Maryland Grade 7 Math

This original classroom activity is independent practice.

Try the problem

Two fictional printing plans charge for n posters. Plan A costs 2 dollars per poster with no setup fee. Plan B costs 2 dollars per poster plus a 5-dollar setup fee. Compare costs for 1, 2, and 4 posters. Decide which cost is proportional to poster count, identify its constant of proportionality, and explain what the origin represents in the model. These are invented plans, not current commercial prices.

Work through the explanation

Plan A costs 2, 4, and 8 dollars for 1, 2, and 4 posters. The ratios cost/count are all 2 dollars per poster, and its equation is c = 2n. With no posters, its modeled cost is 0, so the relationship passes through (0, 0). Plan B costs 7, 9, and 13 dollars. Its ratios are 7, 4.5, and 3.25 dollars per poster, which are not constant. Its equation is c = 2n + 5. Although both plans increase by 2 dollars for each additional poster, the setup fee prevents Plan B’s total cost from being proportional to count. The constant increase alone is not enough.

Check the reasoning

A student may identify 2 as the constant of proportionality for both plans because each extra poster adds 2 dollars. Ask whether doubling poster count doubles total cost. For Plan B, moving from one to two posters changes 7 dollars to 9 dollars, not 14. For Plan A, (1, 2) shows the unit cost, and (4, 8) means four posters cost eight dollars in the stated model. Poster counts are nonnegative whole numbers, so the actual context uses discrete points even though a supporting line can illustrate the relationship. The setup-fee equation gives 5 at n = 0 as a model extension; whether a real provider charges for an order of zero posters would require its actual terms.

Try a related task

Compare a new no-fee plan charging 3 dollars per poster with a plan charging 1 dollar per poster plus a 4-dollar fee. Write tables, test ratios for positive counts, and label the meaning of a point. Explain why a straight graph through the origin supports proportionality while a nonzero intercept does not. Maryland’s revised references separate identifying proportional relationships from representing them with equations and explaining graph points; practice both ideas within the school’s course sequence.

Selected references from revised Maryland mathematics standards

The Maryland mathematics standards directory links grade-specific 2025 crosswalk documents. Their covers identify adoption in July 2025 and implementation in SY 2026–27. Read the 2025 standards columns; the 2010 columns show previous requirements. 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.

Grade 7 is within Maryland’s statewide mathematics testing range. The linked learning resources have their own directions and scoring; a practice score does not establish an official state performance level. Maryland announced a transition from MCAP to MSTAR beginning in 2026–27. Older MCAP-named books and practice retain their published names and are independent supplements. Their timers, question counts, tools, and scoring are not official MSTAR specifications or predictions of a state performance level. Read the May 2026 state board report, PDF page 12 (archived copy).

The live MSDE site displayed a maintenance notice during review and linked an archived backup. These curriculum references use working archived copies of the revised state documents. Check the school’s sequence and MSDE for later updates. Check MSDE updates.

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.