Oxford High School

Courses in Mathematics

#211     Data and Numerical Reasoning - Academic (9/10)     Full Year    1.0 Credit

In Data and Numerical Reasoning, students will review basic arithmetic concepts that they will build upon as the course progresses.  Students will learn about Algebra, Geometry, Statistics and Probability and Discrete Math content on an introductory level.  They will also learn to model real-world situations in order to solve problems arising from those situations. These math topics often appear on standardized tests, so maintaining students’ familiarity with them is important.  This course is an important part of CAPT and SAT preparation, therefore, instruction, practice and assessments will be presented in a variety of formats – multiple choice, short answer, grid-in and open ended that students will encounter on standardized testing.  There will also be extensive use of technology including the graphing calculator throughout the year.

1. Enduring Understandings (broad ideas, usually grounded in the discipline):

•  Mathematics as Calculation – performing calculations. Knowing when exact verses generalized calculation is appropriate and develop insight into a mathematical theory when they see how it relates to actual calculations.

•  Mathematics as a Field of study – using mathematical vocabulary. Communicate clearly by using the formal vocabulary and rules of mathematics.

•  Mathematics as a Modeling Language – using mathematical models. Understand the various types of models used in mathematics and how to translate real life situations to those mathematical models to obtain a solution and then to translate those solutions back into the context of the real-life application.

•  Mathematics as Logical Thought – thinking logically. Think logically in a world that requires careful thought as a reasoning process

2. Course Specific Goals (aligned with Content Standards):

• Understanding basic arithmetic, algebra, geometry, probability, discrete math and statistical concepts.

• Solve mathematical problems in real life situations

• Use technology to solve mathematical problems

3. Expected Performances (aligned with state Expected Performances)

• Integers, fractions and decimals

• Percents

• Customary and metric measurement

• Equations with one and two variables

• Inequalities

• Exponents

• Probability and data analysis

• Points, lines, and planes

• Figures in a plane

• Triangles

• Sequences

Data and Numerical Reasoning - Academic (9/10):  Scope and Sequence Calendar

First semester material to be covered prior to the midterm exam:

UNIT 1 – Arithmetic

1.     Integers, Fractions and Decimals– students will add, subtract, multiply and divide integers, fractions and decimals.  They will learn about equivalent fractions and how to order fractions using the least common multiple. Students learn how to simplify fractions using the greatest common factor. They will also compare and order integers and decimals.

2.     Percents – students will learn how to convert fractions to decimals and decimals to percents.  They will learn percent increase and percent decrease and how they apply to real world problem solving.

3.     Customary and Metric Measurement – students will learn customary and metric measurements and conversions.  The students will use these units of measurement throughout the course.  Students will also use a ruler to find standard and metric measurement.

Unit 2 – Algebra

4.     Equations in One Variable– students write and evaluate expressions and equations using the order of operations. Students represent functions as rules and as tables.  They also graph functions given a rule or table of values.  Students will learn about the real number system, find square roots, apply properties to evaluate and simplify expressions, and use the Distributive Property to write equivalent expressions.  Students use properties of equality to solve one-step, two-step, and multi-step equations. Students write ratios and proportions, solve proportions using cross products, and solve percent problems, such as finding the percent of a number, a base, and part of a base.  Finally, students rewrite equations in function form and solve formulas and literal equations for a given variable.  

5.     Equations in Two Variables - students learn how to plot points in a coordinate plane and use tables, x- and y- intercepts, and the slope and y- intercept to graph linear equations and functions.  They interpret slope as a rate of change in real-world situations and explore how changing the slope and y- intercept changes the graph.  Students write equations of lines in slope-intercept form given three situations: the slope and y- intercept; the slope and a point; or two points.  Also, they write and graph equations using real-world data. 

6.     Inequalities - Students write, solve, and graph one-step and multi-step inequalities using addition, subtraction, multiplication, and division.  Finally, they learn to reverse an inequality sign when multiplying or dividing by a negative number.

7.     Exponents – students learn and use properties of exponents involving products and quotients.  They learn how to apply the product of powers property, the power of a power property, the power of a product property, the quotient of powers property, and the power of a quotient property.  Students also use zero and negative exponents.  Students learn how to read, write, and compute with numbers in scientific notation. 

Second semester material to be covered prior to the final exam:

Unit 3 – Statistics and Probability

8.     Probability and Data Analysis – students use sample spaces to calculate probabilities.  They identify and use the number of permutations or the number of combinations in a set of objects to calculate the probability of an event.  They find the probability of compound events by identifying whether the events are dependent or independent.  They compare measures of central tendency: the mean, median, and mode.  They look at the range for a set of data and look for outliers. They analyze and display data in circle graphs, stem-and-leaf plots, histograms, and box-and-whisker plots.

Unit 4 – Geometry

9.     Points, Lines and Planes - students will name and sketch geometric figures,  find lengths of segments in the coordinate plane, and find the midpoint of a segment.  Students will also name, measure and classify angles, identify complementary and supplementary angles, and classify polygons.  Finally, they will find circumference and area of circles, and area and perimeter of rectangles.  Students will classify angle pairs formed by three intersecting lines and study angle pairs formed by a line that intersects two parallel lines.

10. Triangles - students will classify triangles, find measures of angles of triangles and identify congruent figures. Students use ratios to find the scale of a drawing and then use the scale to find the actual distance on a map or the actual height of a building. 

11. Figures in a Plane - students investigate side lengths by using the Pythagorean Theorem to find the length of the third side in a right triangle. Students will find angle measures in polygons.  They will investigate properties of parallelograms and learn what information they can use to conclude that a quadrilateral is a parallelogram. Students will also study special quadrilaterals such as rhombuses, rectangles, squares, trapezoids, and kites. Finally, students will perform translations, reflect figures in a give line, rotate figures about a point and identify line and rotational symmetry.

Unit 5 – Discrete Mathematics

      13.  Sequences – students will investigate arithmetic and geometric sequences.