Operations on Integers

Lesson 1 of 2: Integers

In this lesson:

• Plot and order integers on a number line
• Add and subtract integers using forward/backward movement
• Multiply integers and apply the sign rules

What You Will Learn Today

By the end of this lesson, you should be able to:

1. Plot positive and negative integers on a number line and order them
2. Add and subtract integers using forward and backward movement
3. Multiply integers by applying the sign rules
4. Solve real-life word problems involving integers

Last Night It Was −2 °C

The temperature was −2 °C at midnight.

By morning it had risen 7 °C.

What is the temperature now?

You can probably get close — but can you be certain, and can you show why?

Which Side Are the Negatives On?

• Negative integers are to the left of zero
• Positive integers are to the right of zero
• Zero is neither positive nor negative

Integers on the Number Line

• An integer is a whole number: positive, negative, or zero — no fractions
• Opposite integers are the same distance from 0 on different sides
• +3 and −3 are opposites; the opposite of 0 is 0

Which Is Larger: −5 or −2?

Predict before reading on.

• A learner says: "−5 is larger because 5 is bigger than 2"
• Is this correct?

Look at the number line and decide: which one sits further to the RIGHT?

Ordering Integers from Smallest to Largest

Order these integers from smallest to largest:

Use the number line: find each number's position, then read left to right.

Answer on the next slide — try first.

Movement on the Number Line

The movement rule:

• To add → step RIGHT (forward) — the number gets larger
• To subtract → step LEFT (backward) — the number gets smaller

Start at the first number. The second number tells you how many steps.

Two Worked Examples: Adding and Subtracting

Example 1:

Start at −3, step 5 right → land on +2

Example 2:

Start at 4, step 6 left → land on −2

Why Add = Right and Subtract = Left

• Further right is larger (from Chunk 1)
• Adding increases your value → step right
• Subtracting decreases your value → step left

Movement direction follows from ordering — not a separate rule to memorise.

Subtracting a Negative: The Key Idea

What happens when you subtract a negative?

• Subtracting reverses direction
• A backward step reversed is a forward step
• Removing a debt makes you richer

Which direction do you move? Predict before the next slide.

Worked Example: Subtracting a Negative

(start at 2, step 3 left → −1)

(start at 2, step 3 right → +5)

Subtracting a negative flips the direction: LEFT becomes RIGHT.

Find and Fix the Error Here

A student writes:

They started at 1 and stepped 4 places LEFT.

Where did they go wrong? What is the correct answer?

Work it out on your own before the next slide.

Practice: Adding and Subtracting Integers

Work these out independently. Draw a number line if it helps.

Write each answer with its sign.

Multiplication as Repeated Forward or Backward Steps

Multiplication is repeated movement on the number line:

• means: take the step three times
• Three steps of each =

What do you get moving backward by 4, three times in a row?

Negative × Negative: Each Step Rises by +4

The Sign Rule for Multiplication

• : different → negative
• : same → positive

Practice: Applying the Sign Rule for Multiplication

Apply the sign rule to each:

State the sign first, then compute the magnitude.

Solving Word Problems: The Three Steps

Every integer word problem follows the same cycle:

1. Translate — write the signed operation from the words
2. Compute — carry out the operation
3. Interpret — state what the sign means in context

Step 3 is where marks are lost: correct number, missing sign = wrong answer.

Worked: Translate, Compute, Then Interpret the Sign

Temperature: −2 °C, rises 7 °C.

Banking: Balance −3000 shillings, deposit 5000.

The number gives the amount; the sign gives the direction.

Your Turn: Altitude Word Problem

A diver is 150 metres below sea level.

She climbs 200 metres upward.

Your task:

1. Write the signed operation
2. Compute the answer
3. State what the sign of the answer means

Do all three steps before advancing.

Key Takeaways: Integers Are Movement and Direction

✓ Further right = larger · add = right · subtract = left

✓ Subtract a negative = step right

✓ Same signs → positive · different signs → negative

✓ Word problems: translate → compute → interpret

−5 < −2 · not −1 ·

Coming Up in Lesson 2: Clock Arithmetic

The next lesson asks: what if the number line wraps around?

• Move past 12 on a clock → you're back at 1
• The same forward and backward language applies
• But the line is now a circle, not a line

Your forward/backward movement from today drives clock arithmetic.