Student Learning Outcomes

1. Fractions, Decimals, Percents

1a. Students can add/subtract/multiply/divide integers and fractions without calculator assistance. Students can simplify expressions using parentheses.

1b. Students can convert between fractions (in lowest terms), decimals, and percents.

1c. Given the total quantity, students can convert between percent and quantity.

1d. Students can convert between percent change and absolute change.

2. Variables and equations

2a. Students can convert between a linear algebraic equation and a written/verbal description of a scenario, including identifying variable meaning.

2b. Students can convert between equivalent equations involving addition and multiplication of rational numbers.

2c. Students can solve one-step equations with rational coefficients using additive or multiplicative inverses.

2d. Students can solve two-step equations of the form \[ ax + b = c\quad\text{ and }\quad a(x+b)=c. \]

3. Geometry

3a. Students can use geometric formulas for area and perimeter of rectangles, solving for one quantity when others are given.

3b. Students can use geometric formulas for area and perimeter of squares, solving for one quantity when others are given. This includes the use of square root.

3c. Students can use geometric formulas for area and circumference of circles, solving for one quantity when others are given.

3d. Students can use Pythagorean Theorem to find one side of a right triangle when the other two are given.

3e. Students can use geometric formulas for area and perimeter of right triangles, solving for one quantity when others are given.

4. Modeling relations

4a. Students can interpret a data table showing pairs of values for two variables.

4b. Students can create a data table from a formula.

4c. Students can plot values from a data table on Cartesian plane, including choosing appropriate horizontal and vertical scales.

4d. Students can interpret points on the plane in terms of data table context.

5. Linear relations

5a. Students can distinguish between linear and nonlinear scenarios.

5b. Students can identify “base” and “rate” of linear modeling scenarios and construct corresponding linear models.

5c. Given a linear model, students can construct a data table and corresponding plot.

5d. Given a linear model and the value of one quantity, students can identify which variable has been provided and solve for the other variable.

5e. Given two data points, students can compute the “rate” (slope) of the corresponding linear model, and subsequently deduce the “base”, thus obtaining the equation of the model.

5f. Given the graph of a model, students can obtain and interpret the equation of the model.

6. Exponential relations

6a. Students can identify “starting amount” and “ratio” for exponential relation and construct corresponding data table and linear model \(y = A\cdot R^x\).

6b. Given an exponential relation, students can construct data table and corresponding plot.

6c. Students can interpret the plot of an exponential relation, computing/estimating the value of one variable if the other is given.