Negative numbers and absolute value

Practice 5 items →

Negative numbers enter through context: temperature, elevation, debt. Minus three is not “less than nothing”; it is three units to the left of zero. Absolute value is distance from zero, so |−4| is 4 and never −4. Students order integers, negative fractions, and negative decimals on one number line, where −7 is less than −3 because it is farther left. Operations on negative numbers (adding, multiplying) are Math 7; this unit is about position, comparison, and opposites. Do not skip it to get to algebra sooner — negative numbers leak into every later unit.

Specification · for a parent or teacher
Part no.
integers-absolute-value
Course
Advanced Math 6 · Unit 4
Also in
High School Math 1
Realm
Foundations
Difficulty
2 of 4 — Grade 4–5. Two steps, or one idea in a story.
Qty
5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

integers in context (temperature, elevation, debt); opposites; ∣x∣\lvert x\rvert; order integers, negative fractions, and negative decimals on one line.

Ready when

they can order 12,−2,0,−2.5,−32\frac{1}{2}, -2, 0, -2.5, -\frac{3}{2} from least to greatest (answer: −2.5,−2,−32,0,12-2.5, -2, -\frac{3}{2}, 0, \frac{1}{2}) and explain ∣−2.5∣=2.5\lvert -2.5\rvert = 2.5 as distance.

Formulas

Absolute value
∣x∣=distance from 0\lvert x \rvert = \text{distance from } 0

Always non-negative.

Opposites
−(−a)=a-(-a) = a

Watch for

−7>−3-7 > -3; ∣−4∣=−4\lvert -4\rvert = -4; “two minuses make a plus” used before operations are taught (operations on negatives are Math 7).

Before · requires

After · used by

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integers-absolute-value

Items: integers-absolute-value-01 · integers-absolute-value-02 · integers-absolute-value-03 · integers-absolute-value-04 · integers-absolute-value-05