PA.N.1 Read, write, compare, classify, and represent real numbers and use them to solve problems in various contexts. PA.N.1.1 PA.N.1.2 PA.N.1.3 PA.N.1.4 PA.N.1.5 Develop and apply the properties of integer exponents, including a 0 = 1, to generate equivalent numerical and algebraic expressions Express and compare approximations of very large and very small numbers using scientific notation Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation Classify Real s as rational or irrational. Explain why the rational number system is closed under addition and multiplication and why the irrational system is not. Explain why the sum of a rational and an irrational number is irrational; and the product of a non-zero rational number and an irrational number is irrational. Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 4000 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers. 1: Exponents and Scientific 1: Exponents and Scientific 1: Exponents and Scientific 1: The Real System 1: The Real System 1: It s a Generational Thing (M5-7) 2: Show What You Know (M5-29) 3: The Big and Small of It (M5-43) 4: How Much Larger (M5-61) 2: Rational Decisions (M4-17) 3: What Are Those? (M4-31) 1: So Many s, So Little Time (M4-7) 3: What are Those?! (M4-31) 7: Exponents 7: Exponents 1: Properties of Whole Exponents 2: Scientific 1: Rational and Irrational s 1: Rational and Irrational s 1: Using the Product Rule and the Quotient Rule 2: Using the Power to a Power Rule 3: Using the Product to a Power Rule and the Quotient to a Power Rule 4: Using Properties of Exponents with Whole 5: Simplifying with Negative and Zero Exponents 1: Using Scientific 2: Comparing s using Scientific 1: Introduction to Irrational s 2: Graphing Real s on a Line 3: Ordering Rational and Irrational s Pre-Algebra Middle School Math Solution: Alignment to OAS 1
PA.A.1 Understand the concept of function in real-world and mathematical situations, and distinguish between linear and nonlinear functions PA.A.1.1 PA.A.1.2 PA.A.1.3 Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable Use Linear to represent and explain real-world and mathematical situations Identify a function as linear if it can be expressed in the form y = mx + b or if its graph is a straight line 3: Determining Unknown Quantities 3: Graphing Quantitative 1: Every Graph Tells a Story (M3-155) 3: One or More Xs to One Y (M2-205) 5: Comparing Apples to Oranges (M2-241) 1: Relations and Models 3: Graphs of Linear in Two-Variables of 1: Exploring 1: Graphing Given an Integer Slope and 2: Graphing Given a Decimal Slope and 3: Modeling Linear in Standard Form 1: Graphing Linear Using a Given Method 2: Graphing Linear using a Chosen Method 1: Modeling Given Slope and a Point 3: Modeling Given Two Points using Multiple Pre-Algebra Middle School Math Solution: Alignment to OAS 2
PA.A.2 Recognize linear functions in real-world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols, and graphs; solve problems involving linear functions and interpret the result in the original context PA.A.2.1 PA.A.2.2 PA.A.2.3 Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another Identify, describe and analyze linear relationships between two variables Identify the graphical properties of linear functions, including slope and intercepts. Know that the slope equals the rate of change, and the y intercept is zero when the function represents a proportional relationship 1: Thinking Proportionally 3: Proportionality 1: From Proportions to Linear 5: Comparing Apples to Oranges (M2-241) 1: U.S. Shirts (M2-81) 2: At the Arcade (M2-93) 3: Dining, Dancing, Driving (M2-109) 5: What s the Point (M2-135) 6: The Arts Are Alive (M2-151) 5: Comparing Apples to Oranges (M2-241) 1: How Does Your Garden Grow? (M1-91) 3: Fish-Inches (M1-137) 1: Post-Secondary Proportions (M2-7) 2: Jack and Jill Went Up the Hill (M2-23) 3: Slippery Slopes (M2-43) 2: At the Arcade (M2-93) 1: Proportional 4: Two-Step and of Models 3: Graphs of Linear in Two-Variables of 3: Representing Proportional by 2: The Coordinate Plane and Two- Step 1: Relations and using Multiple 1: Graphing Given an Integer Slope and 2: Graphing Given a Decimal Slope and 3: Modeling Linear in Standard Form 1: Graphing Linear Using a Given Method 2: Graphing Linear using a Chosen Method 1: Modeling Given Slope and a Point 3: Modeling Given Two Points using Multiple 5: Determining Characteristics of Direct Variation Graphs 1: Graphs of 4: Identifying Key Characteristics from Graphs Pre-Algebra Middle School Math Solution: Alignment to OAS 3
PA.A.2 (cont d) PA.A.3 Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions PA.A.2.4 PA.A.2.5 PA.A.3.1 PA.A.3.2 Predict the effect on the graph of a linear function when the slope or y-intercept changes. Use appropriate tools to examine these effects. Solve problems involving linear functions and interpret the results in the original context Use substitution to simplify and evaluate algebraic expressions Justify steps in generating equivalent expressions by identifying the properties used, including the properties of operations (associative, commutative, and distributive laws) and the order of operations including grouping symbols 1: Proportions to Linear 1: Algebraic 1: Algebraic 2: Jack and Jill Went Up the Hill (M2-23) 3: Slippery Slope (M2-43) 4: Up, Down, and All Around (M2-53) 3: Dining, Dancing, Driving (M2-109) 6: The Arts Are Alive (M2-151) 1: No Substitute for Hard Work (M3-7) 2: Mathematics Gymnastics (M3-19) 3: All My Xs (M3-33 4: Two-Step and of Models and the Distributive Property 1: Variable Using Multiple 1: Modeling with Integer Rates of Change 2: Modeling with Fractional Rates of Change 3: Modeling using the Distributive Property over Division 1: Factoring Linear 2: Using Order of Operations to Simplify Algebraic (No Type In) 3: Using Order of Operations to Simplify Algebraic (Type In) Pre-Algebra Middle School Math Solution: Alignment to OAS 4
PA.A.4 Represent real-world and mathematical problems using equations and inequalities involving linear expressions. Solve and graph equations and inequalities symbolically and graphically. Interpret solutions in the original context. PA.A.4.1 PA.A.4.2 PA.A.4.3 Illustrate, write, and solve mathematical problems using linear equations with one variable with one solution, infinitely many solutions, or no solutions. Interpret the solutions in the original context Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form px + q > r and px + q < r, where p, q, and r are rational numbers Represent real-world situations using equations and inequalities in one variable 3: Modeling Linear 1: Solving Linear 2: Two-Step and 2: Two-Step and 1: Strategic Solving (M3-7) 2: MP3s and DVDs (M3-17) 3: Tic-Tac-Bingo (M3-31) 4: Be Greater Than (M3-95) 4: Be Greater Than (M3-95) 1: U.S. Shirts (M2-81) 2: At the Arcade (M2-93) 3: Dining, Dancing, Driving (M2-109) 5: What s the Point (M2-135) 6: The Arts Are Alive (M2-151) 6: of Linear 4: Two-Step and 1: Solving Linear with Variables on Both Sides 4: Solving Two-Step Models and the Distributive Property of 1: Exploring Two-Step 2: Solving Multi-Step 1: Solving with Integers (No Type In) 2: Solving with Integers (Type In) 3: Solving with One Solution, Infinite, and No Solutions 4: Sorting by of Solutions 1: Graphing with Rational s 2: Solving Two-Step Linear 1: Modeling with Integer Rates of Change 2: Modeling with Fractional Rates of Change 3: Modeling using the Distributive Property over Division Using Multiple Pre-Algebra Middle School Math Solution: Alignment to OAS 5
PA.GM.1 Solve problems involving right triangles using the Pythagorean PA.GM.2 Calculate Surface Area and Volume of three-dimensional figures PA.GM.1.1 PA.GM.1.2 PA.GM.2.1 PA.GM.2.2 PA.GM.2.3 PA.GM.2.4 Informally justify the Pythagorean using measurements, diagrams, or dynamic software and use the Pythagorean to solve problems in two and three dimensions involving right triangles Use the Pythagorean to find the distance between any two points in a coordinate plane Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate measurement. Calculate the surface area of a cylinder, in terms of Pi and using approximations for Pi, using decomposition or nets. Use appropriate units Develop and use the formulas v = lwh and v Bh to determine the volume of rectangular prisms. Justify why the base and height are multiplied to find the volume of a rectangular prism. Use appropriate units. Develop and use the formulas v = πr 2 and V = Bh to determine the volume of right cylinders, in terms of Pi and using approximations for Pi. Justify why base area and height are multiplied to find the volume of a right cylinder. Use appropriate measurements. 1: Composing and Decomposing 1: Composing and Decomposing 2: Pythagorean 2: Pythagorean 3: Decimals and Volume 2: Volume of Curved Figures 3: Decimals and Volume 2: Volume of Curved Figures 1: Right Triangle Connection (M4-55) 2: Can That Be Right? (M4-75) 3: Pythagoras Meets Descartes (M4-87) 4: Catty Corner (M4-99) 3: Pythagoras Meets Descartes (M4-87) 3: Breaking the Fourth Wall (M1-143) 1: Drum Roll, Please! (M5-85) 4: Silos, Frozen Yogurt, and Popcorn (M5-123) 3: Breaking the Fourth Wall (M1-143) 1: Drum Roll, Please! (M5-85) 4: Silos, Frozen Yogurt, and Popcorn (M5-123) 6: Geometric Measurement 2: The Pythagorean 2: The Pythagorean 3: Volume and Surface Area 8: Volume 1: Volume 6: Geometric Measurement 3: Volume and Surface Area 8: Volume 1: Volume 1: Exploring the Pythagorean 2: Applying the Pythagorean 3: Problem Solving Using the Pythagorean 4: Calculating Distances on the Coordinate Plane 3: Calculating Surface Area of Right Prisms 1: Calculating Volume of 2: Using Volume of 3: Calculating Surface Area of Right Prisms 1: Calculating Volume of 2: Using Volume of Pre-Algebra Middle School Math Solution: Alignment to OAS 6
PA.D.1 Display and interpret data in a variety of ways, including scatterplots and approximate line of best fit. Use line of best fit and average rate of change to make predictions and draw conclusions about data. PA.D.1.1 PA.D.1.2 PA.D.1.3 PA.D.2.1 PA.D.2.2 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet and use a calculator to examine this impact. Explain how outliers affect measures of central tendency Collect, display, and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit, make statements about average rate of change, and make a prediction about values not in the original data set. Use appropriate titles, labels, and units. Calculate experimental probabilities and represent them as percents, fractions, and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown. Determine how samples are chosen to draw conclusions about generating a sample to a population Algebra 1* Algebra I 4: Analyzing Populations and 4: Analyzing Populations and 8: Analyzing Data Sets for One Variable 4: Patterns in Bivariate Data 1: Introduction to Probability 3: Drawing Inferences 8.3: You Are Too Far Away! (p. 479) 1: Pass the Squeeze (M2-267) 2: Where Do you Buy Your Books? (M2-289) 3: Mia is Growing Like a Weed (M2-305) 4: The Stroop Test (M2-319) 3: Toss the Cup (M4-33) 1: We Want to Hear From You (M4-133) 2: Tiles, Gumballs, and Pumpkins (M4-151) 3: Spicy or Dark? (M4-169) 4: Finding Your Spot to Live (M4-181) 7: Measures of Central Tendency and Data Displays 1: Measures of Central Tendency 9: Bivariate Data 1: Line of Best Fit 6: Data Comparisons and 2: Introduction to Probability 3: Determining the Effects of Changing Data Sets 1: Estimating Lines of Best Fit 2: Using Lines of Best Fit 2: Comparing Experimental to Theoretical Pre-Algebra Middle School Math Solution: Alignment to OAS 7