Chapter 34: Equality and Number Sentences
Learn Grade 3 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Equality and Number Sentences with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Meaning of the equal sign (a Grade 3 idea used in this chapter)
- Both sides must have the same value (a Grade 3 idea used in this chapter)
- True number sentences (a Grade 3 idea used in this chapter)
- False number sentences (a Grade 3 idea used in this chapter)
- Missing addends (a Grade 3 idea used in this chapter)
- Missing subtrahends (a Grade 3 idea used in this chapter)
- Balancing simple equations (a Grade 3 idea used in this chapter)
- Using models for equality (a Grade 3 idea used in this chapter)
- Writing equal number sentences (a Grade 3 idea used in this chapter)
- Checking equality (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.
34.1 Meaning of the equal sign
Meaning of the equal sign 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 Meaning of the equal sign?
- 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: Meaning of the equal sign helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Meaning of the equal sign 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 Meaning of the equal sign?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Meaning of the equal sign 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 Meaning of the equal sign.
- 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: Meaning of the equal sign 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 Meaning of the equal sign 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: Meaning of the equal sign 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 Meaning of the equal sign.
- 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: Meaning of the equal sign helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Meaning of the equal sign can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the mean of [4, 6, 8].
- Add the values: 18.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 6
Worked Example 7
Problem: Find the mean of [5, 9, 10, 12].
- Add the values: 36.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 9
Worked Example 8
Problem: Find the mean of [3, 7, 7, 11].
- Add the values: 28.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 7
Worked Example 9
Problem: Find the mean of [20, 25, 30].
- Add the values: 75.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 25
Worked Example 10
Problem: Find the mean of [6, 8, 9, 12, 15].
- Add the values: 50.
- Divide by 5.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 10
Practice Exercise
Create one new question about Meaning of the equal sign. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
34.2 Both sides must have the same value
Both sides must have the same value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Both sides must have the same value?
- 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: Both sides must have the same value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Both sides must have the same value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Worked Example 2
Problem: What should you identify first before solving a problem about Both sides must have the same value?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Both sides must have the same value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Both sides must have the same value.
- 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: Both sides must have the same value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Both sides must have the same value 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: Both sides must have the same value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Both sides must have the same value.
- 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: Both sides must have the same value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Both sides must have the same value can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Both sides must have the same value 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: Both sides must have the same value 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 Both sides must have the same value 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: Both sides must have the same value 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 Both sides must have the same value 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: Both sides must have the same value 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 Both sides must have the same value 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: Both sides must have the same value 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 Both sides must have the same value 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: Both sides must have the same value 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 Both sides must have the same value. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
34.3 True number sentences
True number sentences 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 True number sentences?
- 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: True number sentences 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: True number sentences 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 True number sentences?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: True number sentences 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 True number sentences.
- 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: True number sentences 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 True number sentences 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: True number sentences 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 True number sentences.
- 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: True number sentences 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: True number sentences can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain True number sentences 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: True number sentences 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 True number sentences 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: True number sentences 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 True number sentences 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: True number sentences 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 True number sentences 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: True number sentences 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 True number sentences 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: True number sentences 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 True number sentences. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
34.4 False number sentences
False number sentences 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 False number sentences?
- 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: False number sentences 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: False number sentences 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 False number sentences?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: False number sentences 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 False number sentences.
- 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: False number sentences 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 False number sentences 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: False number sentences 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 False number sentences.
- 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: False number sentences 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: False number sentences can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain False number sentences 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: False number sentences 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 False number sentences 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: False number sentences 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 False number sentences 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: False number sentences 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 False number sentences 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: False number sentences 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 False number sentences 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: False number sentences 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 False number sentences. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
34.5 Missing addends
Missing addends 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 Missing addends?
- 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: Missing addends 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: Missing addends 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 Missing addends?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Missing addends 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 Missing addends.
- 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: Missing addends 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 Missing addends 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: Missing addends 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 Missing addends.
- 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: Missing addends 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: Missing addends can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Missing addends 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: Missing addends 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 Missing addends 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: Missing addends 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 Missing addends 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: Missing addends 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 Missing addends 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: Missing addends 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 Missing addends 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: Missing addends 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 Missing addends. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
34.6 Missing subtrahends
Missing subtrahends 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 Missing subtrahends?
- 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: Missing subtrahends 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: Missing subtrahends 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 Missing subtrahends?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Missing subtrahends 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 Missing subtrahends.
- 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: Missing subtrahends 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 Missing subtrahends 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: Missing subtrahends 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 Missing subtrahends.
- 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: Missing subtrahends 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: Missing subtrahends can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Missing subtrahends 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: Missing subtrahends 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 Missing subtrahends 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: Missing subtrahends 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 Missing subtrahends 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: Missing subtrahends 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 Missing subtrahends 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: Missing subtrahends 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 Missing subtrahends 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: Missing subtrahends 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 Missing subtrahends. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
34.7 Balancing simple equations
Balancing simple equations 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 Balancing simple equations?
- 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: Balancing simple equations introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
Answer: Balancing simple equations 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 Balancing simple equations?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Balancing simple equations 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 Balancing simple equations.
- 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: Balancing simple equations 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 Balancing simple equations 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: Balancing simple equations 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 Balancing simple equations.
- 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: Balancing simple equations introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
Answer: Balancing simple equations 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 Balancing simple equations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
34.8 Using models for equality
Using models for equality uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
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 Using models for equality?
- 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: Using models for equality uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
Answer: Using models for equality uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
Worked Example 2
Problem: What should you identify first before solving a problem about Using models for equality?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Using models for equality uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Using models for equality.
- 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: Using models for equality uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
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 Using models for equality 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: Using models for equality uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
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 Using models for equality.
- 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: Using models for equality uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
Answer: Using models for equality 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 Using models for equality. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
34.9 Writing equal number sentences
Writing equal number sentences 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 Writing equal number sentences?
- 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 equal number sentences 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: Writing equal number sentences 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 Writing equal number sentences?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Writing equal number sentences 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 Writing equal number sentences.
- 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 equal number sentences 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 Writing equal number sentences 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 equal number sentences 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 Writing equal number sentences.
- 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 equal number sentences 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: Writing equal number sentences can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Writing equal number sentences 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: Writing equal number sentences 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 Writing equal number sentences 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: Writing equal number sentences 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 Writing equal number sentences 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: Writing equal number sentences 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 Writing equal number sentences 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: Writing equal number sentences 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 Writing equal number sentences 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: Writing equal number sentences 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 Writing equal number sentences. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
34.10 Checking equality
Checking equality 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 equality?
- 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 equality 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 equality 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 equality?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Checking equality 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 equality.
- 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 equality 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 equality 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 equality 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 equality.
- 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 equality 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 equality 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 Checking equality. 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 Meaning of the equal sign.
- Create and solve one original problem about Both sides must have the same value.
- Create and solve one original problem about True number sentences.
- Create and solve one original problem about False number sentences.
- Create and solve one original problem about Missing addends.
- Create and solve one original problem about Missing subtrahends.
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 Meaning of the equal sign?
Answer: Meaning of the equal sign helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Q2. What is the key idea in Both sides must have the same value?
Answer: Both sides must have the same value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Q3. What is the key idea in True number sentences?
Answer: True number sentences 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.
Q4. What is the key idea in False number sentences?
Answer: False number sentences 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.
Q5. What is the key idea in Missing addends?
Answer: Missing addends 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.
Q6. What is the key idea in Missing subtrahends?
Answer: Missing subtrahends 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.
Q7. What is the key idea in Balancing simple equations?
Answer: Balancing simple equations introduces algebraic thinking by describing relationships, using symbols for unknown values, and checking whether mathematical statements are true.
Q8. What is the key idea in Using models for equality?
Answer: Using models for equality uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
Q9. What is the key idea in Writing equal number sentences?
Answer: Writing equal number sentences 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 Checking equality?
Answer: Checking equality 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.
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 Equality and Number Sentences 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 Equality and Number Sentences 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 Equality and Number Sentences 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 Equality and Number Sentences 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 Equality and Number Sentences effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.