Washington Grade 3 Math

Two parts can have different sizes

Two equal-length paper strips represent the same unit whole. One is partitioned into three equal parts and the other into six equal parts. Shade two parts on each. Compare 2/3 and 2/6. Explain why counting two shaded parts on each does not make the fractions equal.

Follow the reasoning

Each third is larger than each sixth of the same whole. Two sixths occupy one third of the strip, while two thirds occupy twice that length. Thus 2/3 > 2/6. The numerator counts selected equal parts, and the denominator tells how many of those parts compose the unit whole. Equal numerators do not make differently sized parts equal. The strips must represent equal wholes for this portion comparison. Dividing thirds in half also shows 2/3 = 4/6, so four sixths exceed two sixths.

Check the explanation

The diagram uses equal-length wholes and equal partitions within each strip. Two sixths of a much longer strip could physically exceed two thirds of a shorter strip; that would be a different comparison of objects. The number comparison keeps the unit fixed.

Try the next step

Compare 1/3 and 1/6 using the same strips, then compare 2/6 and 1/3. Explain both the size difference and the equivalent-value pair by matching equal lengths.

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 3 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.