement is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Enlargement: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Enlargement is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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 Enlargement 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: Enlargement 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 Enlargement 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: Enlargement 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 Enlargement 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: Enlargement 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 Enlargement 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: Enlargement 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 Enlargement 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: Enlargement 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 Enlargement. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.4 Reduction
Reduction is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Reduction: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Reduction is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Reduction: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Reduction is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Reduction: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Reduction is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Reduction: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Reduction is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Reduction: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Reduction is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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 Reduction 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: Reduction 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 Reduction 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: Reduction 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 Reduction 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: Reduction 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 Reduction 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: Reduction 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 Reduction 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: Reduction 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 Reduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.5 Scale drawings
Scale drawings is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Scale factor 2; original side 6 cm. Find image side.
- Multiply 6 by 2.
Very beginner explanation: Scale drawings is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12 cm
Worked Example 2
Problem: Scale factor 1.5; original side 8 cm. Find image side.
- Multiply 8 by 1.5.
Very beginner explanation: Scale drawings is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12 cm
Worked Example 3
Problem: Scale factor 0.5; original side 14 cm. Find image side.
- Multiply 14 by 0.5.
Very beginner explanation: Scale drawings is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7 cm
Worked Example 4
Problem: Scale factor 3; original side 5 cm. Find image side.
- Multiply 5 by 3.
Very beginner explanation: Scale drawings is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 15 cm
Worked Example 5
Problem: Scale factor 4; original side 2.5 cm. Find image side.
- Multiply 2.5 by 4.
Very beginner explanation: Scale drawings is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 10 cm
Worked Example 6
Problem: An original length is 8 cm and the scale factor is 0.5. Find the image length.
- Multiply the original length by the scale factor.
- 8 × 0.5 = 4.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 4 cm
Worked Example 7
Problem: An original length is 12 cm and the scale factor is 1.5. Find the image length.
- Multiply the original length by the scale factor.
- 12 × 1.5 = 18.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 18 cm
Worked Example 8
Problem: An original length is 19 cm and the scale factor is 2. Find the image length.
- Multiply the original length by the scale factor.
- 19 × 2 = 38.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 38 cm
Worked Example 9
Problem: An original length is 22 cm and the scale factor is 2.5. Find the image length.
- Multiply the original length by the scale factor.
- 22 × 2.5 = 55.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 55 cm
Worked Example 10
Problem: An original length is 25 cm and the scale factor is 3. Find the image length.
- Multiply the original length by the scale factor.
- 25 × 3 = 75.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 75 cm
Practice Exercise
Create one new question about Scale drawings. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.6 Maps
Maps is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Maps: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Maps is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Maps: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Maps is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Maps: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Maps is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Maps: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Maps is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Maps: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Maps is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: An original length is 8 cm and the scale factor is 0.5. Find the image length.
- Multiply the original length by the scale factor.
- 8 × 0.5 = 4.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 4 cm
Worked Example 7
Problem: An original length is 12 cm and the scale factor is 1.5. Find the image length.
- Multiply the original length by the scale factor.
- 12 × 1.5 = 18.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 18 cm
Worked Example 8
Problem: An original length is 19 cm and the scale factor is 2. Find the image length.
- Multiply the original length by the scale factor.
- 19 × 2 = 38.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 38 cm
Worked Example 9
Problem: An original length is 22 cm and the scale factor is 2.5. Find the image length.
- Multiply the original length by the scale factor.
- 22 × 2.5 = 55.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 55 cm
Worked Example 10
Problem: An original length is 25 cm and the scale factor is 3. Find the image length.
- Multiply the original length by the scale factor.
- 25 × 3 = 75.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 75 cm
Practice Exercise
Create one new question about Maps. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.7 Floor plans
Floor plans is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: 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: Floor plans is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
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: Floor plans is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
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: Floor plans is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
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: Floor plans is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
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: Floor plans is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Predict when a goal is reached
Worked Example 6
Problem: An original length is 8 cm and the scale factor is 0.5. Find the image length.
- Multiply the original length by the scale factor.
- 8 × 0.5 = 4.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 4 cm
Worked Example 7
Problem: An original length is 12 cm and the scale factor is 1.5. Find the image length.
- Multiply the original length by the scale factor.
- 12 × 1.5 = 18.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 18 cm
Worked Example 8
Problem: An original length is 19 cm and the scale factor is 2. Find the image length.
- Multiply the original length by the scale factor.
- 19 × 2 = 38.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 38 cm
Worked Example 9
Problem: An original length is 22 cm and the scale factor is 2.5. Find the image length.
- Multiply the original length by the scale factor.
- 22 × 2.5 = 55.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 55 cm
Worked Example 10
Problem: An original length is 25 cm and the scale factor is 3. Find the image length.
- Multiply the original length by the scale factor.
- 25 × 3 = 75.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 75 cm
Practice Exercise
Create one new question about Floor plans. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.8 Models
The mode is the value that occurs most often. This topic focuses on Models .
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: The mode is the value that occurs most often. This topic focuses on Models .
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: The mode is the value that occurs most often. This topic focuses on Models .
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: The mode is the value that occurs most often. This topic focuses on Models .
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: The mode is the value that occurs most often. This topic focuses on Models .
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: The mode is the value that occurs most often. This topic focuses on Models .
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 Models. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.9 Finding actual dimensions
Finding actual dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Finding actual dimensions: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Finding actual dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Finding actual dimensions: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Finding actual dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Finding actual dimensions: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Finding actual dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Finding actual dimensions: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Finding actual dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Finding actual dimensions: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Finding actual dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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 Finding actual dimensions 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: Finding actual dimensions 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 Finding actual dimensions 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: Finding actual dimensions 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 Finding actual dimensions 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: Finding actual dimensions 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 Finding actual dimensions 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: Finding actual dimensions 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 Finding actual dimensions 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: Finding actual dimensions 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 Finding actual dimensions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.10 Finding drawing dimensions
Finding drawing dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Finding drawing dimensions: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Finding drawing dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Finding drawing dimensions: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Finding drawing dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Finding drawing dimensions: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Finding drawing dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Finding drawing dimensions: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Finding drawing dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Finding drawing dimensions: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Finding drawing dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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 Finding drawing dimensions 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: Finding drawing dimensions 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 Finding drawing dimensions 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: Finding drawing dimensions 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 Finding drawing dimensions 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: Finding drawing dimensions 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 Finding drawing dimensions 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: Finding drawing dimensions 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 Finding drawing dimensions 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: Finding drawing dimensions 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 Finding drawing dimensions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.11 Similar figures
Similar figures have the same shape and proportional corresponding lengths. This topic focuses on Similar figures .
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: Scale factor 2; original side 6 cm. Find image side.
- Multiply 6 by 2.
Very beginner explanation: Similar figures have the same shape and proportional corresponding lengths. This topic focuses on Similar figures .
Answer: 12 cm
Worked Example 2
Problem: Scale factor 1.5; original side 8 cm. Find image side.
- Multiply 8 by 1.5.
Very beginner explanation: Similar figures have the same shape and proportional corresponding lengths. This topic focuses on Similar figures .
Answer: 12 cm
Worked Example 3
Problem: Scale factor 0.5; original side 14 cm. Find image side.
- Multiply 14 by 0.5.
Very beginner explanation: Similar figures have the same shape and proportional corresponding lengths. This topic focuses on Similar figures .
Answer: 7 cm
Worked Example 4
Problem: Scale factor 3; original side 5 cm. Find image side.
- Multiply 5 by 3.
Very beginner explanation: Similar figures have the same shape and proportional corresponding lengths. This topic focuses on Similar figures .
Answer: 15 cm
Worked Example 5
Problem: Scale factor 4; original side 2.5 cm. Find image side.
- Multiply 2.5 by 4.
Very beginner explanation: Similar figures have the same shape and proportional corresponding lengths. This topic focuses on Similar figures .
Answer: 10 cm
Worked Example 6
Problem: An original length is 8 cm and the scale factor is 0.5. Find the image length.
- Multiply the original length by the scale factor.
- 8 × 0.5 = 4.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 4 cm
Worked Example 7
Problem: An original length is 12 cm and the scale factor is 1.5. Find the image length.
- Multiply the original length by the scale factor.
- 12 × 1.5 = 18.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 18 cm
Worked Example 8
Problem: An original length is 19 cm and the scale factor is 2. Find the image length.
- Multiply the original length by the scale factor.
- 19 × 2 = 38.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 38 cm
Worked Example 9
Problem: An original length is 22 cm and the scale factor is 2.5. Find the image length.
- Multiply the original length by the scale factor.
- 22 × 2.5 = 55.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 55 cm
Worked Example 10
Problem: An original length is 25 cm and the scale factor is 3. Find the image length.
- Multiply the original length by the scale factor.
- 25 × 3 = 75.
Very beginner explanation: A scale factor multiplies every corresponding length by the same amount.
Answer: 75 cm
Practice Exercise
Create one new question about Similar figures. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.12 Corresponding sides
Corresponding sides is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Scale factor 2; original side 6 cm. Find image side.
- Multiply 6 by 2.
Very beginner explanation: Corresponding sides is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12 cm
Worked Example 2
Problem: Scale factor 1.5; original side 8 cm. Find image side.
- Multiply 8 by 1.5.
Very beginner explanation: Corresponding sides is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12 cm
Worked Example 3
Problem: Scale factor 0.5; original side 14 cm. Find image side.
- Multiply 14 by 0.5.
Very beginner explanation: Corresponding sides is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7 cm
Worked Example 4
Problem: Scale factor 3; original side 5 cm. Find image side.
- Multiply 5 by 3.
Very beginner explanation: Corresponding sides is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 15 cm
Worked Example 5
Problem: Scale factor 4; original side 2.5 cm. Find image side.
- Multiply 2.5 by 4.
Very beginner explanation: Corresponding sides is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 10 cm
Worked Example 6
Problem: Explain Corresponding sides 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: Corresponding sides 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 Corresponding sides 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: Corresponding sides 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 Corresponding sides 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: Corresponding sides 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 Corresponding sides 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: Corresponding sides 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 Corresponding sides 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: Corresponding sides 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 Corresponding sides. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.13 Perimeter and scale
Perimeter and scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Scale factor 2; original side 6 cm. Find image side.
- Multiply 6 by 2.
Very beginner explanation: Perimeter and scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12 cm
Worked Example 2
Problem: Scale factor 1.5; original side 8 cm. Find image side.
- Multiply 8 by 1.5.
Very beginner explanation: Perimeter and scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12 cm
Worked Example 3
Problem: Scale factor 0.5; original side 14 cm. Find image side.
- Multiply 14 by 0.5.
Very beginner explanation: Perimeter and scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7 cm
Worked Example 4
Problem: Scale factor 3; original side 5 cm. Find image side.
- Multiply 5 by 3.
Very beginner explanation: Perimeter and scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 15 cm
Worked Example 5
Problem: Scale factor 4; original side 2.5 cm. Find image side.
- Multiply 2.5 by 4.
Very beginner explanation: Perimeter and scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 10 cm
Worked Example 6
Problem: Find the perimeter of a rectangle 5 cm by 2 cm.
- Use P = 2(l + w).
- P = 2(5+2).
Very beginner explanation: Perimeter measures the total distance around a 2D figure.
Answer: 14 cm
Worked Example 7
Problem: Find the perimeter of a rectangle 6 cm by 3 cm.
- Use P = 2(l + w).
- P = 2(6+3).
Very beginner explanation: Perimeter measures the total distance around a 2D figure.
Answer: 18 cm
Worked Example 8
Problem: Find the perimeter of a rectangle 7 cm by 4 cm.
- Use P = 2(l + w).
- P = 2(7+4).
Very beginner explanation: Perimeter measures the total distance around a 2D figure.
Answer: 22 cm
Worked Example 9
Problem: Find the perimeter of a rectangle 8 cm by 5 cm.
- Use P = 2(l + w).
- P = 2(8+5).
Very beginner explanation: Perimeter measures the total distance around a 2D figure.
Answer: 26 cm
Worked Example 10
Problem: Find the perimeter of a rectangle 9 cm by 6 cm.
- Use P = 2(l + w).
- P = 2(9+6).
Very beginner explanation: Perimeter measures the total distance around a 2D figure.
Answer: 30 cm
Practice Exercise
Create one new question about Perimeter and scale. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
20.14 Real-life design applications
Real-life design applications is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Real-life design applications: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Real-life design applications is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Real-life design applications: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Real-life design applications is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Real-life design applications: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Real-life design applications is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Real-life design applications: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Real-life design applications is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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: Real-life design applications: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Real-life design applications is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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 Real-life design applications 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: Real-life design applications 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 Real-life design applications 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: Real-life design applications 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 Real-life design applications 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: Real-life design applications 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 Real-life design applications 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: Real-life design applications 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 Real-life design applications 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: Real-life design applications 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 Real-life design applications. 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 Scale . Show your reasoning and check your answer.
- Create and solve a new question about Scale factor . Show your reasoning and check your answer.
- Create and solve a new question about Enlargement . Show your reasoning and check your answer.
- Create and solve a new question about Reduction . Show your reasoning and check your answer.
- Create and solve a new question about Scale drawings . Show your reasoning and check your answer.
- Create and solve a new question about Maps . Show your reasoning and check your answer.
- Create and solve a new question about Floor plans . Show your reasoning and check your answer.
- Create and solve a new question about Models . Show your reasoning and check your answer.
- Create and solve a new question about Finding actual dimensions . Show your reasoning and check your answer.
- Create and solve a new question about Finding drawing dimensions . Show your reasoning and check your answer.
- Create and solve a new question about Similar figures . Show your reasoning and check your answer.
- Create and solve a new question about Corresponding sides . Show your reasoning and check your answer.
Common Mistakes
- Changing only one part of an equivalent fraction or ratio.
- Moving a decimal point without a mathematical reason.
- Using the new amount instead of the original amount for percent change.
- Mixing units when comparing rates or scale.
30 Review Questions and Answers
Q1. What is important to remember about Scale?
Answer: Scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q2. What is important to remember about Scale factor?
Answer: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Scale factor.
Q3. What is important to remember about Enlargement?
Answer: Enlargement is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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 Reduction?
Answer: Reduction is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q5. What is important to remember about Scale drawings?
Answer: Scale drawings is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Maps?
Answer: Maps is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q7. What is important to remember about Floor plans?
Answer: Floor plans is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Models?
Answer: The mode is the value that occurs most often. This topic focuses on Models.
Q9. What is important to remember about Finding actual dimensions?
Answer: Finding actual dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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 Finding drawing dimensions?
Answer: Finding drawing dimensions is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. 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 Similar figures?
Answer: Similar figures have the same shape and proportional corresponding lengths. This topic focuses on Similar figures.
Q12. What is important to remember about Corresponding sides?
Answer: Corresponding sides is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q13. What is important to remember about Perimeter and scale?
Answer: Perimeter and scale is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q14. What is important to remember about Real-life design applications?
Answer: Real-life design applications is an important Grade 7 idea in Scale Factors, Scale Drawings, and Similarity. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q15. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q16. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q17. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q18. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q19. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q20. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q21. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q22. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q23. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q24. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q25. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q26. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q27. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q28. 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.
Q29. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q30. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.