Chapter 27: Whole-Number Patterns
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Whole-Number Patterns with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Rational Number (a number that can be written as a fraction of integers with a nonzero denominator)
- Prime Number (a whole number greater than 1 with exactly two positive factors)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
27.1 Repeating patterns
A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Repeating patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Show why 3/4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Repeating patterns .
Answer: 3/4 = 0.75
Worked Example 2
Problem: Show why -2 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Repeating patterns .
Answer: -2 = -2/1
Worked Example 3
Problem: Show why 0.4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Repeating patterns .
Answer: 0.4 = 2/5
Worked Example 4
Problem: Show why 0.333… is rational.
- Write it as a fraction of integers.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Repeating patterns .
Answer: 0.333… = 1/3
Worked Example 5
Problem: Show why 1.25 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Repeating patterns .
Answer: 1.25 = 5/4
Worked Example 6
Problem: Show why 3/5 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 3/5 = 0.6
Worked Example 7
Problem: Show why -7 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: -7 = -7/1
Worked Example 8
Problem: Show why 0.25 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.25 = 1/4
Worked Example 9
Problem: Show why 0.666… is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.666… = 2/3
Worked Example 10
Problem: Show why 1.4 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 1.4 = 7/5
Practice Exercise
Create one new question about Repeating patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.2 Growing patterns
A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Growing patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Extend the pattern 2, 5, 8, ... two more terms.
- Common difference = 3.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Growing patterns .
Answer: 11, 14
Worked Example 2
Problem: Extend the pattern 5, 9, 13, ... two more terms.
- Common difference = 4.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Growing patterns .
Answer: 17, 21
Worked Example 3
Problem: Extend the pattern 10, 8, 6, ... two more terms.
- Common difference = -2.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Growing patterns .
Answer: 4, 2
Worked Example 4
Problem: Extend the pattern 1.5, 2, 2.5, ... two more terms.
- Common difference = 0.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Growing patterns .
Answer: 3, 3.5
Worked Example 5
Problem: Extend the pattern 20, 17.5, 15, ... two more terms.
- Common difference = -2.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Growing patterns .
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Growing patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.3 Shrinking patterns
A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Shrinking patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Extend the pattern 2, 5, 8, ... two more terms.
- Common difference = 3.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Shrinking patterns .
Answer: 11, 14
Worked Example 2
Problem: Extend the pattern 5, 9, 13, ... two more terms.
- Common difference = 4.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Shrinking patterns .
Answer: 17, 21
Worked Example 3
Problem: Extend the pattern 10, 8, 6, ... two more terms.
- Common difference = -2.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Shrinking patterns .
Answer: 4, 2
Worked Example 4
Problem: Extend the pattern 1.5, 2, 2.5, ... two more terms.
- Common difference = 0.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Shrinking patterns .
Answer: 3, 3.5
Worked Example 5
Problem: Extend the pattern 20, 17.5, 15, ... two more terms.
- Common difference = -2.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Shrinking patterns .
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Shrinking patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.4 Arithmetic sequences
Arithmetic sequences is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Extend the pattern 2, 5, 8, ... two more terms.
- Common difference = 3.
- Keep adding the same difference.
Very beginner explanation: Arithmetic sequences is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 11, 14
Worked Example 2
Problem: Extend the pattern 5, 9, 13, ... two more terms.
- Common difference = 4.
- Keep adding the same difference.
Very beginner explanation: Arithmetic sequences is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 17, 21
Worked Example 3
Problem: Extend the pattern 10, 8, 6, ... two more terms.
- Common difference = -2.
- Keep adding the same difference.
Very beginner explanation: Arithmetic sequences is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 4, 2
Worked Example 4
Problem: Extend the pattern 1.5, 2, 2.5, ... two more terms.
- Common difference = 0.5.
- Keep adding the same difference.
Very beginner explanation: Arithmetic sequences is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3, 3.5
Worked Example 5
Problem: Extend the pattern 20, 17.5, 15, ... two more terms.
- Common difference = -2.5.
- Keep adding the same difference.
Very beginner explanation: Arithmetic sequences is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Arithmetic sequences. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.5 Common difference
Common difference is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Extend the pattern 2, 5, 8, ... two more terms.
- Common difference = 3.
- Keep adding the same difference.
Very beginner explanation: Common difference is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 11, 14
Worked Example 2
Problem: Extend the pattern 5, 9, 13, ... two more terms.
- Common difference = 4.
- Keep adding the same difference.
Very beginner explanation: Common difference is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 17, 21
Worked Example 3
Problem: Extend the pattern 10, 8, 6, ... two more terms.
- Common difference = -2.
- Keep adding the same difference.
Very beginner explanation: Common difference is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 4, 2
Worked Example 4
Problem: Extend the pattern 1.5, 2, 2.5, ... two more terms.
- Common difference = 0.5.
- Keep adding the same difference.
Very beginner explanation: Common difference is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3, 3.5
Worked Example 5
Problem: Extend the pattern 20, 17.5, 15, ... two more terms.
- Common difference = -2.5.
- Keep adding the same difference.
Very beginner explanation: Common difference is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Common difference. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.6 Finding missing terms
A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Finding missing terms .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Finding missing terms .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Finding missing terms .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Finding missing terms .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Finding missing terms .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Finding missing terms .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Finding missing terms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.7 Pattern rules
A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Pattern rules .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Extend the pattern 2, 5, 8, ... two more terms.
- Common difference = 3.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Pattern rules .
Answer: 11, 14
Worked Example 2
Problem: Extend the pattern 5, 9, 13, ... two more terms.
- Common difference = 4.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Pattern rules .
Answer: 17, 21
Worked Example 3
Problem: Extend the pattern 10, 8, 6, ... two more terms.
- Common difference = -2.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Pattern rules .
Answer: 4, 2
Worked Example 4
Problem: Extend the pattern 1.5, 2, 2.5, ... two more terms.
- Common difference = 0.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Pattern rules .
Answer: 3, 3.5
Worked Example 5
Problem: Extend the pattern 20, 17.5, 15, ... two more terms.
- Common difference = -2.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Pattern rules .
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Pattern rules. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.8 Recursive rules
Recursive rules is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Recursive rules: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Recursive rules is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Recursive rules: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Recursive rules is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Recursive rules: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Recursive rules is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Recursive rules: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Recursive rules is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Recursive rules: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Recursive rules is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Recursive rules. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.9 Explicit rules introduction
Explicit rules introduction is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Explicit rules introduction: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Explicit rules introduction is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Explicit rules introduction: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Explicit rules introduction is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Explicit rules introduction: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Explicit rules introduction is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Explicit rules introduction: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Explicit rules introduction is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Explicit rules introduction: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Explicit rules introduction is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Explicit rules introduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.10 Tables of values
Tables of values is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Tables of values: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Tables of values is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Tables of values: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Tables of values is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Tables of values: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Tables of values is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Tables of values: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Tables of values is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Tables of values: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Tables of values is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Tables of values. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.11 Visual patterns
A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Visual patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Extend the pattern 2, 5, 8, ... two more terms.
- Common difference = 3.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Visual patterns .
Answer: 11, 14
Worked Example 2
Problem: Extend the pattern 5, 9, 13, ... two more terms.
- Common difference = 4.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Visual patterns .
Answer: 17, 21
Worked Example 3
Problem: Extend the pattern 10, 8, 6, ... two more terms.
- Common difference = -2.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Visual patterns .
Answer: 4, 2
Worked Example 4
Problem: Extend the pattern 1.5, 2, 2.5, ... two more terms.
- Common difference = 0.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Visual patterns .
Answer: 3, 3.5
Worked Example 5
Problem: Extend the pattern 20, 17.5, 15, ... two more terms.
- Common difference = -2.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Visual patterns .
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Visual patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.12 Predicting later terms
A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Predicting later terms .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Predicting later terms .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Predicting later terms .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Predicting later terms .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Predicting later terms .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Predicting later terms .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Predicting later terms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
27.13 Real-life patterns
A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Real-life patterns .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Extend the pattern 2, 5, 8, ... two more terms.
- Common difference = 3.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Real-life patterns .
Answer: 11, 14
Worked Example 2
Problem: Extend the pattern 5, 9, 13, ... two more terms.
- Common difference = 4.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Real-life patterns .
Answer: 17, 21
Worked Example 3
Problem: Extend the pattern 10, 8, 6, ... two more terms.
- Common difference = -2.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Real-life patterns .
Answer: 4, 2
Worked Example 4
Problem: Extend the pattern 1.5, 2, 2.5, ... two more terms.
- Common difference = 0.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Real-life patterns .
Answer: 3, 3.5
Worked Example 5
Problem: Extend the pattern 20, 17.5, 15, ... two more terms.
- Common difference = -2.5.
- Keep adding the same difference.
Very beginner explanation: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Real-life patterns .
Answer: 12.5, 10
Worked Example 6
Problem: Continue the pattern 2, 5, 8, ... for two more terms.
- The common difference is 3.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 11, 14
Worked Example 7
Problem: Continue the pattern 5, 9, 13, ... for two more terms.
- The common difference is 4.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 17, 21
Worked Example 8
Problem: Continue the pattern 10, 8, 6, ... for two more terms.
- The common difference is -2.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 4, 2
Worked Example 9
Problem: Continue the pattern 1.5, 2, 2.5, ... for two more terms.
- The common difference is 0.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 3, 3.5
Worked Example 10
Problem: Continue the pattern 20, 17.5, 15, ... for two more terms.
- The common difference is -2.5.
- Add the same difference each time.
Very beginner explanation: A constant-difference pattern changes by the same amount from one term to the next.
Answer: 12.5, 10
Practice Exercise
Create one new question about Real-life patterns. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Repeating patterns . Show your reasoning and check your answer.
- Create and solve a new question about Growing patterns . Show your reasoning and check your answer.
- Create and solve a new question about Shrinking patterns . Show your reasoning and check your answer.
- Create and solve a new question about Arithmetic sequences . Show your reasoning and check your answer.
- Create and solve a new question about Common difference . Show your reasoning and check your answer.
- Create and solve a new question about Finding missing terms . Show your reasoning and check your answer.
- Create and solve a new question about Pattern rules . Show your reasoning and check your answer.
- Create and solve a new question about Recursive rules . Show your reasoning and check your answer.
- Create and solve a new question about Explicit rules introduction . Show your reasoning and check your answer.
- Create and solve a new question about Tables of values . Show your reasoning and check your answer.
- Create and solve a new question about Visual patterns . Show your reasoning and check your answer.
- Create and solve a new question about Predicting later terms . Show your reasoning and check your answer.
Common Mistakes
- Combining unlike terms.
- Changing only one side of an equation.
- Forgetting to distribute to every term.
- Using a pattern rule that works only for the first few terms.
- Writing code without tracing variable values.
- Using a mathematical model without stating assumptions.
30 Review Questions and Answers
Q1. What is important to remember about Repeating patterns?
Answer: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Repeating patterns.
Q2. What is important to remember about Growing patterns?
Answer: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Growing patterns.
Q3. What is important to remember about Shrinking patterns?
Answer: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Shrinking patterns.
Q4. What is important to remember about Arithmetic sequences?
Answer: Arithmetic sequences is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q5. What is important to remember about Common difference?
Answer: Common difference is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Finding missing terms?
Answer: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Finding missing terms.
Q7. What is important to remember about Pattern rules?
Answer: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Pattern rules.
Q8. What is important to remember about Recursive rules?
Answer: Recursive rules is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q9. What is important to remember about Explicit rules introduction?
Answer: Explicit rules introduction is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Tables of values?
Answer: Tables of values is an important Grade 7 idea in Whole-Number Patterns. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q11. What is important to remember about Visual patterns?
Answer: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Visual patterns.
Q12. What is important to remember about Predicting later terms?
Answer: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Predicting later terms.
Q13. What is important to remember about Real-life patterns?
Answer: A pattern follows a rule that can be used to predict missing or future terms. This topic focuses on Real-life patterns.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q26. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q27. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q28. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q29. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q30. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.