Distinguish Distance from Zero and Numerical Order

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: For −9 and −4, absolute values are nine and four, so |−9|>|−4|.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Absolute value measures distance from zero and is never negative. Number order instead follows left-to-right position. A number can be smaller while having a larger absolute value. This distinction prevents a debt-size or below-reference comparison from being confused with which signed number is greater.

Find the nonnegative distance of each supplied number from zero. Compare those distances separately from the signed values. Explain which question is about magnitude and which is about position on the increasing number line.

Separate magnitude comparison from signed-number comparison. Absolute value never retains a negative sign. Draw the signed points and bracket each point’s distance to zero.

1. Draw the signed points and bracket each point’s distance to zero.
2. Work through the supplied example and label what each number or attribute represents.
3. Find the nonnegative distance of each supplied number from zero.
4. Answer the check, then try the three changed-input practice questions and explain one correction.

Check your reasoning

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Take it further

Compare −12 and −5 in both ways. Expected: −12<−5 but 12>5 for their absolute values.

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