# Ideas for Progress: Mathematics, Range 24–27

To enhance their skills in each mathematics-related strand, students who score in the 24–27 score range on the ACT® college readiness assessment may benefit from activities that encourage them to do the following:

Number and Quantity apply and use elementary number concepts and properties to model real-world and mathematical problems describe the difference between a rational number and an irrational number use integer exponents to express repeated multiplication describe the relationship between exponents and roots understand the meaning of a vector, and identify examples of vector quantities model real-world and mathematical problems that involve a combination of rates, proportions, and/or percents create functions, and use characteristics of basic function families (e.g., linear, absolute value, quadratic) to model real-world and mathematical problems graph linear equations and inequalities, determine slopes of lines, identify parallel and perpendicular lines, and find distances apply algebraic properties to rewrite simple expressions in equivalent forms (e.g., rationalize denominators) model real-world and mathematical problems, using systems of two linear equations or inequalities explore and use different methods to solve systems of equations write expressions for composite functions apply a variety of strategies that use relationships between perimeter, area, and volume to calculate desired measures model appropriate geometric objects as a composite of circles, semicircles, triangles, and/or rectangles apply special right-triangle properties and the Pythagorean theorem to solve real-world and mathematical problems involving congruent and similar shapes use basic trigonometric ratios to solve problems involving indirect measurement graph linear equations and inequalities, determine slopes of lines, identify parallel and perpendicular lines, and find distances identify characteristics of figures from a general equation find the probability of simple, disjoint, compound, and independent events in a variety of real-world and mathematical problems, using a variety of counting techniques construct and analyze Venn diagrams to help determine simple probabilities distinguish between independent and dependent events, and provide examples of each identify and describe examples of events that are conditional