In this lesson
Signed value vs magnitude
A real situation can frame the same arithmetic two ways. Asked one way, you answer with a sign. Asked the other way, the sign drops out.
A January morning in Calgary. The temperature starts at −15°C and a chinook pushes it to +9°C by mid-afternoon.
The dial below knows the change — but it won't say until you do. Predict it first, sign included; the sign is half the answer.
Try it
Drag the marker around the dial. The equation updates as you move.
Drag with the mouse, or focus the marker and use ←/→.
Two reasonable questions:
- What is the temperature change?
+24°C. The sign matters:+means it went up. If the temperature had dropped instead, the change would be−24°C. Direction is part of the answer. - By how many degrees did the temperature rise?
24°C. Same scenario, but the question already names the direction ("rise"), so the answer only needs the size.
That second answer is the magnitude: the absolute value of the change. The first answer is the signed value.
Mirror pairs across zero
Every signed value has a partner the same distance from zero on the
other side. +3 and −3. +7.5 and −7.5. +½ and −½. The
two have the same magnitude and opposite signs. The pair is called
an additive inverse.
Find three of them yourself. The line below gives you a dot and nothing else — place your marker where its inverse lives and lock it in. Same distance, opposite side: both halves have to be right.
Challenge 1 of 3
The dot sits at 4. Drag YOUR marker to its additive inverse, then lock it in.
Click anywhere on the line to place the marker, or use ← / → from the keyboard.
This mirror-pair rule does not stop with integers. Every fraction and decimal has an additive inverse: the same absolute value, the opposite sign.
So +3/4 and −3/4 are opposites. +0.6 and −0.6 are opposites.
Each pair lands the same distance from zero, one on each side.
Negative decimals outside the thermometer
Negative decimals show up anywhere a zero point has a meaning:
- a bank balance of
−$12.50means a debt of$12.50; - a stock-price change of
−$2.75means the price fell by$2.75; - an elevation of
−4.6 mmeans4.6 mbelow sea level.
The signed value tells the side of zero. The magnitude tells the size:
|−12.50| = 12.50, |−2.75| = 2.75, and |−4.6| = 4.6.
Worksheet
These aren't graded. The same scenarios show up in different framings. Get used to reading the question for direction.
Practice · Not graded
MA.7.NUM.1Practice the idea
01 / 10
'What is the temperature outside?' Signed answer or magnitude?
Classify the question: does it want a signed answer or a magnitude? 'What is the temperature outside?'Show common mistakes
Student says
“For 'how cold did it get?', I answered −18°C.”
What it reveals
Framing error. That answer is right for 'what was the temperature.'
Targeted response
Temperature Gauge: read the value with the sign for one question, the magnitude for the other. Two readouts, one scenario.
Student says
“The change was 24°C. I dropped the sign because the answer was already positive.”
What it reveals
Treating signs as optional. A signed value carries direction even when the sign happens to be positive.
Targeted response
If the chinook had reversed and the temperature had dropped, the magnitude would still be 24. The sign is what tells you which one happened.
Going further
The next lesson, comparing and ordering rationals, uses the same number line, this time placing two markers and asking which one sits further to the right.