Washington Grade 7 Math

A fixed charge changes the relationship

In a fictional model, Plan A charges 3 tokens per kit. Plan B charges 3 tokens per kit plus a fixed 2-token setup charge, including at zero kits. Compare their costs for one, two, and three kits. Which relationship is proportional to the number of kits? Explain through ratios and equations.

Follow the reasoning

Plan A gives costs 3, 6, and 9; each cost-to-kit ratio is 3, so y = 3x is proportional. Plan B gives 5, 8, and 11, with ratios 5, 4, and 11/3; these are not constant. Its equation y = 3x + 2 includes the fixed charge. At zero kits A costs zero and B costs two, so only A passes through the origin. Both costs increase by three for each extra kit, but equal increments do not make both relationships proportional. Proportionality requires the same multiplier relating the quantities, not merely a constant difference between consecutive costs.

Check the explanation

These are invented token rules. The setup charge is explicitly included at zero; an actual provider might have different conditions. The listed points illustrate the equations. A few points alone would not determine an unspecified rule outside the table.

Try the next step

Change Plan A’s rate to 4 tokens per kit. Its equation becomes y = 4x, still proportional. Keep Plan B unchanged and find the kit count where the two costs agree: 4x = 3x + 2 gives x = 2, with both costs eight tokens. One agreement does not make the rules identical.

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 7 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.