# Math Foundations IIB Grade Levels 9-12

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1 Math Foundations IIB Grade Levels 9-12 Math Foundations IIB introduces students to the following concepts: integers coordinate graphing ratio and proportion multi-step equations and inequalities points, lines, rays, and angles area and volume Pythagorean Theorem scientific notation rational numbers percent probability statistics 1

2 TEACHERS' GUIDE COURSE DESCRIPTION: The Anywhere Learning System (ALS) Math Foundations IIB full semester course is the second semester of Math Foundations II. It is designed to guide students through foundational math skills typically found in sixth to eighth grade instruction. It is appropriate for use as remediation at the high school level, as a bridge to high school, or as middle school curriculum. Carefully paced, guided instruction is accompanied by interactive practice. When used in combination with Math Foundations I (addressing skills typically found in grade 3 to 5), the course effectively remediates the computational skills and conceptual understanding needed to undertake high school-level math courses with confidence. COURSE FEATURES: Math Foundations IIB is presented as a full semester course. All fifty-two lessons contain a study guide, a practice test, and a mastery test. A math unit review assignment is presented at the end of each unit. Answer keys are available to assist teachers in grading the unit assignments. This course is split into seven units: Operations and Real Numbers; Ratio, Proportion, and Probability; Concepts in Algebra; Geometric Concepts; Expressions and Equations; Elements of Algebra; and Geometry. All lessons contain introduction and reinforcement of mathematical skills and concepts. 2

3 TEACHERS' GUIDE COURSE OBJECTIVES: The content in this course is based on Common Core Standards. Students learn about absolute value and how to add, subtract, multiply, and divide integers. Students will understand numbers, ways of representing numbers, relationships among numbers, and number systems. Students review simplifying expression and solving multistep equations and inequalities. They also review plane and space figures and learn formulas for the area of plane figures and volume of space figures. Students use number lines to identify, locate, and compare integers, as well as determine absolute value. Students learn rules for solving equations by adding/subtracting/multiplying/dividing integers with the same or different sign. Students review the definitions of point, line, ray, line segment, and angle. Students find area of polygons and surface area of pyramids, prisms, and cones. COURSE CONTENT Course Name Number of Lessons Length of Course in Semesters Grade Levels Unit Assignments Math Foundations IIB

4 Unit 1: Operations and Real Numbers 1.01 Integers Negative and positive numbers; comparing and ordering integers; using a number line; absolute value Adding and Subtracting Integers Multiplying & Dividing Integers Coordinate Graphing Number Concepts Review Finding sums and differences with integers; additional properties of integers Finding products and quotients with integers; using multiplication properties with integers Graphing ordered pairs on a coordinate axis Place value; rounding; estimation; compatible numbers 1.06 Properties Commutative property of addition; associative property of addition; commutative property of multiplication; associative property of multiplication; identity properties; distributive property Problem Solving: The 5-Step Plan Basic Operations with Rational Numbers Basic Operations with Fractions Five-step thinking plan; problem solving strategies Positive and negative rational numbers; equivalent fractions; cross products; absolute value; order of operations; fractions to decimals; comparing and ordering. Addition; subtraction; multiplication; division 1.10 Unit 1 Assignment Math review of Unit 1 Study: Math Assignment 4

5 Unit 2: Ratio, Proportion, and Probability Ratio and Proportion Problem Solving: Ratio and Proportion Ratio; rates; equivalent ratios; proportion Practical problems dealing with ratio, proportion, unit rates, rates, and scale 2.03 Percent Concepts Percent to decimals; percent to fractions; finding percents 2.04 Percent: Practical uses Percent of increase or decrease; sales tax and discounts 2.05 Probability Probability; finding samples; randomly occurring events; compound events; independent and dependent events; making predictions; capture and recapture method; tree diagrams; counting principle factorials; Venn diagrams 2.06 Unit 2 Assignment Math review of Unit 2 Study: Math Assignment Unit 3: Concepts in Algebra 3.01 Algebra: Expressions, Equations, Order of Operations Numerical expressions; variables; variable expressions; order of operations; equations; solutions 3.02 Algebra: Simplifying Simplifying numerical and variable expressions; coefficients; constants; evaluating algebraic expressions 3.03 Algebra: Equalities and Inequalities Properties of equality; inverse operations; inequalities; solving inequalities 5

6 Algebra: Multi-Step Equalities and Inequalities Algebra: Translating Data to Equations Guides for practice in solving multi-step equations and inequalities Translating data into equations and inequalities; using equations and inequalities to solve practical problems 3.06 Unit 3 Assignment Math review of Unit 3 Study: Math Assignment Unit 4: Geometric Concepts 4.01 Geometric Concepts: Points, Lines, Rays, Angles Point, line, ray; line relationships; angles; angle relationships; angle measurement and classifications; bisecting line segments and angles 4.02 Plane Figures: Polygons and Circles Regular polygons; triangles; quadrilaterals; congruent figures; circles Space Figures: Polyhedrons, Cones, and Spheres Geometric Measurement Square Roots and Triangles Coordinate Graphing Polyhedrons; prisms; pyramids; cylinders; cones; spheres Perimeter and circumference; formulas for area of plane figures; surface area of polyhedrons; volume of space figures Square roots; principal square roots; perfect squares; irrational numbers and real numbers; Pythagorean Theorem; similar triangles; special right triangles; trigonometry Coordinate planes; ordered pairs; solutions; graphing equations; linear equations; slope; slope formula 6

7 4.07 Coordinate Graphing to Solve Problems Using coordinate graphing to solve problems; solving and graphing equations and inequalities; quadrants 4.08 Unit 4 Assignment Math review of Unit 4 Study: Math Assignment Unit 5: Expressions and Equations 5.01 Number Notation Writing numbers in standard, written, expanded, and factor form; scientific notation 5.02 Expressions and Equations Writing numerical expressions; introduction to variables; writing algebraic expressions; evaluating algebraic expressions 5.03 Properties Review Review of commutative, associative, distributive, zero, and identity properties and examples of steps in solving problems using each one; multiplicative property of zero Simplifying Expressions Solving Equations using Properties Solving Equations with Multiplication and Division Terms; operational symbols; numerical coefficients; identifying like terms and constants; using various properties to simplify expressions Properties of equality; using inverse operations; using equivalent equations and inverse operations to solve problems Inverse operations of multiplication and division; the multiplication and division properties of equality 5.07 Unit 5 Assignment Math review of Unit 5 Study: Math Assignment 7

8 Unit 6: Elements of Algebra 6.01 Integers Integers and their opposites; using number lines to identify, locate, and compare integers; absolute value of integers; using integers in real life situations 6.02 Equations with Integers by Adding and Subtracting Rules for solving equations by adding and subtracting integers with the same sign or different signs; examples of strategies to solve equations 6.03 Equations with Integers by Multiplying and Dividing Rules for solving equations by multiplying and dividing integers with the same or different signs; examples of strategies to solve equations 6.04 Inequalities Definition and examples of inequalities; signs that indicate inequality 6.05 Solving Inequalities with Inverse Operations Solving inequalities by reversing signs Solving Inequalities with Multiplication and Division Factors and Exponents Other strategies for solving inequalities; checking for reasonability Identifying laws of exponents; writing numbers in exponential form; writing exponents and variables; rules for determining exponents when adding, subtracting, multiplying, and dividing 6.08 Rational Numbers Identifying parts of fractions; relating fractions to rational numbers; locating rational numbers on the number line; comparing rational numbers; writing rational numbers in decimal form; algebraic fractions 8

9 6.09 Equations- Inequalities by Adding and Subtracting Solving equations and inequalities with addition and subtraction; two-step equations; solving equations with variables on both sides Equations- Inequalities by Multiplying and Dividing Graphing on the Coordinate Plane Ratio and Proportion Solving equations and inequalities with multiplication and division; two-step equations; solving equations with variables on both sides with combined operations Graphing on the coordinate plane; graphing linear equations; slope and intercept; graphing linear equalities Definition and examples of ratios; writing ratios in lowest terms; rates; unit rates; equivalent ratios; cross products; definition of proportions; solving proportions 6.13 Percent Decimals and percents; figuring percents; place value in percent problems; relating percent to wholes Problem Solving with Percent Probability: Permutations and Combinations Examples of solving percent problems in everyday life; discounts; commission; checking answers for reasonableness; numbers larger than one hundred percent The counting principle; permutations; combinations; independent events; dependent events 6.16 Unit 6 Assignment Math review of Unit 6 Study: Math Assignment Unit 7: Geometry 7.01 Algebra with Geometry Definitions of point, line, ray, line segment, angles, and angle measures; parallel and perpendicular lines 9

10 7.02 Polygons and Circles Triangles, quadrilaterals, and other polygons; congruent figures; similar triangles; circles 7.03 Area and Volume Finding area of polygons; finding volume and surface area of pyramids, prisms, and cones 7.04 Special Triangles Square roots; Pythagorean theorem; tangents; sine and cosine ratios 7.05 Statistics and Graphing Frequency tables; range, mean, mode, and median; bar, line, and circle graphs; scatter plots; stem and leaf plots 7.06 Unit 7 Assignment Math review of Unit 7 Study: Math Assignment 10

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