District of Columbia Grade 5 Math

Work through the example

A whole rectangle is divided into three equal columns and four equal rows. The first two columns show two thirds of the whole. Take three fourths of that two-thirds region by keeping its first three rows. What fraction of the original whole is in the overlap?

Connect the model and calculation

The whole has 3 × 4 = 12 equal small rectangles. Two of its three columns contain eight of those parts. Taking three of their four equal rows keeps six parts. The overlap is therefore 6/12 of the original whole, or 1/2. The equation 3/4 × 2/3 = 6/12 = 1/2 records the model. If the whole is a unit square, the overlap also forms a rectangle with side lengths 3/4 and 2/3 unit; its area is 1/2 square unit. The fraction describes a share, while the area statement includes a measurement unit.

Understand an incorrect answer

Counting every part with either kind of shading finds a combined region, not three fourths of the two-thirds region. Count only the six parts where the row and column selections overlap. Dividing by eight gives the share of the selected two-thirds region: six of its eight parts are three fourths of that region. The task asks for a fraction of the original whole, whose denominator is twelve. Name the whole whenever changing the comparison.

Transfer the idea to another example

Keep the same partition but take one fourth of two thirds. The overlap contains two of twelve parts, so 1/4 × 2/3 = 2/12 = 1/6. Then explain why three fourths of a positive amount is smaller than the starting amount: it retains only three of four equal shares. Compare 1/2 with 2/3 on the model rather than assuming that multiplication must make a quantity larger. Choose another pair of proper fractions and show how each denominator contributes to the whole partition.

Selected DC Grade 5 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.