Core Skills Analysis
Mathematics
Ella practiced simplifying algebraic expressions by combining like terms, including expressions such as 4n − n, −9k + 8k, and 15n − 19n. Ella also used the distributive property to expand parentheses, then grouped variable terms and constants in examples such as −4 + 7(1 − 3m) and 10 − 5(9n − 9). Through this work, Ella learned that coefficients can be added or subtracted when terms have the same variable, while constants are combined separately, and that signs must be carried through each operation. The written grouping marks and intermediate steps showed Ella using a visible strategy to track the simplification process.
Tips
Tips Build on Ella’s practice with a “like-term sort”: write variable terms and constants on separate cards, then have Ella group and simplify them before checking the result. Next, connect the distributive property to an area model by drawing a rectangle with one side split into terms such as (x + 3), and label the partial areas to show how multiplication expands parentheses. For a real-world connection, invite Ella to create and simplify expressions for the cost of several identical items plus a fixed fee, then explain each term in a short written or spoken walkthrough.
Book Recommendations
- The Cartoon Guide to Algebra by Larry Gonick: A humorous, illustrated introduction to algebra that makes variables, expressions, and algebraic procedures approachable.
Learning Standards
- MA.7.AR.1.1: Ella’s work with adding and subtracting linear expressions, including combining terms with matching variables and combining constants, aligned with applying properties of operations to linear expressions with rational coefficients.
- MA.7.AR.1.2: Ella’s expansion of expressions with parentheses aligned with applying properties of operations to multiply linear expressions with rational coefficients.
Try This Next
- Create a like-term sorting worksheet: group variable terms and constants, then simplify each expression.
- Draw an area model for 4(x + 3) and label the partial products before writing the expanded expression.
- Write a short quiz with expressions such as −6a + 9a − 4 and 3(2x − 5) + x; simplify and explain each step.