Mathematics

Algebra: from expressions to functions.

Algebra is the language of relationships. Students learn to write expressions, solve equations, and describe change with graphs and tables.

Core skills

Begin with equivalent expressions and the distributive property. Solve one-step and two-step equations, then inequalities on a number line. Use ratio tables before slope-intercept form so students see rate of change in numbers they already trust. Graph proportional relationships, then non-proportional lines. Finish with systems of two equations and a first look at exponential growth.

Every lesson includes a worked example, a near-twin practice item, and an error-analysis prompt such as “Jordan distributed 3 to only the first term. Rewrite the step that failed.” Students must explain why a common mistake does not keep both sides equal.

Sample lesson: slope as unit rate

If a plant grows 6 centimeters in 2 weeks at a constant rate, the unit rate is 3 centimeters per week. On a graph, that rate is the slope: rise over run. Connect the table (week, height) to the equation h = 3w + starting height. Ask: what does the intercept mean in the story? If the plant was 4 cm at week 0, the intercept is 4, not 0.