Chapter 54: Metric Measurement and Conversions
Learn Grade 5 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
- Choosing metric units for length (a Grade 5 idea used in this chapter)
- Choosing metric units for area (a Grade 5 idea used in this chapter)
- Choosing metric units for mass (a Grade 5 idea used in this chapter)
- Choosing metric units for capacity (a Grade 5 idea used in this chapter)
- Estimating measurements (a Grade 5 idea used in this chapter)
- Millimetres, centimetres, metres, and kilometres (a Grade 5 idea used in this chapter)
- Grams and kilograms (a Grade 5 idea used in this chapter)
- Millilitres and litres (a Grade 5 idea used in this chapter)
- Converting larger units to smaller units (a Grade 5 idea used in this chapter)
- Base-ten relationships among metric units (a Grade 5 idea used in this chapter)
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.
54.1 Choosing metric units for length
Choosing metric units for length develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Choosing metric units for length?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Choosing metric units for length develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Choosing metric units for length develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Choosing metric units for length?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Choosing metric units for length develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Choosing metric units for length.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Choosing metric units for length develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Choosing metric units for length problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Choosing metric units for length develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Choosing metric units for length.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Choosing metric units for length develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Choosing metric units for length can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 Choosing metric units for length. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
54.2 Choosing metric units for area
Choosing metric units for area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Choosing metric units for area?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Choosing metric units for area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Choosing metric units for area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Choosing metric units for area?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Choosing metric units for area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Choosing metric units for area.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Choosing metric units for area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Choosing metric units for area problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Choosing metric units for area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Choosing metric units for area.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Choosing metric units for area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Choosing metric units for area can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 Choosing metric units for area. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
54.3 Choosing metric units for mass
Choosing metric units for mass develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Choosing metric units for mass?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Choosing metric units for mass develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Choosing metric units for mass develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Choosing metric units for mass?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Choosing metric units for mass develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Choosing metric units for mass.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Choosing metric units for mass develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Choosing metric units for mass problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Choosing metric units for mass develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Choosing metric units for mass.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Choosing metric units for mass develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Choosing metric units for mass can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 Choosing metric units for mass. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
54.4 Choosing metric units for capacity
Choosing metric units for capacity develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Choosing metric units for capacity?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Choosing metric units for capacity develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Choosing metric units for capacity develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Choosing metric units for capacity?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Choosing metric units for capacity develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Choosing metric units for capacity.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Choosing metric units for capacity develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Choosing metric units for capacity problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Choosing metric units for capacity develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Choosing metric units for capacity.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Choosing metric units for capacity develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Choosing metric units for capacity can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 Choosing metric units for capacity. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
54.5 Estimating measurements
Estimating measurements is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Estimating measurements?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Estimating measurements is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Estimating measurements is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Estimating measurements?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Estimating measurements is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Estimating measurements.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Estimating measurements is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Estimating measurements problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Estimating measurements is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Estimating measurements.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Estimating measurements is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Estimating measurements can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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.
54.6 Millimetres, centimetres, metres, and kilometres
Millimetres, centimetres, metres, and kilometres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Millimetres, centimetres, metres, and kilometres?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Millimetres, centimetres, metres, and kilometres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Millimetres, centimetres, metres, and kilometres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Millimetres, centimetres, metres, and kilometres?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Millimetres, centimetres, metres, and kilometres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Millimetres, centimetres, metres, and kilometres.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Millimetres, centimetres, metres, and kilometres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Millimetres, centimetres, metres, and kilometres problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Millimetres, centimetres, metres, and kilometres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Millimetres, centimetres, metres, and kilometres.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Millimetres, centimetres, metres, and kilometres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Millimetres, centimetres, metres, and kilometres can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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, centimetres, metres, and kilometres. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
54.7 Grams and kilograms
Grams and kilograms is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Grams and kilograms?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Grams and kilograms is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Grams and kilograms is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Grams and kilograms?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Grams and kilograms is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Grams and kilograms.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Grams and kilograms is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Grams and kilograms problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Grams and kilograms is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Grams and kilograms.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Grams and kilograms is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Grams and kilograms can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 and kilograms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
54.8 Millilitres and litres
Millilitres and litres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Millilitres and litres?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Millilitres and litres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Millilitres and litres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Millilitres and litres?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Millilitres and litres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Millilitres and litres.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Millilitres and litres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Millilitres and litres problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Millilitres and litres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Millilitres and litres.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Millilitres and litres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Millilitres and litres can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 and litres. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
54.9 Converting larger units to smaller units
Converting larger units to smaller units is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Converting larger units to smaller units?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Converting larger units to smaller units is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Converting larger units to smaller units is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Converting larger units to smaller units?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Converting larger units to smaller units is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Converting larger units to smaller units.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Converting larger units to smaller units is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Converting larger units to smaller units problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Converting larger units to smaller units is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Converting larger units to smaller units.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Converting larger units to smaller units is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Converting larger units to smaller units can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Converting larger units to smaller 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: Converting larger units to smaller 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 Converting larger units to smaller 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: Converting larger units to smaller 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 Converting larger units to smaller 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: Converting larger units to smaller 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 Converting larger units to smaller 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: Converting larger units to smaller 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 Converting larger units to smaller 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: Converting larger units to smaller 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 Converting larger units to smaller units. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
54.10 Base-ten relationships among metric units
Base-ten relationships among metric units develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Base-ten relationships among metric units?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Base-ten relationships among metric units develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Base-ten relationships among metric units develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Base-ten relationships among metric units?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Base-ten relationships among metric units develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Base-ten relationships among metric units.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Base-ten relationships among metric units develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Base-ten relationships among metric units problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Base-ten relationships among metric units develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Base-ten relationships among metric units.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Base-ten relationships among metric units develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Base-ten relationships among metric units can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: For y = 2x + (1), find y when x = 3.
- Substitute x = 3.
- y = 2(3) + (1).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 7
Worked Example 7
Problem: For y = -1x + (4), find y when x = 3.
- Substitute x = 3.
- y = -1(3) + (4).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 1
Worked Example 8
Problem: For y = 0.5x + (-2), find y when x = 3.
- Substitute x = 3.
- y = 0.5(3) + (-2).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -0.5
Worked Example 9
Problem: For y = 3x + (0), find y when x = 3.
- Substitute x = 3.
- y = 3(3) + (0).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 9
Worked Example 10
Problem: For y = -2x + (5), find y when x = 3.
- Substitute x = 3.
- y = -2(3) + (5).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -1
Practice Exercise
Create one new question about Base-ten relationships among metric 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 question before calculating.
- Represent the mathematics with a model, table, graph, diagram, number line, or equation when useful.
- Show the reasoning and check the final answer with a second method when possible.
Extra Practice
- Create and solve one original problem about Choosing metric units for length.
- Create and solve one original problem about Choosing metric units for area.
- Create and solve one original problem about Choosing metric units for mass.
- Create and solve one original problem about Choosing metric units for capacity.
- Create and solve one original problem about Estimating measurements.
- Create and solve one original problem about Millimetres, centimetres, metres, and kilometres.
Common Mistakes
- Skipping the meaning and trying to memorize a rule only.
- Using the wrong operation because the question was not read completely.
- Ignoring units, labels, place values, or the context of the problem.
- Not estimating or checking whether the final answer is reasonable.
30 Review Questions and Answers
Q1. What is the key idea in Choosing metric units for length?
Answer: Choosing metric units for length develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q2. What is the key idea in Choosing metric units for area?
Answer: Choosing metric units for area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q3. What is the key idea in Choosing metric units for mass?
Answer: Choosing metric units for mass develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q4. What is the key idea in Choosing metric units for capacity?
Answer: Choosing metric units for capacity develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q5. What is the key idea in Estimating measurements?
Answer: Estimating measurements is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q6. What is the key idea in Millimetres, centimetres, metres, and kilometres?
Answer: Millimetres, centimetres, metres, and kilometres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q7. What is the key idea in Grams and kilograms?
Answer: Grams and kilograms is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q8. What is the key idea in Millilitres and litres?
Answer: Millilitres and litres is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q9. What is the key idea in Converting larger units to smaller units?
Answer: Converting larger units to smaller units is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q10. What is the key idea in Base-ten relationships among metric units?
Answer: Base-ten relationships among metric units develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q11. Why should you estimate before or after a calculation?
Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.
Q12. Why are labels and units important?
Answer: They show what a number represents and help prevent mixing unlike quantities.
Q13. How can a diagram help solve a problem?
Answer: A diagram makes quantities and relationships visible before calculation.
Q14. How can inverse operations check an answer?
Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.
Q15. Why should you show steps?
Answer: Showing steps makes reasoning clear and helps find where an error happened.
Q16. What should you do after making a mistake?
Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.
Q17. How can a number line support reasoning?
Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.
Q18. When is a table useful?
Answer: A table organizes related values so patterns and comparisons are easier to see.
Q19. When is a graph useful?
Answer: A graph makes trends, comparisons, locations, or data patterns visible.
Q20. How do you decide which operation to use?
Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.
Q21. Why should you check place value?
Answer: A digit or decimal has a different value depending on its position.
Q22. What makes an answer reasonable?
Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.
Q23. How can you explain mathematical reasoning clearly?
Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.
Q24. Why can more than one strategy be correct?
Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.
Q25. How should you approach a difficult Grade 5 problem?
Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.
Q26. How can you practise Metric Measurement and Conversions effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q27. How can you practise Metric Measurement and Conversions effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q28. How can you practise Metric Measurement and Conversions effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q29. How can you practise Metric Measurement and Conversions effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q30. How can you practise Metric Measurement and Conversions effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.