Washington Grade 8 Math

Counts and proportions answer different questions

A fictional club asks each of forty volunteers two questions: whether they attended a demonstration and whether they chose a folding design afterward. Of ten attendees, eight choose folding and two do not. Of thirty non-attendees, twelve choose folding and eighteen do not. Compare the groups’ folding choices using counts and within-group proportions. Does the record prove that attending caused the choice?

Follow the reasoning

The non-attendee group contains more folding choices in raw count: twelve versus eight. But it is also three times as large. Within the attendee group, 8/10 = 80% choose folding; within the non-attendee group, 12/30 = 40% do. The table therefore shows a higher folding-choice proportion among attendees in this invented volunteer record. The correct denominator is the size of the group being described. Attendance was not randomly assigned, so different existing interests could affect both attendance and choice. The association does not establish a cause or represent every club member.

Check the explanation

The two categorical variables are recorded for the same forty fictional volunteers, each counted once. Neither a row percentage nor a raw count alone explains why a choice occurs. Self-selection and volunteer coverage limit generalization. The totals are ten attendees, thirty non-attendees, twenty folding choices, and twenty other choices.

Try the next step

Construct a second table with ten attendees choosing folding four times and thirty non-attendees choosing folding twelve times. The raw counts still differ, but both within-group proportions are 40%. Explain why unequal counts alone do not establish a difference in proportions.

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 8 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.