Year 9 maths lesson · Integers

Adding and Subtracting Integers

Add and subtract positive and negative numbers using a number line. Learn the two sign-pair shortcuts (+ − becomes −, and − − becomes +) and how to handle calculations that cross zero.

  • About 6–9 minutes
  • 12 quick questions as you go
  • Then about 6 minutes of practice
Practice questions → Set for Class

Worked examples

3 + 5

  1. Start at 3, hop right 5
  2. Land on 8

−5 + 3

  1. Start at −5, hop right 3
  2. Land on −2

−14 + 20

  1. Break the hop into stages
  2. From −14, hop 14 right to reach 0
  3. Then 6 more right — land on 6

5 + (−3)

  1. Adding a negative flips the direction — hop left
  2. From 5, hop 3 left to land on 2
  3. Shortcut: + − becomes −, so 5 + (−3) = 5 − 3 = 2

5 + (−9)

  1. + − becomes −: rewrite as 5 − 9
  2. From 5, hop 5 left to reach 0, then 4 more
  3. Land on −4

−5 − (−3)

  1. Subtracting a negative moves us right
  2. From −5, hop 3 right to land on −2

−5 − (−9)

  1. − − becomes +: rewrite as −5 + 9
  2. From −5, hop 5 right to reach 0, then 4 more
  3. Land on 4

Before this lesson

It helps to be comfortable with:

  • Addition and subtraction of whole numbers
  • Reading a number line
  • Familiarity with negative numbers as positions left of zero

Lesson transcript

Everything the lesson says, word for word

Student: Hey Alex! What are we working on today?

Teacher: Adding and subtracting integers — positive and negative numbers.

Student: Do we need the number line?

Teacher: Yep. Let’s start easy. Three plus five — start at 3, hop right five places.

Student: Eight. That’s simple.

Teacher: Now watch what happens when we start in the negatives. Negative 5 plus 3.

Teacher: We still hop right — three times. Hop… hop… hop.

Student: Negative 2! Same idea — just starting left of zero.

Teacher: Negative 14 plus 20. Let’s add in stages. First we use up 14 hops to reach zero. How many more do we need to add?

Student: 6 more. That takes us to positive 6!

Teacher: Exactly. Negative 14 plus 20 equals 6.

Teacher: Good. Now — adding a positive moves us right. What should adding a negative do?

Student: The opposite… move left?

Teacher: Exactly! Five plus negative 3. We start at 5 and hop left 3 places.

Student: So five plus negative 3 equals 2. Adding a negative pulls you left.

Teacher: Notice the two signs in the middle of that expression. A plus next to a minus.

Teacher: Circle them.

Teacher: Plus then minus just means subtract. They simplify to a single minus sign.

Student: So five plus negative 3 is the same as 5 minus 3?

Teacher: Exactly the same thing.

Teacher: Now try five plus negative 9. Remember, plus minus becomes minus. So this is really five minus 9.

Teacher: First hop takes us to zero — that uses up 5 of our 9 steps.

Teacher: Four more steps left and we land at negative 4.

Student: Five plus negative 9 equals negative 4. Two hops makes crossing zero easy.

Teacher: Your turn, Jamie. Try 7 plus negative 9.

Student: Looking at the middle symbols. Plus and minus become minus. So it's really 7 minus 9. 7 hops to zero, then 2 more. That's negative 2.

Teacher: Nice! Now try negative 5 plus negative 13.

Student: Same here. The plus and minus become minus. Negative 5 minus 13. Starting at negative 5, 13 to the left lands at negative 18.

Teacher: Great job! Let's see how you do with some practice questions.

Teacher: Last big idea. Subtracting a positive moves us left. So what does subtracting a negative do?

Student: The opposite of left… so right?

Teacher: Yes! Subtracting a negative moves us right. Negative 5 minus negative 3 — start at negative 5, move right 3.

Student: Negative 5 minus negative 3 equals negative 2. Moving right from a negative — nice.

Teacher: Another example. 5 minus 3 takes us 3 steps left to land at 2. So what about 5 minus negative 3?

Teacher: Subtracting a negative moves us right. 5 minus negative 3 equals 8.

Student: 5 minus negative 3 equals 8!

Teacher: Look at the two middle signs. Subtracting a negative just means plus. We can replace them with a single plus sign.

Teacher: Here's a nice way to remember it. If you rotate one minus sign and put them together, they make a plus sign.

Student: Oh that’s a cool way to see it!

Teacher: Let’s put it together. Negative 5 minus negative 9.

Teacher: Circle those two middle signs.

Teacher: They become a plus — so it’s negative 5 plus 9.

Teacher: Now move right 9 from negative 5. First hop: add 5 to reach zero.

Teacher: Then 4 more to land at positive 4.

Student: Negative 5 minus negative 9 equals 4. Convert the signs, then use the number line.

Teacher: Here’s the full picture.

Student: If I see a plus next to a minus, they just become minus. So 5 plus negative 3 is the same as 5 minus 3.

Student: And two minuses next to each other become a plus. So negative 5 minus negative 9 is the same as negative 5 plus 9.

Teacher: Exactly. Have a go at these.

More Integers lessons

Next lesson: Multiplying and Dividing Integers →All Year 9 Number lessonsAll lessons