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Ideas for Progress: Mathematics, Range 28–32

To enhance their skills in each mathematics-related strand, students who score in the 28–32 score range on the ACT® college readiness assessment may benefit from activities that encourage them to do the following:

Score Range 28–32
Number and Quantity
  • use relationships and elementary number concepts to explain, solve, and/or draw conclusions for complex real-world and mathematical problems
  • compare the characteristics of the real number system and the complex number system
  • recognize, identify, and apply basic properties of matrices
  • recognize and identify inverse, zero, and identity matrices
Algebra and Functions
  • solve real-world and mathematical problems that require combining multiple algebraic concepts
  • formulate expressions, equations, and inequalities that require planning to accurately model real-world and mathematical problems (e.g., direct and inverse variation)
  • create algebraic models that involve planning, strategic manipulation, or integrating concepts
  • use algebraic expressions to model real-world and mathematical problems
Algebra
  • compare the characteristics of basic function families (e.g., linear, power, exponential)
  • compare explicit and recursive formulas for arithmetic and geometric sequences
  • explore geometric models where unit circle trigonometry and basic identities can be used to solve real-world and mathematical problems
  • describe the relationship between exponents and logarithms
Functions
  • compare the characteristics of basic function families (e.g., linear, power, exponential)
  • compare explicit and recursive formulas for arithmetic and geometric sequences
  • explore geometric models where unit circle trigonometry and basic identities can be used to solve real-world and mathematical problems
  • describe the relationship between exponents and logarithms
Geometry
  • investigate angle and arc relationships for circles
  • examine and compare a variety of methods to find areas of composite figures and construct scale drawings
  • model appropriate geometric objects as a composite of rectangular solids, pyramids, cylinders, cones, spheres, half cylinders, and/or hemispheres
  • model appropriate geometric objects as a composite of sectors of circles, circles, semicircles, triangles, and/or rectangles
  • make generalizations, draw conclusions based on conditional statements, and offer solutions that involve connecting mathematics with other content areas
Statistics and Probability
  • describe how a measure of central tendency for a numerical data set summarizes all of its values with a single number
  • design and conduct probability investigations (e.g., identify how the margin of error is determined), and then determine, analyze, and communicate the results
  • identify techniques for generating a random sample
  • organize and interpret data generated from a random sample
  • create statistical models that involve planning, strategic manipulation, and/or integrating concepts
  • compare actual values and model values to judge the fit of the model