Chapter 29: Fraction Problem Solving
Learn Grade 3 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Fraction Problem Solving with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Equal-sharing problems (a Grade 3 idea used in this chapter)
- Fraction of a shape problems (a Grade 3 idea used in this chapter)
- Fraction of a set problems (a Grade 3 idea used in this chapter)
- Equivalent-fraction problems (a Grade 3 idea used in this chapter)
- Comparing-fraction problems (a Grade 3 idea used in this chapter)
- Fraction number-line problems (a Grade 3 idea used in this chapter)
- Drawing a fraction model (a Grade 3 idea used in this chapter)
- Writing a fraction from a story (a Grade 3 idea used in this chapter)
- Checking if parts are equal (a Grade 3 idea used in this chapter)
- Explaining fraction reasoning (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.
29.1 Equal-sharing problems
Equal-sharing problems is an important Grade 3 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 Equal-sharing problems?
- 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: Equal-sharing problems is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Equal-sharing problems is an important Grade 3 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 Equal-sharing problems?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Equal-sharing problems is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Equal-sharing problems.
- 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: Equal-sharing problems is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Equal-sharing problems 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: Equal-sharing problems is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Equal-sharing problems.
- 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: Equal-sharing problems is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Equal-sharing problems can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Equal-sharing problems in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Equal-sharing problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Equal-sharing problems and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Equal-sharing problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Equal-sharing problems using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Equal-sharing problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Equal-sharing problems problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Equal-sharing problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Equal-sharing problems could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Equal-sharing problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Equal-sharing problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.2 Fraction of a shape problems
Fraction of a shape problems 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 Fraction of a shape problems?
- 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: Fraction of a shape problems 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: Fraction of a shape problems 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 Fraction of a shape problems?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Fraction of a shape problems 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 Fraction of a shape problems.
- 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: Fraction of a shape problems 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 Fraction of a shape problems 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: Fraction of a shape problems 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 Fraction of a shape problems.
- 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: Fraction of a shape problems 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: Fraction of a shape problems 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 Fraction of a shape problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.3 Fraction of a set problems
Fraction of a set problems 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 Fraction of a set problems?
- 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: Fraction of a set problems 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: Fraction of a set problems 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 Fraction of a set problems?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Fraction of a set problems 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 Fraction of a set problems.
- 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: Fraction of a set problems 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 Fraction of a set problems 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: Fraction of a set problems 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 Fraction of a set problems.
- 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: Fraction of a set problems 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: Fraction of a set problems 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 Fraction of a set problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.4 Equivalent-fraction problems
Equivalent-fraction problems 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 Equivalent-fraction problems?
- 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: Equivalent-fraction problems 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: Equivalent-fraction problems 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 Equivalent-fraction problems?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Equivalent-fraction problems 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 Equivalent-fraction problems.
- 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: Equivalent-fraction problems 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 Equivalent-fraction problems 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: Equivalent-fraction problems 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 Equivalent-fraction problems.
- 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: Equivalent-fraction problems 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: Equivalent-fraction problems 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 Equivalent-fraction problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.5 Comparing-fraction problems
Comparing-fraction problems 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 Comparing-fraction problems?
- 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: Comparing-fraction problems 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: Comparing-fraction problems 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 Comparing-fraction problems?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Comparing-fraction problems 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 Comparing-fraction problems.
- 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: Comparing-fraction problems 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 Comparing-fraction problems 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: Comparing-fraction problems 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 Comparing-fraction problems.
- 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: Comparing-fraction problems 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: Comparing-fraction problems 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 Comparing-fraction problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.6 Fraction number-line problems
Fraction number-line problems 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 Fraction number-line problems?
- 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: Fraction number-line problems 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: Fraction number-line problems 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 Fraction number-line problems?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Fraction number-line problems 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 Fraction number-line problems.
- 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: Fraction number-line problems 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 Fraction number-line problems 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: Fraction number-line problems 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 Fraction number-line problems.
- 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: Fraction number-line problems 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: Fraction number-line problems 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 Fraction number-line problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.7 Drawing a fraction model
Drawing a fraction model 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 Drawing a fraction model?
- 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: Drawing a fraction model 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: Drawing a fraction model 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 Drawing a fraction model?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Drawing a fraction model 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 Drawing a fraction model.
- 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: Drawing a fraction model 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 Drawing a fraction model 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: Drawing a fraction model 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 Drawing a fraction model.
- 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: Drawing a fraction model 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: Drawing a fraction model 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 Drawing a fraction model. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.8 Writing a fraction from a story
Writing a fraction from a story 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 Writing a fraction from a story?
- 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: Writing a fraction from a story 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: Writing a fraction from a story 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 Writing a fraction from a story?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Writing a fraction from a story 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 Writing a fraction from a story.
- 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: Writing a fraction from a story 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 Writing a fraction from a story 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: Writing a fraction from a story 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 Writing a fraction from a story.
- 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: Writing a fraction from a story 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: Writing a fraction from a story 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 Writing a fraction from a story. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.9 Checking if parts are equal
Checking if parts are equal is an important Grade 3 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 Checking if parts are equal?
- 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: Checking if parts are equal is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Checking if parts are equal is an important Grade 3 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 Checking if parts are equal?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Checking if parts are equal is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Checking if parts are equal.
- 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: Checking if parts are equal is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Checking if parts are equal 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: Checking if parts are equal is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Checking if parts are equal.
- 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: Checking if parts are equal is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Checking if parts are equal can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Checking if parts are equal 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: Checking if parts are equal 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 Checking if parts are equal 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: Checking if parts are equal 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 Checking if parts are equal 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: Checking if parts are equal 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 Checking if parts are equal 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: Checking if parts are equal 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 Checking if parts are equal 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: Checking if parts are equal 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 Checking if parts are equal. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.10 Explaining fraction reasoning
Explaining fraction reasoning 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 Explaining fraction reasoning?
- 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: Explaining fraction reasoning 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: Explaining fraction reasoning 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 Explaining fraction reasoning?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Explaining fraction reasoning 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 Explaining fraction reasoning.
- 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: Explaining fraction reasoning 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 Explaining fraction reasoning 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: Explaining fraction reasoning 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 Explaining fraction reasoning.
- 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: Explaining fraction reasoning 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: Explaining fraction reasoning 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 Explaining fraction reasoning. 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 Equal-sharing problems.
- Create and solve one original problem about Fraction of a shape problems.
- Create and solve one original problem about Fraction of a set problems.
- Create and solve one original problem about Equivalent-fraction problems.
- Create and solve one original problem about Comparing-fraction problems.
- Create and solve one original problem about Fraction number-line problems.
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 Equal-sharing problems?
Answer: Equal-sharing problems is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q2. What is the key idea in Fraction of a shape problems?
Answer: Fraction of a shape problems 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.
Q3. What is the key idea in Fraction of a set problems?
Answer: Fraction of a set problems 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.
Q4. What is the key idea in Equivalent-fraction problems?
Answer: Equivalent-fraction problems 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 Comparing-fraction problems?
Answer: Comparing-fraction problems 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.
Q6. What is the key idea in Fraction number-line problems?
Answer: Fraction number-line problems 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.
Q7. What is the key idea in Drawing a fraction model?
Answer: Drawing a fraction model 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.
Q8. What is the key idea in Writing a fraction from a story?
Answer: Writing a fraction from a story 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.
Q9. What is the key idea in Checking if parts are equal?
Answer: Checking if parts are equal is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q10. What is the key idea in Explaining fraction reasoning?
Answer: Explaining fraction reasoning 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.
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 Fraction Problem Solving 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 Fraction Problem Solving 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 Fraction Problem Solving 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 Fraction Problem Solving 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 Fraction Problem Solving effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.