Chapter 13: Introduction to Multiplication
Learn Grade 3 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Introduction to Multiplication with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Equal groups (a Grade 3 idea used in this chapter)
- Repeated addition (a Grade 3 idea used in this chapter)
- Writing multiplication sentences (a Grade 3 idea used in this chapter)
- Factors and products (a Grade 3 idea used in this chapter)
- Making equal groups with objects (a Grade 3 idea used in this chapter)
- Drawing equal groups (a Grade 3 idea used in this chapter)
- Skip counting for multiplication (a Grade 3 idea used in this chapter)
- Connecting addition and multiplication (a Grade 3 idea used in this chapter)
- Multiplication in everyday situations (a Grade 3 idea used in this chapter)
- Checking a multiplication model (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.
13.1 Equal groups
Equal groups 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 groups?
- 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 groups 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 groups 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 groups?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Equal groups 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 groups.
- 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 groups 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 groups 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 groups 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 groups.
- 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 groups 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 groups 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 groups 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 groups 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 groups 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 groups 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 groups 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 groups 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 groups 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 groups 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 groups 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 groups 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 groups. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.2 Repeated addition
Repeated addition develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Repeated addition?
- 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: Repeated addition develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Repeated addition develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Worked Example 2
Problem: What should you identify first before solving a problem about Repeated addition?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Repeated addition develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Repeated addition.
- 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: Repeated addition develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Repeated addition 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: Repeated addition develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Repeated addition.
- 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: Repeated addition develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Repeated addition can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Repeated addition 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: Repeated addition 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 Repeated addition 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: Repeated addition 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 Repeated addition 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: Repeated addition 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 Repeated addition 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: Repeated addition 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 Repeated addition 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: Repeated addition 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 Repeated addition. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.3 Writing multiplication sentences
Writing multiplication sentences develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Writing multiplication 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 multiplication sentences develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Writing multiplication sentences develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Worked Example 2
Problem: What should you identify first before solving a problem about Writing multiplication sentences?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Writing multiplication sentences develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Writing multiplication 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 multiplication sentences develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Writing multiplication 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 multiplication sentences develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Writing multiplication 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 multiplication sentences develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Writing multiplication sentences can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Writing multiplication sentences. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.4 Factors and products
Factors and products 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 Factors and products?
- 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: Factors and products 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: Factors and products 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 Factors and products?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Factors and products 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 Factors and products.
- 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: Factors and products 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 Factors and products 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: Factors and products 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 Factors and products.
- 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: Factors and products 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: Factors and products can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Calculate 84 × 7.
- Break one factor into easier parts if helpful.
- Multiply carefully.
- Check with division.
Very beginner explanation: Multiplication combines equal groups and can be checked with the inverse operation, division.
Answer: 588
Worked Example 7
Problem: Calculate 125 × 8.
- Break one factor into easier parts if helpful.
- Multiply carefully.
- Check with division.
Very beginner explanation: Multiplication combines equal groups and can be checked with the inverse operation, division.
Answer: 1000
Worked Example 8
Problem: Calculate 936 × 9.
- Break one factor into easier parts if helpful.
- Multiply carefully.
- Check with division.
Very beginner explanation: Multiplication combines equal groups and can be checked with the inverse operation, division.
Answer: 8424
Worked Example 9
Problem: Calculate 48 × 12.
- Break one factor into easier parts if helpful.
- Multiply carefully.
- Check with division.
Very beginner explanation: Multiplication combines equal groups and can be checked with the inverse operation, division.
Answer: 576
Worked Example 10
Problem: Calculate 315 × 5.
- Break one factor into easier parts if helpful.
- Multiply carefully.
- Check with division.
Very beginner explanation: Multiplication combines equal groups and can be checked with the inverse operation, division.
Answer: 1575
Practice Exercise
Create one new question about Factors and products. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.5 Making equal groups with objects
Making equal groups with objects 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 Making equal groups with objects?
- 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: Making equal groups with objects 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: Making equal groups with objects 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 Making equal groups with objects?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Making equal groups with objects 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 Making equal groups with objects.
- 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: Making equal groups with objects 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 Making equal groups with objects 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: Making equal groups with objects 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 Making equal groups with objects.
- 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: Making equal groups with objects 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: Making equal groups with objects can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Making equal groups with objects 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: Making equal groups with objects 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 Making equal groups with objects 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: Making equal groups with objects 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 Making equal groups with objects 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: Making equal groups with objects 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 Making equal groups with objects 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: Making equal groups with objects 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 Making equal groups with objects 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: Making equal groups with objects 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 Making equal groups with objects. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.6 Drawing equal groups
Drawing equal groups 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 Drawing equal groups?
- 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 equal groups 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: Drawing equal groups 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 Drawing equal groups?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Drawing equal groups 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 Drawing equal groups.
- 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 equal groups 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 Drawing equal groups 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 equal groups 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 Drawing equal groups.
- 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 equal groups 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: Drawing equal groups can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Drawing equal groups 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: Drawing equal groups 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 Drawing equal groups 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: Drawing equal groups 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 Drawing equal groups 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: Drawing equal groups 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 Drawing equal groups 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: Drawing equal groups 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 Drawing equal groups 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: Drawing equal groups 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 Drawing equal groups. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.7 Skip counting for multiplication
Skip counting for multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Skip counting for multiplication?
- 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: Skip counting for multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Skip counting for multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Worked Example 2
Problem: What should you identify first before solving a problem about Skip counting for multiplication?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Skip counting for multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Skip counting for multiplication.
- 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: Skip counting for multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Skip counting for multiplication 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: Skip counting for multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Skip counting for multiplication.
- 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: Skip counting for multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Skip counting for multiplication can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Skip counting for multiplication. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.8 Connecting addition and multiplication
Connecting addition and multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Connecting addition and multiplication?
- 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: Connecting addition and multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Connecting addition and multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Worked Example 2
Problem: What should you identify first before solving a problem about Connecting addition and multiplication?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Connecting addition and multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Connecting addition and multiplication.
- 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: Connecting addition and multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Connecting addition and multiplication 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: Connecting addition and multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Connecting addition and multiplication.
- 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: Connecting addition and multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Connecting addition and multiplication can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Connecting addition and multiplication. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.9 Multiplication in everyday situations
Multiplication in everyday situations develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Multiplication in everyday situations?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Multiplication in everyday situations develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Multiplication in everyday situations develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Worked Example 2
Problem: What should you identify first before solving a problem about Multiplication in everyday situations?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Multiplication in everyday situations develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Multiplication in everyday situations.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Multiplication in everyday situations develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Multiplication in everyday situations problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Multiplication in everyday situations develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Multiplication in everyday situations.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Multiplication in everyday situations develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Multiplication in everyday situations can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Multiplication in everyday situations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.10 Checking a multiplication model
Checking a multiplication model develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Checking a multiplication 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: Checking a multiplication model develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Checking a multiplication model develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Worked Example 2
Problem: What should you identify first before solving a problem about Checking a multiplication model?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Checking a multiplication model develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Checking a multiplication 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: Checking a multiplication model develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Checking a multiplication 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: Checking a multiplication model develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Checking a multiplication 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: Checking a multiplication model develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Checking a multiplication model can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Checking a multiplication model. 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 groups.
- Create and solve one original problem about Repeated addition.
- Create and solve one original problem about Writing multiplication sentences.
- Create and solve one original problem about Factors and products.
- Create and solve one original problem about Making equal groups with objects.
- Create and solve one original problem about Drawing equal groups.
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 groups?
Answer: Equal groups 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 Repeated addition?
Answer: Repeated addition develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Q3. What is the key idea in Writing multiplication sentences?
Answer: Writing multiplication sentences develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Q4. What is the key idea in Factors and products?
Answer: Factors and products 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 Making equal groups with objects?
Answer: Making equal groups with objects 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 Drawing equal groups?
Answer: Drawing equal groups 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 Skip counting for multiplication?
Answer: Skip counting for multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Q8. What is the key idea in Connecting addition and multiplication?
Answer: Connecting addition and multiplication develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Q9. What is the key idea in Multiplication in everyday situations?
Answer: Multiplication in everyday situations develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Q10. What is the key idea in Checking a multiplication model?
Answer: Checking a multiplication model develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
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 Introduction to Multiplication 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 Introduction to Multiplication 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 Introduction to Multiplication 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 Introduction to Multiplication 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 Introduction to Multiplication effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.