Math Foundations IIA Grade Levels 9-12

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1 Math Foundations IIA Grade Levels 9-12 Math Foundations IIA introduces students to the following concepts: order of operations squares and square root multiplying decimals organizing and graphing data graphing in the coordinate plane similar and congruent figures prime and composite numbers ratio and proportion variables equations inequalities 1

2 TEACHERS' GUIDE COURSE DESCRIPTION: The Anywhere Learning System (ALS) Math Foundations IIA full semester course guides 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. This course builds computational skills and conceptual understanding needed to undertake high schoollevel math courses with confidence. Carefully paced, guided instruction is accompanied by interactive practice. COURSE FEATURES: Math Foundations IIA is presented as a full semester course. All fifty-five 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 six units: Numbers and Operations; Data, Measurement, and Geometry; Ration, Proportion, and Decimals; Numbers and Properties; Concepts in Algebra; and Geometry and Statistics. 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 rounding numbers, order of operations, square numbers and square roots, five-step thinking plan to solving word problems, multiplication properties, division, factoring, comparing fractions, addition/subtraction of fractions, and multiplication/division of fractions. Students learn about types of graphs, solving equations, solving inequalities, metric measures, customary measures, time, temperature, planes, polygons, circles, space figures, and calculating perimeter, circumference, area, surface area, and volume. Students learn how to solve proportion problems, find percents of whole numbers, predict outcomes, add and subtract integers, graph ordered pairs, and express numbers in expanded and scientific notation. Students review commutative, associative, zero, one, and distributive properties as well as learn about solving problems with decimals, writing fractions in simplest form, and performing operations on fractions and mixed numbers. Students learn about evaluating expressions, solving multistep equations and solving problems involving measurement. Students learn basic geometric concepts, as well as how to identify plane figures, calculate circumference and area of a circle, determine similarity or congruency, measure length, area, volume, and surface area of geometric figures, find mean, median, mode, and range in a set of data, and organize data on various graphs and plots. COURSE CONTENT Course Name Number of Lessons Length of Course in Semesters Grade Levels Unit Assignments Math Foundations IIA

4 Unit 1: Numbers and Operations 1.01 Number Sense: Rounding, Estimating, and Range Rounding numbers; number ranges; estimation 1.02 Number Operations Order of operations; exponents and powers of numbers Number Sense: Squares and Square Root The 5-Step Plan Application Multiplication: Properties Multiplication: Decimals Square numbers and square roots Five-step thinking plan; strategies solving problems Review of 5-step plan; selecting relevant information; working with misleading or unnecessary data; finding strategy in patterns; choosing strategy to solve problems Estimating products; commutative, zero, associative, and one properties Multiplying decimals; zeros in multiplication 1.08 Division Estimating quotients; multiplying and dividing by powers of ten; dividing by one-digit numbers; dividing by two-digit numbers; dividing decimals 1.09 Number Sense: Factors Factors; divisibility; prime numbers; composite numbers; factor trees; prime factorization; greatest common factors; multiples; least common multiples 4

5 1.10 Fractions: Equivalent Fractions Equivalent fractions; comparing fractions; simplest form; relating fractions to decimals 1.11 Fractions: Estimating with Fractions Estimating sums and differences; adding and subtracting like fractions; adding and subtracting unlike fractions; adding and subtracting mixed numbers 1.12 Fractions: Multiplying & Dividing Fractions Estimating products; multiplying fractions and mixed numbers; simplifying; dividing fractions and mixed numbers 1.13 Unit 1 Assignment Math review of Unit 1 Study: Math Assignment Unit 2: Data, Measurement, and Geometry 2.01 Organizing Data Collecting data; tallies; frequency tables; mean, median, mode, and range 2.02 Graphing Data Bar graphs; pictographs, line graphs, circle graphs, and stem and leaf plots; analyzing graphed information 2.03 Metric Measures Metric place value; comparing metric units; length units; capacity units; mass units 2.04 Customary Measures Length units; capacity units; weight units 2.05 Other Measures Time and temperature 2.06 Plane Geometry Points, lines, rays; angles; parallel, intersecting, perpendicular, and skew lines; bisecting lines 5

6 2.07 Polygons Triangle classifications; quadrilateral classifications; other polygons; congruence; similar figures; symmetry; motion geometry 2.08 Space Figures Prisms; pyramids; faces, edges, vertices, and bases 2.09 Geometric Measurements Perimeter; circumference; area; surface area; volume 2.10 Circles Parts of a circle; pi; formulas 2.11 Unit 2 Assignment Math review of Unit 2 Study: Math Assignment Unit 3: Ratio, Proportion, & Decimals 3.01 Ratio and Proportion Ratio; proportion; solving proportions; rates; using scales 3.02 Percent Percents and decimals; percents and fractions; estimation; finding percents of whole numbers 3.03 Probability: Predicting Outcomes Outcomes; predicting outcomes; identifying independent events 3.04 Integers Positive integers; negative integers; zero; comparing integers; adding and subtracting integers 3.05 Coordinate Graphing Ordered pairs; coordinate planes; x-axis; y-axis 3.06 Number Values Place value through billions; decimal place value through thousandths; word form; standard form; expanded form; comparing and ordering numbers 6

7 3.07 Decimal Number Concepts Place value, exponents, powers of ten, expanded notation, scientific notation 3.08 Unit 3 Assignment Math review of Unit 3 Study: Math Assignment Unit 4: Numbers and Properties 4.01 Number Operations Commutative, associative, zero, one, and distributive properties; inverse operations; order of operations Decimal Number Operations Decimals Expanding skills in addition, subtraction, multiplication, and division using decimals Solving practical problems that deal with decimal numbers 4.04 Number Theory Prime and composite numbers; prime factorization; divisibility rules; common factors; greatest common factor; common multiples; least common multiple; square numbers; square roots 4.05 Number Theory Practical application of number theory in problem solving 4.06 Fraction Concepts 4.07 Fraction Operations Simplest form; equivalent fractions; like and unlike fractions, comparing fractions; improper fractions; mixed numbers; relating fractions to decimals; reciprocals Expanding skills in addition, subtraction, multiplication, and division with fractions and mixed numbers 4.08 Fractions Practical situations dealing with fractions in problem solving 7

8 Ratio and Proportion Ratio, Rates, Proportions Probability: Properties Ratios; equivalent ratios; cross products; rates; proportions; solving proportions Problem solving with ratios, rates, proportions, and scale drawings Properties of probability; making predictions; outcomes and permutations 4.12 Percent Concepts Percent; decimals; fractions; finding percents of a whole; finding parts of a whole; finding the whole 4.13 Percents Problem solving with percents; percent of increase or decrease; discounts, markups, commissions, interest, and sales tax 4.14 Unit 4 Assignment Math review of Unit 4 Study: Math Assignment Unit 5: Concepts in Algebra 5.01 Algebra Concepts Numerical expressions, variables, equations, algebraic expressions, inequalities, inverse operations Variables and Equations Equations and Inequalities Expressions and Equations Identifying variables; numerical expressions; algebraic expressions; addition and subtraction equations; multiplication and division equations Rational numbers in equations; solving equations; solving Inequalities Replacing variables to evaluate expressions; steps to solving equations 8

9 Equations Measurement Writing equations to solve word problems; solving multi-step equations Problem solving applications of measurement 5.07 Unit 5 Assignment Math review of Unit 5 Study: Math Assignment Unit 6: Geometry and Statistics 6.01 Geometric Concepts Definitions and examples of points, lines, planes, and angles; bisecting lines and planes; relationships of lines; relationships of angles 6.02 Plane Figures Polygons: triangles, quadrilaterals, pentagon, octagon, decagon; diagonal; circles: parts of a circle, calculate circumference and area 6.03 Motion Geometry Similar and congruent figures; rotation; translation; reflection Space Figures: A Review Geometric Measurement: A Review Review and expansion of ideas about prisms, pyramids, cones, and cylinders Length, area, volume, surface area of geometric figures 6.06 Statistics Data collection; mean, median, mode, and range 6.07 Graphs and Plots Bar, circle, and line graphs; stem and leaf plots; box and whisker plots; frequency plots 6.08 Unit 6 Assignment Math review of Unit 6 Study: Math Assignment 9

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