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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:

Score Range 20–23
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
Algebra and Functions
  • 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
Algebra
  • 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
Functions
  • 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)
Geometry
  • 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)
Statistics and Probability
  • 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