Washington Grade 6 Math

Farther from zero does not mean greater

Two invented markers lie at −7 and +4 on a horizontal number line. Zero is the chosen reference position, with positive values to the right. Which marker has the greater number? Which is farther from zero? A student says −7 is greater because its distance is seven. Explain the two comparisons.

Follow the reasoning

The marker at +4 is to the right of −7, so +4 > −7. Their distances from zero are |−7| = 7 and |+4| = 4, so −7 is farther from zero. The distance comparison drops direction and compares magnitudes; the order comparison retains the signed positions. The student answers the distance question while using language for number order. Both statements can be true at once: +4 is the greater number, and −7 has the greater absolute value. Locate the points and zero before deciding which relationship is being asked about.

Check the explanation

The reference and direction are fixed for this model. An absolute value is nonnegative and represents distance from zero, not a replacement for the original signed number in every comparison. These are invented positions, not a measurement of an actual site.

Try the next step

Compare −3 and −9. The greater number is −3, while −9 has the greater absolute value. Explain both using their positions relative to zero, then give a pair of opposite numbers with equal absolute values.

Washington reference for this worked activity

The Washington mathematics standards directory links the adopted 2026 standards. The PDF records adoption on June 18, 2026. OSPI says educators can explore, learn about, and begin using the new standards during 2026–27, with required use with students in 2027–28. Ask the school which learning sequence it follows during the transition. Read the complete requirements and the school’s current curriculum sequence. The reference below selects one worked focus.

This selected reference identifies the activity focus. The complete standard and grade curriculum include additional work. These labels do not certify alignment of every independent lesson, worksheet, or quiz in the broader directory.

Choose a next task from the student’s explanation

Use changed values or a different figure to check whether the student can explain the same relationship. If the explanation is unclear, return to the model; if the reasoning is sound but a calculation is wrong, work through a shorter calculation and check it against the model. Use the related learning resources alongside the teacher’s assigned goals.

OSPI’s state-testing overview lists Smarter Balanced mathematics and English in Grades 3–8 and 10. Grade 6 is included in that listed mathematics range; follow current school directions and accommodations. Independently published practice has its own timing, tools, question count, and scoring. This original activity is not an official state assessment question, and a practice result does not establish a state performance level. Read Washington assessment guidance.

State sources and the selected complete PDF page checked October 6, 2026. OSPI separates classroom standards implementation from assessment updates: new media-literacy, digital-citizenship, and data-science assessment changes are planned no earlier than 2028–29, beginning with pilots. This does not establish a changed current test format or question count. Read standards and assessment transition guidance. Confirm later guidance and local assignments.