Chapter 50: Metric Measurement and Conversions
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Metric Measurement and Conversions 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)
- 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.
50.1 Millimetres
Millimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Millimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Millimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Millimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Millimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Millimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 50 cm
Worked Example 7
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 120 cm
Worked Example 8
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 275 cm
Worked Example 9
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 360 cm
Worked Example 10
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 405 cm
Practice Exercise
Create one new question about Millimetres. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.2 Centimetres
Centimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Centimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Centimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Centimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Centimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Centimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 50 cm
Worked Example 7
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 120 cm
Worked Example 8
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 275 cm
Worked Example 9
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 360 cm
Worked Example 10
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 405 cm
Practice Exercise
Create one new question about Centimetres. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.3 Metres
Metres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Metres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Metres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Metres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Metres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Metres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 50 cm
Worked Example 7
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 120 cm
Worked Example 8
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 275 cm
Worked Example 9
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 360 cm
Worked Example 10
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 405 cm
Practice Exercise
Create one new question about Metres. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.4 Kilometres
Kilometres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Kilometres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Kilometres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Kilometres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Kilometres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Kilometres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 50 cm
Worked Example 7
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 120 cm
Worked Example 8
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 275 cm
Worked Example 9
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 360 cm
Worked Example 10
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 405 cm
Practice Exercise
Create one new question about Kilometres. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.5 Milligrams
Milligrams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Milligrams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Milligrams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Milligrams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Milligrams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Milligrams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 50 cm
Worked Example 7
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 120 cm
Worked Example 8
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 275 cm
Worked Example 9
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 360 cm
Worked Example 10
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 405 cm
Practice Exercise
Create one new question about Milligrams. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.6 Grams
Grams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Grams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Grams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Grams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Grams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Grams is an important Grade 7 idea in Metric Measurement and Conversions. 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: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 50 cm
Worked Example 7
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 120 cm
Worked Example 8
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 275 cm
Worked Example 9
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 360 cm
Worked Example 10
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 405 cm
Practice Exercise
Create one new question about Grams. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.7 Kilograms
Kilograms is an important Grade 7 idea in Metric Measurement and Conversions. 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: Kilograms is an important Grade 7 idea in Metric Measurement and Conversions. 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: Kilograms is an important Grade 7 idea in Metric Measurement and Conversions. 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: Kilograms is an important Grade 7 idea in Metric Measurement and Conversions. 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: Kilograms is an important Grade 7 idea in Metric Measurement and Conversions. 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: Kilograms is an important Grade 7 idea in Metric Measurement and Conversions. 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: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 50 cm
Worked Example 7
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 120 cm
Worked Example 8
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 275 cm
Worked Example 9
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 360 cm
Worked Example 10
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 405 cm
Practice Exercise
Create one new question about Kilograms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.8 Millilitres
Millilitres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Millilitres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Millilitres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Millilitres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Millilitres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Millilitres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 50 cm
Worked Example 7
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 120 cm
Worked Example 8
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 275 cm
Worked Example 9
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 360 cm
Worked Example 10
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 405 cm
Practice Exercise
Create one new question about Millilitres. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.9 Litres
Litres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Litres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Litres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Litres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Litres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Litres is an important Grade 7 idea in Metric Measurement and Conversions. 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: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 50 cm
Worked Example 7
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 120 cm
Worked Example 8
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 275 cm
Worked Example 9
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 360 cm
Worked Example 10
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 405 cm
Practice Exercise
Create one new question about Litres. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.10 Metric prefixes
The metric system is a base-10 measurement system used for length, mass, and capacity. This topic focuses on Metric prefixes .
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: The metric system is a base-10 measurement system used for length, mass, and capacity. This topic focuses on Metric prefixes .
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: The metric system is a base-10 measurement system used for length, mass, and capacity. This topic focuses on Metric prefixes .
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: The metric system is a base-10 measurement system used for length, mass, and capacity. This topic focuses on Metric prefixes .
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: The metric system is a base-10 measurement system used for length, mass, and capacity. This topic focuses on Metric prefixes .
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: The metric system is a base-10 measurement system used for length, mass, and capacity. This topic focuses on Metric prefixes .
Answer: 45 cm
Worked Example 6
Problem: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 50 cm
Worked Example 7
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 120 cm
Worked Example 8
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 275 cm
Worked Example 9
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 360 cm
Worked Example 10
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10.
Answer: 405 cm
Practice Exercise
Create one new question about Metric prefixes. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.11 Length conversions
Length conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Length conversions: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Length conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Length conversions: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Length conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Length conversions: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Length conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Length conversions: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Length conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Length conversions: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Length conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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 Length conversions 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: Length conversions 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 Length conversions 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: Length conversions 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 Length conversions 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: Length conversions 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 Length conversions 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: Length conversions 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 Length conversions 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: Length conversions 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 Length conversions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.12 Mass conversions
Mass conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Mass conversions: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Mass conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Mass conversions: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Mass conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Mass conversions: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Mass conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Mass conversions: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Mass conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Mass conversions: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Mass conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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 Mass conversions 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: Mass conversions 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 Mass conversions 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: Mass conversions 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 Mass conversions 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: Mass conversions 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 Mass conversions 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: Mass conversions 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 Mass conversions 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: Mass conversions 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 Mass conversions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.13 Capacity conversions
Capacity conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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: Cylinder radius 2 cm, height 5 cm. Find volume.
- Use V=πr²h.
- V≈62.83.
Very beginner explanation: Capacity conversions is an important Grade 7 idea in Metric Measurement and Conversions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 62.83 cm³
Worked Example 2
Problem: Cylinder radius 3 cm, height 6 cm. Find volume.
- Use V=πr²h.
- V≈169.65.
Very beginner explanation: Capacity conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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 cm³
Worked Example 3
Problem: Cylinder radius 4 cm, height 8 cm. Find volume.
- Use V=πr²h.
- V≈402.12.
Very beginner explanation: Capacity conversions is an important Grade 7 idea in Metric Measurement and Conversions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 402.12 cm³
Worked Example 4
Problem: Cylinder radius 5 cm, height 10 cm. Find volume.
- Use V=πr²h.
- V≈785.40.
Very beginner explanation: Capacity conversions is an important Grade 7 idea in Metric Measurement and Conversions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 785.40 cm³
Worked Example 5
Problem: Cylinder radius 6 cm, height 12 cm. Find volume.
- Use V=πr²h.
- V≈1357.17.
Very beginner explanation: Capacity conversions is an important Grade 7 idea in Metric Measurement and Conversions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1357.17 cm³
Worked Example 6
Problem: Find the volume of a cylinder with radius 2 cm and height 5 cm.
- Use V = πr²h.
- V = π(2)²(5).
Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.
Answer: 62.83 cm³
Worked Example 7
Problem: Find the volume of a cylinder with radius 3 cm and height 6 cm.
- Use V = πr²h.
- V = π(3)²(6).
Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.
Answer: 169.65 cm³
Worked Example 8
Problem: Find the volume of a cylinder with radius 4 cm and height 7 cm.
- Use V = πr²h.
- V = π(4)²(7).
Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.
Answer: 351.86 cm³
Worked Example 9
Problem: Find the volume of a cylinder with radius 5 cm and height 8 cm.
- Use V = πr²h.
- V = π(5)²(8).
Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.
Answer: 628.32 cm³
Worked Example 10
Problem: Find the volume of a cylinder with radius 6 cm and height 9 cm.
- Use V = πr²h.
- V = π(6)²(9).
Very beginner explanation: Cylinder volume equals the area of the circular base multiplied by height.
Answer: 1017.88 cm³
Practice Exercise
Create one new question about Capacity conversions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.14 Area-unit conversions introduction
Area-unit conversions introduction is an important Grade 7 idea in Metric Measurement and Conversions. 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: Area-unit conversions introduction is an important Grade 7 idea in Metric Measurement and Conversions. 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: Area-unit conversions introduction is an important Grade 7 idea in Metric Measurement and Conversions. 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: Area-unit conversions introduction is an important Grade 7 idea in Metric Measurement and Conversions. 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: Area-unit conversions introduction is an important Grade 7 idea in Metric Measurement and Conversions. 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: Area-unit conversions introduction is an important Grade 7 idea in Metric Measurement and Conversions. 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: Find the area of a rectangle 6 cm by 3 cm.
- Use A = length × width.
- A = 6 × 3.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 18 cm²
Worked Example 7
Problem: Find the area of a rectangle 7 cm by 4 cm.
- Use A = length × width.
- A = 7 × 4.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 28 cm²
Worked Example 8
Problem: Find the area of a rectangle 8 cm by 5 cm.
- Use A = length × width.
- A = 8 × 5.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 40 cm²
Worked Example 9
Problem: Find the area of a rectangle 9 cm by 6 cm.
- Use A = length × width.
- A = 9 × 6.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 54 cm²
Worked Example 10
Problem: Find the area of a rectangle 10 cm by 7 cm.
- Use A = length × width.
- A = 10 × 7.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 70 cm²
Practice Exercise
Create one new question about Area-unit conversions introduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.15 Choosing appropriate units
Choosing appropriate units is an important Grade 7 idea in Metric Measurement and Conversions. 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 appropriate units: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Choosing appropriate units is an important Grade 7 idea in Metric Measurement and Conversions. 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 appropriate units: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Choosing appropriate units is an important Grade 7 idea in Metric Measurement and Conversions. 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 appropriate units: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Choosing appropriate units is an important Grade 7 idea in Metric Measurement and Conversions. 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 appropriate units: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Choosing appropriate units is an important Grade 7 idea in Metric Measurement and Conversions. 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 appropriate units: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Choosing appropriate units is an important Grade 7 idea in Metric Measurement and Conversions. 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 appropriate units 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 appropriate units 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 appropriate units 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 appropriate units 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 appropriate units 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 appropriate units 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 appropriate units 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 appropriate units 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 appropriate units 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 appropriate units 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 appropriate units. 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 Millimetres . Show your reasoning and check your answer.
- Create and solve a new question about Centimetres . Show your reasoning and check your answer.
- Create and solve a new question about Metres . Show your reasoning and check your answer.
- Create and solve a new question about Kilometres . Show your reasoning and check your answer.
- Create and solve a new question about Milligrams . Show your reasoning and check your answer.
- Create and solve a new question about Grams . Show your reasoning and check your answer.
- Create and solve a new question about Kilograms . Show your reasoning and check your answer.
- Create and solve a new question about Millilitres . Show your reasoning and check your answer.
- Create and solve a new question about Litres . Show your reasoning and check your answer.
- Create and solve a new question about Metric prefixes . Show your reasoning and check your answer.
- Create and solve a new question about Length conversions . Show your reasoning and check your answer.
- Create and solve a new question about Mass conversions . 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 Millimetres?
Answer: Millimetres is an important Grade 7 idea in Metric Measurement and Conversions. 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 Centimetres?
Answer: Centimetres is an important Grade 7 idea in Metric Measurement and Conversions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q3. What is important to remember about Metres?
Answer: Metres is an important Grade 7 idea in Metric Measurement and Conversions. 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 Kilometres?
Answer: Kilometres is an important Grade 7 idea in Metric Measurement and Conversions. 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 Milligrams?
Answer: Milligrams is an important Grade 7 idea in Metric Measurement and Conversions. 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 Grams?
Answer: Grams is an important Grade 7 idea in Metric Measurement and Conversions. 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 Kilograms?
Answer: Kilograms is an important Grade 7 idea in Metric Measurement and Conversions. 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 Millilitres?
Answer: Millilitres is an important Grade 7 idea in Metric Measurement and Conversions. 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 Litres?
Answer: Litres is an important Grade 7 idea in Metric Measurement and Conversions. 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 Metric prefixes?
Answer: The metric system is a base-10 measurement system used for length, mass, and capacity. This topic focuses on Metric prefixes.
Q11. What is important to remember about Length conversions?
Answer: Length conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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 Mass conversions?
Answer: Mass conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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 Capacity conversions?
Answer: Capacity conversions is an important Grade 7 idea in Metric Measurement and Conversions. 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 Area-unit conversions introduction?
Answer: Area-unit conversions introduction is an important Grade 7 idea in Metric Measurement and Conversions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q15. What is important to remember about Choosing appropriate units?
Answer: Choosing appropriate units is an important Grade 7 idea in Metric Measurement and Conversions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q16. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q17. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q18. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q19. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q20. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q21. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q22. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q23. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q24. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q25. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q26. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q27. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q28. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q29. 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.
Q30. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.