District of Columbia Grade 7 Math

Work through the example

An invented supply order contains two notebooks at the same unknown price and one pen costing $3. The total is $17, with no other charges. Let x be the price of one notebook in dollars. Write an equation for the order and find x.

Connect the model and calculation

The two notebooks cost 2x dollars together. The pen adds $3 once, so the equation is 2x + 3 = 17. Subtract 3 from both sides to isolate the notebooks’ combined cost: 2x = 14. Divide both sides by 2 to obtain x = 7. One notebook costs $7. An arithmetic explanation reaches the same answer by removing the pen’s $3 from the $17 total, then sharing the remaining $14 equally between the two notebooks. The equation records those quantity relationships.

Understand an incorrect answer

Writing 2(x + 3) = 17 charges $3 for each of two groups, describing two pens rather than the single pen in the order. Writing x + 3 = 17 leaves out one notebook. A result of x = 14 is the pair’s cost, not one notebook’s price. Before calculating, ask the student what x represents and what each term counts. Subtracting from only one side changes the equality instead of preserving the same relationship.

Transfer the idea to another example

Substitute the answer into the original equation: 2 × 7 + 3 = 17. Then change only the total to $19. The notebooks together now cost $16, so each costs $8. Compare that with a different order containing two identical notebook-and-pen sets. If each set has a notebook at x dollars plus a $3 pen and the two sets total $20, the equation is 2(x + 3) = 20 and x = 7. Explain why parentheses fit the second story but not the first. Check both the arithmetic and the meaning of the answer.

Selected DC Grade 7 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.