Unit 4 · Topic 02 · Integers
The temperature was −3°C. It rose by 8 degrees.
Kabir added: −3 + 8, and hesitated — negative numbers still felt like a trick.
Anaya pulled out a number line and just walked the steps — no trick needed at all.
"The temperature was −3°C this morning and rose by 8 degrees by noon. What's the new temperature?" asked Ms. Rao.
Kabir froze. "Do I add or subtract? Negative numbers always confuse me."
Anaya drew a number line on her notebook. "Start at −3. Rising by 8 means moving RIGHT 8 steps, since warmer is always to the right." She counted: −3, −2, −1, 0, 1, 2, 3, 4, 5. "Landed on 5. So −3 + 8 = 5."
"The number line never lies," said Ms. Rao. "Adding a positive number always means moving RIGHT. Adding a negative number means moving LEFT."
She posed the reverse: "Now the temperature is 5°C and drops by 9 degrees. Where do you land?"
Kabir tried the number line himself. "Dropping means moving LEFT. Start at 5, move left 9 steps: 5, 4, 3, 2, 1, 0, −1, −2, −3, −4." He counted carefully. "Lands on −4. So 5 − 9 = −4."
"Exactly. And here's the deeper trick," said Ms. Rao. "Subtracting a number is the SAME as adding its opposite. 5 − 9 is the same move as 5 + (−9). Once you see subtraction as 'add the opposite,' every integer problem becomes the same kind of number-line walk."
Anaya tested it on a trickier one: −4 − (−6). "Subtracting a NEGATIVE number... that means adding the opposite of −6, which is +6. So it's −4 + 6." She walked the line: −4, −3, −2, −1, 0, 1, 2. "Lands on 2."
"Two negatives next to each other flip into a plus," said Ms. Rao. "Subtracting a negative is the same as adding a positive — the two 'minus' signs cancel into one 'plus.'"
By the end, Kabir had a rule written in his notebook: 'Adding a negative = moving left. Subtracting = add the opposite. Two minuses together = a plus.'
On a number line, adding a positive number moves RIGHT; adding a negative number moves LEFT.
Subtracting a number is the same as adding its opposite: a − b = a + (−b).
Subtracting a negative number becomes addition, because the two negative signs combine into a positive: a − (−b) = a + b.
The number line is a reliable way to check any integer addition or subtraction by physically counting the steps.
Draw a number line and solve −5 + 7 and 3 − 8 by physically counting the steps.
Find 3 real temperature or elevation examples and write them as integer addition/subtraction problems.
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