Washington Grade 4 Math

A diagonal divides equally but does not make a matching fold

Use an ideal rectangle 8 units long and 4 units wide. Compare a fold along its vertical middle line with a fold along a diagonal joining opposite corners. A student says both are lines of symmetry because each divides the area in half. Explain what the fold must do.

Follow the reasoning

The middle line divides the rectangle into two 4-by-4 regions. Folding across it matches corresponding edges and corners, so it is a line of symmetry. A diagonal also divides the rectangle into two equal-area triangles, but folding over that diagonal does not superimpose the non-square rectangle’s boundary. The remaining corners do not match: reflecting a corner across that slanted line places it away from the opposite corner. Equal area is therefore insufficient. A symmetry fold requires the two parts to match in position after the fold, not merely to contain the same amount of area. The horizontal middle line also gives a matching fold.

Check the explanation

The figure is an ideal non-square rectangle. Its diagonal is not a symmetry line, although a square’s diagonal is. The equal-area triangles are congruent through a different motion; that fact does not make reflection in this particular diagonal a symmetry of the rectangle.

Try the next step

Compare with a square. Explain why its middle lines and diagonals match the parts after folding. Use a teacher-approved paper model or trace corresponding corners, keeping the fold line visible.

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 4 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.