New Mexico Grade 7 Math

A plane section is the two-dimensional shape where a plane passes through a solid. Its shape depends on the solid and the direction of the cut. This original rectangular-prism model specifies that direction rather than treating every section as identical.

Try this original activity

A right rectangular prism has a six-unit by four-unit base and height three units. Describe the section from a horizontal plane halfway up, parallel to the base. Then describe a vertical section through the interior, parallel to a six-unit by three-unit face. Sketch and label each section.

Work through the reasoning

The horizontal section is a rectangle measuring six units by four units. Because the sides are vertical and the plane is parallel to the base, the width and depth do not change at half the height. The vertical section parallel to the six-by-three face is a six-unit by three-unit rectangle: it spans the full six-unit direction and the full three-unit height. The first section has area 24 square units and the second 18, if those areas are calculated as a check. Neither is a box or another three-dimensional prism; the section has no thickness in the mathematical model. A drawing of the solid in perspective may make a rectangular face look slanted on the screen. Describe its mathematical shape from the specified perpendicular edges and dimensions.

Check the common mistake

Halfway up does not halve the section’s width or depth. It locates the cutting plane along the height. Similarly, cutting through the interior is different from counting an outside face, even when the shapes and dimensions match. Do not conclude that every possible tilted cut of every prism must produce the same rectangle. The direction specified in each case is essential.

Try a related case

Change the prism’s height to four units while keeping its six-by-four base. The horizontal section remains six by four, while the parallel vertical section becomes six by four too. Explain why equal section shapes in this new case do not mean the two cutting planes have the same orientation. For a different solid, use a teacher-guided paper model to examine a cut before predicting its section.

Selected New Mexico mathematics references for this activity

The current New Mexico adopted content standards directory links the Common Core mathematics standards. The selected references below were checked in the state-hosted 2010 standards document. They identify this activity’s focus, rather than a complete course. Read the full requirements, mathematical practices, examples, and progression alongside the school’s curriculum.

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.

The current state NM-MSSA resource page describes statewide mathematics and ELA assessment at the end of Grades 3–8, including Grade 7. Scores are one measure and should be considered alongside classroom and other assessment evidence. Confirm the learner’s assigned pathway and school directions. The assessment directory is updating resources for 2026–2027; this guide does not claim Spring2027 administration specifications from a Spring2026 manual. 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 official NM-MSSA resource page.

Read New Mexico adopted content standards 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.