# Ideas for Progress: Mathematics, Range 20–23

To enhance their skills in each mathematics-related strand, students who score in the 20–23 score range on the ACT® college readiness assessment may benefit from activities that encourage them to do the following:

Number and Quantity compare two fractions use whole number exponents to express examples of repeated multiplication identify and use factors of whole numbers identify and use multiples of whole numbers describe the meaning of i, the unit imaginary number perform basic operations with complex numbers apply number properties to model real-world and mathematical problems that involve reasoning with proportions select and use appropriate units when solving real-world and mathematical problems that involve one or more units of measure solve literal equations (e.g., P = 2l + 2w) for any variable identify, interpret, and generate symbolic representations that model the contexts of real-world and mathematical problems represent and interpret relationships defined by equations and formulas; translate between representations as ordered pairs, graphs, and equations; and investigate symmetry and transformations (e.g., reflections, translations) identify characteristics of figures from a general equation graph and interpret simple inequalities on the number line model real-world and mathematical problems using linear equations and inequalities attend to the difference between values from an algebraic model and actual outcomes factor and perform the basic operations on second-degree polynomials identify basic characteristics of a quadratic equation (e.g., second-degree polynomial) use the inverse relationships for the four basic operations, exponentiation, and root extractions to determine unknown quantities model real-world and mathematical problems, using scientific notation describe the result of division by zero describe why square roots of negative numbers do not yield real number values evaluate algebraic expressions and solve multistep first-degree equations describe simple numerical patterns by writing explicit and recursive formulas recognize that values may be different than predictions made using a model describe the difference between an equation and a function describe examples where a function is undefined (e.g., division by zero, square roots of negative numbers) recognize when to apply geometric properties and relationships of parallel lines to find unknown angle measures recognize when to apply geometric properties and relationships of triangles to find unknown angle measures and side lengths apply the definition of symmetry (e.g., line, rotational) to describe plane and solid figures use appropriate units and degrees of precision to measure and describe real-world objects apply a variety of strategies to determine the circumference or perimeter and the area for circles, triangles, rectangles, and composite geometric figures identify the basic trigonometric ratios describe the relative locations of two points in the coordinate plane in terms of horizontal (e.g., run) and vertical (e.g., rise) distances identify and describe midpoints and bisectors investigate symmetry and transformations of points (e.g., reflections, translations, rotations) use several computations with data to solve real-world and mathematical problems use data presented in different displays (e.g., table, chart, histogram) to solve real-world and mathematical problems calculate simple probabilities to solve real-world and mathematical problems read and interpret information presented in a Venn diagram consider the impact of outliers and deviations when describing data trends choose the best measures of central tendency and variability to describe a data set based on the shape of its distribution