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Chapter 23: Variables, Constants, and Terms

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 Variables, Constants, and Terms in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Meaning of variable (A variable is a symbol used to represent a number that may change or may be unknown.)
  • Meaning of constant (A constant is a value that stays the same.)
  • Meaning of term (The mean is found by adding all values and dividing by the number of values.)
  • Meaning of coefficient (A coefficient is the number multiplying a variable.)
  • Algebraic expressions (An algebraic expression combines numbers, variables, and operations without an equals sign.)
  • Identifying terms (Identifying terms is a Grade 6 mathematics idea in Variables, Constants, and Terms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)

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.

23.1 Meaning of variable

A variable is a symbol used to represent a number that may change or may be unknown. 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 Meaning of variable. 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.

23.2 Meaning of constant

A constant is a value that stays the same. 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 Meaning of constant. 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.

23.3 Meaning of term

The mean is found by adding all values and dividing by the number of values. 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 Meaning of term. 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.

23.4 Meaning of coefficient

A coefficient is the number multiplying a variable. 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 Meaning of coefficient. 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.

23.5 Algebraic expressions

An algebraic expression combines numbers, variables, and operations without an equals sign. 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 Algebraic expressions. 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.

23.6 Writing expressions from words

An algebraic expression combines numbers, variables, and operations without an equals sign. 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 Writing expressions from words. 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.

23.7 Writing words from expressions

An algebraic expression combines numbers, variables, and operations without an equals sign. 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 Writing words from expressions. 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.

23.8 Variables in real-life situations

A variable is a symbol used to represent a number that may change or may be unknown. 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 Variables in real-life situations. 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.

23.9 Constants in real-life situations

A constant is a value that stays the same. 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 Constants in real-life situations. 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.

23.10 Identifying terms

Identifying terms is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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: 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 Identifying terms. 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.

23.11 Identifying coefficients

A coefficient is the number multiplying a variable. 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 Identifying coefficients. 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.

23.12 Using symbols to represent unknowns

Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns to analyze the values 4 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: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns to analyze the values 24 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: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns to analyze the values 19 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: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns to analyze the values 22 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: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns to analyze the values 19 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: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns to analyze the values 22 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: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns to analyze the values 30 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: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns to analyze the values 30 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: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns to analyze the values 18 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: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns to analyze the values 9 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: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. 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 Using symbols to represent unknowns. 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 Meaning of variable?

Answer: A variable is a symbol used to represent a number that may change or may be unknown.

Q2. What is important to understand about Meaning of constant?

Answer: A constant is a value that stays the same.

Q3. What is important to understand about Meaning of term?

Answer: The mean is found by adding all values and dividing by the number of values.

Q4. What is important to understand about Meaning of coefficient?

Answer: A coefficient is the number multiplying a variable.

Q5. What is important to understand about Algebraic expressions?

Answer: An algebraic expression combines numbers, variables, and operations without an equals sign.

Q6. What is important to understand about Writing expressions from words?

Answer: An algebraic expression combines numbers, variables, and operations without an equals sign.

Q7. What is important to understand about Writing words from expressions?

Answer: An algebraic expression combines numbers, variables, and operations without an equals sign.

Q8. What is important to understand about Variables in real-life situations?

Answer: A variable is a symbol used to represent a number that may change or may be unknown.

Q9. What is important to understand about Constants in real-life situations?

Answer: A constant is a value that stays the same.

Q10. What is important to understand about Identifying terms?

Answer: Identifying terms is a Grade 6 mathematics idea in Variables, Constants, and Terms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q11. What is important to understand about Identifying coefficients?

Answer: A coefficient is the number multiplying a variable.

Q12. What is important to understand about Using symbols to represent unknowns?

Answer: Using symbols to represent unknowns is a Grade 6 mathematics idea in Variables, Constants, and Terms. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. Why should you show your steps?

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

Q14. Why is estimation useful?

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

Q15. Why do units matter?

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

Q16. When should you round?

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

Q17. How can you check an answer?

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

Q18. What should you identify first in a word problem?

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

Q19. What makes a final answer complete?

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

Q20. What should you do if an answer seems unreasonable?

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

Q21. Why are diagrams useful?

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

Q22. Why are tables useful?

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

Q23. Why are graphs useful?

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

Q24. Why should you explain your reasoning?

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

Q25. Why can more than one strategy be correct?

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

Q26. What should you do before using a formula or rule?

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

Q27. How does practice help in mathematics?

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

Q28. What is a good way to learn from a mistake?

Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.

Q29. Why should you compare an exact answer with an estimate?

Answer: The estimate gives a quick reasonableness check for the exact calculation.

Q30. What does representing mathematics mean?

Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.