Montana Grade 6 Math

The greater signed number is not always the number farther from zero. Compare both ideas in this invented height model. Zero is a shared reference level; positive values are above it and negative values are below it.

Try this original activity

Platform A is at −3 meters relative to the reference level. Platform B is at +2 meters. Which is higher? Which is farther from the reference level? Write an inequality for the signed heights and a comparison of their absolute values.

Work through the reasoning

Platform B is higher because +2 is greater than −3. On the horizontal number line, −3 is left of +2, so −3 < 2. Platform A is farther from the reference level: its distance is |−3| = 3 meters, while B’s distance is |2| = 2 meters. Thus |−3| > |2| even though −3 < 2. The sign describes the direction relative to the reference; absolute value describes magnitude without that direction. The comparison questions therefore ask different things. A complete explanation names the reference level, includes meters for distance, and distinguishes higher from farther.

Check the common mistake

Absolute value does not make every negative height greater in the signed order. It gives distance from zero. Nor does the negative sign mean that A is below the ground: the reference level has not been identified as ground level. Do not use 3 > 2 as the signed comparison when A’s recorded height is −3. The number line is a model of signed heights; its horizontal orientation does not change the specified meaning of above and below in the context.

Try a related case

Compare −1.5 meters and +2.5 meters relative to the same reference. The positive height is greater and also farther from zero in this case. Explain why that result does not change the earlier example: compare the actual magnitudes each time.

Selected references from Montana mathematics standards

Montana’s Office of Public Instruction identifies July 1, 2026 as the implementation date for its revised mathematics standards. The selected references below were checked in the current PK–12 mathematics document linked from the OPI mathematics directory. Use the 2026 implementation document when checking a code; earlier Montana documents use a different set of references. These selected references identify the worked activity’s focus. The expectations include numbered requirements, examples, and mathematical practices. Read the full document and confirm the school’s current instructional sequence.

Sources checked October 6, 2026. Read complete requirements, clarifications, limitations, and mathematical practices alongside the school’s sequence. This selected activity is an entry point for instruction.

Connect the explanation with practice

Use the lesson, worksheet, and quiz directory to choose a related skill. The existing resource links remain available; open each activity’s directions to understand its timer, tools, question count, and scoring.

OPI identifies MAST English language arts and mathematics assessment for Grades 3–8, including Grade 6. The required-assessments directory also identifies alternate assessment pathways. Follow the school’s current assigned pathway, instructional sequence, and administration directions. Independently published practice may use its own timer, tools, question count, and scoring; these are not official administration specifications or a prediction of a state performance level. Read the current OPI assessment overview.

Read OPI mathematics guidance for later guidance. Keep one example of the student’s reasoning with the practice result. Choose a smaller model, a related question, or a new context according to the difficulty revealed in the worked activity.