Year 7 NSW Maths Integers Worksheet | Compare, Order and Calculate

Instructions

1. Complete the questions in order. They begin with comparing integers and build toward solving real-world problems.
2. Remember that integers include positive numbers, negative numbers, and zero.
3. Use a number line when helpful. Numbers farther to the right are greater than numbers to the left.
4. Show your working for calculation and problem-solving questions.
5. Complete the optional challenge if you are ready for a harder task.

Learning goals:

• Compare integers using >, <, or =.
• Order integers from least to greatest and greatest to least.
• Add, subtract, multiply, and divide integers.
• Use integers to solve practical problems involving temperature, elevation, money, and scores.

Mission 1: Integer Investigators

Helpful example: Since -3 is to the left of 2 on a number line, -3 < 2.

A. Compare the integers

Write >, <, or = in each box.

1. -6 [ ] 2
2. -4 [ ] -9
3. 0 [ ] -7
4. 5 [ ] 5
5. -12 [ ] -3
6. 8 [ ] -1
7. -15 [ ] -18
8. 0 [ ] 4

B. Circle the greater integer

1. -8 or -2
2. -11 or -15
3. 3 or -3
4. -1 or 0
5. -20 or -7

C. Number-line thinking

Use the number line to answer the questions.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

1. Which integer is 4 spaces to the left of 1? __
2. Which integer is 6 spaces to the right of -5? __
3. How many spaces are between -7 and 3? __
4. Write an integer between -4 and 2: __
5. Write an integer less than -8: __

Mission 2: Sort the Scores

A. Order the integers

Write each group from least to greatest.

1. 4, -2, 0, -7, 5 Answer: __

2. -10, -3, -12, 1, 0 Answer: __

3. 9, -1, 6, -8, -4 Answer: __

4. -5, 5, -15, 0, 10 Answer: __

B. Order the integers in reverse

Write each group from greatest to least.

1. -3, 7, 0, -9, 4 Answer: __

2. 12, -6, -2, 8, -10 Answer: __

Mission 3: Integer Operations

Hints:

• Adding a positive moves right on a number line.
• Adding a negative moves left.
• Subtracting a negative is the same as adding a positive.
• When multiplying or dividing, integers with the same signs give a positive answer. Different signs give a negative answer.

Calculate. Show a number-line jump or another method for at least two questions.

1. 7 + (-3) = __
2. -5 + 9 = __
3. -8 + (-6) = __
4. 12 - 17 = __
5. -4 - 7 = __
6. -9 - (-5) = __
7. (-6) × 4 = __
8. (-7) × (-3) = __
9. 36 ÷ (-6) = __
10. (-48) ÷ (-8) = __
11. 5 + (-12) - (-4) = __
12. (-3) × 5 + 8 = __

Mission 4: Real-World Integer Problems

Read each situation carefully. Choose an operation, calculate, and write your answer with a suitable unit.

1. The temperature is -2°C in the morning. By midday, it rises 9°C. What is the midday temperature?

   Working: __ Answer: ___

2. A diver is at -18 metres. She rises 7 metres. What is her new position?

   Working: __ Answer: ___

3. A hiker starts at an elevation of 250 metres. He descends 430 metres. What is his new elevation?

   Working: __ Answer: ___

4. Liam has $15 in his account. He spends $23. Represent his balance as an integer. What is his new balance?

   Working: __ Answer: ___

5. A quiz awards 4 points for a correct answer and subtracts 2 points for an incorrect answer. Mia gets 6 correct answers and 3 incorrect answers. What is her total score?

   Working: __ Answer: ___

6. A lift begins on level 3. It travels down 8 levels, then up 5 levels. Which level does it reach?

   Working: __ Answer: ___

Mission 5: Show What You Know

Complete the organizer. The first row is an example.

Mission 6: Explain Your Thinking

Answer in complete sentences.

1. Why is -10 less than -4 even though 10 is greater than 4?

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2. Write two different integer calculations that have an answer of -6.

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3. Give an everyday example where a negative integer would be useful.

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Optional Challenge: The Mountain Rescue Route

A rescue team begins at an elevation of 120 metres. They travel down 185 metres, climb 70 metres, descend 260 metres, and then climb 90 metres.

1. Write one integer expression for the entire journey.

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2. What is the team’s final elevation?

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3. What is the lowest elevation reached during the journey?

   ---

4. How many metres higher or lower is the final elevation than the starting elevation?

   ---

Reflection

Complete these sentences.

• One strategy that helped me compare integers was ____.
• I can use negative numbers in real life when _____ ____.
• The skill I would like to practise more is ____.

Answer Key

Mission 1

A.

1. -6 < 2
2. -4 > -9
3. 0 > -7
4. 5 = 5
5. -12 < -3
6. 8 > -1
7. -15 > -18
8. 0 < 4

B.

1. -2
2. -11
3. 3
4. 0
5. -7

C.

1. -3
2. 1
3. 10 spaces
4. Any integer from -3 to 1, such as -2
5. Any integer less than -8, such as -9

Mission 2

A. Least to greatest

1. -7, -2, 0, 4, 5
2. -12, -10, -3, 0, 1
3. -8, -4, -1, 6, 9
4. -15, -5, 0, 5, 10

B. Greatest to least

1. 7, 4, 0, -3, -9
2. 12, 8, -2, -6, -10

Mission 3

1. 4
2. 4
3. -14
4. -5
5. -11
6. -4
7. -24
8. 21
9. -6
10. 6
11. -3
12. -7

Mission 4

1. -2 + 9 = 7; the midday temperature is 7°C.
2. -18 + 7 = -11; the diver is at -11 metres.
3. 250 - 430 = -180; the new elevation is -180 metres.
4. 15 - 23 = -8; the new balance is -$8, or $8 below zero.
5. 6 × 4 + 3 × (-2) = 24 - 6 = 18; Mia’s score is 18 points.
6. 3 - 8 + 5 = 0; the lift reaches level 0.

Mission 5

Mission 6

1. -10 is to the left of -4 on a number line, so -10 is less than -4.
2. Possible answers include -2 + (-4) = -6 and 3 - 9 = -6.
3. Possible answers include temperatures below zero, money owed, being below sea level, or a decrease in points.

Optional Challenge

1. 120 - 185 + 70 - 260 + 90
2. 120 - 185 + 70 - 260 + 90 = -165 metres. The final elevation is -165 metres.
3. After descending 185 metres, the team is at -65 metres. After climbing 70 metres, it is at 5 metres. After descending 260 metres, it reaches -255 metres, the lowest elevation.
4. The final elevation is 285 metres lower than the starting elevation: -165 - 120 = -285.