West Virginia Grade 3 Math

Two partitions of the same L-shaped region

An L-shaped region fits inside a 5-unit by 5-unit square. Its bottom strip is 5 units wide and 2 units high. Above that strip, its left arm is 2 units wide and 3 units high. Find the region’s area by adding non-overlapping rectangles. Check with a second partition.

Follow the reasoning

The bottom strip has area 5 × 2 = 10 square units. The left arm above it has area 2 × 3 = 6 square units. They meet at an edge and have no overlapping interior, so the total is 10 + 6 = 16 square units. Another partition uses the entire left strip, 2 × 5 = 10, plus the bottom-right piece, 3 × 2 = 6, again giving 16. Adding the entire left strip to the entire bottom strip would give 20, but their 2 × 2 corner would be counted twice. The correct partitions show why each part of the region contributes once. The outside square also provides a check: 25 − 9 = 16, subtracting its missing 3 × 3 corner.

Check the explanation

The drawing represents a flat region with whole-number lengths, not a volume or perimeter. Each square unit belongs to the region once. The 5-unit outside square includes a missing corner; its full area is not the L-shape’s area.

Try the next step

Keep the bottom strip 5 by 2 units, but make the left arm above it 2 by 4 units. Explain 10 + 8 = 18 square units. Check using the whole left strip, 2 by 6, and the bottom-right piece, 3 by 2: 12 + 6 = 18.

West Virginia reference for this worked activity

The West Virginia mathematics policy and standards page provides grade-specific documents under Policy 2520.2B. The linked Grade 3 document includes Mathematical Habits of Mind and content standards. These should be developed together in classroom work. 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 a different set of numbers 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.

The West Virginia Department of Education General Summative Assessment overview lists English language arts and mathematics in Grades 3–8, with science in Grades 5 and 8. Grade 3 is included in that mathematics range. Follow the school’s current directions and accommodations. Independently published practice follows its own timing, tools, question count, and scoring; its result does not establish a state performance level. This original activity is not an official state assessment question. Read West Virginia assessment guidance.

State sources and the selected complete PDF page checked October 6, 2026. Confirm later guidance and local assignments before planning assessment preparation.