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Chapter 60: Comprehensive Grade 6 Review and Mathematical Processes

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

This chapter teaches Comprehensive Grade 6 Review and Mathematical Processes in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Whole-number review (Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Integer review (An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.)
  • Decimal review (A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.)
  • Fraction review (A fraction represents equal parts of a whole, set, or quantity.)
  • Percent ratio and rate review (Percent means 'per hundred' and compares a quantity with 100 equal parts.)
  • Operations review (A ratio compares two quantities by division.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

60.1 Whole-number review

Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Whole-number review to analyze the values 9 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Whole-number review to analyze the values 8 and 8. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Whole-number review to analyze the values 15 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Whole-number review to analyze the values 23 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Whole-number review to analyze the values 23 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Whole-number review to analyze the values 13 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Whole-number review to analyze the values 20 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Whole-number review to analyze the values 18 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Whole-number review to analyze the values 30 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Whole-number review to analyze the values 26 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Whole-number review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.2 Integer review

An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A temperature starts at 9° and changes by -5°. What is the new temperature?

  1. Start at the original integer.
  2. Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 4°

Worked Example 2

Problem: A temperature starts at 7° and changes by -7°. What is the new temperature?

  1. Start at the original integer.
  2. Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 0°

Worked Example 3

Problem: A temperature starts at 9° and changes by -5°. What is the new temperature?

  1. Start at the original integer.
  2. Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 4°

Worked Example 4

Problem: A temperature starts at 2° and changes by -5°. What is the new temperature?

  1. Start at the original integer.
  2. Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -3°

Worked Example 5

Problem: A temperature starts at -6° and changes by +1°. What is the new temperature?

  1. Start at the original integer.
  2. Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -5°

Worked Example 6

Problem: A temperature starts at -3° and changes by +4°. What is the new temperature?

  1. Start at the original integer.
  2. Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 1°

Worked Example 7

Problem: A temperature starts at 7° and changes by -5°. What is the new temperature?

  1. Start at the original integer.
  2. Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 2°

Worked Example 8

Problem: A temperature starts at 6° and changes by -5°. What is the new temperature?

  1. Start at the original integer.
  2. Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 1°

Worked Example 9

Problem: A temperature starts at -5° and changes by +5°. What is the new temperature?

  1. Start at the original integer.
  2. Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 0°

Worked Example 10

Problem: A temperature starts at 2° and changes by -4°. What is the new temperature?

  1. Start at the original integer.
  2. Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -2°

Practice Exercise

Create one new Grade 6 problem about Integer review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.3 Decimal review

A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: What digit is in the tenths place of 35.676?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 6

Worked Example 2

Problem: What digit is in the tenths place of 86.727?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 7

Worked Example 3

Problem: What digit is in the tenths place of 35.378?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 3

Worked Example 4

Problem: What digit is in the tenths place of 45.716?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 7

Worked Example 5

Problem: What digit is in the tenths place of 4.528?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 5

Worked Example 6

Problem: What digit is in the tenths place of 80.247?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 2

Worked Example 7

Problem: What digit is in the tenths place of 4.841?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 8

Worked Example 8

Problem: What digit is in the tenths place of 10.042?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 0

Worked Example 9

Problem: What digit is in the tenths place of 36.587?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 5

Worked Example 10

Problem: What digit is in the tenths place of 60.89?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 8

Practice Exercise

Create one new Grade 6 problem about Decimal review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is lining up the last digits instead of lining up decimal points and place values.

60.4 Fraction review

A fraction represents equal parts of a whole, set, or quantity. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide 1 by 2.

Very beginner explanation: The fraction bar means division.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide 2 by 3.

Very beginner explanation: The fraction bar means division.

Answer: 0.667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide 3 by 5.

Very beginner explanation: The fraction bar means division.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide 5 by 8.

Very beginner explanation: The fraction bar means division.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide 7 by 10.

Very beginner explanation: The fraction bar means division.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide 4 by 9.

Very beginner explanation: The fraction bar means division.

Answer: 0.444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide 5 by 6.

Very beginner explanation: The fraction bar means division.

Answer: 0.833

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide 3 by 4.

Very beginner explanation: The fraction bar means division.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide 2 by 5.

Very beginner explanation: The fraction bar means division.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide 7 by 12.

Very beginner explanation: The fraction bar means division.

Answer: 0.583

Practice Exercise

Create one new Grade 6 problem about Fraction review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is combining numerators and denominators without first applying the correct fraction rule.

60.5 Percent ratio and rate review

Percent means 'per hundred' and compares a quantity with 100 equal parts. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find 1% of 80.

  1. Think of 1% as 1/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 0.8

Worked Example 2

Problem: Find 5% of 120.

  1. Think of 5% as 5/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6

Worked Example 3

Problem: Find 10% of 64.

  1. Think of 10% as 10/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6.4

Worked Example 4

Problem: Find 20% of 250.

  1. Think of 20% as 20/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 50

Worked Example 5

Problem: Find 25% of 96.

  1. Think of 25% as 25/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 24

Worked Example 6

Problem: Find 50% of 40.

  1. Think of 50% as 50/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 20

Worked Example 7

Problem: Find 75% of 200.

  1. Think of 75% as 75/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 150

Worked Example 8

Problem: Find 15% of 60.

  1. Think of 15% as 15/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 9

Worked Example 9

Problem: Find 30% of 150.

  1. Think of 30% as 30/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 45

Worked Example 10

Problem: Find 40% of 90.

  1. Think of 40% as 40/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 36

Practice Exercise

Create one new Grade 6 problem about Percent ratio and rate review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.

60.6 Operations review

A ratio compares two quantities by division. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Simplify the ratio 2:9.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 2:9

Worked Example 2

Problem: Simplify the ratio 3:14.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 3:14

Worked Example 3

Problem: Simplify the ratio 2:7.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 2:7

Worked Example 4

Problem: Simplify the ratio 9:8.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 9:8

Worked Example 5

Problem: Simplify the ratio 8:11.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 8:11

Worked Example 6

Problem: Simplify the ratio 9:7.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 9:7

Worked Example 7

Problem: Simplify the ratio 2:11.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 2:11

Worked Example 8

Problem: Simplify the ratio 3:14.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 3:14

Worked Example 9

Problem: Simplify the ratio 9:6.

  1. Find the greatest common factor, 3.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 3:2

Worked Example 10

Problem: Simplify the ratio 9:12.

  1. Find the greatest common factor, 3.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 3:4

Practice Exercise

Create one new Grade 6 problem about Operations review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.7 Algebra and equation review

An equation states that two mathematical expressions have the same value. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate 3x + 4 when x = 5.

  1. Replace x with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 2

Problem: Evaluate 2n + 7 when n = 6.

  1. Replace n with 6.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 3

Problem: Evaluate 5a - 3 when a = 4.

  1. Replace a with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 17

Worked Example 4

Problem: Evaluate 4p + 1 when p = 8.

  1. Replace p with 8.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 33

Worked Example 5

Problem: Evaluate 6m - 5 when m = 3.

  1. Replace m with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 13

Worked Example 6

Problem: Evaluate 2.5x + 1 when x = 4.

  1. Replace x with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 11

Worked Example 7

Problem: Evaluate 7q + 2 when q = 2.

  1. Replace q with 2.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 16

Worked Example 8

Problem: Evaluate 3r - 1 when r = 9.

  1. Replace r with 9.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 9

Problem: Evaluate 4y + 6 when y = 5.

  1. Replace y with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 10

Problem: Evaluate 8k - 4 when k = 3.

  1. Replace k with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 20

Practice Exercise

Create one new Grade 6 problem about Algebra and equation review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is changing only one side of a relationship or forgetting to check the solution.

60.8 Coding and modelling review

The mode is the value that appears most often. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A simple cost model is C = 20 + 3n. Find the cost when n = 5.

  1. Substitute n = 5.
  2. Multiply 3 × 5.
  3. Add the fixed amount.

Very beginner explanation: A model is a simplified mathematical representation of a real situation.

Answer: $35

Worked Example 2

Problem: A simple cost model is C = 25 + 4n. Find the cost when n = 6.

  1. Substitute n = 6.
  2. Multiply 4 × 6.
  3. Add the fixed amount.

Very beginner explanation: A model is a simplified mathematical representation of a real situation.

Answer: $49

Worked Example 3

Problem: A simple cost model is C = 30 + 5n. Find the cost when n = 7.

  1. Substitute n = 7.
  2. Multiply 5 × 7.
  3. Add the fixed amount.

Very beginner explanation: A model is a simplified mathematical representation of a real situation.

Answer: $65

Worked Example 4

Problem: A simple cost model is C = 35 + 6n. Find the cost when n = 8.

  1. Substitute n = 8.
  2. Multiply 6 × 8.
  3. Add the fixed amount.

Very beginner explanation: A model is a simplified mathematical representation of a real situation.

Answer: $83

Worked Example 5

Problem: A simple cost model is C = 40 + 7n. Find the cost when n = 9.

  1. Substitute n = 9.
  2. Multiply 7 × 9.
  3. Add the fixed amount.

Very beginner explanation: A model is a simplified mathematical representation of a real situation.

Answer: $103

Worked Example 6

Problem: A simple cost model is C = 45 + 8n. Find the cost when n = 10.

  1. Substitute n = 10.
  2. Multiply 8 × 10.
  3. Add the fixed amount.

Very beginner explanation: A model is a simplified mathematical representation of a real situation.

Answer: $125

Worked Example 7

Problem: A simple cost model is C = 50 + 9n. Find the cost when n = 11.

  1. Substitute n = 11.
  2. Multiply 9 × 11.
  3. Add the fixed amount.

Very beginner explanation: A model is a simplified mathematical representation of a real situation.

Answer: $149

Worked Example 8

Problem: A simple cost model is C = 55 + 10n. Find the cost when n = 12.

  1. Substitute n = 12.
  2. Multiply 10 × 12.
  3. Add the fixed amount.

Very beginner explanation: A model is a simplified mathematical representation of a real situation.

Answer: $175

Worked Example 9

Problem: A simple cost model is C = 60 + 11n. Find the cost when n = 13.

  1. Substitute n = 13.
  2. Multiply 11 × 13.
  3. Add the fixed amount.

Very beginner explanation: A model is a simplified mathematical representation of a real situation.

Answer: $203

Worked Example 10

Problem: A simple cost model is C = 65 + 12n. Find the cost when n = 14.

  1. Substitute n = 14.
  2. Multiply 12 × 14.
  3. Add the fixed amount.

Very beginner explanation: A model is a simplified mathematical representation of a real situation.

Answer: $233

Practice Exercise

Create one new Grade 6 problem about Coding and modelling review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.9 Data and graph review

Data and graph review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify the data values [4, 6, 8, 10] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 2

Problem: Classify the data values [5, 7, 7, 9, 12] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 3

Problem: Classify the data values [3, 5, 8, 8, 11] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 4

Problem: Classify the data values [10, 12, 14, 16] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 5

Problem: Classify the data values [2, 4, 6, 8, 10] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 6

Problem: Classify the data values [1, 5, 5, 6, 13] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 7

Problem: Classify the data values [20, 25, 25, 30] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 8

Problem: Classify the data values [7, 8, 9, 10, 11] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 9

Problem: Classify the data values [3, 3, 4, 5, 9] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Worked Example 10

Problem: Classify the data values [12, 15, 18, 21] as quantitative or qualitative.

  1. They are numerical values.
  2. Numerical counts or measurements are quantitative.

Very beginner explanation: Quantitative data use numbers to represent counts or measurements.

Answer: Quantitative

Practice Exercise

Create one new Grade 6 problem about Data and graph review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is ignoring the scale, labels, units, or the type of data shown.

60.10 Probability review

Probability describes how likely an event is to happen. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the probability to roll an even number on a fair six-sided die.

  1. Count favourable outcomes: 3.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 2

Problem: Find the probability to flip heads on a fair coin.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 3

Problem: Find the probability to draw red from 4 red and 6 blue counters.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 2/5

Worked Example 4

Problem: Find the probability to choose a vowel from A B C E.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 4.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 5

Problem: Find the probability to spin one section on 5 equal sections.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 5.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/5

Worked Example 6

Problem: Find the probability to roll a number greater than 4.

  1. Count favourable outcomes: 2.
  2. Count total equally likely outcomes: 6.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Worked Example 7

Problem: Find the probability to choose an odd number from 1 through 10.

  1. Count favourable outcomes: 5.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 8

Problem: Find the probability to draw green from 7 green and 3 yellow counters.

  1. Count favourable outcomes: 7.
  2. Count total equally likely outcomes: 10.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 7/10

Worked Example 9

Problem: Find the probability to flip tails.

  1. Count favourable outcomes: 1.
  2. Count total equally likely outcomes: 2.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/2

Worked Example 10

Problem: Find the probability to choose a multiple of 3 from 1 through 12.

  1. Count favourable outcomes: 4.
  2. Count total equally likely outcomes: 12.
  3. Write favourable ÷ total and simplify.

Very beginner explanation: Probability compares favourable outcomes with all equally likely outcomes.

Answer: 1/3

Practice Exercise

Create one new Grade 6 problem about Probability review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is counting favourable outcomes but forgetting to count all possible outcomes.

60.11 Geometry and measurement review

Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Geometry and measurement review to analyze the values 22 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Geometry and measurement review to analyze the values 10 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Geometry and measurement review to analyze the values 6 and 11. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Geometry and measurement review to analyze the values 9 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Geometry and measurement review to analyze the values 4 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Geometry and measurement review to analyze the values 11 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Geometry and measurement review to analyze the values 29 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Geometry and measurement review to analyze the values 27 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Geometry and measurement review to analyze the values 8 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Geometry and measurement review to analyze the values 16 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Geometry and measurement review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.12 Financial literacy review

Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Financial literacy review to analyze the values 26 and 12. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Financial literacy review to analyze the values 2 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Financial literacy review to analyze the values 13 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Financial literacy review to analyze the values 9 and 3. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Financial literacy review to analyze the values 12 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Financial literacy review to analyze the values 16 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Financial literacy review to analyze the values 28 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Financial literacy review to analyze the values 7 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Financial literacy review to analyze the values 2 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Financial literacy review to analyze the values 14 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Financial literacy review. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is comparing only one number and ignoring fees, timing, limits, or the full context.

60.13 Problem solving

Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Problem solving to analyze the values 17 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Problem solving to analyze the values 29 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Problem solving to analyze the values 7 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Problem solving to analyze the values 26 and 8. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Problem solving to analyze the values 8 and 9. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Problem solving to analyze the values 6 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Problem solving to analyze the values 3 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Problem solving to analyze the values 13 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Problem solving to analyze the values 14 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Problem solving to analyze the values 9 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Problem solving. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.14 Reasoning and proving

Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Reasoning and proving to analyze the values 13 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Reasoning and proving to analyze the values 3 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Reasoning and proving to analyze the values 8 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Reasoning and proving to analyze the values 7 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Reasoning and proving to analyze the values 11 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Reasoning and proving to analyze the values 28 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Reasoning and proving to analyze the values 9 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Reasoning and proving to analyze the values 10 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Reasoning and proving to analyze the values 23 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Reasoning and proving to analyze the values 26 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Reasoning and proving. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.15 Reflecting

Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Reflecting to analyze the values 4 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Reflecting to analyze the values 26 and 8. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Reflecting to analyze the values 29 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Reflecting to analyze the values 16 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Reflecting to analyze the values 7 and 3. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Reflecting to analyze the values 22 and 9. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Reflecting to analyze the values 25 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Reflecting to analyze the values 20 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Reflecting to analyze the values 6 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Reflecting to analyze the values 9 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Reflecting. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.16 Selecting tools and strategies

A rate compares two quantities measured in different units. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: 88 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 88 ÷ 8 = 11.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 11 per group

Worked Example 2

Problem: 80 units are used in 10 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 80 ÷ 10 = 8.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 8 per group

Worked Example 3

Problem: 96 units are used in 12 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 96 ÷ 12 = 8.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 8 per group

Worked Example 4

Problem: 120 units are used in 15 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 120 ÷ 15 = 8.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 8 per group

Worked Example 5

Problem: 22 units are used in 11 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 22 ÷ 11 = 2.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 2 per group

Worked Example 6

Problem: 90 units are used in 10 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 90 ÷ 10 = 9.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 9 per group

Worked Example 7

Problem: 39 units are used in 13 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 39 ÷ 13 = 3.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 3 per group

Worked Example 8

Problem: 33 units are used in 11 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 33 ÷ 11 = 3.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 3 per group

Worked Example 9

Problem: 88 units are used in 11 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 88 ÷ 11 = 8.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 8 per group

Worked Example 10

Problem: 25 units are used in 5 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 25 ÷ 5 = 5.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 5 per group

Practice Exercise

Create one new Grade 6 problem about Selecting tools and strategies. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.17 Connecting

Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Connecting to analyze the values 5 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Connecting to analyze the values 13 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Connecting to analyze the values 20 and 3. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Connecting to analyze the values 14 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Connecting to analyze the values 19 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Connecting to analyze the values 29 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Connecting to analyze the values 4 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Connecting to analyze the values 23 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Connecting to analyze the values 20 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Connecting to analyze the values 6 and 3. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Connecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Connecting. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.18 Representing

Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Representing to analyze the values 27 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Representing to analyze the values 14 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Representing to analyze the values 23 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Representing to analyze the values 12 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Representing to analyze the values 12 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Representing to analyze the values 18 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Representing to analyze the values 29 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Representing to analyze the values 26 and 12. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Representing to analyze the values 26 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Representing to analyze the values 22 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Representing is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Representing. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

60.19 Communicating

Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Communicating to analyze the values 22 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Communicating to analyze the values 26 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Communicating to analyze the values 2 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Communicating to analyze the values 13 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Communicating to analyze the values 26 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Communicating to analyze the values 28 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Communicating to analyze the values 7 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Communicating to analyze the values 9 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Communicating to analyze the values 29 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Communicating to analyze the values 11 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Communicating is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Communicating. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

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30 Review Questions and Answers

Q1. What is important to understand about Whole-number review?

Answer: Whole-number review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q2. What is important to understand about Integer review?

Answer: An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.

Q3. What is important to understand about Decimal review?

Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.

Q4. What is important to understand about Fraction review?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q5. What is important to understand about Percent ratio and rate review?

Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.

Q6. What is important to understand about Operations review?

Answer: A ratio compares two quantities by division.

Q7. What is important to understand about Algebra and equation review?

Answer: An equation states that two mathematical expressions have the same value.

Q8. What is important to understand about Coding and modelling review?

Answer: The mode is the value that appears most often.

Q9. What is important to understand about Data and graph review?

Answer: Data and graph review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q10. What is important to understand about Probability review?

Answer: Probability describes how likely an event is to happen.

Q11. What is important to understand about Geometry and measurement review?

Answer: Geometry and measurement review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q12. What is important to understand about Financial literacy review?

Answer: Financial literacy review is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. What is important to understand about Problem solving?

Answer: Problem solving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q14. What is important to understand about Reasoning and proving?

Answer: Reasoning and proving is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q15. What is important to understand about Reflecting?

Answer: Reflecting is a Grade 6 mathematics idea in Comprehensive Grade 6 Review and Mathematical Processes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q16. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q17. Why is estimation useful?

Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.

Q18. Why do units matter?

Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.

Q19. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q20. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.

Q21. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the relationship connecting them.

Q22. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q23. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.

Q24. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships that are harder to see in words alone.

Q25. Why are tables useful?

Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.

Q26. Why are graphs useful?

Answer: Graphs make relationships, changes, trends, and comparisons visible.

Q27. Why should you explain your reasoning?

Answer: An explanation shows why a method works instead of only giving a final number.

Q28. Why can more than one strategy be correct?

Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.

Q29. What should you do before using a formula or rule?

Answer: Check what each quantity means and whether the rule matches the situation.

Q30. How does practice help in mathematics?

Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.