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:

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 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 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 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 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 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