Integrated Math

This course is designed to bridge the mathematical gap from 8^th grade to high school. A considerable amount of time will be spent reviewing basic operations on whole numbers, fractions, and decimals. Elementary ideas from geometry, algebra, statistics, and measurement are integrated into the course.

Integrated Math is intended to prepare students who struggled in pre-algebra for success in algebra and geometry. Number and operation sense, estimation skills, and the ability to judge reasonableness of results will be strengthened in the context of practical applications and problem solving. Students will apply mathematical ideas to real-world situations. This course revolves around a broadened approach to core topics integrating algebra, geometry, and statistics in orders to meet Grade 9 Idaho Achievement Standards. Direct instruction (using PH Math, Course 3, 2004), Accelerated Math, and PLATO will be the primary instructional resources.

Quarter 1

Basic Skills and Introductory Algebra Concepts

• Apply properties of rational numbers. (347.01.b)
• Use positive and negative numbers, absolute value, fractions, decimals, percentages, and scientific notation, including application in real world situations. (347.01.a)
• Apply properties of exponents. (347.01.c)
• Identify exact and approximate roots without simplification.
• Solve problems using number theory concepts (factors, multiples, primes).
• Use the order of operations and perform operations with rational numbers. (347.02.a)
• Apply number sense to everyday situations and judge reasonableness of results. (347.03.a)
• Identify that error accumulates in a computation when there is rounding. (349.05.b)
• Represent mathematical relationships using variables, expressions, linear equations and inequalities
• Use appropriate procedures for manipulating and simplifying algebraic expressions involving variables, integers, rational numbers, and for solving multi-step, first-degree equations and inequalities.

Quarter 2

Geometry and Measurement

• Formulate and use proportions, ratios, percents, discounts, markup, and scaling. (Students will need to solve equations using division.)
• Students apply concepts of rates and direct and indirect measurements.
• Students evaluate given measurement formulas for two- and three- dimensional objects.
• Understand and use U.S. customary and metric measurements
• Determine and use appropriate units. (349.01.a)
• Approximate error in measurement situations.
• Define and use basic geometric terms, including point, ray, line segment, plane, supplementary, complementary, parallel, perpendicular, vertical and adjacent angles.
• Use protractors to measure angles.
• Given the formulas, find the circumference, perimeter, or area of triangles, circles, and quadrilaterals, and the volume and surface area of rectangular prisms and cylinders. (349.01.a)
• Solve word problems involving circumference, perimeter, or area of triangles, circles, and rectangles.
• Given the Pythagorean Theorem, calculate a missing side length of a right triangle where the legs and hypotenuse are real numbers. (351.02.c) (Students will need to find square roots and simplify radicals)

Quarter 3

Probability, Statistics, and Data Analysis

· Interpret and use basic statistical concepts including mean, median, mode, range, and distribution of data, including outliers. (352.03.a)

• Students make predictions and draw conclusions based on statistical measures and students make predictions based on randomness, chance, equally likely events, and probability.
• Students find probabilities based on dependent, independent, and compound events and students make predictions based on randomness, chance, equally likely events, and probability.
• Analyze and interpret tables, charts, and graphs, including scatter plots, broken line graphs, and box-and-whisker plots. (352.01.a)
• Collect, organize, and display data in tables, charts, and graphs. (352.02.a)
• Make predictions and draw conclusions based on statistical measures. (352.05.a)
• Find probabilities based on dependent, independent, and compound events.
• Contrast experimental and theoretical probability. (352.04.a)
• Make predictions based on randomness, chance, equally likely events, and probability. (352.04.c)
• Use appropriate tools/technology to conduct simulations and employ graphical models to make predictions or decisions based on data. (352.05.a)
• Conduct and interpret results of statistical experiments. (352.05.b)

Quarter 4

More Algebraic Concepts

• Students understand the concept and applications of functions and mathematical models.
• Given graphs, charts, ordered pairs, mappings, or equations, students determine whether a relation is a function.
• Students evaluate functions written in functional notation and, given a function, students identify domain and range.
• Use appropriate graphing procedures to solve multi-step, first-degree equations and inequalities; such as 3(2x – 5) = 5x + 7 or 3(2x – 5) > 5x + 7. (350.03.a)
• Differentiate between linear and non-linear equations and graphs
• Use appropriate procedures to solve linear systems of equations involving two variables; such as x + y = 7 and 2x + 3y = 21. (350.04.a)
• Given graphs, charts, ordered pairs, mappings, or equations, determine whether a relation is a function.
• Evaluate functions written in functional notation.
• Given a function, identify domain and range.
• Model and solve real-world phenomena using multi-step, first degree, single variable equations and inequalities, linear equations, and two-variable linear systems of equations. (353.01.a)
• Identify attributes of the Cartesian Coordinate System, such as quadrants, origin, and axes. (351.03.a)
• Graph scatter plots and identify informal trend lines (e.g., eyeball fit lines).
• Identify positive and negative correlations.
• Create graphs and equations for linear relationships.
• Represent linear relationships using tables, graphs, and mathematical symbols.
• Interpret attributes of linear relationships such as slope (rate of change) and intercepts