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Chapter 11: Related Division Facts from 0 to 12

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

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

This chapter teaches Related Division Facts from 0 to 12 with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.

Key Technical Terms

  • Division as equal sharing (a Grade 5 idea used in this chapter)
  • Division as grouping (a Grade 5 idea used in this chapter)
  • Fact families (a Grade 5 idea used in this chapter)
  • Division facts related to twos, fives, and tens (a Grade 5 idea used in this chapter)
  • Division facts related to threes and fours (a Grade 5 idea used in this chapter)
  • Division facts related to sixes (a Grade 5 idea used in this chapter)
  • Division facts related to sevens (a Grade 5 idea used in this chapter)
  • Division facts related to eights and nines (a Grade 5 idea used in this chapter)
  • Division facts related to elevens and twelves (a Grade 5 idea used in this chapter)
  • Checking division with multiplication (a Grade 5 idea used in this chapter)

How to Learn This Chapter

Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

11.1 Division as equal sharing

Division as equal sharing 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 Division as equal sharing?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Division as equal sharing 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: Division as equal sharing 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 Division as equal sharing?

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

Very beginner explanation: Division as equal sharing 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 Division as equal sharing.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Division as equal sharing 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 Division as equal sharing problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Division as equal sharing 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 Division as equal sharing.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Division as equal sharing 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: Division as equal sharing can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Division as equal sharing in one simple sentence.

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

Very beginner explanation: Division as equal sharing 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 Division as equal sharing and explain why.

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

Very beginner explanation: Division as equal sharing 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 Division as equal sharing using a table, diagram, number line, graph, or equation.

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

Very beginner explanation: Division as equal sharing 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 Division as equal sharing problem, how can you check the answer?

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

Very beginner explanation: Division as equal sharing 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 Division as equal sharing could be useful.

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

Very beginner explanation: Division as equal sharing 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 Division as equal sharing. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

11.2 Division as grouping

Division as grouping 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 Division as grouping?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Division as grouping 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: Division as grouping 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 Division as grouping?

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

Very beginner explanation: Division as grouping 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 Division as grouping.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Division as grouping 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 Division as grouping problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Division as grouping 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 Division as grouping.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Division as grouping 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: Division as grouping can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.

Worked Example 6

Problem: Explain Division as grouping in one simple sentence.

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

Very beginner explanation: Division as grouping 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 Division as grouping and explain why.

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

Very beginner explanation: Division as grouping 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 Division as grouping using a table, diagram, number line, graph, or equation.

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

Very beginner explanation: Division as grouping 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 Division as grouping problem, how can you check the answer?

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

Very beginner explanation: Division as grouping 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 Division as grouping could be useful.

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

Very beginner explanation: Division as grouping 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 Division as grouping. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

11.3 Fact families

Fact families is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Beginner Note

Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In your own words, what is the main idea of Fact families?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Fact families is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: Fact families is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Worked Example 2

Problem: What should you identify first before solving a problem about Fact families?

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

Very beginner explanation: Fact families is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

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

Worked Example 3

Problem: Choose a useful representation for Fact families.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Fact families is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: Use the representation that makes the important relationship easiest to see and check.

Worked Example 4

Problem: A learner gets an answer in a Fact families problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Fact families is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Answer: The answer should agree with an estimate, the problem conditions, and a second check.

Worked Example 5

Problem: Give a real-life use for Fact families.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Fact families is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

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

Worked Example 6

Problem: Explain Fact families in one simple sentence.

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

Very beginner explanation: Fact families 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 Fact families and explain why.

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

Very beginner explanation: Fact families 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 Fact families using a table, diagram, number line, graph, or equation.

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

Very beginner explanation: Fact families 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 Fact families problem, how can you check the answer?

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

Very beginner explanation: Fact families 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 Fact families could be useful.

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

Very beginner explanation: Fact families 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 Fact families. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

11.4 Division facts related to twos, fives, and tens

Division facts related to twos, fives, and tens 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 Division facts related to twos, fives, and tens?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Division facts related to twos, fives, and tens 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: Division facts related to twos, fives, and tens 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 Division facts related to twos, fives, and tens?

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

Very beginner explanation: Division facts related to twos, fives, and tens 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 Division facts related to twos, fives, and tens.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Division facts related to twos, fives, and tens 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 Division facts related to twos, fives, and tens problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Division facts related to twos, fives, and tens 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 Division facts related to twos, fives, and tens.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Division facts related to twos, fives, and tens 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: Division facts related to twos, fives, and tens 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.

  1. Ask how many groups of 7 fit in 84.
  2. 7 × 12 = 84.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 12

Worked Example 7

Problem: Calculate 125 ÷ 8.

  1. Ask how many groups of 8 fit in 125.
  2. 8 × 15 = 120.
  3. Remainder = 5.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 15 R 5

Worked Example 8

Problem: Calculate 936 ÷ 9.

  1. Ask how many groups of 9 fit in 936.
  2. 9 × 104 = 936.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 104

Worked Example 9

Problem: Calculate 48 ÷ 12.

  1. Ask how many groups of 12 fit in 48.
  2. 12 × 4 = 48.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 4

Worked Example 10

Problem: Calculate 315 ÷ 5.

  1. Ask how many groups of 5 fit in 315.
  2. 5 × 63 = 315.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 63

Practice Exercise

Create one new question about Division facts related to twos, fives, and tens. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

11.5 Division facts related to threes and fours

Division facts related to threes and fours 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 Division facts related to threes and fours?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Division facts related to threes and fours 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: Division facts related to threes and fours 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 Division facts related to threes and fours?

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

Very beginner explanation: Division facts related to threes and fours 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 Division facts related to threes and fours.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Division facts related to threes and fours 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 Division facts related to threes and fours problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Division facts related to threes and fours 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 Division facts related to threes and fours.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Division facts related to threes and fours 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: Division facts related to threes and fours 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.

  1. Ask how many groups of 7 fit in 84.
  2. 7 × 12 = 84.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 12

Worked Example 7

Problem: Calculate 125 ÷ 8.

  1. Ask how many groups of 8 fit in 125.
  2. 8 × 15 = 120.
  3. Remainder = 5.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 15 R 5

Worked Example 8

Problem: Calculate 936 ÷ 9.

  1. Ask how many groups of 9 fit in 936.
  2. 9 × 104 = 936.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 104

Worked Example 9

Problem: Calculate 48 ÷ 12.

  1. Ask how many groups of 12 fit in 48.
  2. 12 × 4 = 48.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 4

Worked Example 10

Problem: Calculate 315 ÷ 5.

  1. Ask how many groups of 5 fit in 315.
  2. 5 × 63 = 315.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 63

Practice Exercise

Create one new question about Division facts related to threes and fours. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

11.6 Division facts related to sixes

Division facts related to sixes 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 Division facts related to sixes?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Division facts related to sixes 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: Division facts related to sixes 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 Division facts related to sixes?

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

Very beginner explanation: Division facts related to sixes 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 Division facts related to sixes.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Division facts related to sixes 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 Division facts related to sixes problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Division facts related to sixes 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 Division facts related to sixes.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Division facts related to sixes 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: Division facts related to sixes 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.

  1. Ask how many groups of 7 fit in 84.
  2. 7 × 12 = 84.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 12

Worked Example 7

Problem: Calculate 125 ÷ 8.

  1. Ask how many groups of 8 fit in 125.
  2. 8 × 15 = 120.
  3. Remainder = 5.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 15 R 5

Worked Example 8

Problem: Calculate 936 ÷ 9.

  1. Ask how many groups of 9 fit in 936.
  2. 9 × 104 = 936.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 104

Worked Example 9

Problem: Calculate 48 ÷ 12.

  1. Ask how many groups of 12 fit in 48.
  2. 12 × 4 = 48.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 4

Worked Example 10

Problem: Calculate 315 ÷ 5.

  1. Ask how many groups of 5 fit in 315.
  2. 5 × 63 = 315.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 63

Practice Exercise

Create one new question about Division facts related to sixes. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

11.7 Division facts related to sevens

Division facts related to sevens 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 Division facts related to sevens?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Division facts related to sevens 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: Division facts related to sevens 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 Division facts related to sevens?

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

Very beginner explanation: Division facts related to sevens 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 Division facts related to sevens.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Division facts related to sevens 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 Division facts related to sevens problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Division facts related to sevens 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 Division facts related to sevens.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Division facts related to sevens 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: Division facts related to sevens 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.

  1. Ask how many groups of 7 fit in 84.
  2. 7 × 12 = 84.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 12

Worked Example 7

Problem: Calculate 125 ÷ 8.

  1. Ask how many groups of 8 fit in 125.
  2. 8 × 15 = 120.
  3. Remainder = 5.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 15 R 5

Worked Example 8

Problem: Calculate 936 ÷ 9.

  1. Ask how many groups of 9 fit in 936.
  2. 9 × 104 = 936.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 104

Worked Example 9

Problem: Calculate 48 ÷ 12.

  1. Ask how many groups of 12 fit in 48.
  2. 12 × 4 = 48.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 4

Worked Example 10

Problem: Calculate 315 ÷ 5.

  1. Ask how many groups of 5 fit in 315.
  2. 5 × 63 = 315.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 63

Practice Exercise

Create one new question about Division facts related to sevens. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

11.8 Division facts related to eights and nines

Division facts related to eights and nines 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 Division facts related to eights and nines?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Division facts related to eights and nines 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: Division facts related to eights and nines 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 Division facts related to eights and nines?

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

Very beginner explanation: Division facts related to eights and nines 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 Division facts related to eights and nines.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Division facts related to eights and nines 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 Division facts related to eights and nines problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Division facts related to eights and nines 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 Division facts related to eights and nines.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Division facts related to eights and nines 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: Division facts related to eights and nines 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.

  1. Ask how many groups of 7 fit in 84.
  2. 7 × 12 = 84.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 12

Worked Example 7

Problem: Calculate 125 ÷ 8.

  1. Ask how many groups of 8 fit in 125.
  2. 8 × 15 = 120.
  3. Remainder = 5.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 15 R 5

Worked Example 8

Problem: Calculate 936 ÷ 9.

  1. Ask how many groups of 9 fit in 936.
  2. 9 × 104 = 936.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 104

Worked Example 9

Problem: Calculate 48 ÷ 12.

  1. Ask how many groups of 12 fit in 48.
  2. 12 × 4 = 48.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 4

Worked Example 10

Problem: Calculate 315 ÷ 5.

  1. Ask how many groups of 5 fit in 315.
  2. 5 × 63 = 315.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 63

Practice Exercise

Create one new question about Division facts related to eights and nines. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

11.9 Division facts related to elevens and twelves

Division facts related to elevens and twelves 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 Division facts related to elevens and twelves?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Division facts related to elevens and twelves 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: Division facts related to elevens and twelves 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 Division facts related to elevens and twelves?

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

Very beginner explanation: Division facts related to elevens and twelves 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 Division facts related to elevens and twelves.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Division facts related to elevens and twelves 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 Division facts related to elevens and twelves problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Division facts related to elevens and twelves 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 Division facts related to elevens and twelves.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Division facts related to elevens and twelves 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: Division facts related to elevens and twelves 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.

  1. Ask how many groups of 7 fit in 84.
  2. 7 × 12 = 84.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 12

Worked Example 7

Problem: Calculate 125 ÷ 8.

  1. Ask how many groups of 8 fit in 125.
  2. 8 × 15 = 120.
  3. Remainder = 5.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 15 R 5

Worked Example 8

Problem: Calculate 936 ÷ 9.

  1. Ask how many groups of 9 fit in 936.
  2. 9 × 104 = 936.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 104

Worked Example 9

Problem: Calculate 48 ÷ 12.

  1. Ask how many groups of 12 fit in 48.
  2. 12 × 4 = 48.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 4

Worked Example 10

Problem: Calculate 315 ÷ 5.

  1. Ask how many groups of 5 fit in 315.
  2. 5 × 63 = 315.
  3. Remainder = 0.

Very beginner explanation: Division can be checked by multiplying the quotient by the divisor and adding any remainder.

Answer: 63

Practice Exercise

Create one new question about Division facts related to elevens and twelves. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

11.10 Checking division with multiplication

Checking division with 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 Checking division with multiplication?

  1. Read the topic name carefully.
  2. Identify the quantity, relationship, shape, or process it describes.
  3. Explain the idea without using a memorized sentence.

Very beginner explanation: Checking division with 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: Checking division with 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 Checking division with multiplication?

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

Very beginner explanation: Checking division with 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 Checking division with multiplication.

  1. Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
  2. Label the representation clearly.
  3. Check that it matches the mathematical relationship.

Very beginner explanation: Checking division with 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 Checking division with multiplication problem. How can the learner check it?

  1. Estimate the expected size or direction of the answer.
  2. Check units, labels, signs, and place values.
  3. Use an inverse operation or a second method when possible.

Very beginner explanation: Checking division with 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 Checking division with multiplication.

  1. Think about money, measurement, data, patterns, design, or everyday quantities.
  2. Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
  3. Explain the connection in one sentence.

Very beginner explanation: Checking division with 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: Checking division with 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.

  1. Convert 10% to 0.1.
  2. 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.

  1. Convert 25% to 0.25.
  2. 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.

  1. Convert 15% to 0.15.
  2. 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.

  1. Convert 5% to 0.05.
  2. 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.

  1. Convert 20% to 0.2.
  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 division with multiplication. 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

  1. Create and solve one original problem about Division as equal sharing.
  2. Create and solve one original problem about Division as grouping.
  3. Create and solve one original problem about Fact families.
  4. Create and solve one original problem about Division facts related to twos, fives, and tens.
  5. Create and solve one original problem about Division facts related to threes and fours.
  6. Create and solve one original problem about Division facts related to sixes.

Common Mistakes

  • Skipping the meaning and trying to memorize a rule only.
  • Using the wrong operation because the question was not read completely.
  • Ignoring units, labels, place values, or the context of the problem.
  • Not estimating or checking whether the final answer is reasonable.
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30 Review Questions and Answers

Q1. What is the key idea in Division as equal sharing?

Answer: Division as equal sharing 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.

Q2. What is the key idea in Division as grouping?

Answer: Division as grouping 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 Fact families?

Answer: Fact families is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.

Q4. What is the key idea in Division facts related to twos, fives, and tens?

Answer: Division facts related to twos, fives, and tens 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.

Q5. What is the key idea in Division facts related to threes and fours?

Answer: Division facts related to threes and fours 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.

Q6. What is the key idea in Division facts related to sixes?

Answer: Division facts related to sixes 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.

Q7. What is the key idea in Division facts related to sevens?

Answer: Division facts related to sevens 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 Division facts related to eights and nines?

Answer: Division facts related to eights and nines 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 Division facts related to elevens and twelves?

Answer: Division facts related to elevens and twelves 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 division with multiplication?

Answer: Checking division with 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.

Q11. Why should you estimate before or after a calculation?

Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.

Q12. Why are labels and units important?

Answer: They show what a number represents and help prevent mixing unlike quantities.

Q13. How can a diagram help solve a problem?

Answer: A diagram makes quantities and relationships visible before calculation.

Q14. How can inverse operations check an answer?

Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.

Q15. Why should you show steps?

Answer: Showing steps makes reasoning clear and helps find where an error happened.

Q16. What should you do after making a mistake?

Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.

Q17. How can a number line support reasoning?

Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.

Q18. When is a table useful?

Answer: A table organizes related values so patterns and comparisons are easier to see.

Q19. When is a graph useful?

Answer: A graph makes trends, comparisons, locations, or data patterns visible.

Q20. How do you decide which operation to use?

Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.

Q21. Why should you check place value?

Answer: A digit or decimal has a different value depending on its position.

Q22. What makes an answer reasonable?

Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.

Q23. How can you explain mathematical reasoning clearly?

Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.

Q24. Why can more than one strategy be correct?

Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.

Q25. How should you approach a difficult Grade 5 problem?

Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.

Q26. How can you practise Related Division Facts from 0 to 12 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 Related Division Facts from 0 to 12 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 Related Division Facts from 0 to 12 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 Related Division Facts from 0 to 12 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 Related Division Facts from 0 to 12 effectively?

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