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Chapter 19: Growing and Shrinking Patterns

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

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

This chapter teaches Growing and Shrinking Patterns in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Growing patterns (A pattern follows a rule that can be described, extended, and used to make predictions.)
  • Finding the change between terms (Finding the change between terms is a Grade 6 mathematics idea in Growing and Shrinking Patterns. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Number sequences (Number sequences is a Grade 6 mathematics idea in Growing and Shrinking Patterns. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Predicting later terms (Predicting later terms is a Grade 6 mathematics idea in Growing and Shrinking Patterns. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Real-life growing and shrinking situations (Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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.

19.1 Growing 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 -1, 1, 3, ... 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: 5, 7

Worked Example 2

Problem: Continue the pattern 11, 16, 21, ... 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: 26, 31

Worked Example 3

Problem: Continue the pattern 3, 12, 21, ... 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: 30, 39

Worked Example 4

Problem: Continue the pattern 3, 12, 21, ... 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: 30, 39

Worked Example 5

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

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

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

Answer: 33, 41

Worked Example 6

Problem: Continue the pattern 13, 15, 17, ... 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: 19, 21

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 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 9

Problem: Continue the pattern 2, 11, 20, ... 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: 29, 38

Worked Example 10

Problem: Continue the pattern 3, 12, 21, ... 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: 30, 39

Practice Exercise

Create one new Grade 6 problem about Growing 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.

19.2 Shrinking 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, 17, 20, ... 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: 23, 26

Worked Example 2

Problem: Continue the pattern 6, 11, 16, ... 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: 21, 26

Worked Example 3

Problem: Continue the pattern 8, 13, 18, ... 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: 23, 28

Worked Example 4

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 5

Problem: Continue the pattern 6, 13, 20, ... 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: 27, 34

Worked Example 6

Problem: Continue the pattern 1, 9, 17, ... 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: 25, 33

Worked Example 7

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

Worked Example 8

Problem: Continue the pattern 2, 7, 12, ... 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: 17, 22

Worked Example 9

Problem: Continue the pattern 14, 17, 20, ... 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: 23, 26

Worked Example 10

Problem: Continue the pattern 8, 13, 18, ... 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: 23, 28

Practice Exercise

Create one new Grade 6 problem about Shrinking 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.

19.3 Finding the change between terms

Finding the change between terms is a Grade 6 mathematics idea in Growing and Shrinking 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: Evaluate 3x + 4 when x = 5.

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

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

Answer: 19

Worked Example 2

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

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

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

Answer: 19

Worked Example 3

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

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

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

Answer: 17

Worked Example 4

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

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

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

Answer: 33

Worked Example 5

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

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

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

Answer: 13

Worked Example 6

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

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

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

Answer: 11

Worked Example 7

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

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

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

Answer: 16

Worked Example 8

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

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

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

Answer: 26

Worked Example 9

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

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

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

Answer: 26

Worked Example 10

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

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

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

Answer: 20

Practice Exercise

Create one new Grade 6 problem about Finding the change between terms. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

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

19.4 Extending growing 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, 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 2

Problem: Continue the pattern 2, 8, 14, ... 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: 20, 26

Worked Example 3

Problem: Continue the pattern -4, 1, 6, ... 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: 11, 16

Worked Example 4

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 5

Problem: Continue the pattern 2, 9, 16, ... 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: 23, 30

Worked Example 6

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 7

Problem: Continue the pattern 1, 6, 11, ... 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: 16, 21

Worked Example 8

Problem: Continue the pattern -4, 3, 10, ... 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: 17, 24

Worked Example 9

Problem: Continue the pattern 12, 19, 26, ... 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: 33, 40

Worked Example 10

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

Practice Exercise

Create one new Grade 6 problem about Extending growing 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.

19.5 Extending shrinking 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, 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 2

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 3

Problem: Continue the pattern 15, 17, 19, ... 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: 21, 23

Worked Example 4

Problem: Continue the pattern 13, 22, 31, ... 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: 40, 49

Worked Example 5

Problem: Continue the pattern 6, 12, 18, ... 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: 24, 30

Worked Example 6

Problem: Continue the pattern -5, -1, 3, ... 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: 7, 11

Worked Example 7

Problem: Continue the pattern 4, 13, 22, ... 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: 31, 40

Worked Example 8

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

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

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

Answer: 9, 13

Worked Example 9

Problem: Continue the pattern 1, 9, 17, ... 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: 25, 33

Worked Example 10

Problem: Continue the pattern 2, 11, 20, ... 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: 29, 38

Practice Exercise

Create one new Grade 6 problem about Extending shrinking 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.

19.6 Visual growing 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 -4, 4, 12, ... for two more terms.

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

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

Answer: 20, 28

Worked Example 2

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 3

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 4

Problem: Continue the pattern 5, 9, 13, ... 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: 17, 21

Worked Example 5

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 6

Problem: Continue the pattern 12, 15, 18, ... 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: 21, 24

Worked Example 7

Problem: Continue the pattern 4, 10, 16, ... 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: 22, 28

Worked Example 8

Problem: Continue the pattern 4, 12, 20, ... 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: 28, 36

Worked Example 9

Problem: Continue the pattern 3, 7, 11, ... 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: 15, 19

Worked Example 10

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

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

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

Answer: 17, 19

Practice Exercise

Create one new Grade 6 problem about Visual growing 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.

19.7 Number sequences

Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences to analyze the values 21 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: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences to analyze the values 17 and 16. What should be checked first?

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

Very beginner explanation: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences to analyze the values 25 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: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences to analyze the values 26 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: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences 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: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences to analyze the values 26 and 8. What should be checked first?

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

Very beginner explanation: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences to analyze the values 25 and 17. What should be checked first?

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

Very beginner explanation: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences to analyze the values 27 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: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences 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: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences 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: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking 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 Number sequences. 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.

19.8 Tables of pattern values

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 -4, -2, 0, ... 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: 2, 4

Worked Example 2

Problem: Continue the pattern -5, 2, 9, ... 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: 16, 23

Worked Example 3

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 4

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

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

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

Answer: 28, 37

Worked Example 5

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 6

Problem: Continue the pattern 3, 6, 9, ... 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: 12, 15

Worked Example 7

Problem: Continue the pattern 14, 16, 18, ... 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: 20, 22

Worked Example 8

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 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 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

Practice Exercise

Create one new Grade 6 problem about Tables of pattern 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.

19.9 Writing 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 -1, 5, 11, ... 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: 17, 23

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 0, 4, 8, ... for two more terms.

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

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

Answer: 12, 16

Worked Example 4

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

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

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

Answer: 19, 23

Worked Example 5

Problem: Continue the pattern -5, -1, 3, ... 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: 7, 11

Worked Example 6

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

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

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

Answer: 1, 3

Worked Example 7

Problem: Continue the pattern 6, 15, 24, ... 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: 33, 42

Worked Example 8

Problem: Continue the pattern -1, 8, 17, ... 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: 26, 35

Worked Example 9

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

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

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

Answer: 8, 10

Worked Example 10

Problem: Continue the pattern 4, 10, 16, ... 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: 22, 28

Practice Exercise

Create one new Grade 6 problem about Writing 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.

19.10 Predicting later terms

Predicting later terms is a Grade 6 mathematics idea in Growing and Shrinking 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: Evaluate 3x + 4 when x = 5.

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

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

Answer: 19

Worked Example 2

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

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

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

Answer: 19

Worked Example 3

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

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

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

Answer: 17

Worked Example 4

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

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

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

Answer: 33

Worked Example 5

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

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

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

Answer: 13

Worked Example 6

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

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

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

Answer: 11

Worked Example 7

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

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

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

Answer: 16

Worked Example 8

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

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

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

Answer: 26

Worked Example 9

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

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

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

Answer: 26

Worked Example 10

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

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

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

Answer: 20

Practice Exercise

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

Common Mistake

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

19.11 Comparing two 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.

  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 -5, 2, 9, ... 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: 16, 23

Worked Example 3

Problem: Continue the pattern -3, 6, 15, ... 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: 24, 33

Worked Example 4

Problem: Continue the pattern 15, 24, 33, ... 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: 42, 51

Worked Example 5

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

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

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

Answer: 1, 3

Worked Example 6

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 7

Problem: Continue the pattern 3, 12, 21, ... 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: 30, 39

Worked Example 8

Problem: Continue the pattern 4, 8, 12, ... 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: 16, 20

Worked Example 9

Problem: Continue the pattern 10, 18, 26, ... 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: 34, 42

Worked Example 10

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

Practice Exercise

Create one new Grade 6 problem about Comparing two 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.

19.12 Real-life growing and shrinking situations

Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations to analyze the values 13 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: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations to analyze the values 3 and 7. What should be checked first?

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

Very beginner explanation: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations to analyze the values 24 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: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations to analyze the values 20 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: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations to analyze the values 12 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: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations to analyze the values 22 and 13. What should be checked first?

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

Very beginner explanation: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations to analyze the values 4 and 10. What should be checked first?

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

Very beginner explanation: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations to analyze the values 17 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: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations to analyze the values 9 and 6. What should be checked first?

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

Very beginner explanation: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations to analyze the values 13 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: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking 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 Real-life growing and shrinking situations. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

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

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30 Review Questions and Answers

Q1. What is important to understand about Growing patterns?

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

Q2. What is important to understand about Shrinking patterns?

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

Q3. What is important to understand about Finding the change between terms?

Answer: Finding the change between terms is a Grade 6 mathematics idea in Growing and Shrinking Patterns. 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 Extending growing patterns?

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

Q5. What is important to understand about Extending shrinking patterns?

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

Q6. What is important to understand about Visual growing patterns?

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

Q7. What is important to understand about Number sequences?

Answer: Number sequences is a Grade 6 mathematics idea in Growing and Shrinking Patterns. 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 Tables of pattern values?

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

Q9. What is important to understand about Writing pattern rules?

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

Q10. What is important to understand about Predicting later terms?

Answer: Predicting later terms is a Grade 6 mathematics idea in Growing and Shrinking Patterns. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q11. What is important to understand about Comparing two patterns?

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

Q12. What is important to understand about Real-life growing and shrinking situations?

Answer: Real-life growing and shrinking situations is a Grade 6 mathematics idea in Growing and Shrinking Patterns. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. Why should you show your steps?

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

Q14. Why is estimation useful?

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

Q15. Why do units matter?

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

Q16. When should you round?

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

Q17. How can you check an answer?

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

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

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

Q19. What makes a final answer complete?

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

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

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

Q21. Why are diagrams useful?

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

Q22. Why are tables useful?

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

Q23. Why are graphs useful?

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

Q24. Why should you explain your reasoning?

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

Q25. Why can more than one strategy be correct?

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

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

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

Q27. How does practice help in mathematics?

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

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

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

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

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

Q30. What does representing mathematics mean?

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