Chapter 18: Repeating Patterns
Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Repeating Patterns in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
Key Technical Terms
- Meaning of a repeating pattern (A pattern follows a rule that can be described, extended, and used to make predictions.)
- Finding missing elements (Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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.
18.1 Meaning of a repeating pattern
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 0, 4, 8, ... for two more terms.
- Find the constant change: +4.
- 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 2
Problem: Continue the pattern 4, 11, 18, ... for two more terms.
- Find the constant change: +7.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 25, 32
Worked Example 3
Problem: Continue the pattern 15, 19, 23, ... for two more terms.
- Find the constant change: +4.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 27, 31
Worked Example 4
Problem: Continue the pattern 8, 14, 20, ... for two more terms.
- Find the constant change: +6.
- 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 5
Problem: Continue the pattern 12, 20, 28, ... for two more terms.
- Find the constant change: +8.
- 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 -2, 6, 14, ... for two more terms.
- Find the constant change: +8.
- 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 7
Problem: Continue the pattern 1, 5, 9, ... for two more terms.
- Find the constant change: +4.
- 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
Worked Example 8
Problem: Continue the pattern 4, 8, 12, ... for two more terms.
- Find the constant change: +4.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 16, 20
Worked Example 9
Problem: Continue the pattern 12, 16, 20, ... for two more terms.
- Find the constant change: +4.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 24, 28
Worked Example 10
Problem: Continue the pattern 3, 7, 11, ... for two more terms.
- Find the constant change: +4.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 15, 19
Practice Exercise
Create one new Grade 6 problem about Meaning of a repeating pattern. 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.
18.2 Core of a repeating pattern
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 -1, 2, 5, ... for two more terms.
- Find the constant change: +3.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 8, 11
Worked Example 2
Problem: Continue the pattern 10, 16, 22, ... for two more terms.
- Find the constant change: +6.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 28, 34
Worked Example 3
Problem: Continue the pattern 3, 10, 17, ... for two more terms.
- Find the constant change: +7.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 24, 31
Worked Example 4
Problem: Continue the pattern 10, 18, 26, ... for two more terms.
- Find the constant change: +8.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 34, 42
Worked Example 5
Problem: Continue the pattern -3, 2, 7, ... for two more terms.
- Find the constant change: +5.
- 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 6
Problem: Continue the pattern 5, 12, 19, ... for two more terms.
- Find the constant change: +7.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 26, 33
Worked Example 7
Problem: Continue the pattern 9, 14, 19, ... for two more terms.
- Find the constant change: +5.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 24, 29
Worked Example 8
Problem: Continue the pattern 1, 7, 13, ... for two more terms.
- Find the constant change: +6.
- 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 9
Problem: Continue the pattern 14, 17, 20, ... for two more terms.
- Find the constant change: +3.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 23, 26
Worked Example 10
Problem: Continue the pattern 3, 11, 19, ... for two more terms.
- Find the constant change: +8.
- 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 Core of a repeating pattern. 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.
18.3 Extending repeating 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 15, 23, 31, ... for two more terms.
- Find the constant change: +8.
- 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 -3, 1, 5, ... for two more terms.
- Find the constant change: +4.
- 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 3
Problem: Continue the pattern -4, 5, 14, ... for two more terms.
- Find the constant change: +9.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 23, 32
Worked Example 4
Problem: Continue the pattern 3, 6, 9, ... for two more terms.
- Find the constant change: +3.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 12, 15
Worked Example 5
Problem: Continue the pattern 11, 13, 15, ... for two more terms.
- Find the constant change: +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 6
Problem: Continue the pattern -1, 4, 9, ... for two more terms.
- Find the constant change: +5.
- 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 7
Problem: Continue the pattern 6, 10, 14, ... for two more terms.
- Find the constant change: +4.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 18, 22
Worked Example 8
Problem: Continue the pattern 12, 18, 24, ... for two more terms.
- Find the constant change: +6.
- 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 -5, 1, 7, ... for two more terms.
- Find the constant change: +6.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 13, 19
Worked Example 10
Problem: Continue the pattern -1, 6, 13, ... for two more terms.
- Find the constant change: +7.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 20, 27
Practice Exercise
Create one new Grade 6 problem about Extending repeating 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.
18.4 Finding missing elements
Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements to analyze the values 24 and 19. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements to analyze the values 2 and 19. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements to analyze the values 4 and 18. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements to analyze the values 9 and 5. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements to analyze the values 3 and 4. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements to analyze the values 4 and 3. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements to analyze the values 19 and 7. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements to analyze the values 27 and 16. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements to analyze the values 21 and 5. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements to analyze the values 4 and 15. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 missing elements. 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.
18.5 Representing patterns with symbols
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, 13, 18, ... for two more terms.
- Find the constant change: +5.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 23, 28
Worked Example 2
Problem: Continue the pattern 12, 17, 22, ... for two more terms.
- Find the constant change: +5.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 27, 32
Worked Example 3
Problem: Continue the pattern 8, 16, 24, ... for two more terms.
- Find the constant change: +8.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 32, 40
Worked Example 4
Problem: Continue the pattern 11, 18, 25, ... for two more terms.
- Find the constant change: +7.
- 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 5
Problem: Continue the pattern 5, 12, 19, ... for two more terms.
- Find the constant change: +7.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 26, 33
Worked Example 6
Problem: Continue the pattern 2, 10, 18, ... for two more terms.
- Find the constant change: +8.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 26, 34
Worked Example 7
Problem: Continue the pattern 10, 18, 26, ... for two more terms.
- Find the constant change: +8.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 34, 42
Worked Example 8
Problem: Continue the pattern -2, 7, 16, ... for two more terms.
- Find the constant change: +9.
- 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 9
Problem: Continue the pattern 9, 12, 15, ... for two more terms.
- Find the constant change: +3.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 18, 21
Worked Example 10
Problem: Continue the pattern 9, 14, 19, ... for two more terms.
- Find the constant change: +5.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 24, 29
Practice Exercise
Create one new Grade 6 problem about Representing patterns with symbols. 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.
18.6 Representing patterns with numbers
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 6, 8, 10, ... for two more terms.
- Find the constant change: +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, 14
Worked Example 2
Problem: Continue the pattern 4, 8, 12, ... for two more terms.
- Find the constant change: +4.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 16, 20
Worked Example 3
Problem: Continue the pattern 7, 16, 25, ... for two more terms.
- Find the constant change: +9.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 34, 43
Worked Example 4
Problem: Continue the pattern 3, 7, 11, ... for two more terms.
- Find the constant change: +4.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 15, 19
Worked Example 5
Problem: Continue the pattern 3, 11, 19, ... for two more terms.
- Find the constant change: +8.
- 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 6
Problem: Continue the pattern 11, 16, 21, ... for two more terms.
- Find the constant change: +5.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 26, 31
Worked Example 7
Problem: Continue the pattern 14, 18, 22, ... for two more terms.
- Find the constant change: +4.
- 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 8
Problem: Continue the pattern 6, 14, 22, ... for two more terms.
- Find the constant change: +8.
- 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 9
Problem: Continue the pattern 1, 7, 13, ... for two more terms.
- Find the constant change: +6.
- 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 10
Problem: Continue the pattern 7, 12, 17, ... for two more terms.
- Find the constant change: +5.
- 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
Practice Exercise
Create one new Grade 6 problem about Representing patterns with numbers. 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.
18.7 Position in a repeating pattern
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 9, 16, 23, ... for two more terms.
- Find the constant change: +7.
- 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 2
Problem: Continue the pattern 9, 14, 19, ... for two more terms.
- Find the constant change: +5.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 24, 29
Worked Example 3
Problem: Continue the pattern 3, 10, 17, ... for two more terms.
- Find the constant change: +7.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 24, 31
Worked Example 4
Problem: Continue the pattern 8, 16, 24, ... for two more terms.
- Find the constant change: +8.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 32, 40
Worked Example 5
Problem: Continue the pattern 4, 13, 22, ... for two more terms.
- Find the constant change: +9.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 31, 40
Worked Example 6
Problem: Continue the pattern 10, 13, 16, ... for two more terms.
- Find the constant change: +3.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 19, 22
Worked Example 7
Problem: Continue the pattern 7, 13, 19, ... for two more terms.
- Find the constant change: +6.
- 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 8
Problem: Continue the pattern -4, 1, 6, ... for two more terms.
- Find the constant change: +5.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 11, 16
Worked Example 9
Problem: Continue the pattern 7, 14, 21, ... for two more terms.
- Find the constant change: +7.
- 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 10
Problem: Continue the pattern 9, 14, 19, ... for two more terms.
- Find the constant change: +5.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 24, 29
Practice Exercise
Create one new Grade 6 problem about Position in a repeating pattern. 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.
18.8 Comparing repeating 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 14, 23, 32, ... for two more terms.
- Find the constant change: +9.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 41, 50
Worked Example 2
Problem: Continue the pattern 2, 6, 10, ... for two more terms.
- Find the constant change: +4.
- 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 3
Problem: Continue the pattern 1, 10, 19, ... for two more terms.
- Find the constant change: +9.
- 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 6, 13, 20, ... for two more terms.
- Find the constant change: +7.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 27, 34
Worked Example 5
Problem: Continue the pattern 10, 16, 22, ... for two more terms.
- Find the constant change: +6.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 28, 34
Worked Example 6
Problem: Continue the pattern 12, 14, 16, ... for two more terms.
- Find the constant change: +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, 20
Worked Example 7
Problem: Continue the pattern 6, 9, 12, ... for two more terms.
- Find the constant change: +3.
- 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 8
Problem: Continue the pattern 4, 10, 16, ... for two more terms.
- Find the constant change: +6.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 22, 28
Worked Example 9
Problem: Continue the pattern 0, 8, 16, ... for two more terms.
- Find the constant change: +8.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 24, 32
Worked Example 10
Problem: Continue the pattern 2, 9, 16, ... for two more terms.
- Find the constant change: +7.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 23, 30
Practice Exercise
Create one new Grade 6 problem about Comparing repeating 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.
18.9 Creating repeating 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 10, 12, 14, ... for two more terms.
- Find the constant change: +2.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 16, 18
Worked Example 2
Problem: Continue the pattern 4, 10, 16, ... for two more terms.
- Find the constant change: +6.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 22, 28
Worked Example 3
Problem: Continue the pattern -3, 1, 5, ... for two more terms.
- Find the constant change: +4.
- 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 4
Problem: Continue the pattern 1, 3, 5, ... for two more terms.
- Find the constant change: +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, 9
Worked Example 5
Problem: Continue the pattern 10, 14, 18, ... for two more terms.
- Find the constant change: +4.
- 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 6
Problem: Continue the pattern 0, 6, 12, ... for two more terms.
- Find the constant change: +6.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 18, 24
Worked Example 7
Problem: Continue the pattern 8, 17, 26, ... for two more terms.
- Find the constant change: +9.
- 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 8
Problem: Continue the pattern -2, 0, 2, ... for two more terms.
- Find the constant change: +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 9
Problem: Continue the pattern -2, 4, 10, ... for two more terms.
- Find the constant change: +6.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 16, 22
Worked Example 10
Problem: Continue the pattern -2, 1, 4, ... for two more terms.
- Find the constant change: +3.
- 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
Practice Exercise
Create one new Grade 6 problem about Creating repeating 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.
18.10 Real-life repeating 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 -3, 2, 7, ... for two more terms.
- Find the constant change: +5.
- 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 2
Problem: Continue the pattern -3, -1, 1, ... for two more terms.
- Find the constant change: +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 3
Problem: Continue the pattern 8, 17, 26, ... for two more terms.
- Find the constant change: +9.
- 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 4
Problem: Continue the pattern -3, 0, 3, ... for two more terms.
- Find the constant change: +3.
- 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 5
Problem: Continue the pattern -4, 5, 14, ... for two more terms.
- Find the constant change: +9.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 23, 32
Worked Example 6
Problem: Continue the pattern 5, 14, 23, ... for two more terms.
- Find the constant change: +9.
- 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
Worked Example 7
Problem: Continue the pattern -5, -3, -1, ... for two more terms.
- Find the constant change: +2.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 1, 3
Worked Example 8
Problem: Continue the pattern -5, 4, 13, ... for two more terms.
- Find the constant change: +9.
- 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 9
Problem: Continue the pattern 10, 19, 28, ... for two more terms.
- Find the constant change: +9.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 37, 46
Worked Example 10
Problem: Continue the pattern 13, 15, 17, ... for two more terms.
- Find the constant change: +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, 21
Practice Exercise
Create one new Grade 6 problem about Real-life repeating 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.
18.11 Explaining a pattern rule
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 12, 18, 24, ... for two more terms.
- Find the constant change: +6.
- 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 2
Problem: Continue the pattern -1, 1, 3, ... for two more terms.
- Find the constant change: +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, 7
Worked Example 3
Problem: Continue the pattern 7, 13, 19, ... for two more terms.
- Find the constant change: +6.
- 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 4
Problem: Continue the pattern 9, 14, 19, ... for two more terms.
- Find the constant change: +5.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 24, 29
Worked Example 5
Problem: Continue the pattern 1, 10, 19, ... for two more terms.
- Find the constant change: +9.
- 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 6
Problem: Continue the pattern -3, 4, 11, ... for two more terms.
- Find the constant change: +7.
- 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
Worked Example 7
Problem: Continue the pattern 5, 8, 11, ... for two more terms.
- Find the constant change: +3.
- 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 8
Problem: Continue the pattern -4, -2, 0, ... for two more terms.
- Find the constant change: +2.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 2, 4
Worked Example 9
Problem: Continue the pattern 1, 8, 15, ... for two more terms.
- Find the constant change: +7.
- Add the same amount each time.
Very beginner explanation: A constant-rate numerical pattern changes by the same amount for each step.
Answer: 22, 29
Worked Example 10
Problem: Continue the pattern 9, 16, 23, ... for two more terms.
- Find the constant change: +7.
- 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
Practice Exercise
Create one new Grade 6 problem about Explaining a pattern rule. 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.
30 Review Questions and Answers
Q1. What is important to understand about Meaning of a repeating pattern?
Answer: A pattern follows a rule that can be described, extended, and used to make predictions.
Q2. What is important to understand about Core of a repeating pattern?
Answer: A pattern follows a rule that can be described, extended, and used to make predictions.
Q3. What is important to understand about Extending repeating patterns?
Answer: A pattern follows a rule that can be described, extended, and used to make predictions.
Q4. What is important to understand about Finding missing elements?
Answer: Finding missing elements is a Grade 6 mathematics idea in Repeating Patterns. 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 Representing patterns with symbols?
Answer: A pattern follows a rule that can be described, extended, and used to make predictions.
Q6. What is important to understand about Representing patterns with numbers?
Answer: A pattern follows a rule that can be described, extended, and used to make predictions.
Q7. What is important to understand about Position in a repeating pattern?
Answer: A pattern follows a rule that can be described, extended, and used to make predictions.
Q8. What is important to understand about Comparing repeating patterns?
Answer: A pattern follows a rule that can be described, extended, and used to make predictions.
Q9. What is important to understand about Creating repeating patterns?
Answer: A pattern follows a rule that can be described, extended, and used to make predictions.
Q10. What is important to understand about Real-life repeating patterns?
Answer: A pattern follows a rule that can be described, extended, and used to make predictions.
Q11. What is important to understand about Explaining a pattern rule?
Answer: A pattern follows a rule that can be described, extended, and used to make predictions.
Q12. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q13. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q14. Why do units matter?
Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.
Q15. When should you round?
Answer: Usually round near the end unless the question specifically asks for earlier rounding.
Q16. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.
Q17. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q18. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q19. What should you do if an answer seems unreasonable?
Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.
Q20. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships that are harder to see in words alone.
Q21. Why are tables useful?
Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.
Q22. Why are graphs useful?
Answer: Graphs make relationships, changes, trends, and comparisons visible.
Q23. Why should you explain your reasoning?
Answer: An explanation shows why a method works instead of only giving a final number.
Q24. Why can more than one strategy be correct?
Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.
Q25. What should you do before using a formula or rule?
Answer: Check what each quantity means and whether the rule matches the situation.
Q26. How does practice help in mathematics?
Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.
Q27. 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.
Q28. Why should you compare an exact answer with an estimate?
Answer: The estimate gives a quick reasonableness check for the exact calculation.
Q29. What does representing mathematics mean?
Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.
Q30. What does connecting mathematics mean?
Answer: It means linking one math idea to another or to a real-life situation.