Grade 7 Math Chapter 55: Nets, Composite Solids, and Measurement Problems

Chapter Overview

This chapter teaches Nets, Composite Solids, and Measurement Problems with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.

Key Technical Terms

Unit Rate (a rate per one unit)
Surface Area (total area of the outside of a 3D object)
Volume (amount of 3D space inside an object)
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.

55.1 Nets of prisms

Nets of prisms is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈87.96.

Very beginner explanation: Nets of prisms is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈169.65.

Very beginner explanation: Nets of prisms is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈301.59.

Very beginner explanation: Nets of prisms is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈471.24.

Very beginner explanation: Nets of prisms is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈678.58.

Very beginner explanation: Nets of prisms is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 678.58 cm²

Worked Example 6

Problem: Find the surface area of a rectangular prism 4 cm × 3 cm × 2 cm.

Find the areas of the three different face pairs.
SA = 2(12+8+6).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 52 cm²

Worked Example 7

Problem: Find the surface area of a rectangular prism 5 cm × 4 cm × 3 cm.

Find the areas of the three different face pairs.
SA = 2(20+15+12).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 94 cm²

Worked Example 8

Problem: Find the surface area of a rectangular prism 6 cm × 5 cm × 4 cm.

Find the areas of the three different face pairs.
SA = 2(30+24+20).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 148 cm²

Worked Example 9

Problem: Find the surface area of a rectangular prism 7 cm × 6 cm × 5 cm.

Find the areas of the three different face pairs.
SA = 2(42+35+30).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 214 cm²

Worked Example 10

Problem: Find the surface area of a rectangular prism 8 cm × 7 cm × 6 cm.

Find the areas of the three different face pairs.
SA = 2(56+48+42).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 292 cm²

Practice Exercise

Create one new question about Nets of prisms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.2 Nets of cylinders

A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Nets of cylinders .

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: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈87.96.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Nets of cylinders .

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈169.65.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Nets of cylinders .

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈301.59.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Nets of cylinders .

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈471.24.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Nets of cylinders .

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈678.58.

Very beginner explanation: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Nets of cylinders .

Answer: 678.58 cm²

Worked Example 6

Problem: Find the surface area of a rectangular prism 4 cm × 3 cm × 2 cm.

Find the areas of the three different face pairs.
SA = 2(12+8+6).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 52 cm²

Worked Example 7

Problem: Find the surface area of a rectangular prism 5 cm × 4 cm × 3 cm.

Find the areas of the three different face pairs.
SA = 2(20+15+12).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 94 cm²

Worked Example 8

Problem: Find the surface area of a rectangular prism 6 cm × 5 cm × 4 cm.

Find the areas of the three different face pairs.
SA = 2(30+24+20).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 148 cm²

Worked Example 9

Problem: Find the surface area of a rectangular prism 7 cm × 6 cm × 5 cm.

Find the areas of the three different face pairs.
SA = 2(42+35+30).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 214 cm²

Worked Example 10

Problem: Find the surface area of a rectangular prism 8 cm × 7 cm × 6 cm.

Find the areas of the three different face pairs.
SA = 2(56+48+42).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 292 cm²

Practice Exercise

Create one new question about Nets of cylinders. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.3 Building 3D objects from nets

Building 3D objects from nets is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Closed cylinder radius 2 cm, height 5 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈87.96.

Very beginner explanation: Building 3D objects from nets is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 87.96 cm²

Worked Example 2

Problem: Closed cylinder radius 3 cm, height 6 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈169.65.

Very beginner explanation: Building 3D objects from nets is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 169.65 cm²

Worked Example 3

Problem: Closed cylinder radius 4 cm, height 8 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈301.59.

Very beginner explanation: Building 3D objects from nets is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 301.59 cm²

Worked Example 4

Problem: Closed cylinder radius 5 cm, height 10 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈471.24.

Very beginner explanation: Building 3D objects from nets is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 471.24 cm²

Worked Example 5

Problem: Closed cylinder radius 6 cm, height 12 cm. Find surface area.

Use SA=2πr²+2πrh.
SA≈678.58.

Very beginner explanation: Building 3D objects from nets is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 678.58 cm²

Worked Example 6

Problem: Find the surface area of a rectangular prism 4 cm × 3 cm × 2 cm.

Find the areas of the three different face pairs.
SA = 2(12+8+6).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 52 cm²

Worked Example 7

Problem: Find the surface area of a rectangular prism 5 cm × 4 cm × 3 cm.

Find the areas of the three different face pairs.
SA = 2(20+15+12).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 94 cm²

Worked Example 8

Problem: Find the surface area of a rectangular prism 6 cm × 5 cm × 4 cm.

Find the areas of the three different face pairs.
SA = 2(30+24+20).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 148 cm²

Worked Example 9

Problem: Find the surface area of a rectangular prism 7 cm × 6 cm × 5 cm.

Find the areas of the three different face pairs.
SA = 2(42+35+30).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 214 cm²

Worked Example 10

Problem: Find the surface area of a rectangular prism 8 cm × 7 cm × 6 cm.

Find the areas of the three different face pairs.
SA = 2(56+48+42).

Very beginner explanation: Surface area measures all outside faces and uses square units.

Answer: 292 cm²

Practice Exercise

Create one new question about Building 3D objects from nets. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.4 Composite solids

Composite solids is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: List the factors of 18.

Find all whole numbers that divide exactly.

Very beginner explanation: Composite solids is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

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: Composite solids is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

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: Composite solids is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

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: Composite solids is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

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: Composite solids is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Worked Example 6

Problem: Is 18 prime or composite?

List its factors: 1, 2, 3, 6, 9, 18.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 7

Problem: Is 24 prime or composite?

List its factors: 1, 2, 3, 4, 6, 8, 12, 24.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 8

Problem: Is 30 prime or composite?

List its factors: 1, 2, 3, 5, 6, 10, 15, 30.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 9

Problem: Is 42 prime or composite?

List its factors: 1, 2, 3, 6, 7, 14, 21, 42.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 10

Problem: Is 60 prime or composite?

List its factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Practice Exercise

Create one new question about Composite solids. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.5 Surface area of composite objects

Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of composite objects .

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: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of composite objects .

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: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of composite objects .

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: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of composite objects .

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: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of composite objects .

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: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of composite objects .

Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Worked Example 6

Problem: Is 18 prime or composite?

List its factors: 1, 2, 3, 6, 9, 18.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 7

Problem: Is 24 prime or composite?

List its factors: 1, 2, 3, 4, 6, 8, 12, 24.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 8

Problem: Is 30 prime or composite?

List its factors: 1, 2, 3, 5, 6, 10, 15, 30.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 9

Problem: Is 42 prime or composite?

List its factors: 1, 2, 3, 6, 7, 14, 21, 42.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 10

Problem: Is 60 prime or composite?

List its factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Practice Exercise

Create one new question about Surface area of composite objects. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.6 Volume of composite objects introduction

Volume measures the 3D space inside an object and uses cubic units. This topic focuses on Volume of composite objects introduction .

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: Volume measures the 3D space inside an object and uses cubic units. This topic focuses on Volume of composite objects introduction .

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: Volume measures the 3D space inside an object and uses cubic units. This topic focuses on Volume of composite objects introduction .

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: Volume measures the 3D space inside an object and uses cubic units. This topic focuses on Volume of composite objects introduction .

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: Volume measures the 3D space inside an object and uses cubic units. This topic focuses on Volume of composite objects introduction .

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: Volume measures the 3D space inside an object and uses cubic units. This topic focuses on Volume of composite objects introduction .

Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Worked Example 6

Problem: Is 18 prime or composite?

List its factors: 1, 2, 3, 6, 9, 18.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 7

Problem: Is 24 prime or composite?

List its factors: 1, 2, 3, 4, 6, 8, 12, 24.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 8

Problem: Is 30 prime or composite?

List its factors: 1, 2, 3, 5, 6, 10, 15, 30.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 9

Problem: Is 42 prime or composite?

List its factors: 1, 2, 3, 6, 7, 14, 21, 42.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Worked Example 10

Problem: Is 60 prime or composite?

List its factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
A prime number has exactly two positive factors.

Very beginner explanation: Factor counting is a reliable way to classify a positive whole number as prime or composite.

Answer: Composite

Practice Exercise

Create one new question about Volume of composite objects introduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.7 Missing dimensions

Missing dimensions is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Missing dimensions: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Missing dimensions is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Missing dimensions: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Missing dimensions is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Missing dimensions: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Missing dimensions is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Missing dimensions: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Missing dimensions is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Missing dimensions: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Missing dimensions is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 Missing 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: Missing 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 Missing 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: Missing 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 Missing 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: Missing 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 Missing 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: Missing 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 Missing 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: Missing 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 Missing dimensions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.8 Unit conversions in measurement

Unit conversions in measurement is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Convert 3.6 m to cm.

Use the metric relationship and multiply or divide by a power of 10.

Very beginner explanation: Unit conversions in measurement is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 360 cm

Worked Example 2

Problem: Convert 2.5 km to m.

Use the metric relationship and multiply or divide by a power of 10.

Very beginner explanation: Unit conversions in measurement is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 2500 m

Worked Example 3

Problem: Convert 7500 g to kg.

Use the metric relationship and multiply or divide by a power of 10.

Very beginner explanation: Unit conversions in measurement is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 7.5 kg

Worked Example 4

Problem: Convert 1.8 L to mL.

Use the metric relationship and multiply or divide by a power of 10.

Very beginner explanation: Unit conversions in measurement is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 1800 mL

Worked Example 5

Problem: Convert 450 mm to cm.

Use the metric relationship and multiply or divide by a power of 10.

Very beginner explanation: Unit conversions in measurement is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 45 cm

Worked Example 6

Problem: Explain Unit conversions in measurement 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: Unit conversions in measurement 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 Unit conversions in measurement 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: Unit conversions in measurement 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 Unit conversions in measurement 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: Unit conversions in measurement 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 Unit conversions in measurement 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: Unit conversions in measurement 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 Unit conversions in measurement 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: Unit conversions in measurement 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 Unit conversions in measurement. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.9 Estimating measurements

Estimating measurements is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Estimating measurements: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Estimating measurements is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Estimating measurements: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Estimating measurements is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Estimating measurements: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Estimating measurements is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Estimating measurements: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Estimating measurements is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Estimating measurements: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Estimating measurements is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 Estimating measurements 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: Estimating measurements 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 Estimating measurements 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: Estimating measurements 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 Estimating measurements 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: Estimating measurements 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 Estimating measurements 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: Estimating measurements 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 Estimating measurements 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: Estimating measurements 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 Estimating measurements. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.10 Choosing formulas

Choosing formulas is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Choosing formulas: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Choosing formulas is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Choosing formulas: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Choosing formulas is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Choosing formulas: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Choosing formulas is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Choosing formulas: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Choosing formulas is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Choosing formulas: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Choosing formulas is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 Choosing formulas 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: Choosing formulas 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 Choosing formulas 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: Choosing formulas 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 Choosing formulas 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: Choosing formulas 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 Choosing formulas 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: Choosing formulas 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 Choosing formulas 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: Choosing formulas 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 Choosing formulas. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.11 Multi-step measurement problems

Multi-step measurement problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Multi-step measurement problems: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Multi-step measurement problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Multi-step measurement problems: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Multi-step measurement problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Multi-step measurement problems: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Multi-step measurement problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Multi-step measurement problems: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Multi-step measurement problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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: Multi-step measurement problems: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Multi-step measurement problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 Multi-step measurement 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: Multi-step measurement 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 Multi-step measurement 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: Multi-step measurement 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 Multi-step measurement 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: Multi-step measurement 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 Multi-step measurement 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: Multi-step measurement 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 Multi-step measurement 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: Multi-step measurement 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 Multi-step measurement problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

55.12 Real-life design problems

Real-life design problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 problems: Identify a correct example.

State the definition and show why the example fits.
Show all important reasoning.

Very beginner explanation: Real-life design problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 problems: Identify a non-example.

Explain which requirement is missing.
Show all important reasoning.

Very beginner explanation: Real-life design problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 problems: Compare two cases.

State one similarity and one difference.
Show all important reasoning.

Very beginner explanation: Real-life design problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 problems: Apply the idea in a real situation.

Translate the situation into mathematical language.
Show all important reasoning.

Very beginner explanation: Real-life design problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 problems: Create and check your own example.

Use the definition, then verify each condition.
Show all important reasoning.

Very beginner explanation: Real-life design problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 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: Real-life design 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 Real-life design 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: Real-life design 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 Real-life design 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: Real-life design 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 Real-life design 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: Real-life design 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 Real-life design 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: Real-life design 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 Real-life design problems. 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 Nets of prisms . Show your reasoning and check your answer.
Create and solve a new question about Nets of cylinders . Show your reasoning and check your answer.
Create and solve a new question about Building 3D objects from nets . Show your reasoning and check your answer.
Create and solve a new question about Composite solids . Show your reasoning and check your answer.
Create and solve a new question about Surface area of composite objects . Show your reasoning and check your answer.
Create and solve a new question about Volume of composite objects introduction . Show your reasoning and check your answer.
Create and solve a new question about Missing dimensions . Show your reasoning and check your answer.
Create and solve a new question about Unit conversions in measurement . Show your reasoning and check your answer.
Create and solve a new question about Estimating measurements . Show your reasoning and check your answer.
Create and solve a new question about Choosing formulas . Show your reasoning and check your answer.
Create and solve a new question about Multi-step measurement problems . Show your reasoning and check your answer.
Create and solve a new question about Real-life design problems . Show your reasoning and check your answer.

Common Mistakes

Assuming a diagram is drawn to scale.
Confusing radius and diameter.
Using square units for volume or cubic units for area.
Applying a scale factor to only one dimension.
Forgetting the circular bases in cylinder surface area.

30 Review Questions and Answers

Q1. What is important to remember about Nets of prisms?

Answer: Nets of prisms is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 Nets of cylinders?

Answer: A cylinder is a 3D object with two congruent circular bases connected by a curved surface. This topic focuses on Nets of cylinders.

Q3. What is important to remember about Building 3D objects from nets?

Answer: Building 3D objects from nets is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 Composite solids?

Answer: Composite solids is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 Surface area of composite objects?

Answer: Surface area is the total area covering the outside of a 3D object. This topic focuses on Surface area of composite objects.

Q6. What is important to remember about Volume of composite objects introduction?

Answer: Volume measures the 3D space inside an object and uses cubic units. This topic focuses on Volume of composite objects introduction.

Q7. What is important to remember about Missing dimensions?

Answer: Missing dimensions is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 Unit conversions in measurement?

Answer: Unit conversions in measurement is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q9. What is important to remember about Estimating measurements?

Answer: Estimating measurements is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 Choosing formulas?

Answer: Choosing formulas is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. 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 Multi-step measurement problems?

Answer: Multi-step measurement problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q12. What is important to remember about Real-life design problems?

Answer: Real-life design problems is an important Grade 7 idea in Nets, Composite Solids, and Measurement Problems. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q13. Why should you show your steps?

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

Q14. Why is estimation useful?

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

Q15. Why do units matter?

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

Q16. When should you round?

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

Q17. How can you check an answer?

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

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

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

Q19. What makes a final answer complete?

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

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

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

Q21. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.

Q22. Why are tables useful?

Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.

Q23. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer you obtained.

Q24. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.

Q25. How should you study this chapter?

Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.

Q26. 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.

Q27. Why compare more than one strategy?

Answer: Different strategies can make a problem easier and provide a way to verify the result.

Q28. What is a mathematical model?

Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.

Q29. Why should assumptions be stated?

Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.

Q30. Why should sources be checked in data problems?

Answer: Reliable sources and fair collection methods make conclusions more trustworthy.