Chapter 60: Taxes, Community Services, and Comprehensive Grade 5 Review

Learn Grade 5 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.

Grade 5Beginner Friendly10 Examples Per Topic30 Q&APractice + Review

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Chapter Overview

This chapter teaches Taxes, Community Services, and Comprehensive Grade 5 Review with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.

Key Technical Terms

Different levels of government and taxes (a Grade 5 idea used in this chapter)
Why taxes are collected (a Grade 5 idea used in this chapter)
Community services supported by tax revenue (a Grade 5 idea used in this chapter)
Responsible consumer decisions (a Grade 5 idea used in this chapter)
Whole-number review (a Grade 5 idea used in this chapter)
Fractions, decimals, and percents review (a Grade 5 idea used in this chapter)
Algebra, coding, and modelling review (a Grade 5 idea used in this chapter)
Data and probability review (a Grade 5 idea used in this chapter)
Spatial sense and measurement review (a Grade 5 idea used in this chapter)
Financial literacy and mathematical processes review (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.

60.1 Different levels of government and taxes

Different levels of government and taxes builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

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 Different levels of government and taxes?

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: Different levels of government and taxes builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Answer: Different levels of government and taxes builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Worked Example 2

Problem: What should you identify first before solving a problem about Different levels of government and taxes?

Read the complete problem.
Mark the information that is given.
Identify exactly what the question asks you to find.

Very beginner explanation: Different levels of government and taxes builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Different levels of government and taxes.

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: Different levels of government and taxes builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

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 Different levels of government and taxes 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: Different levels of government and taxes builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

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 Different levels of government and taxes.

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: Different levels of government and taxes builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Answer: Different levels of government and taxes can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Different levels of government and taxes 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: Different levels of government and taxes 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 Different levels of government and taxes 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: Different levels of government and taxes 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 Different levels of government and taxes 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: Different levels of government and taxes 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 Different levels of government and taxes 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: Different levels of government and taxes 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 Different levels of government and taxes 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: Different levels of government and taxes 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 Different levels of government and taxes. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

60.2 Why taxes are collected

Why taxes are collected builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

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 Why taxes are collected?

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: Why taxes are collected builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Answer: Why taxes are collected builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Worked Example 2

Problem: What should you identify first before solving a problem about Why taxes are collected?

Read the complete problem.
Mark the information that is given.
Identify exactly what the question asks you to find.

Very beginner explanation: Why taxes are collected builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Why taxes are collected.

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: Why taxes are collected builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

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 Why taxes are collected 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: Why taxes are collected builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

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 Why taxes are collected.

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: Why taxes are collected builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Answer: Why taxes are collected can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Why taxes are collected 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: Why taxes are collected 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 Why taxes are collected 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: Why taxes are collected 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 Why taxes are collected 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: Why taxes are collected 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 Why taxes are collected 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: Why taxes are collected 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 Why taxes are collected 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: Why taxes are collected 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 Why taxes are collected. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

60.3 Community services supported by tax revenue

Community services supported by tax revenue builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

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 Community services supported by tax revenue?

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: Community services supported by tax revenue builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Answer: Community services supported by tax revenue builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Worked Example 2

Problem: What should you identify first before solving a problem about Community services supported by tax revenue?

Read the complete problem.
Mark the information that is given.
Identify exactly what the question asks you to find.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Community services supported by tax revenue.

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.

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 Community services supported by tax revenue 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.

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 Community services supported by tax revenue.

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.

Answer: Community services supported by tax revenue can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Community services supported by tax revenue 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: Community services supported by tax revenue 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 Community services supported by tax revenue 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: Community services supported by tax revenue 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 Community services supported by tax revenue 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: Community services supported by tax revenue 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 Community services supported by tax revenue 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: Community services supported by tax revenue 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 Community services supported by tax revenue 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: Community services supported by tax revenue 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 Community services supported by tax revenue. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

60.4 Responsible consumer decisions

Responsible consumer decisions 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 Responsible consumer decisions?

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: Responsible consumer decisions 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: Responsible consumer decisions 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 Responsible consumer decisions?

Read the complete problem.
Mark the information that is given.
Identify exactly what the question asks you to find.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Responsible consumer decisions.

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.

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 Responsible consumer decisions 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.

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 Responsible consumer decisions.

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.

Answer: Responsible consumer decisions can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Responsible consumer decisions 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: Responsible consumer decisions 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 Responsible consumer decisions 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: Responsible consumer decisions 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 Responsible consumer decisions 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: Responsible consumer decisions 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 Responsible consumer decisions 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: Responsible consumer decisions 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 Responsible consumer decisions 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: Responsible consumer decisions 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 Responsible consumer decisions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

60.5 Whole-number review

Whole-number review 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 Whole-number review?

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: Whole-number review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.

Answer: Whole-number review 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 Whole-number review?

Read the complete problem.
Mark the information that is given.
Identify exactly what the question asks you to find.

Very beginner explanation: Whole-number review 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 Whole-number review.

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: Whole-number review 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 Whole-number review 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: Whole-number review 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 Whole-number review.

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: Whole-number review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.

Answer: Whole-number review can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Whole-number review in one simple sentence.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Whole-number review becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Whole-number review and explain why.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Whole-number review becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Whole-number review using a table, diagram, number line, graph, or equation.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Whole-number review becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Whole-number review problem, how can you check the answer?

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Whole-number review becomes easier to understand when you connect its definition to examples, non-examples, and representations.

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

Worked Example 10

Problem: Give one real-life situation where Whole-number review could be useful.

Read the definition of the topic.
Use the definition to build the response.
Check that the response matches every important condition.

Very beginner explanation: Whole-number review becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

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

60.6 Fractions, decimals, and percents review

Fractions, decimals, and percents review focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

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 Fractions, decimals, and percents review?

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: Fractions, decimals, and percents review focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

Answer: Fractions, decimals, and percents review focuses on equal parts of a whole or set. Learners use models, number lines, and equivalent forms so the fraction has a clear meaning before using a rule.

Worked Example 2

Problem: What should you identify first before solving a problem about Fractions, decimals, and percents review?

Read the complete problem.
Mark the information that is given.
Identify exactly what the question asks you to find.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Fractions, decimals, and percents review.

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.

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 Fractions, decimals, and percents review 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.

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 Fractions, decimals, and percents review.

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.

Answer: Fractions, decimals, and percents review can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Write 1/3 as a decimal.

A fraction bar means division.
Divide 1 by 3.

Very beginner explanation: Fractions and decimals can represent the same rational number.

Answer: 0.3333

Worked Example 7

Problem: Write 2/5 as a decimal.

A fraction bar means division.
Divide 2 by 5.

Very beginner explanation: Fractions and decimals can represent the same rational number.

Answer: 0.4

Worked Example 8

Problem: Write 3/8 as a decimal.

A fraction bar means division.
Divide 3 by 8.

Very beginner explanation: Fractions and decimals can represent the same rational number.

Answer: 0.375

Worked Example 9

Problem: Write 5/12 as a decimal.

A fraction bar means division.
Divide 5 by 12.

Very beginner explanation: Fractions and decimals can represent the same rational number.

Answer: 0.4167

Worked Example 10

Problem: Write 7/9 as a decimal.

A fraction bar means division.
Divide 7 by 9.

Very beginner explanation: Fractions and decimals can represent the same rational number.

Answer: 0.7778

Practice Exercise

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

60.7 Algebra, coding, and modelling review

Algebra, coding, and modelling review uses clear step-by-step instructions to represent mathematics. Learners trace, test, and revise instructions to understand how changes affect results.

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 Algebra, coding, and modelling review?

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: Algebra, coding, and modelling review uses clear step-by-step instructions to represent mathematics. Learners trace, test, and revise instructions to understand how changes affect results.

Answer: Algebra, coding, and modelling review uses clear step-by-step instructions to represent mathematics. Learners trace, test, and revise instructions to understand how changes affect results.

Worked Example 2

Problem: What should you identify first before solving a problem about Algebra, coding, and modelling review?

Read the complete problem.
Mark the information that is given.
Identify exactly what the question asks you to find.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Algebra, coding, and modelling review.

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.

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 Algebra, coding, and modelling review 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.

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 Algebra, coding, and modelling review.

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.

Answer: Algebra, coding, and modelling review can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Tile a floor

Write a simple rule: area = length × width.
State any assumptions.
Use the rule on sample values.
Check whether the result is realistic.

Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.

Answer: Estimate tile quantity and include a small waste allowance.

Worked Example 7

Problem: Plan monthly savings

Write a simple rule: total = starting amount + monthly deposit × months.
State any assumptions.
Use the rule on sample values.
Check whether the result is realistic.

Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.

Answer: Predict when the savings goal is reached.

Worked Example 8

Problem: Simulate a die

Write a simple rule: generate a random whole number from 1 to 6.
State any assumptions.
Use the rule on sample values.
Check whether the result is realistic.

Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.

Answer: Repeat many times and compare frequencies.

Worked Example 9

Problem: Translate a point

Write a simple rule: new x = x + 3; new y = y - 2.
State any assumptions.
Use the rule on sample values.
Check whether the result is realistic.

Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.

Answer: Apply the same rule to every point.

Worked Example 10

Problem: Estimate paint needed

Write a simple rule: paint = wall area ÷ coverage per can.
State any assumptions.
Use the rule on sample values.
Check whether the result is realistic.

Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.

Answer: Round up because a partial can may not be enough.

Practice Exercise

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

60.8 Data and probability review

Data and probability review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

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 Data and probability review?

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: Data and probability review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Data and probability review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Worked Example 2

Problem: What should you identify first before solving a problem about Data and probability review?

Read the complete problem.
Mark the information that is given.
Identify exactly what the question asks you to find.

Very beginner explanation: Data and probability review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Identify the known information and the unknown before choosing an operation or rule.

Worked Example 3

Problem: Choose a useful representation for Data and probability review.

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: Data and probability review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

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 Data and probability review 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: Data and probability review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

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 Data and probability review.

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: Data and probability review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Answer: Data and probability review can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Classify the data [4, 6, 8].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 7

Problem: Classify the data [5, 9, 10, 12].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 8

Problem: Classify the data [3, 7, 7, 11].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 9

Problem: Classify the data [20, 25, 30].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Worked Example 10

Problem: Classify the data [6, 8, 9, 12, 15].

These values are numerical.
Decide whether they represent counts or measurements.

Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.

Answer: Quantitative data

Practice Exercise

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

60.9 Spatial sense and measurement review

Spatial sense and measurement review 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 Spatial sense and measurement review?

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: Spatial sense and measurement review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.

Answer: Spatial sense and measurement review 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 Spatial sense and measurement review?

Read the complete problem.
Mark the information that is given.
Identify exactly what the question asks you to find.

Very beginner explanation: Spatial sense and measurement review 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 Spatial sense and measurement review.

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: Spatial sense and measurement review 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 Spatial sense and measurement review 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: Spatial sense and measurement review 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 Spatial sense and measurement review.

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: Spatial sense and measurement review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.

Answer: Spatial sense and measurement review can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Spatial sense and measurement review 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: Spatial sense and measurement review 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 Spatial sense and measurement review 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: Spatial sense and measurement review 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 Spatial sense and measurement review 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: Spatial sense and measurement review 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 Spatial sense and measurement review 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: Spatial sense and measurement review 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 Spatial sense and measurement review 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: Spatial sense and measurement review 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 Spatial sense and measurement review. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

60.10 Financial literacy and mathematical processes review

Financial literacy and mathematical processes review 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 Financial literacy and mathematical processes review?

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: Financial literacy and mathematical processes review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.

Answer: Financial literacy and mathematical processes review 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 Financial literacy and mathematical processes review?

Read the complete problem.
Mark the information that is given.
Identify exactly what the question asks you to find.

Very beginner explanation: Financial literacy and mathematical processes review 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 Financial literacy and mathematical processes review.

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: Financial literacy and mathematical processes review 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 Financial literacy and mathematical processes review 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: Financial literacy and mathematical processes review 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 Financial literacy and mathematical processes review.

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: Financial literacy and mathematical processes review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.

Answer: Financial literacy and mathematical processes review can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Financial literacy and mathematical processes review 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: Financial literacy and mathematical processes review 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 Financial literacy and mathematical processes review 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: Financial literacy and mathematical processes review 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 Financial literacy and mathematical processes review 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: Financial literacy and mathematical processes review 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 Financial literacy and mathematical processes review 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: Financial literacy and mathematical processes review 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 Financial literacy and mathematical processes review 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: Financial literacy and mathematical processes review 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 Financial literacy and mathematical processes review. 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 Different levels of government and taxes.
Create and solve one original problem about Why taxes are collected.
Create and solve one original problem about Community services supported by tax revenue.
Create and solve one original problem about Responsible consumer decisions.
Create and solve one original problem about Whole-number review.
Create and solve one original problem about Fractions, decimals, and percents review.

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.

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30 Review Questions and Answers

Q1. What is the key idea in Different levels of government and taxes?

Answer: Different levels of government and taxes builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Q2. What is the key idea in Why taxes are collected?

Answer: Why taxes are collected builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Q3. What is the key idea in Community services supported by tax revenue?

Answer: Community services supported by tax revenue builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.

Q4. What is the key idea in Responsible consumer decisions?

Answer: Responsible consumer decisions 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.

Q5. What is the key idea in Whole-number review?

Answer: Whole-number review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.

Q6. What is the key idea in Fractions, decimals, and percents review?

Q7. What is the key idea in Algebra, coding, and modelling review?

Q8. What is the key idea in Data and probability review?

Answer: Data and probability review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.

Q9. What is the key idea in Spatial sense and measurement review?

Answer: Spatial sense and measurement review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.

Q10. What is the key idea in Financial literacy and mathematical processes review?

Answer: Financial literacy and mathematical processes review 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 Taxes, Community Services, and Comprehensive Grade 5 Review 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 Taxes, Community Services, and Comprehensive Grade 5 Review 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 Taxes, Community Services, and Comprehensive Grade 5 Review 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 Taxes, Community Services, and Comprehensive Grade 5 Review 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 Taxes, Community Services, and Comprehensive Grade 5 Review effectively?

Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.