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Chapter 20: Constant-Rate Patterns

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 Constant-Rate Patterns in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Meaning of constant rate (A rate compares two quantities measured in different units.)
  • Constant addition (A constant is a value that stays the same.)
  • Distance-time patterns (A pattern follows a rule that can be described, extended, and used to make predictions.)

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.

20.1 Meaning of constant rate

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: 70 units are used in 14 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 70 ÷ 14 = 5.

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

Answer: 5 per group

Worked Example 2

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

Worked Example 3

Problem: 42 units are used in 6 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 42 ÷ 6 = 7.

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

Answer: 7 per group

Worked Example 4

Problem: 35 units are used in 5 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 35 ÷ 5 = 7.

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

Answer: 7 per group

Worked Example 5

Problem: 16 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 16 ÷ 8 = 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: 26 units are used in 13 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 26 ÷ 13 = 2.

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

Answer: 2 per group

Worked Example 7

Problem: 18 units are used in 9 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 18 ÷ 9 = 2.

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

Answer: 2 per group

Worked Example 8

Problem: 126 units are used in 14 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 126 ÷ 14 = 9.

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

Answer: 9 per group

Worked Example 9

Problem: 132 units are used in 11 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 132 ÷ 11 = 12.

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

Answer: 12 per group

Worked Example 10

Problem: 60 units are used in 15 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 60 ÷ 15 = 4.

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

Answer: 4 per group

Practice Exercise

Create one new Grade 6 problem about Meaning of constant rate. 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.

20.2 Constant addition

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 Constant addition. 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.

20.3 Constant subtraction

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 Constant subtraction. 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.

20.4 Distance-time patterns

A pattern follows a rule that can be described, extended, and used to make predictions. 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: Continue the pattern 5, 7, 9, ... for two more terms.

  1. Find the constant change: +2.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 11, 13

Worked Example 2

Problem: Continue the pattern 2, 4, 6, ... for two more terms.

  1. Find the constant change: +2.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 8, 10

Worked Example 3

Problem: Continue the pattern 1, 10, 19, ... for two more terms.

  1. Find the constant change: +9.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 28, 37

Worked Example 4

Problem: Continue the pattern 11, 15, 19, ... for two more terms.

  1. Find the constant change: +4.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 23, 27

Worked Example 5

Problem: Continue the pattern 0, 4, 8, ... for two more terms.

  1. Find the constant change: +4.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 12, 16

Worked Example 6

Problem: Continue the pattern 2, 4, 6, ... for two more terms.

  1. Find the constant change: +2.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 8, 10

Worked Example 7

Problem: Continue the pattern -3, 1, 5, ... for two more terms.

  1. Find the constant change: +4.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 9, 13

Worked Example 8

Problem: Continue the pattern 7, 11, 15, ... for two more terms.

  1. Find the constant change: +4.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 19, 23

Worked Example 9

Problem: Continue the pattern 9, 17, 25, ... for two more terms.

  1. Find the constant change: +8.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 33, 41

Worked Example 10

Problem: Continue the pattern 1, 10, 19, ... for two more terms.

  1. Find the constant change: +9.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 28, 37

Practice Exercise

Create one new Grade 6 problem about Distance-time patterns. 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.

20.5 Cost-per-item patterns

A pattern follows a rule that can be described, extended, and used to make predictions. 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: Continue the pattern 7, 13, 19, ... for two more terms.

  1. Find the constant change: +6.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 25, 31

Worked Example 2

Problem: Continue the pattern 7, 15, 23, ... for two more terms.

  1. Find the constant change: +8.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 31, 39

Worked Example 3

Problem: Continue the pattern -4, 4, 12, ... for two more terms.

  1. Find the constant change: +8.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 20, 28

Worked Example 4

Problem: Continue the pattern 11, 13, 15, ... for two more terms.

  1. Find the constant change: +2.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 17, 19

Worked Example 5

Problem: Continue the pattern 6, 9, 12, ... for two more terms.

  1. Find the constant change: +3.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 15, 18

Worked Example 6

Problem: Continue the pattern -2, 7, 16, ... for two more terms.

  1. Find the constant change: +9.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 25, 34

Worked Example 7

Problem: Continue the pattern 13, 17, 21, ... for two more terms.

  1. Find the constant change: +4.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 25, 29

Worked Example 8

Problem: Continue the pattern 11, 14, 17, ... for two more terms.

  1. Find the constant change: +3.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 20, 23

Worked Example 9

Problem: Continue the pattern -3, -1, 1, ... for two more terms.

  1. Find the constant change: +2.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 3, 5

Worked Example 10

Problem: Continue the pattern -3, 4, 11, ... for two more terms.

  1. Find the constant change: +7.
  2. Add the same amount each time.

Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.

Answer: 18, 25

Practice Exercise

Create one new Grade 6 problem about Cost-per-item patterns. 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.

20.6 Tables of constant rate

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

  1. Divide the first quantity by the second.
  2. 150 ÷ 15 = 10.

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

Answer: 10 per group

Worked Example 2

Problem: 63 units are used in 9 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 63 ÷ 9 = 7.

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

Answer: 7 per group

Worked Example 3

Problem: 36 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 36 ÷ 3 = 12.

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

Answer: 12 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: 70 units are used in 10 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 70 ÷ 10 = 7.

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

Answer: 7 per group

Worked Example 6

Problem: 27 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 27 ÷ 3 = 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: 132 units are used in 12 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 132 ÷ 12 = 11.

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

Answer: 11 per group

Worked Example 8

Problem: 65 units are used in 13 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 65 ÷ 13 = 5.

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

Answer: 5 per group

Worked Example 9

Problem: 132 units are used in 12 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 132 ÷ 12 = 11.

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

Answer: 11 per group

Worked Example 10

Problem: 66 units are used in 11 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 66 ÷ 11 = 6.

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

Answer: 6 per group

Practice Exercise

Create one new Grade 6 problem about Tables of constant rate. 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.

20.7 Graphs of constant rate

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: 63 units are used in 9 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 63 ÷ 9 = 7.

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

Answer: 7 per group

Worked Example 2

Problem: 56 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 56 ÷ 8 = 7.

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

Answer: 7 per group

Worked Example 3

Problem: 72 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 72 ÷ 8 = 9.

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

Answer: 9 per group

Worked Example 4

Problem: 45 units are used in 15 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 45 ÷ 15 = 3.

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

Answer: 3 per group

Worked Example 5

Problem: 66 units are used in 6 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 66 ÷ 6 = 11.

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

Answer: 11 per group

Worked Example 6

Problem: 110 units are used in 11 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 110 ÷ 11 = 10.

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

Answer: 10 per group

Worked Example 7

Problem: 64 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 64 ÷ 8 = 8.

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

Answer: 8 per group

Worked Example 8

Problem: 40 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 40 ÷ 8 = 5.

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

Answer: 5 per group

Worked Example 9

Problem: 104 units are used in 13 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 104 ÷ 13 = 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: 8 units are used in 4 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 8 ÷ 4 = 2.

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

Answer: 2 per group

Practice Exercise

Create one new Grade 6 problem about Graphs of constant rate. 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.

20.8 Finding the rate from a table

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: 21 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 21 ÷ 3 = 7.

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

Answer: 7 per group

Worked Example 2

Problem: 70 units are used in 10 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 70 ÷ 10 = 7.

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

Answer: 7 per group

Worked Example 3

Problem: 110 units are used in 11 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 110 ÷ 11 = 10.

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

Answer: 10 per group

Worked Example 4

Problem: 48 units are used in 4 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 48 ÷ 4 = 12.

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

Answer: 12 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: 55 units are used in 5 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 55 ÷ 5 = 11.

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

Answer: 11 per group

Worked Example 7

Problem: 30 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 30 ÷ 3 = 10.

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

Answer: 10 per group

Worked Example 8

Problem: 56 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 56 ÷ 7 = 8.

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

Answer: 8 per group

Worked Example 9

Problem: 12 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 12 ÷ 3 = 4.

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

Answer: 4 per group

Worked Example 10

Problem: 48 units are used in 12 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 48 ÷ 12 = 4.

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

Answer: 4 per group

Practice Exercise

Create one new Grade 6 problem about Finding the rate from a table. 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.

20.9 Finding the rate from a graph

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

  1. Divide the first quantity by the second.
  2. 15 ÷ 5 = 3.

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

Answer: 3 per group

Worked Example 2

Problem: 14 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 14 ÷ 7 = 2.

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

Answer: 2 per group

Worked Example 3

Problem: 84 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 84 ÷ 7 = 12.

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

Answer: 12 per group

Worked Example 4

Problem: 60 units are used in 5 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 60 ÷ 5 = 12.

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

Answer: 12 per group

Worked Example 5

Problem: 44 units are used in 4 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 44 ÷ 4 = 11.

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

Answer: 11 per group

Worked Example 6

Problem: 36 units are used in 9 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 36 ÷ 9 = 4.

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

Answer: 4 per group

Worked Example 7

Problem: 140 units are used in 14 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 140 ÷ 14 = 10.

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

Answer: 10 per group

Worked Example 8

Problem: 42 units are used in 14 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 42 ÷ 14 = 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: 36 units are used in 4 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 36 ÷ 4 = 9.

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

Answer: 9 per group

Worked Example 10

Problem: 21 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 21 ÷ 7 = 3.

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

Answer: 3 per group

Practice Exercise

Create one new Grade 6 problem about Finding the rate from a graph. 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.

20.10 Predicting with a constant rate

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: 35 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 35 ÷ 7 = 5.

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

Answer: 5 per group

Worked Example 2

Problem: 28 units are used in 4 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 28 ÷ 4 = 7.

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

Answer: 7 per group

Worked Example 3

Problem: 45 units are used in 15 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 45 ÷ 15 = 3.

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

Answer: 3 per group

Worked Example 4

Problem: 35 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 35 ÷ 7 = 5.

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

Answer: 5 per group

Worked Example 5

Problem: 108 units are used in 9 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 108 ÷ 9 = 12.

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

Answer: 12 per group

Worked Example 6

Problem: 18 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 18 ÷ 3 = 6.

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

Answer: 6 per group

Worked Example 7

Problem: 15 units are used in 5 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 15 ÷ 5 = 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: 20 units are used in 5 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 20 ÷ 5 = 4.

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

Answer: 4 per group

Worked Example 9

Problem: 56 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 56 ÷ 7 = 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: 28 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 28 ÷ 7 = 4.

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

Answer: 4 per group

Practice Exercise

Create one new Grade 6 problem about Predicting with a constant rate. 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.

20.11 Comparing constant rates

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: 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 2

Problem: 30 units are used in 6 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 30 ÷ 6 = 5.

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

Answer: 5 per group

Worked Example 3

Problem: 33 units are used in 3 equal groups. Find the unit rate.

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

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

Answer: 11 per group

Worked Example 4

Problem: 105 units are used in 15 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 105 ÷ 15 = 7.

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

Answer: 7 per group

Worked Example 5

Problem: 75 units are used in 15 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 75 ÷ 15 = 5.

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

Answer: 5 per group

Worked Example 6

Problem: 72 units are used in 6 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 72 ÷ 6 = 12.

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

Answer: 12 per group

Worked Example 7

Problem: 60 units are used in 10 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 60 ÷ 10 = 6.

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

Answer: 6 per group

Worked Example 8

Problem: 135 units are used in 15 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 135 ÷ 15 = 9.

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

Answer: 9 per group

Worked Example 9

Problem: 100 units are used in 10 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 100 ÷ 10 = 10.

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

Answer: 10 per group

Worked Example 10

Problem: 72 units are used in 12 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 72 ÷ 12 = 6.

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

Answer: 6 per group

Practice Exercise

Create one new Grade 6 problem about Comparing constant rates. 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.

20.12 Real-life constant-rate problems

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

  1. Divide the first quantity by the second.
  2. 35 ÷ 5 = 7.

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

Answer: 7 per group

Worked Example 2

Problem: 70 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 70 ÷ 7 = 10.

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

Answer: 10 per group

Worked Example 3

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 4

Problem: 72 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 72 ÷ 8 = 9.

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

Answer: 9 per group

Worked Example 5

Problem: 108 units are used in 9 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 108 ÷ 9 = 12.

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

Answer: 12 per group

Worked Example 6

Problem: 121 units are used in 11 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 121 ÷ 11 = 11.

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

Answer: 11 per group

Worked Example 7

Problem: 50 units are used in 5 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 50 ÷ 5 = 10.

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

Answer: 10 per group

Worked Example 8

Problem: 144 units are used in 12 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 144 ÷ 12 = 12.

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

Answer: 12 per group

Worked Example 9

Problem: 121 units are used in 11 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 121 ÷ 11 = 11.

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

Answer: 11 per group

Worked Example 10

Problem: 36 units are used in 9 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 36 ÷ 9 = 4.

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

Answer: 4 per group

Practice Exercise

Create one new Grade 6 problem about Real-life constant-rate problems. 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 constant rate?

Answer: A rate compares two quantities measured in different units.

Q2. What is important to understand about Constant addition?

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

Q3. What is important to understand about Constant subtraction?

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

Q4. What is important to understand about Distance-time patterns?

Answer: A pattern follows a rule that can be described, extended, and used to make predictions.

Q5. What is important to understand about Cost-per-item patterns?

Answer: A pattern follows a rule that can be described, extended, and used to make predictions.

Q6. What is important to understand about Tables of constant rate?

Answer: A rate compares two quantities measured in different units.

Q7. What is important to understand about Graphs of constant rate?

Answer: A rate compares two quantities measured in different units.

Q8. What is important to understand about Finding the rate from a table?

Answer: A rate compares two quantities measured in different units.

Q9. What is important to understand about Finding the rate from a graph?

Answer: A rate compares two quantities measured in different units.

Q10. What is important to understand about Predicting with a constant rate?

Answer: A rate compares two quantities measured in different units.

Q11. What is important to understand about Comparing constant rates?

Answer: A rate compares two quantities measured in different units.

Q12. What is important to understand about Real-life constant-rate problems?

Answer: A rate compares two quantities measured in different units.

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.