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📗 Class 7 maths · session 1 of 12 · 60 minutes · free

Integers

Welcome aboard, Hero! Captain Calc needs your math superpowers to defeat negative confusion and master integers.

🎯 Practice mode🖨 Print a worksheet

🤖 Written with Google's Gemini AI. A second AI solved all 55 questions without seeing the answers, and both agree. One of our teachers has not read it yet, so if something looks wrong, please tell us.

A complete lesson · 60 minutes

Teach it, see it, practise it, all on this page.

Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.

See the teacher's plan
  1. Warm-up3 min
  2. Warm-up games5 min
  3. Adding and Subtracting Integers8 min
  4. Properties of Addition and Subtraction7 min
  5. Multiplying Integers7 min
  6. Dividing Integers7 min
  7. Operation Deep Freeze6 min
  8. The Bank Vault Mission5 min
  9. Submarine Navigation Code6 min
  10. Quiz5 min
  11. Set the project1 min

By the end you can

  • Add and subtract positive and negative integers accurately
  • Apply properties of integer addition and multiplication
  • Multiply and divide integers using correct sign rules
  • Solve real-world integer problems involving money, temperature, and elevation

Before you start

  • Basic operations with natural numbers and whole numbers
  • Understanding of basic number lines and profit or loss concepts

Have ready

  • Red and green counters or buttons to represent negative and positive numbers
  • A notebook and pen for calculation missions

Class 7 · CBSE, ICSE and state boards

Warm-up · think first

A freezer drops temperature by 3 degrees every hour. If it starts at 0 degrees, what is the temperature after 4 hours?

Show the answer

-12 degrees. Dropping 3 degrees 4 times means 4 × (-3) = -12.

Teacher tip: Ask students if a negative number makes sense for temperatures below zero.

More warm-ups for every class →

🎮 Warm-up games · 5 quick games

Play with Captain Calc

Six minutes with Captain Calc. Vote, say why, then show the answer.

  1. Which one does not belong: -15, -9, 4, -21? (-15 · -9 · 4 · -21)
    Answer: 4 does not belong because it is a positive integer while all others are negative integers.
  2. Would you rather have a bank account balance of -₹500 or -₹100? (-₹500 · -₹100)
    Answer: -₹100 is better because owing ₹100 is a smaller debt than owing ₹500.
  3. The product of two negative integers is a positive integer. (Always · Sometimes · Never)
    Answer: Always. Multiplying two negative numbers always yields a positive result, such as (-2) × (-3) = 6.
  4. I am an integer. Multiply me by -4, then add 10, and you get -2. What number am I?
    Answer: 3. If -4 × x + 10 = -2, then -4 × x = -12, which means x = 3.
  5. Where do we use negative integers in everyday life in India?
    Answer: We use them in bank overdrafts, test score penalties, underground building floors, and mountain freezing temperatures.

Part 1 of 4 · learn, see, practise

Adding and Subtracting Integers

Integers include zero, positive numbers, and negative numbers.

When adding integers with the same sign, add their values and keep the common sign.

When adding integers with different signs, subtract the smaller value from the larger value and keep the sign of the larger value.

Example 1

Find the value of -7 + (-5).

  1. Both numbers are negative.
  2. Add their absolute values: 7 + 5 = 12.
  3. Keep the negative sign: -12.

Answer: -12

Example 2

Find the value of 14 - (-8).

  1. Subtracting a negative number is equivalent to adding a positive number.
  2. Change 14 - (-8) to 14 + 8.
  3. Add the values: 14 + 8 = 22.

Answer: 22

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. -5
  2. 7
  3. -5
  4. -29
  5. 9
  6. -45

Part 2 of 4 · learn, see, practise

Properties of Addition and Subtraction

Integers are closed under addition and subtraction, meaning the result is always an integer.

Addition is commutative because changing the order of numbers gives the exact same sum.

Zero is the additive identity because adding zero to any integer does not change its value.

Example 1

Verify the commutative property for -6 and 9.

  1. Add -6 + 9 to get 3.
  2. Add 9 + (-6) to get 3.
  3. Both orders give 3, proving addition is commutative.

Answer: 3

Example 2

Find the additive inverse of -17.

  1. The additive inverse of a number gives a sum of zero when added to it.
  2. Since -17 + 17 = 0, the additive inverse is 17.

Answer: 17

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 23
  2. -45
  3. 14
  4. 0
  5. 0
  6. 0

Part 3 of 4 · learn, see, practise

Multiplying Integers

The product of two integers with the same sign is always a positive integer.

The product of two integers with opposite signs is always a negative integer.

The distributive property states that a × (b + c) = (a × b) + (a × c).

Example 1

Calculate: (-7) × (-8).

  1. Both factors are negative.
  2. Multiply absolute values: 7 × 8 = 56.
  3. Same signs yield a positive product: 56.

Answer: 56

Example 2

Solve using distributive property: 15 × (-4) + 15 × (-6).

  1. Group terms: 15 × [(-4) + (-6)].
  2. Add inside brackets: -4 + (-6) = -10.
  3. Multiply: 15 × (-10) = -150.

Answer: -150

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. -45
  2. 48
  3. -40
  4. -32
  5. -1
  6. -140

Part 4 of 4 · learn, see, practise

Dividing Integers

Dividing two integers with the same sign gives a positive quotient.

Dividing two integers with different signs gives a negative quotient.

Dividing zero by any non-zero integer equals zero, but division by zero is undefined.

Example 1

Calculate: (-72) ÷ 8.

  1. The signs are different, so the quotient will be negative.
  2. Divide values: 72 ÷ 8 = 9.
  3. Attach the negative sign: -9.

Answer: -9

Example 2

Calculate: (-60) ÷ (-12).

  1. Both numbers are negative, so the quotient will be positive.
  2. Divide values: 60 ÷ 12 = 5.
  3. The result is positive 5.

Answer: 5

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. -5
  2. 8
  3. 0
  4. -5
  5. 6
  6. 7

Watch out

Common mistakes

Writing (-5) - (-3) as -8.

Remember that subtracting a negative number changes the sign to addition: -5 + 3 = -2.

Thinking that the product of two negative numbers is negative.

Use the sign rule: two negatives multiplied together always make a positive.

Dividing a number by zero to get zero.

Any number divided by zero is undefined, whereas zero divided by a non-zero number is zero.

Class activity 1 of 3

Operation Deep Freeze

Captain Calc needs your help tracking temperatures at the Himalayan Outpost!

  1. Read each temperature change carefully.
  2. Use addition or subtraction rules to find the final temperature.
  3. Write your final integer answer clearly.

Answers (for the teacher)
  1. -9
  2. -4
  3. -7
  4. -12
  5. 0

Class activity 2 of 3

The Bank Vault Mission

Help Captain Calc calculate ledger balances at the Super Math Bank!

  1. Treat deposits as positive integers and debts as negative integers.
  2. Multiply or divide to calculate total transaction changes.
  3. Write the net balance as an integer.

Answers (for the teacher)
  1. -200
  2. -200
  3. -100
  4. -50
  5. -200

Class activity 3 of 3

Submarine Navigation Code

Decode the secret coordinates of Captain Calc's submarine using integer operations!

  1. Solve each integer expression following correct order of operations.
  2. Pay close attention to signs during multiplication and division.
  3. Enter the final numerical value.

Answers (for the teacher)
  1. -2
  2. -2
  3. -24
  4. -4
  5. -8

After class · project

Captain Calc's City Temperature Tracker

Track temperature fluctuations in five Indian hill stations and calculate average integer changes.

What to make: A temperature log report with complete integer calculations and sign steps shown.

Stretch: Graph the temperature values on a vertical number line showing positions above and below zero.

How it is marked

Look forDone well when
Data CollectionAccurately lists 5 temperatures using proper integer signs.
Calculation AccuracyCorrectly computes temperature sum of integers.
Average CalculationUses integer division correctly to find the mean temperature.

Project template

Copy it onto paper or print the practice sheet.

City 1 Temperature: ___ degrees C
City 2 Temperature: ___ degrees C
City 3 Temperature: ___ degrees C
Total sum of temperatures: ___ degrees C
Average minimum temperature: ___ degrees C

Homework

Practise at home

Try each on paper, then tap to see the answer and working. Or print the practice sheet.

  1. Calculate: -14 + (-18)

    -32: Add absolute values 14 + 18 = 32 and attach the common negative sign.

  2. Calculate: 25 - (-15)

    40: Rewrite subtraction of negative as 25 + 15 = 40.

  3. Calculate: (-12) × (-6)

    72: Multiplying two negative integers gives a positive product.

  4. Calculate: (-81) ÷ 9

    -9: Dividing negative by positive gives a negative quotient.

  5. Use distributive property to evaluate: (-15) × 8 + (-15) × 2

    -150: Rewrite as (-15) × (8 + 2) = (-15) × 10 = -150.

  6. In a test, +3 marks are given for every correct answer and -1 mark for every wrong answer. Ananya got 12 correct and 5 wrong. What is her total score?

    31: Calculate (12 × 3) + (5 × -1) = 36 - 5 = 31.

🔥 Challenge round · finished early?

The hardest questions of the lesson, no notes

Cover the notes and try these from memory. They are meant to make you think hard: draw, try small cases, and check your answer.

Stretch 🔥

Stretch 🔥

Stretch 🔥

Stretch 🔥

Stretch 🔥

Stretch 🔥

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 9
  2. -45
  3. 0
  4. 0
  5. -1
  6. -140
  7. 6
  8. 7

🧠 Think-hard question

Determine whether the product of 99 negative integers and 5 positive integers is positive or negative. Explain why without calculating the actual product.

Talk it through or use the drawing board. There is more than one way to get there.

🎯 Practice mode: one question at a time🧩 Brain warm-ups🎮 Maths and logic games

Quiz · 10 questions

Final quiz: check what you learned

Pick an answer to see if it is right and why. Your best score is saved on this device.

1What is the value of -15 + 9?
Show the answer

-6. Subtract 9 from 15 and keep the negative sign from the larger absolute value.

2Which of the following equals -12 - (-5)?
Show the answer

-7. Subtracting -5 is equivalent to adding 5, so -12 + 5 = -7.

3What is the product of (-9) and (-4)?
Show the answer

36. The product of two negative integers is always positive.

4What is (-48) ÷ 6?
Show the answer

-8. Dividing a negative integer by a positive integer yields a negative result.

5What is the additive inverse of -35?
Show the answer

35. The additive inverse of a number is its opposite sign value that sums to zero.

6Which property is shown by (-5) + 8 = 8 + (-5)?
Show the answer

Commutative property of addition. Changing the order of two added integers does not change the sum.

7Evaluate: (-2) × 5 × (-3).
Show the answer

30. Multiply (-2) × 5 = -10, then (-10) × (-3) = 30.

8What is the result of 0 ÷ (-18)?
Show the answer

0. Zero divided by any non-zero integer is equal to zero.

9A submarine descends at 4 m per second. What is its depth change after 10 seconds?
Show the answer

-40 m. Descending 4 m ten times is represented by 10 × (-4) = -40 m.

10Evaluate using distributive property: 7 × (-12) + 7 × 2.
Show the answer

-70. 7 × [(-12) + 2] = 7 × (-10) = -70.

🖨 Print what we learned

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For parents and teachers

The 60-minute lesson plan

Use it as it is, or stretch any part over two sessions. Each row links to the part of the page you need.

TimePartThe teacherThe learner
0–3 minWarm-upAsk the question and wait for a guess before any hint.Guess, then explain.
3–8 minWarm-up gamesPlay three or four games. Ask for a reason each time.Vote and say why.
8–16 minAdding and Subtracting IntegersExplain, then reveal the examples one step at a time.Practise up to the stretch question.
16–23 minProperties of Addition and SubtractionExplain, then show the examples.Practise.
23–30 minMultiplying IntegersExplain, then show the examples.Practise.
30–37 minDividing IntegersExplain, then show the examples.Practise; the stretch can be homework.
37–43 minOperation Deep FreezeLet learners work alone; hint only after a wrong check.Solve and check.
43–48 minThe Bank Vault MissionDo the first item together.Finish the activity.
48–54 minSubmarine Navigation CodeSet as homework if time is short.Solve the mission.
54–59 minQuizRead each question aloud; vote, then check.Answer and read why.
59–60 minSet the projectShow the template and agree a due date.Start the project.

Questions to ask

  • How does subtracting a negative integer differ from subtracting a positive integer?
  • Why is the product of two negative integers positive?
  • Can you give a real-life example where a negative answer indicates a loss or debt?

If it feels hard

Use two-sided colored counters where green represents +1 and red represents -1. Pair one green and one red counter to form zero pairs when adding or subtracting.

If it feels easy

Determine whether the product of 99 negative integers and 5 positive integers is positive or negative. Explain why without calculating the actual product.

FAQ

Integers: questions

Why do two negative signs make a positive when multiplying?

Multiplying by a negative flips the direction on a number line. Flipping direction twice restores the original positive direction.

What is the difference between absolute value and an integer?

An integer includes a sign indicating direction, while absolute value measures only distance from zero without sign.

Why is division by zero not allowed for integers?

Dividing by zero has no meaningful integer answer because no number multiplied by zero can equal a non-zero number.

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