Unit 1 · Number Foundations
Adding Integers
Model integer addition with movement and counters, then apply efficient sign rules with understanding.
Recommended prerequisites
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. 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.
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.
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.Calculate 8 + (−3).
- 2.Calculate −12 + (−7).
- 3.A submarine is at −18 m and rises 25 m. What is its new elevation?
- 4.A game score changes by −6 points and then +10 points. What is the total change?
Check independent-practice answers
- 1. 5
- 2. −19
- 3. 7 m
- 4. +4 points
40–45 minutes
Lesson Check
Answer every question. A score of 80% or higher marks this lesson complete.
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.