District of Columbia Grade 4 Math

Work through the example

A classroom model has 42 columns and 18 rows of equal unit squares. How many squares are there? Split 42 into 40 + 2 and split 18 into 10 + 8. Each table cell records the number of squares in one part of this mathematical rectangle.

Connect the model and calculation

The four parts contain 40 × 10 = 400, 2 × 10 = 20, 40 × 8 = 320, and 2 × 8 = 16 squares. Adding them gives 400 + 20 + 320 + 16 = 756. Every square belongs to one part, and no part is counted twice. Grouping the first two products gives 42 × 10 = 420; grouping the last two gives 42 × 8 = 336. Thus 42 × 18 = 420 + 336 = 756. The four-part and two-part methods describe the same total.

Understand an incorrect answer

An answer of 416 comes from using only 40 × 10 and 2 × 8. Those are two parts of the rectangle; the two cross-products are missing. Point to the 40-by-8 and 2-by-10 regions before repeating the calculation. If a student writes 42 × 10 as 42, name the groups: ten groups of 42 contain 420. The zero records the changed place value, rather than being an unexplained rule about attaching a digit.

Transfer the idea to another example

Estimate with 40 × 20 = 800. A total of 756 is reasonably close, although the estimate alone cannot prove the exact answer. Then change 18 to 19. One additional row of 42 squares gives 756 + 42 = 798; verify it with 42 × (10 + 9). Ask a student to choose a useful split for 36 × 14 and label every partial product. Keep the labels when moving to a written multiplication method so the algorithm remains connected to the quantities.

Selected DC Grade 4 references

The OSSE standards directory links the Common Core mathematics standards. DC adopted Common Core in July 2010. Use the adopted document and the school’s instructional sequence for planning. These labels describe the activity’s focus; the publisher’s mathematics document supplies the full expectations and mathematical practices.

Sources checked October 5, 2026. This selected activity supports instruction; it does not cover the whole grade’s curriculum.

Connect the explanation with practice

Choose a related skill from the lesson, worksheet, and quiz directory. Use the worked example to decide what needs support, then read the selected resource’s directions before assigning it.

DC CAPE Next begins with the spring 2027 administration. OSSE lists mathematics assessments in Grades 3–8 and says the educational standards have not changed. Confirm current participation and preparation guidance with the school. Read the DC CAPE Next changes and 2026–27 assessment policy.

The linked practice and books are independently published. Some editions may predate DC CAPE Next; check their contents and directions alongside current OSSE guidance rather than assuming their timer, question count, tools, or scoring matches the new assessment.

Keep one example of the student’s explanation with the practice result. Choose a smaller model, another related task, or a new context according to the difficulty shown in the activity.