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Chapter 22: Pattern Rules, Tables, and Relationships

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 Pattern Rules, Tables, and Relationships in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Pattern rules (A pattern follows a rule that can be described, extended, and used to make predictions.)
  • Recursive rules (Recursive rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Explicit rule (Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Input-output rules (Input-output rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Completing tables of values (Completing tables of values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Finding a rule from a table (Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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.

22.1 Pattern rules

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, 13, 21, ... 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: 29, 37

Worked Example 2

Problem: Continue the pattern 10, 14, 18, ... 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: 22, 26

Worked Example 3

Problem: Continue the pattern -1, 3, 7, ... 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: 11, 15

Worked Example 4

Problem: Continue the pattern -3, 2, 7, ... for two more terms.

  1. Find the constant change: +5.
  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, 17

Worked Example 5

Problem: Continue the pattern 5, 11, 17, ... 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: 23, 29

Worked Example 6

Problem: Continue the pattern 15, 22, 29, ... 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: 36, 43

Worked Example 7

Problem: Continue the pattern 14, 20, 26, ... 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: 32, 38

Worked Example 8

Problem: Continue the pattern 12, 18, 24, ... 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: 30, 36

Worked Example 9

Problem: Continue the pattern 13, 19, 25, ... 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: 31, 37

Worked Example 10

Problem: Continue the pattern 1, 5, 9, ... 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: 13, 17

Practice Exercise

Create one new Grade 6 problem about Pattern rules. 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.

22.2 Recursive rules

Recursive rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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: Continue the pattern 5, 11, 17, ... 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: 23, 29

Worked Example 2

Problem: Continue the pattern 9, 11, 13, ... 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: 15, 17

Worked Example 3

Problem: Continue the pattern 4, 7, 10, ... 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: 13, 16

Worked Example 4

Problem: Continue the pattern 6, 14, 22, ... 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: 30, 38

Worked Example 5

Problem: Continue the pattern -2, 0, 2, ... 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: 4, 6

Worked Example 6

Problem: Continue the pattern 7, 14, 21, ... 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: 28, 35

Worked Example 7

Problem: Continue the pattern 11, 18, 25, ... 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: 32, 39

Worked Example 8

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 9

Problem: Continue the pattern 0, 2, 4, ... 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: 6, 8

Worked Example 10

Problem: Continue the pattern 12, 21, 30, ... 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: 39, 48

Practice Exercise

Create one new Grade 6 problem about Recursive rules. 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.

22.3 Explicit rule introduction

Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction to analyze the values 5 and 17. What should be checked first?

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

Very beginner explanation: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction to analyze the values 16 and 8. What should be checked first?

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

Very beginner explanation: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction to analyze the values 10 and 17. What should be checked first?

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

Very beginner explanation: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction to analyze the values 17 and 14. What should be checked first?

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

Very beginner explanation: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction to analyze the values 25 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: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction to analyze the values 25 and 18. What should be checked first?

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

Very beginner explanation: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction to analyze the values 14 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: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction to analyze the values 13 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: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction to analyze the values 17 and 2. What should be checked first?

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

Very beginner explanation: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction to analyze the values 26 and 20. What should be checked first?

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

Very beginner explanation: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Explicit rule introduction. 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.

22.4 Input-output rules

Input-output rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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: Continue the pattern 6, 14, 22, ... 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: 30, 38

Worked Example 2

Problem: Continue the pattern 14, 21, 28, ... 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: 35, 42

Worked Example 3

Problem: Continue the pattern -2, 6, 14, ... 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: 22, 30

Worked Example 4

Problem: Continue the pattern 15, 20, 25, ... for two more terms.

  1. Find the constant change: +5.
  2. Add the same amount each time.

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

Answer: 30, 35

Worked Example 5

Problem: Continue the pattern 0, 7, 14, ... 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: 21, 28

Worked Example 6

Problem: Continue the pattern 3, 11, 19, ... 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: 27, 35

Worked Example 7

Problem: Continue the pattern 8, 14, 20, ... 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: 26, 32

Worked Example 8

Problem: Continue the pattern 7, 12, 17, ... for two more terms.

  1. Find the constant change: +5.
  2. Add the same amount each time.

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

Answer: 22, 27

Worked Example 9

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 10

Problem: Continue the pattern 13, 19, 25, ... 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: 31, 37

Practice Exercise

Create one new Grade 6 problem about Input-output rules. 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.

22.5 Completing tables of values

Completing tables of values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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: Continue the pattern -5, 3, 11, ... 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: 19, 27

Worked Example 2

Problem: Continue the pattern 15, 23, 31, ... 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: 39, 47

Worked Example 3

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 4

Problem: Continue the pattern 1, 7, 13, ... 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: 19, 25

Worked Example 5

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 6

Problem: Continue the pattern 12, 18, 24, ... 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: 30, 36

Worked Example 7

Problem: Continue the pattern -5, 4, 13, ... 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: 22, 31

Worked Example 8

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 9

Problem: Continue the pattern -1, 4, 9, ... for two more terms.

  1. Find the constant change: +5.
  2. Add the same amount each time.

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

Answer: 14, 19

Worked Example 10

Problem: Continue the pattern 5, 14, 23, ... 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: 32, 41

Practice Exercise

Create one new Grade 6 problem about Completing tables of values. 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.

22.6 Finding a rule from a table

Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule from a table to analyze the values 18 and 8. What should be checked first?

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

Very beginner explanation: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule from a table 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: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule from a table to analyze the values 5 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: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule from a table to analyze the values 21 and 11. What should be checked first?

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

Very beginner explanation: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule from a table to analyze the values 15 and 18. What should be checked first?

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

Very beginner explanation: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule from a table to analyze the values 9 and 13. What should be checked first?

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

Very beginner explanation: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule from a table to analyze the values 9 and 14. What should be checked first?

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

Very beginner explanation: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule from a table to analyze the values 14 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: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule from a table to analyze the values 25 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: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule from a table to analyze the values 27 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: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Finding a rule 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.

22.7 Comparing two rules

Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules to analyze the values 30 and 3. What should be checked first?

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

Very beginner explanation: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules to analyze the values 18 and 14. What should be checked first?

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

Very beginner explanation: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules to analyze the values 21 and 18. What should be checked first?

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

Very beginner explanation: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules to analyze the values 18 and 3. What should be checked first?

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

Very beginner explanation: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules to analyze the values 17 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: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules to analyze the values 2 and 4. What should be checked first?

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

Very beginner explanation: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules to analyze the values 28 and 17. What should be checked first?

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

Very beginner explanation: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules to analyze the values 8 and 13. What should be checked first?

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

Very beginner explanation: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules to analyze the values 3 and 10. What should be checked first?

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

Very beginner explanation: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules to analyze the values 10 and 17. What should be checked first?

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

Very beginner explanation: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Comparing two rules. 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.

22.8 Equivalent representations

Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations to analyze the values 5 and 10. What should be checked first?

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

Very beginner explanation: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations to analyze the values 21 and 10. What should be checked first?

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

Very beginner explanation: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations to analyze the values 21 and 9. What should be checked first?

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

Very beginner explanation: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations to analyze the values 29 and 11. What should be checked first?

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

Very beginner explanation: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations to analyze the values 4 and 4. What should be checked first?

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

Very beginner explanation: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations to analyze the values 23 and 3. What should be checked first?

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

Very beginner explanation: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations to analyze the values 27 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: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations to analyze the values 3 and 8. What should be checked first?

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

Very beginner explanation: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations to analyze the values 20 and 13. What should be checked first?

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

Very beginner explanation: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations to analyze the values 20 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: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Equivalent representations. 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.

22.9 Words tables and graphs

Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs to analyze the values 18 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: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs to analyze the values 24 and 9. What should be checked first?

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

Very beginner explanation: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs to analyze the values 25 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: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs to analyze the values 26 and 4. What should be checked first?

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

Very beginner explanation: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs to analyze the values 27 and 11. What should be checked first?

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

Very beginner explanation: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs to analyze the values 24 and 9. What should be checked first?

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

Very beginner explanation: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs to analyze the values 8 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: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs to analyze the values 3 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: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs to analyze the values 14 and 11. What should be checked first?

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

Very beginner explanation: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs to analyze the values 8 and 11. What should be checked first?

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

Very beginner explanation: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Words tables and graphs. 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.

22.10 Using variables in pattern rules

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 8, 17, 26, ... 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: 35, 44

Worked Example 2

Problem: Continue the pattern 4, 9, 14, ... for two more terms.

  1. Find the constant change: +5.
  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, 24

Worked Example 3

Problem: Continue the pattern -1, 3, 7, ... 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: 11, 15

Worked Example 4

Problem: Continue the pattern 13, 16, 19, ... 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: 22, 25

Worked Example 5

Problem: Continue the pattern 9, 16, 23, ... 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: 30, 37

Worked Example 6

Problem: Continue the pattern 5, 8, 11, ... 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: 14, 17

Worked Example 7

Problem: Continue the pattern -3, 0, 3, ... 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: 6, 9

Worked Example 8

Problem: Continue the pattern -2, 2, 6, ... 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: 10, 14

Worked Example 9

Problem: Continue the pattern 14, 18, 22, ... 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: 26, 30

Worked Example 10

Problem: Continue the pattern 3, 11, 19, ... 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: 27, 35

Practice Exercise

Create one new Grade 6 problem about Using variables in pattern rules. 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.

22.11 Predicting unknown values

Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values to analyze the values 11 and 11. What should be checked first?

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

Very beginner explanation: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values to analyze the values 15 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: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values to analyze the values 2 and 18. What should be checked first?

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

Very beginner explanation: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values to analyze the values 19 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: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values to analyze the values 17 and 17. What should be checked first?

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

Very beginner explanation: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values to analyze the values 13 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: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values to analyze the values 12 and 13. What should be checked first?

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

Very beginner explanation: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values to analyze the values 3 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: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values to analyze the values 24 and 17. What should be checked first?

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

Very beginner explanation: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values to analyze the values 19 and 2. What should be checked first?

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

Very beginner explanation: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. 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 Predicting unknown values. 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.

22.12 Real-life pattern relationships

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 15, 23, 31, ... 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: 39, 47

Worked Example 2

Problem: Continue the pattern 8, 11, 14, ... 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: 17, 20

Worked Example 3

Problem: Continue the pattern -4, -1, 2, ... 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: 5, 8

Worked Example 4

Problem: Continue the pattern -2, 1, 4, ... 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: 7, 10

Worked Example 5

Problem: Continue the pattern 12, 20, 28, ... 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: 36, 44

Worked Example 6

Problem: Continue the pattern 12, 18, 24, ... 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: 30, 36

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 2, 6, 10, ... 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: 14, 18

Worked Example 9

Problem: Continue the pattern -1, 4, 9, ... for two more terms.

  1. Find the constant change: +5.
  2. Add the same amount each time.

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

Answer: 14, 19

Worked Example 10

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

Practice Exercise

Create one new Grade 6 problem about Real-life pattern relationships. 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 Pattern rules?

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

Q2. What is important to understand about Recursive rules?

Answer: Recursive rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q3. What is important to understand about Explicit rule introduction?

Answer: Explicit rule introduction is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q4. What is important to understand about Input-output rules?

Answer: Input-output rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q5. What is important to understand about Completing tables of values?

Answer: Completing tables of values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q6. What is important to understand about Finding a rule from a table?

Answer: Finding a rule from a table is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q7. What is important to understand about Comparing two rules?

Answer: Comparing two rules is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q8. What is important to understand about Equivalent representations?

Answer: Equivalent representations is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q9. What is important to understand about Words tables and graphs?

Answer: Words tables and graphs is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q10. What is important to understand about Using variables in pattern rules?

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

Q11. What is important to understand about Predicting unknown values?

Answer: Predicting unknown values is a Grade 6 mathematics idea in Pattern Rules, Tables, and Relationships. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q12. What is important to understand about Real-life pattern relationships?

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

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.