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Lesson · Signed numbers · about 20 min Pending teacher review

Adding integers: jumps and zero pairs

Goal: Add any two integers, with the same or different signs, and explain the result with a number-line jump or a chip model.

Before this: Needs Direction on the number line (adding a positive moves right, adding a negative moves left) and Opposites (a number plus its opposite makes 0).

Step 1 · Launch (≈5 min)

A game scores points up and down. You are at $-3$ and you gain $5$. Where are you now?

Try it two ways:

Jump: start at $-3$, jump $5$ to the right.
Chips: 3 negative chips and 5 positive chips. Pair each negative with a positive — each pair is $0$. What is left?

Step 2 · Practice (≈10 min)

Pick the level that fits today. Hints are allowed — each one is recorded as assisted practice, which never changes an independent status.

Add: $\;-6 + (-4)$

Answer

Add: $\;7 + (-10)$

Answer

Add: $\;-8 + 12$

Answer

The temperature is $-9\,°$F. It rises $6\,°$F. What is the temperature now? (number only)

Answer

Show me how it works — worked explanation

Two reliable pictures: **jumps** on a number line and **zero pairs** with chips. The rules fall out of the pictures — you do not have to memorise them first.

Adding a positive = jump right. Adding a negative = jump left.
**Same signs** ($-3 + (-4)$): both jumps go the same way, so the sizes pile up: 3 + 4 = 7 steps left → $-7$.
**Different signs** ($5 + (-8)$): the jumps fight. Pair up chips: 5 positives and 8 negatives make 5 zero pairs; 3 negatives remain → $-3$. Shortcut: subtract the sizes (8 − 5 = 3) and keep the sign of the larger size.
**Opposites** ($6 + (-6)$): every chip pairs off → $0$.

Step 3 · Wrap-up (≈5 min)

Adding a positive moves right; adding a negative moves left. With the same signs, the sizes add and the sign stays. With different signs, the sizes subtract and the sign belongs to the number that is farther from zero. A number plus its opposite is zero — that is why chips pair off.

Step 4 · Independent check

4 fresh problems on this skill, done alone: no hints, no worked solutions, no feedback until the end. This is what moves the skill's status.

You can start the check any time, but the wrap-up is worth reading first.

Parent guide (for the adult)

What to notice

With same-sign problems, does your learner subtract the sizes ("−3 + (−4) = −1")? That is the most common error at this stage.
With different signs, do they add the sizes ("5 + (−8) = 13") or keep the first number's sign no matter what?
Do they reach for a picture (line or chips) when unsure, or guess?

What to ask

"Which direction does adding a negative move you?"
"Which number is farther from zero? So which sign wins?"
"Can you show me that with chips?"

Common errors — and a question that separates a slip from a misconception

Subtracts sizes and keeps the first sign on same-sign problems
Looks like: −3 + (−4) = −1
Ask: "Start at −3. Does adding −4 move you toward zero or away from it?" If they move the right way and self-correct, it was a slip; if they say "two negatives cancel", that is the misconception — use the chip picture (there is nothing to pair).
Adds sizes on different-sign problems
Looks like: 5 + (−8) = 13 or −13
Ask: "Lay out 5 positive and 8 negative chips. How many pairs cancel?"
Always keeps the first number's sign
Looks like: −6 + 9 = −3
Ask: "Which pile is bigger, the negatives or the positives?"

When to show an example

Open the worked explanation after the first wrong same-sign problem — the pile-up picture fixes it faster than re-explaining the rule. Let your learner narrate the next problem with the picture.

Complete solutions (keep closed during the independent check)

Show practice solutions

Support

Same signs: add the sizes (2 + 3 = 5) and keep the sign: $-5$.
Start at $4$, one step left: $3$. Or: one zero pair cancels, 3 positives remain.
A number plus its opposite is $0$.

Core

Same signs → add sizes, keep the sign: $-10$.
Different signs → subtract sizes (10 − 7 = 3) and take the sign of the larger size (negative): $-3$.
$12 - 8 = 4$; the positive has the larger size, so $4$.
$-9 + 6 = -3$: six steps right from $-9$ lands on $-3$.

Extension

$-15 + 9 = -6$; $-6 + (-4) = -10$.
From $-7$ to $2$ is 9 steps right, so add $9$.

Repeat or move on?

Move on when the independent check is 4 of 4, or 3 of 4 with a clear slip. If the same-sign error repeats, repeat the support set with chips for one more session before the check. The next lesson (subtracting) is built on this one.