Foundation · Grade 8+45 minutes

Unit 1 · Number Foundations

Adding Integers

Model integer addition with movement and counters, then apply efficient sign rules with understanding.

0–3 minutes

Learning Objectives

  • Add integers with the same sign.
  • Add integers with different signs.
  • Model addition as movement on a number line.
  • Explain how zero pairs simplify integer sums.

3–10 minutes

Warm-up

The temperature is −2°C and rises by 7°C. What is the new temperature?

Reveal explanation

5°C, because −2 + 7 = 5.

10–23 minutes

Core Teaching

1. Addition as movement

Begin at the first integer on a number line. Adding a positive integer moves right; adding a negative integer moves left.

For −3 + 5, begin at −3 and move five spaces right to reach 2.

2 + 4 = 6
3 + (−5) = −2
−4 + 7 = 3
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Numbers decrease ←→ Numbers increase

2. Adding integers with the same sign

When signs are the same, add the absolute values and keep the common sign.

For −6 + (−8), add 6 + 8 = 14 and keep the negative sign: −14.

5 + 9 = 14
−7 + (−2) = −9
−12 + (−3) = −15

3. Adding integers with different signs

When signs differ, subtract the smaller absolute value from the larger absolute value.

Use the sign of the integer with the greater absolute value. For −10 + 6, calculate 10 − 6 = 4 and use the negative sign, giving −4.

8 + (−3) = 5
−11 + 4 = −7
−5 + 9 = 4

4. Zero pairs

A positive counter and a negative counter cancel because 1 + (−1) = 0.

In 4 + (−6), four zero pairs cancel, leaving two negative counters. Therefore the sum is −2.

23–33 minutes

Guided Practice

1.Calculate −7 + (−5).

Hint: The signs are the same.

Answer: −12

2.Calculate −9 + 14.

Hint: Subtract absolute values and use the sign of the larger absolute value.

Answer: 5

3.Calculate 6 + (−10).

Hint: Ten has the greater absolute value.

Answer: −4

33–40 minutes

Independent Practice

  1. 1.Calculate 8 + (−3).
  2. 2.Calculate −12 + (−7).
  3. 3.A submarine is at −18 m and rises 25 m. What is its new elevation?
  4. 4.A game score changes by −6 points and then +10 points. What is the total change?
Check independent-practice answers
  1. 1. 5
  2. 2. −19
  3. 3. 7 m
  4. 4. +4 points

40–45 minutes

Lesson Check

Answer every question. A score of 80% or higher marks this lesson complete.

1.What is −4 + (−9)?
2.What is −8 + 3?
3.What is 12 + (−12)?
4.Which expression equals 6?
5.A balance of −$20 receives a $35 deposit. What is the new balance?

Lesson Summary

  • Adding a positive integer moves right; adding a negative integer moves left.
  • For equal signs, add absolute values and keep the sign.
  • For different signs, subtract absolute values and use the sign of the larger absolute value.
  • Opposite counters form zero pairs and cancel.
Subtracting Integers · Coming soon