Chapter 4: Factors, Multiples, Prime Numbers, and Divisibility
Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.
What this chapter covers
This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.
4.1 Factors
A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Factors.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Factors: Explain Factors in one simple sentence.
- Look at the words in “Factors”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Factors is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Factors: A student says, “I can use Factors without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Factors: What is the first step when solving a problem about Factors?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Factors: After solving a Factors problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Factors: Give one way Factors could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Factors can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Factors: Which representation could help explain Factors: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Factors: A student gets an answer for Factors but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Factors: Why can estimation help before a detailed Factors calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Factors: How can you test whether your rule for Factors works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Factors: How would you teach Factors to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Factors. Show the important steps, include units when needed, and explain how you checked the answer.
4.2 Factor pairs
A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Factor pairs.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Factor pairs: Explain Factor pairs in one simple sentence.
- Look at the words in “Factor pairs”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Factor pairs is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Factor pairs: A student says, “I can use Factor pairs without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Factor pairs: What is the first step when solving a problem about Factor pairs?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Factor pairs: After solving a Factor pairs problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Factor pairs: Give one way Factor pairs could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Factor pairs can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Factor pairs: Which representation could help explain Factor pairs: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Factor pairs: A student gets an answer for Factor pairs but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Factor pairs: Why can estimation help before a detailed Factor pairs calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Factor pairs: How can you test whether your rule for Factor pairs works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Factor pairs: How would you teach Factor pairs to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Factor pairs. Show the important steps, include units when needed, and explain how you checked the answer.
4.3 Multiples
A multiple (the result of multiplying a number by a whole number) helps with common denominators and repeating schedules. In this section, the focus is Multiples.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Multiples. Show the important steps, include units when needed, and explain how you checked the answer.
4.4 Common factors
A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Common factors.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Common factors: Explain Common factors in one simple sentence.
- Look at the words in “Common factors”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Common factors is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Common factors: A student says, “I can use Common factors without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Common factors: What is the first step when solving a problem about Common factors?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Common factors: After solving a Common factors problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Common factors: Give one way Common factors could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Common factors can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Common factors: Which representation could help explain Common factors: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Common factors: A student gets an answer for Common factors but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Common factors: Why can estimation help before a detailed Common factors calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Common factors: How can you test whether your rule for Common factors works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Common factors: How would you teach Common factors to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Common factors. Show the important steps, include units when needed, and explain how you checked the answer.
4.5 Greatest common factor
A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Greatest common factor.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Greatest common factor: Explain Greatest common factor in one simple sentence.
- Look at the words in “Greatest common factor”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Greatest common factor is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Greatest common factor: A student says, “I can use Greatest common factor without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Greatest common factor: What is the first step when solving a problem about Greatest common factor?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Greatest common factor: After solving a Greatest common factor problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Greatest common factor: Give one way Greatest common factor could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Greatest common factor can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Greatest common factor: Which representation could help explain Greatest common factor: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Greatest common factor: A student gets an answer for Greatest common factor but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Greatest common factor: Why can estimation help before a detailed Greatest common factor calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Greatest common factor: How can you test whether your rule for Greatest common factor works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Greatest common factor: How would you teach Greatest common factor to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Greatest common factor. Show the important steps, include units when needed, and explain how you checked the answer.
4.6 Common multiples
A multiple (the result of multiplying a number by a whole number) helps with common denominators and repeating schedules. In this section, the focus is Common multiples.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Common multiples. Show the important steps, include units when needed, and explain how you checked the answer.
4.7 Least common multiple
A multiple (the result of multiplying a number by a whole number) helps with common denominators and repeating schedules. In this section, the focus is Least common multiple.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Least common multiple. Show the important steps, include units when needed, and explain how you checked the answer.
4.8 Prime numbers
A prime number (a whole number greater than 1 with exactly two positive factors) cannot be broken into smaller whole-number factors except 1 and itself. In this section, the focus is Prime numbers.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Prime numbers: Explain Prime numbers in one simple sentence.
- Look at the words in “Prime numbers”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Prime numbers is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Prime numbers: A student says, “I can use Prime numbers without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Prime numbers: What is the first step when solving a problem about Prime numbers?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Prime numbers: After solving a Prime numbers problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Prime numbers: Give one way Prime numbers could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Prime numbers can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Prime numbers: Which representation could help explain Prime numbers: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Prime numbers: A student gets an answer for Prime numbers but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Prime numbers: Why can estimation help before a detailed Prime numbers calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Prime numbers: How can you test whether your rule for Prime numbers works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Prime numbers: How would you teach Prime numbers to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Prime numbers. Show the important steps, include units when needed, and explain how you checked the answer.
4.9 Composite numbers
Composite numbers is an important Grade 8 concept in Factors, Multiples, Prime Numbers, and Divisibility. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Composite numbers: Explain Composite numbers in one simple sentence.
- Look at the words in “Composite numbers”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Composite numbers is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Composite numbers: A student says, “I can use Composite numbers without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Composite numbers: What is the first step when solving a problem about Composite numbers?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Composite numbers: After solving a Composite numbers problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Composite numbers: Give one way Composite numbers could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Composite numbers can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Composite numbers: Which representation could help explain Composite numbers: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Composite numbers: A student gets an answer for Composite numbers but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Composite numbers: Why can estimation help before a detailed Composite numbers calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Composite numbers: How can you test whether your rule for Composite numbers works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Composite numbers: How would you teach Composite numbers to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Composite numbers. Show the important steps, include units when needed, and explain how you checked the answer.
4.10 Prime factorization
A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Prime factorization.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Prime factorization: Explain Prime factorization in one simple sentence.
- Look at the words in “Prime factorization”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Prime factorization is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Prime factorization: A student says, “I can use Prime factorization without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Prime factorization: What is the first step when solving a problem about Prime factorization?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Prime factorization: After solving a Prime factorization problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Prime factorization: Give one way Prime factorization could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Prime factorization can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Prime factorization: Which representation could help explain Prime factorization: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Prime factorization: A student gets an answer for Prime factorization but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Prime factorization: Why can estimation help before a detailed Prime factorization calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Prime factorization: How can you test whether your rule for Prime factorization works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Prime factorization: How would you teach Prime factorization to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Prime factorization. Show the important steps, include units when needed, and explain how you checked the answer.
4.11 Factor trees
A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Factor trees.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Factor trees: Explain Factor trees in one simple sentence.
- Look at the words in “Factor trees”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Factor trees is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Factor trees: A student says, “I can use Factor trees without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Factor trees: What is the first step when solving a problem about Factor trees?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Factor trees: After solving a Factor trees problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Factor trees: Give one way Factor trees could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Factor trees can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Factor trees: Which representation could help explain Factor trees: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Factor trees: A student gets an answer for Factor trees but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Factor trees: Why can estimation help before a detailed Factor trees calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Factor trees: How can you test whether your rule for Factor trees works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Factor trees: How would you teach Factor trees to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Factor trees. Show the important steps, include units when needed, and explain how you checked the answer.
4.12 Divisibility rules
Divisibility rules is an important Grade 8 concept in Factors, Multiples, Prime Numbers, and Divisibility. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Divisibility rules: Explain Divisibility rules in one simple sentence.
- Look at the words in “Divisibility rules”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Divisibility rules is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Divisibility rules: A student says, “I can use Divisibility rules without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Divisibility rules: What is the first step when solving a problem about Divisibility rules?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Divisibility rules: After solving a Divisibility rules problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Divisibility rules: Give one way Divisibility rules could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Divisibility rules can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Divisibility rules: Which representation could help explain Divisibility rules: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Divisibility rules: A student gets an answer for Divisibility rules but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Divisibility rules: Why can estimation help before a detailed Divisibility rules calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Divisibility rules: How can you test whether your rule for Divisibility rules works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Divisibility rules: How would you teach Divisibility rules to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Divisibility rules. Show the important steps, include units when needed, and explain how you checked the answer.
4.13 Applications of GCF and LCM
Applications of GCF and LCM is an important Grade 8 concept in Factors, Multiples, Prime Numbers, and Divisibility. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Applications of GCF and LCM: Explain Applications of GCF and LCM in one simple sentence.
- Look at the words in “Applications of GCF and LCM”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Applications of GCF and LCM is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Applications of GCF and LCM: A student says, “I can use Applications of GCF and LCM without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Applications of GCF and LCM: What is the first step when solving a problem about Applications of GCF and LCM?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Applications of GCF and LCM: After solving a Applications of GCF and LCM problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Applications of GCF and LCM: Give one way Applications of GCF and LCM could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Applications of GCF and LCM can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Applications of GCF and LCM: Which representation could help explain Applications of GCF and LCM: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Applications of GCF and LCM: A student gets an answer for Applications of GCF and LCM but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Applications of GCF and LCM: Why can estimation help before a detailed Applications of GCF and LCM calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Applications of GCF and LCM: How can you test whether your rule for Applications of GCF and LCM works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Applications of GCF and LCM: How would you teach Applications of GCF and LCM to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Applications of GCF and LCM. Show the important steps, include units when needed, and explain how you checked the answer.
Chapter 4 Review Questions and Answers
Q1. What is important to remember about Factors?
Answer: A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Factors.
Q2. What is important to remember about Factor pairs?
Answer: A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Factor pairs.
Q3. What is important to remember about Multiples?
Answer: A multiple (the result of multiplying a number by a whole number) helps with common denominators and repeating schedules. In this section, the focus is Multiples.
Q4. What is important to remember about Common factors?
Answer: A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Common factors.
Q5. What is important to remember about Greatest common factor?
Answer: A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Greatest common factor.
Q6. What is important to remember about Common multiples?
Answer: A multiple (the result of multiplying a number by a whole number) helps with common denominators and repeating schedules. In this section, the focus is Common multiples.
Q7. What is important to remember about Least common multiple?
Answer: A multiple (the result of multiplying a number by a whole number) helps with common denominators and repeating schedules. In this section, the focus is Least common multiple.
Q8. What is important to remember about Prime numbers?
Answer: A prime number (a whole number greater than 1 with exactly two positive factors) cannot be broken into smaller whole-number factors except 1 and itself. In this section, the focus is Prime numbers.
Q9. What is important to remember about Composite numbers?
Answer: Composite numbers is an important Grade 8 concept in Factors, Multiples, Prime Numbers, and Divisibility. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Prime factorization?
Answer: A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Prime factorization.
Q11. What is important to remember about Factor trees?
Answer: A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Factor trees.
Q12. What is important to remember about Divisibility rules?
Answer: Divisibility rules is an important Grade 8 concept in Factors, Multiples, Prime Numbers, and Divisibility. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q13. What is important to remember about Applications of GCF and LCM?
Answer: Applications of GCF and LCM is an important Grade 8 concept in Factors, Multiples, Prime Numbers, and Divisibility. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a calculated answer is reasonable.
Q16. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the mathematical relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question and check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, rates, relationships, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer was obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.
Q26. When is a calculator useful?
Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.
Q27. Why compare more than one strategy?
Answer: Different strategies may make a problem easier and provide a way to verify the result.
Q28. What is mathematical communication?
Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.
Q29. What is mathematical modelling?
Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.
Q30. Why should assumptions be stated?
Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.