Core Skills Analysis
Mathematics
Ella worked through an eighth-grade lesson on solving one-variable equations, using inverse operations to isolate the variable while keeping both sides of an equation balanced. She practiced undoing addition or subtraction before undoing multiplication or division, as shown in examples such as x/4 + 5 = 7 and 5n/4 + 2 = 7. Ella recorded solutions for equations involving positive and negative numbers, including w = -8 for -3w - 12 = 12 and a = -2 for 4a + 5 = -3. Her highlighting and written calculations showed that she marked key steps and applied a consistent, step-by-step approach to algebra.
Tips
Tips Build on Ella’s equation-solving practice by turning everyday situations into equations—for example, model a purchase with a fixed fee and a per-item cost, then solve for the unknown number of items. Use a balance scale or two equal groups of counters to demonstrate why the same operation must be applied to both sides. Invite Ella to create a set of equations that use fractions, negative numbers, and different operation orders, then explain each inverse-operation choice aloud. Finish with a substitution check: replace the variable with the solution and verify that both sides of each equation are equal.
Learning Standards
- Florida B.E.S.T. Mathematics — MA.8.AR.3.1: Ella solved one-variable linear equations with rational-number coefficients, including equations involving fractions, negative numbers, and multiple operations.
- Mathematical practice—reasoning with equations: Her work reflected the use of inverse operations and equivalent steps to isolate a variable and determine a solution.
Try This Next
- Inverse-Operations Sort: Match equations with the correct first and second steps for isolating the variable.
- Equation Creator: Write three real-life word problems, turn each into a one-variable equation, and solve it.
- Substitution Check: Choose four solved equations, substitute each answer, and show that the two sides are equal.