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ABE 031 PRE-ALGEBRA LEVEL C Number and Operations: Base Ten (+ The Number System) Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Understand the place value system. Perform operations with multi-digit whole numbers and decimals to hundredths. The Number System Compute fluently with multi-digit numbers and find common factors and multiples. Number and Operations: Fractions Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimal fractions. Use equivalent fractions as strategy to add and subtract fractions. Apply and extend previous understanding of multiplication and division to multiply and divide fractions. The Number System Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. Gain familiarity with factors and multiples. Generate and analyze patterns. Write and interpret numerical expressions. Expressions and Equations Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one-variable equations and inequalities. ABE 041 ALGEBRA I LEVEL D Expressions and Equations Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Work with radicals and integer exponents. Understand the connection between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. Functions Define, evaluate, and compare functions. Use functions to model relationships between quantities. LEVEL E Number and Quantity: The Real Number System Extend the properties of exponents to rational exponents. Number and Quantity: Quantities Reason quantitatively and use units to solve problems. Algebra: Seeing Structures in Expressions Interpret structure of expressions. Write expressions in equivalent form to solve problems. Algebra: Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomials. Rewrite rational expressions. Algebra: Creating Equations Create equations that describe numbers or relationships. Algebra: Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explaining reasoning. Solve equations and inequalities in one variable. Represent and solve equations and inequalities graphically. Represent and analyze quantitative relationships between dependent and independent variables. LEVEL D The Number System Apply and extend previous understandings of numbers to the system of rational numbers. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Know that there are numbers that are not rational, and approximate them by rational numbers. Understand ratio concepts and use ratio reasoning to solve problems. Analyze proportional relationships and use them to solve realworld and mathematical problems. ABE 051 GEOMETRY LEVEL C Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Graph points on the coordinate plane to solve real-world and mathematical problems. Classify two-dimensional figures into categories based on their properties. Solve real-world and mathematical problems involving area, surface area, and volume. Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Geometric measurement: understand concepts of angle and measure angles. Convert like measurement units within a given measurement system. Represent and interpret data. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. LEVEL D Geometry Draw, construct, and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle, measure, area, surface area, and volume. Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean Theorem. LEVEL E Geometry: Congruence Experiment with transformations in the plane. Geometry: Similarity, Right Triangles, and Trigonometry Prove theorems involving similarity. Geometry: Geometric Measurement and Dimensions Explain volume formulas and use them to solve problems. Geometry: Modeling with Geometry ABE 061 MODULARIZED MATH **Includes all standards from ABE 031, ABE 041, and ABE 051. ** LEVEL C Statistics and Probability Develop understanding of statistical variability. Summarize and describe distributions. LEVEL D Statistics and Probability Summarize and describe distributions. Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models. Investigate patterns of association in bivariate data. LEVEL E Algebra: Seeing Structures in Expressions Interpret structure of expressions. Write expressions in equivalent form to solve problems. Algebra: Arithmetic with Polynomials and Rational Expressions Perform algebraic operations with polynomials. Rewrite rational expressions. Algebra: Creating Equations Create equations that describe number relationships. Algebra: Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explaining reasoning. Solving equations and inequalities in one variable. Solve systems of equations. Represent and solve equations and inequalities graphically. Functions: Understand the concept of functions and function notation. Interpret functions that arise in applications in terms of context. Analyze functions using different representations. Functions: Building Functions Build a function that models a relationship between two quantities. Functions: Linear, Quadratic, and Exponential Models Construct and compare linear, quadratic, and exponential models to solve problems. Apply geometry concepts in modeling situations. Interpret expressions for functions in terms of the situation they model. Statistics and Probability: Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measureable variable. Summarize, represent, and interpret data on two categorical and quantitative variables.