Descriptions of the Reporting Categories Mathematics

The following descriptions outline what you should know and be able to do in this subject.

Numbers and Operations

You are already very familiar with how to add, subtract, multiply, and divide numbers. Now you can find relationships between number systems such as real numbers and irrational numbers. You should be able to apply your skills with operations to more complex problems such as finding the Greatest Common Factor of a set of polynomials. You should also be able to choose the correct numerical relationship such as proportions, absolute value, and order of operations, etc., to solve word problems.

Put the following numbers in order from smallest to largest: 0.1; 0.1 x 0.1; 0.2 + 0.3 x 0.1; 1.0; and (1.1 + 0.03) x 0.2 - 0.2. Answering this question requires an understanding of decimals and order of operations. For more practice, make up problems that include fractions, exponents, scientific notation, or absolute value, or attempt to put five, six, or seven numbers in order. Answer: The correct order is 1. 0.1 x 0.1 which is 0.01; 2. (1.1 + 0.03) x 0.2 - 0.2. Order of operations tells us to do the parentheses first, then multiply, and finally subtract to get 0.026; 3. 0.1; 4. 0.2 + 0.3 x 0.1 because order of operations tells us to multiply first and then add to get 0.23; 5. 1.0

Measurement

In earlier grades you learned the basics of measurement. You learned how to find distances using the customary and metric measurement systems. You also learned how to measure and compare angles. Now your skills should include finding area and perimeter of simple and complex figures. You can use and understand the formulas for surface area and volume of three-dimensional figures, and understand angle relationships such as complementary, supplementary, and vertical angles.

An angle of 23 degrees is formed by two intersecting lines. What is the measure of the angle's complement? Supplement? Vertical angle? Answering these questions requires an understanding of several angle relationships. For practice, draw two pairs of parallel lines that intersect without forming right angles. Provide one angle measure, and use it to find the measures of all the other angles in the diagram. Answer: Complementary angles add to 90 degrees, so the complement of 23 degrees is 67 degrees. Supplementary angles add to 180 degrees so the supplement of 23 degrees is 157 degrees. Vertical angles are equal so the vertical angle to a 23 degree angle will also measure 23 degrees

Geometry

Geometry in high school involves using geometric properties to solve problems. You have already learned to identify and classify two- and three-dimensional shapes. Now you use the characteristics of these figures in problem solving situations. You should be able to apply the rules of congruence, correspondence, and similarity to solve problems.

The points (-3, -5) and (3, 3) are the endpoints of a line segment. What is the distance between the two points and what is the midpoint of the line segment? To answer this question, use the distance formula and the midpoint formula. For more practice, you could also find the slope of the line segment connecting the two points. You can further challenge yourself by writing two linear equations: one for the line that is parallel to the line segment and another for the line that is perpendicular to the segment. Answer: The distance between the two points is 10 units. The midpoint of the segment is (0, -1).

Algebraic Concepts

In earlier grades you worked with linear equations. Algebraic Concepts involves broadening and deepening your understanding of functions and relations. For example, your study of linear equations includes finding distance and midpoint and writing equivalent forms of an equation. You also study other kinds of functions such as quadratic equations.

Ten years ago the unemployment rate in the United States, rounded to the nearest tenth, was 5.4%. Suppose there were 148,132,000 employable people in the United States last month and 7,988,000 were unemployed. Suppose also that a politician claimed that the unemployment rate was unchanged from ten years ago. Would the politician be telling the truth? Answer: Yes, because 7,988,000 divided by 148,132,000 is 0.0539 which is the same as 5.39%. When rounded to the nearest tenth of a percent, 5.39% = 5.4%

Data Analysis and Probability

You already know how to construct and read bar graphs and line graphs. Now you create and interpret more advanced types of data displays such as box-and-whisker plots and scatter plots. You also analyze a variety of graphs using such statistical measures as mean, median, mode, quartiles, etc. Finally, you should be able to apply your knowledge of permutations and combinations to real life situations.

Twenty-six different letters are placed in a bag. One letter is drawn randomly from the bag. What is the probability of drawing a vowel (a, e, i, o, u)? What are the odds against drawing a vowel? This question requires an understanding of how to calculate probability and convert between probability and odds. For a further challenge in this Assessment Anchor, find the probability of compound events such as drawing two vowels in a row without replacing the first. Answer: The probability of drawing a vowel is 5/26 because there are 26 total letters and 5 of them are vowels. The odds against drawing a vowel are 21 to 5 because there are 21 letters that are not vowels and 5 that are vowels.