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Chapter 4: Integer Foundations

Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.

Grade 7Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
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Chapter Overview

This chapter teaches Integer Foundations 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)
  • Integer (a positive whole number, negative whole number, or zero)
  • 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.

4.1 Meaning of integers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Meaning of integers .

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: Place -7 on a number line.

  1. Start at 0.
  2. Move 7 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Meaning of integers .

Answer: -7 is negative.

Worked Example 2

Problem: Place 4 on a number line.

  1. Start at 0.
  2. Move 4 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Meaning of integers .

Answer: 4 is positive.

Worked Example 3

Problem: Place -6 on a number line.

  1. Start at 0.
  2. Move 6 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Meaning of integers .

Answer: -6 is negative.

Worked Example 4

Problem: Place 12 on a number line.

  1. Start at 0.
  2. Move 12 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Meaning of integers .

Answer: 12 is positive.

Worked Example 5

Problem: Place -15 on a number line.

  1. Start at 0.
  2. Move 15 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Meaning of integers .

Answer: -15 is negative.

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Meaning of integers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.2 Positive integers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Positive integers .

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: Place -7 on a number line.

  1. Start at 0.
  2. Move 7 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Positive integers .

Answer: -7 is negative.

Worked Example 2

Problem: Place 4 on a number line.

  1. Start at 0.
  2. Move 4 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Positive integers .

Answer: 4 is positive.

Worked Example 3

Problem: Place -6 on a number line.

  1. Start at 0.
  2. Move 6 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Positive integers .

Answer: -6 is negative.

Worked Example 4

Problem: Place 12 on a number line.

  1. Start at 0.
  2. Move 12 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Positive integers .

Answer: 12 is positive.

Worked Example 5

Problem: Place -15 on a number line.

  1. Start at 0.
  2. Move 15 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Positive integers .

Answer: -15 is negative.

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Positive integers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.3 Negative integers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Negative integers .

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: Place -7 on a number line.

  1. Start at 0.
  2. Move 7 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Negative integers .

Answer: -7 is negative.

Worked Example 2

Problem: Place 4 on a number line.

  1. Start at 0.
  2. Move 4 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Negative integers .

Answer: 4 is positive.

Worked Example 3

Problem: Place -6 on a number line.

  1. Start at 0.
  2. Move 6 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Negative integers .

Answer: -6 is negative.

Worked Example 4

Problem: Place 12 on a number line.

  1. Start at 0.
  2. Move 12 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Negative integers .

Answer: 12 is positive.

Worked Example 5

Problem: Place -15 on a number line.

  1. Start at 0.
  2. Move 15 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Negative integers .

Answer: -15 is negative.

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Negative integers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.4 Zero

Zero is an important Grade 7 idea in Integer Foundations. 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: Zero: Identify a correct example.

  1. State the definition and show why the example fits.
  2. Show all important reasoning.

Very beginner explanation: Zero is an important Grade 7 idea in Integer Foundations. 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: Zero: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: Zero is an important Grade 7 idea in Integer Foundations. 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: Zero: Compare two cases.

  1. State one similarity and one difference.
  2. Show all important reasoning.

Very beginner explanation: Zero is an important Grade 7 idea in Integer Foundations. 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: Zero: Apply the idea in a real situation.

  1. Translate the situation into mathematical language.
  2. Show all important reasoning.

Very beginner explanation: Zero is an important Grade 7 idea in Integer Foundations. 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: Zero: Create and check your own example.

  1. Use the definition, then verify each condition.
  2. Show all important reasoning.

Very beginner explanation: Zero is an important Grade 7 idea in Integer Foundations. 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: Explain Zero in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Zero becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Zero and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Zero becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Zero using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Zero becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Zero problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Zero becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Zero could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Zero becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Zero. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.5 Opposite integers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Opposite integers .

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: Place -7 on a number line.

  1. Start at 0.
  2. Move 7 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Opposite integers .

Answer: -7 is negative.

Worked Example 2

Problem: Place 4 on a number line.

  1. Start at 0.
  2. Move 4 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Opposite integers .

Answer: 4 is positive.

Worked Example 3

Problem: Place -6 on a number line.

  1. Start at 0.
  2. Move 6 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Opposite integers .

Answer: -6 is negative.

Worked Example 4

Problem: Place 12 on a number line.

  1. Start at 0.
  2. Move 12 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Opposite integers .

Answer: 12 is positive.

Worked Example 5

Problem: Place -15 on a number line.

  1. Start at 0.
  2. Move 15 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Opposite integers .

Answer: -15 is negative.

Worked Example 6

Problem: Calculate -8 - (5).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of 5 is -5.
  3. Compute -8+(-5).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: -13

Worked Example 7

Problem: Calculate 7 - (-12).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -12 is 12.
  3. Compute 7+(12).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 19

Worked Example 8

Problem: Calculate -4 - (-9).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -9 is 9.
  3. Compute -4+(9).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 5

Worked Example 9

Problem: Calculate 15 - (-6).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -6 is 6.
  3. Compute 15+(6).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 21

Worked Example 10

Problem: Calculate -20 - (13).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of 13 is -13.
  3. Compute -20+(-13).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: -33

Practice Exercise

Create one new question about Opposite integers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.6 Integers on a number line

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers on a number line .

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: Place -7 on a number line.

  1. Start at 0.
  2. Move 7 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers on a number line .

Answer: -7 is negative.

Worked Example 2

Problem: Place 4 on a number line.

  1. Start at 0.
  2. Move 4 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers on a number line .

Answer: 4 is positive.

Worked Example 3

Problem: Place -6 on a number line.

  1. Start at 0.
  2. Move 6 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers on a number line .

Answer: -6 is negative.

Worked Example 4

Problem: Place 12 on a number line.

  1. Start at 0.
  2. Move 12 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers on a number line .

Answer: 12 is positive.

Worked Example 5

Problem: Place -15 on a number line.

  1. Start at 0.
  2. Move 15 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers on a number line .

Answer: -15 is negative.

Worked Example 6

Problem: Which is farther right on a number line: 3,000 or 3,750?

  1. Numbers get larger as you move right.
  2. 3,750 is greater than 3,000.

Very beginner explanation: On a standard number line, the greater number is farther to the right.

Answer: 3,750

Worked Example 7

Problem: Which is farther right on a number line: 4,000 or 4,750?

  1. Numbers get larger as you move right.
  2. 4,750 is greater than 4,000.

Very beginner explanation: On a standard number line, the greater number is farther to the right.

Answer: 4,750

Worked Example 8

Problem: Which is farther right on a number line: 5,000 or 5,750?

  1. Numbers get larger as you move right.
  2. 5,750 is greater than 5,000.

Very beginner explanation: On a standard number line, the greater number is farther to the right.

Answer: 5,750

Worked Example 9

Problem: Which is farther right on a number line: 6,000 or 6,750?

  1. Numbers get larger as you move right.
  2. 6,750 is greater than 6,000.

Very beginner explanation: On a standard number line, the greater number is farther to the right.

Answer: 6,750

Worked Example 10

Problem: Which is farther right on a number line: 7,000 or 7,750?

  1. Numbers get larger as you move right.
  2. 7,750 is greater than 7,000.

Very beginner explanation: On a standard number line, the greater number is farther to the right.

Answer: 7,750

Practice Exercise

Create one new question about Integers on a number line. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.7 Comparing integers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Comparing integers .

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: Compare -7 and 5.

  1. The number farther right on a number line is greater.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Comparing integers .

Answer: -7 < 5

Worked Example 2

Problem: Compare 4 and -9.

  1. The number farther right on a number line is greater.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Comparing integers .

Answer: 4 > -9

Worked Example 3

Problem: Compare -6 and -3.

  1. The number farther right on a number line is greater.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Comparing integers .

Answer: -6 < -3

Worked Example 4

Problem: Compare 12 and -8.

  1. The number farther right on a number line is greater.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Comparing integers .

Answer: 12 > -8

Worked Example 5

Problem: Compare -15 and 20.

  1. The number farther right on a number line is greater.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Comparing integers .

Answer: -15 < 20

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Comparing integers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.8 Ordering integers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Ordering integers .

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: Compare -7 and 5.

  1. The number farther right on a number line is greater.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Ordering integers .

Answer: -7 < 5

Worked Example 2

Problem: Compare 4 and -9.

  1. The number farther right on a number line is greater.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Ordering integers .

Answer: 4 > -9

Worked Example 3

Problem: Compare -6 and -3.

  1. The number farther right on a number line is greater.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Ordering integers .

Answer: -6 < -3

Worked Example 4

Problem: Compare 12 and -8.

  1. The number farther right on a number line is greater.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Ordering integers .

Answer: 12 > -8

Worked Example 5

Problem: Compare -15 and 20.

  1. The number farther right on a number line is greater.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Ordering integers .

Answer: -15 < 20

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Ordering integers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.9 Absolute value

Absolute value (distance from zero) is always zero or positive. This topic focuses on Absolute value .

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: Absolute value: Identify a correct example.

  1. State the definition and show why the example fits.
  2. Show all important reasoning.

Very beginner explanation: Absolute value (distance from zero) is always zero or positive. This topic focuses on Absolute value .

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Absolute value: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: Absolute value (distance from zero) is always zero or positive. This topic focuses on Absolute value .

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Absolute value: Compare two cases.

  1. State one similarity and one difference.
  2. Show all important reasoning.

Very beginner explanation: Absolute value (distance from zero) is always zero or positive. This topic focuses on Absolute value .

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Absolute value: Apply the idea in a real situation.

  1. Translate the situation into mathematical language.
  2. Show all important reasoning.

Very beginner explanation: Absolute value (distance from zero) is always zero or positive. This topic focuses on Absolute value .

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Absolute value: Create and check your own example.

  1. Use the definition, then verify each condition.
  2. Show all important reasoning.

Very beginner explanation: Absolute value (distance from zero) is always zero or positive. This topic focuses on Absolute value .

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Find |-8|.

  1. Absolute value means distance from zero.
  2. -8 is 8 units from zero.

Very beginner explanation: Distance is never negative, so absolute value is zero or positive.

Answer: 8

Worked Example 7

Problem: Find |7|.

  1. Absolute value means distance from zero.
  2. 7 is 7 units from zero.

Very beginner explanation: Distance is never negative, so absolute value is zero or positive.

Answer: 7

Worked Example 8

Problem: Find |-4|.

  1. Absolute value means distance from zero.
  2. -4 is 4 units from zero.

Very beginner explanation: Distance is never negative, so absolute value is zero or positive.

Answer: 4

Worked Example 9

Problem: Find |15|.

  1. Absolute value means distance from zero.
  2. 15 is 15 units from zero.

Very beginner explanation: Distance is never negative, so absolute value is zero or positive.

Answer: 15

Worked Example 10

Problem: Find |-20|.

  1. Absolute value means distance from zero.
  2. -20 is 20 units from zero.

Very beginner explanation: Distance is never negative, so absolute value is zero or positive.

Answer: 20

Practice Exercise

Create one new question about Absolute value. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.10 Distance from zero

Distance from zero is an important Grade 7 idea in Integer Foundations. 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: Distance from zero: Identify a correct example.

  1. State the definition and show why the example fits.
  2. Show all important reasoning.

Very beginner explanation: Distance from zero is an important Grade 7 idea in Integer Foundations. 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: Distance from zero: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: Distance from zero is an important Grade 7 idea in Integer Foundations. 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: Distance from zero: Compare two cases.

  1. State one similarity and one difference.
  2. Show all important reasoning.

Very beginner explanation: Distance from zero is an important Grade 7 idea in Integer Foundations. 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: Distance from zero: Apply the idea in a real situation.

  1. Translate the situation into mathematical language.
  2. Show all important reasoning.

Very beginner explanation: Distance from zero is an important Grade 7 idea in Integer Foundations. 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: Distance from zero: Create and check your own example.

  1. Use the definition, then verify each condition.
  2. Show all important reasoning.

Very beginner explanation: Distance from zero is an important Grade 7 idea in Integer Foundations. 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: Explain Distance from zero in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Distance from zero becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Distance from zero and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Distance from zero becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Distance from zero using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Distance from zero becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Distance from zero problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Distance from zero becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Distance from zero could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Distance from zero becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Distance from zero. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.11 Temperature

Temperature is an important Grade 7 idea in Integer Foundations. 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: Place -7 on a number line.

  1. Start at 0.
  2. Move 7 units left.

Very beginner explanation: Temperature is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -7 is negative.

Worked Example 2

Problem: Place 4 on a number line.

  1. Start at 0.
  2. Move 4 units right.

Very beginner explanation: Temperature is an important Grade 7 idea in Integer Foundations. 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 is positive.

Worked Example 3

Problem: Place -6 on a number line.

  1. Start at 0.
  2. Move 6 units left.

Very beginner explanation: Temperature is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -6 is negative.

Worked Example 4

Problem: Place 12 on a number line.

  1. Start at 0.
  2. Move 12 units right.

Very beginner explanation: Temperature is an important Grade 7 idea in Integer Foundations. 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 is positive.

Worked Example 5

Problem: Place -15 on a number line.

  1. Start at 0.
  2. Move 15 units left.

Very beginner explanation: Temperature is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -15 is negative.

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Temperature. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.12 Elevation

Elevation is an important Grade 7 idea in Integer Foundations. 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: Place -7 on a number line.

  1. Start at 0.
  2. Move 7 units left.

Very beginner explanation: Elevation is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -7 is negative.

Worked Example 2

Problem: Place 4 on a number line.

  1. Start at 0.
  2. Move 4 units right.

Very beginner explanation: Elevation is an important Grade 7 idea in Integer Foundations. 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 is positive.

Worked Example 3

Problem: Place -6 on a number line.

  1. Start at 0.
  2. Move 6 units left.

Very beginner explanation: Elevation is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -6 is negative.

Worked Example 4

Problem: Place 12 on a number line.

  1. Start at 0.
  2. Move 12 units right.

Very beginner explanation: Elevation is an important Grade 7 idea in Integer Foundations. 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 is positive.

Worked Example 5

Problem: Place -15 on a number line.

  1. Start at 0.
  2. Move 15 units left.

Very beginner explanation: Elevation is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -15 is negative.

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Elevation. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

4.13 Money and debt contexts

Money and debt contexts is an important Grade 7 idea in Integer Foundations. 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: Place -7 on a number line.

  1. Start at 0.
  2. Move 7 units left.

Very beginner explanation: Money and debt contexts is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -7 is negative.

Worked Example 2

Problem: Place 4 on a number line.

  1. Start at 0.
  2. Move 4 units right.

Very beginner explanation: Money and debt contexts is an important Grade 7 idea in Integer Foundations. 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 is positive.

Worked Example 3

Problem: Place -6 on a number line.

  1. Start at 0.
  2. Move 6 units left.

Very beginner explanation: Money and debt contexts is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -6 is negative.

Worked Example 4

Problem: Place 12 on a number line.

  1. Start at 0.
  2. Move 12 units right.

Very beginner explanation: Money and debt contexts is an important Grade 7 idea in Integer Foundations. 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 is positive.

Worked Example 5

Problem: Place -15 on a number line.

  1. Start at 0.
  2. Move 15 units left.

Very beginner explanation: Money and debt contexts is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -15 is negative.

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Money and debt contexts. 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

  1. Create and solve a new question about Meaning of integers . Show your reasoning and check your answer.
  2. Create and solve a new question about Positive integers . Show your reasoning and check your answer.
  3. Create and solve a new question about Negative integers . Show your reasoning and check your answer.
  4. Create and solve a new question about Zero . Show your reasoning and check your answer.
  5. Create and solve a new question about Opposite integers . Show your reasoning and check your answer.
  6. Create and solve a new question about Integers on a number line . Show your reasoning and check your answer.
  7. Create and solve a new question about Comparing integers . Show your reasoning and check your answer.
  8. Create and solve a new question about Ordering integers . Show your reasoning and check your answer.
  9. Create and solve a new question about Absolute value . Show your reasoning and check your answer.
  10. Create and solve a new question about Distance from zero . Show your reasoning and check your answer.
  11. Create and solve a new question about Temperature . Show your reasoning and check your answer.
  12. Create and solve a new question about Elevation . Show your reasoning and check your answer.

Common Mistakes

  • Ignoring place value or signs.
  • Using an operation before checking what the question asks.
  • Skipping estimation and accepting an unreasonable result.
  • Forgetting the correct order of operations.
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30 Review Questions and Answers

Q1. What is important to remember about Meaning of integers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Meaning of integers.

Q2. What is important to remember about Positive integers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Positive integers.

Q3. What is important to remember about Negative integers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Negative integers.

Q4. What is important to remember about Zero?

Answer: Zero is an important Grade 7 idea in Integer Foundations. 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 Opposite integers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Opposite integers.

Q6. What is important to remember about Integers on a number line?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers on a number line.

Q7. What is important to remember about Comparing integers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Comparing integers.

Q8. What is important to remember about Ordering integers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Ordering integers.

Q9. What is important to remember about Absolute value?

Answer: Absolute value (distance from zero) is always zero or positive. This topic focuses on Absolute value.

Q10. What is important to remember about Distance from zero?

Answer: Distance from zero is an important Grade 7 idea in Integer Foundations. 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 Temperature?

Answer: Temperature is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q12. What is important to remember about Elevation?

Answer: Elevation is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q13. What is important to remember about Money and debt contexts?

Answer: Money and debt contexts is an important Grade 7 idea in Integer Foundations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

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.