Chapter 60: Comprehensive Grade 3 Review and Mathematical Processes
Learn Grade 3 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Comprehensive Grade 3 Review and Mathematical Processes with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Number sense review (a Grade 3 idea used in this chapter)
- Addition and subtraction review (a Grade 3 idea used in this chapter)
- Multiplication and division review (a Grade 3 idea used in this chapter)
- Fractions review (a Grade 3 idea used in this chapter)
- Patterns and equations review (a Grade 3 idea used in this chapter)
- Coding and modelling review (a Grade 3 idea used in this chapter)
- Data review (a Grade 3 idea used in this chapter)
- Spatial sense and measurement review (a Grade 3 idea used in this chapter)
- Financial literacy review (a Grade 3 idea used in this chapter)
- Problem solving reasoning and communication review (a Grade 3 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 Number sense review
Number sense 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 Number sense 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: Number sense review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Number sense 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 Number sense review?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Number sense 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 Number sense 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: Number sense 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 Number sense 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: Number sense 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 Number sense 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: Number sense review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Number sense 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 Number sense 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: Number sense 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 Number sense 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: Number sense 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 Number sense 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: Number sense 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 Number sense 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: Number sense 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 Number sense 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: Number sense 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 Number sense review. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
60.2 Addition and subtraction review
Addition and subtraction review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
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 Addition and subtraction 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: Addition and subtraction review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Addition and subtraction review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Worked Example 2
Problem: What should you identify first before solving a problem about Addition and subtraction review?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Addition and subtraction review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Addition and subtraction 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: Addition and subtraction review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
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 Addition and subtraction 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: Addition and subtraction review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
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 Addition and subtraction 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: Addition and subtraction review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Addition and subtraction 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 Addition and subtraction 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: Addition and subtraction 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 Addition and subtraction 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: Addition and subtraction 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 Addition and subtraction 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: Addition and subtraction 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 Addition and subtraction 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: Addition and subtraction 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 Addition and subtraction 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: Addition and subtraction 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 Addition and subtraction review. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
60.3 Multiplication and division review
Multiplication and division review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
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 Multiplication and division 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: Multiplication and division review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Multiplication and division review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Worked Example 2
Problem: What should you identify first before solving a problem about Multiplication and division review?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Multiplication and division review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Multiplication and division 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: Multiplication and division review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
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 Multiplication and division 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: Multiplication and division review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
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 Multiplication and division 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: Multiplication and division review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Multiplication and division review can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Multiplication and division review. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
60.4 Fractions review
Fractions 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 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 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 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 review?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Fractions 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: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Fractions 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: Fractions 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: 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 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: Fractions 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: 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 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: Fractions 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 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 review. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
60.5 Patterns and equations review
Patterns and equations review introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
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 Patterns and equations 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: Patterns and equations review introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
Answer: Patterns and equations review introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
Worked Example 2
Problem: What should you identify first before solving a problem about Patterns and equations review?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Patterns and equations review introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Patterns and equations 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: Patterns and equations review introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
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 Patterns and equations 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: Patterns and equations review introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
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 Patterns and equations 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: Patterns and equations review introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
Answer: Patterns and equations review can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Solve 2x + 5 = 17.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 6
Worked Example 7
Problem: Solve 3x - 4 = 11.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 8
Problem: Solve 5x + 7 = 2x + 22.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 9
Problem: Solve 4(x + 2) = 24.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 4
Worked Example 10
Problem: Solve 7x - 3 = 4x + 12.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Practice Exercise
Create one new question about Patterns and equations review. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
60.6 Coding and modelling review
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 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: 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: 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 Coding and modelling review?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: 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: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for 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.
Very beginner explanation: 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: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a 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.
Very beginner explanation: 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: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for 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.
Very beginner explanation: 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: 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 Coding and modelling review. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
60.7 Data review
Data 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 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 review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Data 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 review?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Data 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 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 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 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 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 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 review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Data 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 review. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
60.8 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.
60.9 Financial literacy review
Financial literacy 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 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 review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Financial literacy 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 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 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 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 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 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 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 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 review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Financial literacy 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 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 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 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 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 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 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 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 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 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 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 review. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
60.10 Problem solving reasoning and communication review
Problem solving reasoning and communication 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 Problem solving reasoning and communication 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: Problem solving reasoning and communication review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Problem solving reasoning and communication 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 Problem solving reasoning and communication review?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Problem solving reasoning and communication 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 Problem solving reasoning and communication 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: Problem solving reasoning and communication 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 Problem solving reasoning and communication 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: Problem solving reasoning and communication 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 Problem solving reasoning and communication 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: Problem solving reasoning and communication review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Problem solving reasoning and communication 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 Problem solving reasoning and communication 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: Problem solving reasoning and communication 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 Problem solving reasoning and communication 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: Problem solving reasoning and communication 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 Problem solving reasoning and communication 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: Problem solving reasoning and communication 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 Problem solving reasoning and communication 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: Problem solving reasoning and communication 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 Problem solving reasoning and communication 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: Problem solving reasoning and communication 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 Problem solving reasoning and communication 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 Number sense review.
- Create and solve one original problem about Addition and subtraction review.
- Create and solve one original problem about Multiplication and division review.
- Create and solve one original problem about Fractions review.
- Create and solve one original problem about Patterns and equations review.
- Create and solve one original problem about Coding and modelling 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.
30 Review Questions and Answers
Q1. What is the key idea in Number sense review?
Answer: Number sense review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q2. What is the key idea in Addition and subtraction review?
Answer: Addition and subtraction review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Q3. What is the key idea in Multiplication and division review?
Answer: Multiplication and division review develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Q4. What is the key idea in Fractions review?
Answer: Fractions 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.
Q5. What is the key idea in Patterns and equations review?
Answer: Patterns and equations review introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
Q6. What is the key idea in Coding and modelling review?
Answer: 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.
Q7. What is the key idea in Data review?
Answer: Data review helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Q8. 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.
Q9. What is the key idea in Financial literacy review?
Answer: Financial literacy review develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q10. What is the key idea in Problem solving reasoning and communication review?
Answer: Problem solving reasoning and communication 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 3 problem?
Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.
Q26. How can you practise Comprehensive Grade 3 Review and Mathematical Processes 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 Comprehensive Grade 3 Review and Mathematical Processes 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 Comprehensive Grade 3 Review and Mathematical Processes 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 Comprehensive Grade 3 Review and Mathematical Processes 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 Comprehensive Grade 3 Review and Mathematical Processes effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.