Chapter 4: Integer Foundations and Number Lines

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

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review

Estimated reading time0% read

Advertisement area — AdSense / Auto Ads

Chapter Overview

This chapter teaches Integer Foundations and Number Lines in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

Meaning of integers (An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.)
Zero (Zero is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Distance from zero (Distance from zero is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Temperature contexts (Temperature contexts is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Elevation contexts (Elevation contexts is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Money and debt contexts (Money and debt contexts is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

4.1 Meaning of integers

An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A temperature starts at 3° and changes by -4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -1°

Worked Example 2

Problem: A temperature starts at -5° and changes by +2°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -3°

Worked Example 3

Problem: A temperature starts at -2° and changes by +1°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -1°

Worked Example 4

Problem: A temperature starts at -8° and changes by -6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -14°

Worked Example 5

Problem: A temperature starts at -7° and changes by -1°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -8°

Worked Example 6

Problem: A temperature starts at 1° and changes by -4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -3°

Worked Example 7

Problem: A temperature starts at 3° and changes by +2°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 5°

Worked Example 8

Problem: A temperature starts at 9° and changes by +4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 13°

Worked Example 9

Problem: A temperature starts at -1° and changes by -6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -7°

Worked Example 10

Problem: A temperature starts at -3° and changes by +2°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -1°

Practice Exercise

Create one new Grade 6 problem about Meaning of integers. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

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

4.2 Positive integers

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A temperature starts at 8° and changes by -8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 0°

Worked Example 2

Problem: A temperature starts at 3° and changes by -8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -5°

Worked Example 3

Problem: A temperature starts at 5° and changes by -8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -3°

Worked Example 4

Problem: A temperature starts at -1° and changes by +7°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 6°

Worked Example 5

Problem: A temperature starts at -6° and changes by +3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -3°

Worked Example 6

Problem: A temperature starts at -3° and changes by -8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -11°

Worked Example 7

Problem: A temperature starts at -4° and changes by +6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 2°

Worked Example 8

Problem: A temperature starts at 7° and changes by -3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 4°

Worked Example 9

Problem: A temperature starts at 10° and changes by -7°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 3°

Worked Example 10

Problem: A temperature starts at 4° and changes by +2°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 6°

Practice Exercise

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

Common Mistake

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

4.3 Negative integers

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A temperature starts at 0° and changes by -5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -5°

Worked Example 2

Problem: A temperature starts at 2° and changes by +6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 8°

Worked Example 3

Problem: A temperature starts at 2° and changes by -1°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 1°

Worked Example 4

Problem: A temperature starts at -7° and changes by +3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -4°

Worked Example 5

Problem: A temperature starts at 7° and changes by +5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 12°

Worked Example 6

Problem: A temperature starts at 10° and changes by -7°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 3°

Worked Example 7

Problem: A temperature starts at 8° and changes by -5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 3°

Worked Example 8

Problem: A temperature starts at 0° and changes by +5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 5°

Worked Example 9

Problem: A temperature starts at -9° and changes by -4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -13°

Worked Example 10

Problem: A temperature starts at 0° and changes by -4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -4°

Practice Exercise

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

Common Mistake

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

4.4 Zero

Zero is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Zero to analyze the values 18 and 12. What should be checked first?

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

Very beginner explanation: Zero is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Zero to analyze the values 18 and 11. What should be checked first?

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

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Zero to analyze the values 23 and 9. What should be checked first?

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

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Zero to analyze the values 19 and 5. What should be checked first?

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

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Zero to analyze the values 15 and 12. What should be checked first?

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

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Zero to analyze the values 27 and 11. What should be checked first?

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

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Zero to analyze the values 18 and 15. What should be checked first?

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

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Zero to analyze the values 16 and 17. What should be checked first?

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

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Zero to analyze the values 4 and 13. What should be checked first?

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

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Zero to analyze the values 11 and 15. What should be checked first?

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

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

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

Common Mistake

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

4.5 Opposite integers

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: What is the opposite of 7?

Opposite integers are the same distance from zero on different sides.

Very beginner explanation: Changing the sign gives the opposite integer.

Answer: -7

Worked Example 2

Problem: What is the opposite of -4?

Opposite integers are the same distance from zero on different sides.

Very beginner explanation: Changing the sign gives the opposite integer.

Answer: 4

Worked Example 3

Problem: What is the opposite of 3?

Opposite integers are the same distance from zero on different sides.

Very beginner explanation: Changing the sign gives the opposite integer.

Answer: -3

Worked Example 4

Problem: What is the opposite of -16?

Opposite integers are the same distance from zero on different sides.

Very beginner explanation: Changing the sign gives the opposite integer.

Answer: 16

Worked Example 5

Problem: What is the opposite of -5?

Opposite integers are the same distance from zero on different sides.

Very beginner explanation: Changing the sign gives the opposite integer.

Answer: 5

Worked Example 6

Problem: What is the opposite of 10?

Opposite integers are the same distance from zero on different sides.

Very beginner explanation: Changing the sign gives the opposite integer.

Answer: -10

Worked Example 7

Problem: What is the opposite of 4?

Opposite integers are the same distance from zero on different sides.

Very beginner explanation: Changing the sign gives the opposite integer.

Answer: -4

Worked Example 8

Problem: What is the opposite of -14?

Opposite integers are the same distance from zero on different sides.

Very beginner explanation: Changing the sign gives the opposite integer.

Answer: 14

Worked Example 9

Problem: What is the opposite of -14?

Opposite integers are the same distance from zero on different sides.

Very beginner explanation: Changing the sign gives the opposite integer.

Answer: 14

Worked Example 10

Problem: What is the opposite of 13?

Opposite integers are the same distance from zero on different sides.

Very beginner explanation: Changing the sign gives the opposite integer.

Answer: -13

Practice Exercise

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

Common Mistake

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

4.6 Integers on a number line

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A temperature starts at -2° and changes by +4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 2°

Worked Example 2

Problem: A temperature starts at 2° and changes by +6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 8°

Worked Example 3

Problem: A temperature starts at 1° and changes by +5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 6°

Worked Example 4

Problem: A temperature starts at -5° and changes by -6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -11°

Worked Example 5

Problem: A temperature starts at -5° and changes by -3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -8°

Worked Example 6

Problem: A temperature starts at 7° and changes by +8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 15°

Worked Example 7

Problem: A temperature starts at 0° and changes by -7°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -7°

Worked Example 8

Problem: A temperature starts at -3° and changes by -7°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -10°

Worked Example 9

Problem: A temperature starts at -2° and changes by -5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -7°

Worked Example 10

Problem: A temperature starts at -10° and changes by +5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -5°

Practice Exercise

Create one new Grade 6 problem about Integers on a number line. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

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

4.7 Comparing integers

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Compare 3 and 20.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: 3 < 20

Worked Example 2

Problem: Compare -16 and 11.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -16 < 11

Worked Example 3

Problem: Compare 16 and -8.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: 16 > -8

Worked Example 4

Problem: Compare 4 and -14.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: 4 > -14

Worked Example 5

Problem: Compare 4 and 14.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: 4 < 14

Worked Example 6

Problem: Compare -17 and 18.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -17 < 18

Worked Example 7

Problem: Compare -8 and -7.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -8 < -7

Worked Example 8

Problem: Compare 10 and 19.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: 10 < 19

Worked Example 9

Problem: Compare -15 and -10.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -15 < -10

Worked Example 10

Problem: Compare 9 and 10.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: 9 < 10

Practice Exercise

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

Common Mistake

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

4.8 Ordering integers

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Compare 5 and -6.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: 5 > -6

Worked Example 2

Problem: Compare -18 and -9.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -18 < -9

Worked Example 3

Problem: Compare -15 and 4.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -15 < 4

Worked Example 4

Problem: Compare -13 and 9.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -13 < 9

Worked Example 5

Problem: Compare -12 and -7.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -12 < -7

Worked Example 6

Problem: Compare -4 and 16.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -4 < 16

Worked Example 7

Problem: Compare 12 and -15.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: 12 > -15

Worked Example 8

Problem: Compare -11 and 12.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -11 < 12

Worked Example 9

Problem: Compare 10 and -1.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: 10 > -1

Worked Example 10

Problem: Compare -8 and -17.

Place both values mentally on a number line.
The value farther right is greater.

Very beginner explanation: On a number line, values increase as you move right.

Answer: -8 > -17

Practice Exercise

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

Common Mistake

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

4.9 Distance from zero

Distance from zero is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How far is 1 from 0 on a number line?

Distance is counted in positive units.
Use the absolute size of the integer.

Very beginner explanation: Distance from zero is never negative.

Answer: 1

Worked Example 2

Problem: How far is 8 from 0 on a number line?

Distance is counted in positive units.
Use the absolute size of the integer.

Very beginner explanation: Distance from zero is never negative.

Answer: 8

Worked Example 3

Problem: How far is -20 from 0 on a number line?

Distance is counted in positive units.
Use the absolute size of the integer.

Very beginner explanation: Distance from zero is never negative.

Answer: 20

Worked Example 4

Problem: How far is 11 from 0 on a number line?

Distance is counted in positive units.
Use the absolute size of the integer.

Very beginner explanation: Distance from zero is never negative.

Answer: 11

Worked Example 5

Problem: How far is 13 from 0 on a number line?

Distance is counted in positive units.
Use the absolute size of the integer.

Very beginner explanation: Distance from zero is never negative.

Answer: 13

Worked Example 6

Problem: How far is -18 from 0 on a number line?

Distance is counted in positive units.
Use the absolute size of the integer.

Very beginner explanation: Distance from zero is never negative.

Answer: 18

Worked Example 7

Problem: How far is 8 from 0 on a number line?

Distance is counted in positive units.
Use the absolute size of the integer.

Very beginner explanation: Distance from zero is never negative.

Answer: 8

Worked Example 8

Problem: How far is 15 from 0 on a number line?

Distance is counted in positive units.
Use the absolute size of the integer.

Very beginner explanation: Distance from zero is never negative.

Answer: 15

Worked Example 9

Problem: How far is -11 from 0 on a number line?

Distance is counted in positive units.
Use the absolute size of the integer.

Very beginner explanation: Distance from zero is never negative.

Answer: 11

Worked Example 10

Problem: How far is -16 from 0 on a number line?

Distance is counted in positive units.
Use the absolute size of the integer.

Very beginner explanation: Distance from zero is never negative.

Answer: 16

Practice Exercise

Create one new Grade 6 problem about Distance from zero. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

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

4.10 Temperature contexts

Temperature contexts is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A temperature starts at 2° and changes by +4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 6°

Worked Example 2

Problem: A temperature starts at 6° and changes by +6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 12°

Worked Example 3

Problem: A temperature starts at 0° and changes by +4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 4°

Worked Example 4

Problem: A temperature starts at 0° and changes by +5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 5°

Worked Example 5

Problem: A temperature starts at 3° and changes by +6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 9°

Worked Example 6

Problem: A temperature starts at 4° and changes by +1°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 5°

Worked Example 7

Problem: A temperature starts at 4° and changes by -8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -4°

Worked Example 8

Problem: A temperature starts at 7° and changes by +5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 12°

Worked Example 9

Problem: A temperature starts at -8° and changes by -6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -14°

Worked Example 10

Problem: A temperature starts at 2° and changes by -7°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -5°

Practice Exercise

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

Common Mistake

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

4.11 Elevation contexts

Elevation contexts is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A temperature starts at 3° and changes by -4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -1°

Worked Example 2

Problem: A temperature starts at -1° and changes by +3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 2°

Worked Example 3

Problem: A temperature starts at 2° and changes by +4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 6°

Worked Example 4

Problem: A temperature starts at 8° and changes by -6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 2°

Worked Example 5

Problem: A temperature starts at -10° and changes by +1°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -9°

Worked Example 6

Problem: A temperature starts at -8° and changes by -5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -13°

Worked Example 7

Problem: A temperature starts at 9° and changes by +4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 13°

Worked Example 8

Problem: A temperature starts at 3° and changes by +3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 6°

Worked Example 9

Problem: A temperature starts at -7° and changes by +2°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -5°

Worked Example 10

Problem: A temperature starts at -5° and changes by -3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -8°

Practice Exercise

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

Common Mistake

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

4.12 Money and debt contexts

Money and debt contexts is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A temperature starts at 8° and changes by -6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 2°

Worked Example 2

Problem: A temperature starts at -5° and changes by +6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 1°

Worked Example 3

Problem: A temperature starts at 10° and changes by -3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 7°

Worked Example 4

Problem: A temperature starts at -5° and changes by -4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -9°

Worked Example 5

Problem: A temperature starts at 0° and changes by +1°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 1°

Worked Example 6

Problem: A temperature starts at 7° and changes by +1°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 8°

Worked Example 7

Problem: A temperature starts at -5° and changes by +0°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -5°

Worked Example 8

Problem: A temperature starts at 3° and changes by +5°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 8°

Worked Example 9

Problem: A temperature starts at -10° and changes by +8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -2°

Worked Example 10

Problem: A temperature starts at -8° and changes by +3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -5°

Practice Exercise

Create one new Grade 6 problem about Money and debt contexts. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

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

4.13 Integer word problems

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A temperature starts at -6° and changes by +1°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -5°

Worked Example 2

Problem: A temperature starts at 10° and changes by +8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 18°

Worked Example 3

Problem: A temperature starts at 3° and changes by +4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 7°

Worked Example 4

Problem: A temperature starts at -4° and changes by -8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -12°

Worked Example 5

Problem: A temperature starts at 6° and changes by -6°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 0°

Worked Example 6

Problem: A temperature starts at 0° and changes by -3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -3°

Worked Example 7

Problem: A temperature starts at -4° and changes by +3°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: -1°

Worked Example 8

Problem: A temperature starts at -4° and changes by +8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 4°

Worked Example 9

Problem: A temperature starts at -8° and changes by +8°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 0°

Worked Example 10

Problem: A temperature starts at 8° and changes by -4°. What is the new temperature?

Start at the original integer.
Move right for a positive change or left for a negative change.

Very beginner explanation: Integers are useful for quantities above and below a reference point such as 0°.

Answer: 4°

Practice Exercise

Create one new Grade 6 problem about Integer word problems. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

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

Advertisement area — AdSense / Auto Ads

30 Review Questions and Answers

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

Answer: An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.

Q2. What is important to understand about Positive integers?

Answer: An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.

Q3. What is important to understand about Negative integers?

Answer: An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.

Q4. What is important to understand about Zero?

Answer: Zero is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q5. What is important to understand about Opposite integers?

Answer: An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.

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

Answer: An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.

Q7. What is important to understand about Comparing integers?

Answer: An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.

Q8. What is important to understand about Ordering integers?

Answer: An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.

Q9. What is important to understand about Distance from zero?

Answer: Distance from zero is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q10. What is important to understand about Temperature contexts?

Answer: Temperature contexts is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q11. What is important to understand about Elevation contexts?

Answer: Elevation contexts is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q12. What is important to understand about Money and debt contexts?

Answer: Money and debt contexts is a Grade 6 mathematics idea in Integer Foundations and Number Lines. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. What is important to understand about Integer word problems?

Answer: An integer is a whole number, zero, or the opposite of a whole number, such as -4, 0, or 7.

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 help prevent incompatible quantities from being mixed.

Q17. When should you round?

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

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, a table, 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 and check copied values, operations, signs, units, rules, and calculations.

Q22. Why are diagrams useful?

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

Q23. Why are tables useful?

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

Q24. Why are graphs useful?

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

Q25. Why should you explain your reasoning?

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

Q26. Why can more than one strategy be correct?

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

Q27. What should you do before using a formula or rule?

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

Q28. How does practice help in mathematics?

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

Q29. What is a good way to learn from a mistake?

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

Q30. Why should you compare an exact answer with an estimate?

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