# Areas Assessed for the DT-HSM

The DT-HSM yields a score for each student in each of the following areas, as well as an overall score.

• Whole Numbers - Add, subtract, multiply, and divide whole numbers; including carrying, borrowing, and saving a place with a zero.
• Common Fractions - Add, subtract, multiply, divide, and reduce common fractions and mixed numbers; including finding common denominators.
• Decimal Fractions - Add, subtract, multiply, divide, and convert decimal fractions into common fractions and percentages (including multiplying and dividing numbers by 10 and powers of ten).
• Percentages - Add, subtract, multiply, and divide percentages, and convert percentages into common and decimal fractions; determine X percent of a given number; determine what percent X is of a given number; relate percentages to a whole (e.g., 110% is more than 1 unit).
• Signed Numbers - Add, subtract, multiply, and divide signed numbers.
• Powers and Roots - Work with and solve equations containing powers and roots, including use of the laws of exponents.
• Substitution - Substitute values for unknowns in an expression or equation.
• Setting Up Equations - Set up an equation or series of equations when given information in the form of a word problem or a data chart.
• Solving Algebraic Equations - Solve one equation with one unknown, and two equations with two unknowns; solve quadratic equations using factoring; simplify and isolate variables to find the solution (without using the "guess and check" method).
• Geometry - Have knowledge of and be able to work with points, angles, parallel lines, lines of symmetry, surfaces, vertices, different types of triangles, similar figures, Pi, the Pythagorean theorem; find the area and perimeter or circumference of basic shapes; solve problems involving inscribed and circumscribed polygons and circles; know properties of common triangles (e.g., 3/4/5 and 45º/45º/90º).
• Graphs - Understand common types of graphs (Cartesian, bar, pictograph, scatter, pie), read axes and their scales; find and chart points using X and Y coordinates; reflect, rotate, and translate figures across axes; write the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line; interpret a graph; graph a line and extrapolate values; write an equation for the approximate line-of-best-fit for several data points; know the notation for the four quadrants; construct a graph from given tabular or narrative data; use information in a key.
• Tables - Understand how row and column titles correspond to data inside a table, find pertinent information in a table and transfer the information to a graph, be able to match data in a table with graphical representations and written equations, extrapolate from data in a table.
• Estimation - Know when and how to use estimation, round and estimate to check answers.
• Probability - Find the probability of an event based on a narrative description or tabular data, make reasonable predictions using probability, calculate odds, find the probability of the occurrence of two independent events.
• Statistics - Know how to find and interpret the mean, median, mode, and range of a data set; work backwards using the equation for the average (e.g., find the sum from the mean and N); recognize and be able to work with box plots (box-and-whisker graph) and stem and leaf plots.
• Order of Operations - Understand order of operations; know and apply PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
• Ratios and Proportions - Represent data in ratio form and set up ratio problems; add, subtract, multiply, divide, and reduce ratios (including attention to units); understand difference between and be able to convert between ratios and proportions.
• Math Vocabulary - Know words like numerator, denominator, product, sum, meter, reciprocal, absolute value, irrational number, integer, origin, real number and prime number; know geometry vocabulary such as equilateral triangle, congruent, and perpendicular.
• Word Problems - Understand written and diagramed scenarios, translate word problems into equations, discern what information is necessary to solve the problem and what information is superfluous.
• Misc. - Convert between units of measure, calculate the nth term in a data series, solve basic trigonometry problems, solve and graph simple inequalities, be familiar with the notation f(x) = , perform simple matrix arithmetic operations.