Louisiana Grade 7 Math

Which cost rule is proportional to the number of items?

Two fictional print services charge three dollars for each poster. Service A has no setup fee. Service B adds a five-dollar setup fee to each order, regardless of the number of posters. Let n be the number of posters and C the cost in dollars. Compare the relationships for positive whole-number orders; use the zero value as the mathematical rule’s intercept check.

Test the ratio of cost to quantity

For A, three dollars for one poster, six for two, and twelve for four all give a constant three dollars per poster. The equation is C = 3n. For B, the ratios are eight dollars for one poster, eleven divided by two or 5.50 dollars per poster, and seventeen divided by four or 4.25 dollars per poster. Those total-cost-to-quantity ratios differ. B is therefore not proportional to n even though each additional poster adds three dollars to the total. Constant differences alone do not establish proportionality.

Interpret the fixed fee

The equation C = 3n + 5 separates the per-poster charge from the amount paid once per order. On a graph, A’s modeled line passes through the origin; B’s modeled line has a vertical intercept of five. The zero row evaluates the formulas. It is not a claim that a real customer must place an empty order and pay a fee. Actual orders in the task use positive whole numbers, so distinguish the mathematical extension from the service’s practical domain. Both rules have the same increase per added poster, but only A has a constant total-cost-to-quantity ratio.

Check a tempting conclusion

A student may say B is proportional because costs rise by six when posters rise by two. That observation identifies a constant rate of change, which both rules have. Ask the student to compare C divided by n at two positive values. The fixed fee is spread over different numbers of posters, so B’s total average per poster changes. Do not divide by zero when checking ratios. The intercept provides a separate graphical or equation check.

Transfer the reasoning

Change the per-poster charge to four dollars while keeping B’s setup fee at five. A becomes C = 4n and remains proportional; B becomes C = 4n + 5 and remains nonproportional. Explain why changing the rate does not remove the fixed term. Use the school’s current sequence to connect equivalent ratios, tables, equations, and graphs. This independently written example illustrates selected Louisiana Grade 7 references, not a real print-service offer.

Selected references from Louisiana mathematics standards

The Louisiana mathematics standards directory lists current and updated standards. For 2026–27, use the current K–12 document, updated December 21, 2017; the revised standards have full implementation in 2027–28. 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 Louisiana’s general LEAP mathematics testing range. The linked learning resources have their own directions and scoring; a practice score does not establish an official state performance level. Read Louisiana’s assessment overview.

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.