Welcome to the learning progression for Pre-Algebra. This progression incorporates the overall topics of this grade-level's mathematics and is formatted with Overarching Questions, Essential Questions, and Big Ideas for each unit. This progression model takes the work of bundling standards to the next level by grouping together grade-level concepts in the Big Ideas sections. The Big Ideas are designed to represent the critical mathematics of this grade level in a manner that is more coherent and productive as a guide for planning instruction, assessment, and intervention. Big Ideas are for progression and planning and are not a replacement for the OAS-M objectives.
Unit |
Overarching Question |
Essential Questions |
Big Ideas |
Full Objectives |
How does mindset affect learning mathematics? |
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Unit 1: Expressions, Equations, and Inequalities Timing 5-6 weeks Objectives |
How can you use expressions, equations, and inequalities within real-world situations? |
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PA.A.3.1 Use substitution to simplify and evaluate algebraic expressions. PA.A.3.2 Justify steps in generating equivalent expressions by combining like terms and using order of operations (to include grouping symbols). Identify the properties used, including the properties of operations (associative, commutative, and distributive). PA.A.4.1 Solve mathematical problems using linear equations with one variable where there could be one, infinitely many, or no solutions. Represent situations using linear equations and interpret solutions in the original context PA.A.4.2 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. PA.A.4.3 Represent real-world situations using equations and inequalities involving one variable. |
Linear Equations and Functions Timing 5-6 weeks Objectives |
How can we use graphs and other representations to gain knowledge of real-world situations? |
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PA.A.1.1 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. PA.A.1.2 Use linear functions to represent and model mathematical situations. PA.A.1.3 Identify a function as linear if it can be expressed in the form y=mx + b or if its graph is a non-vertical straight line. PA.A.2.1 Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. PA.A.2.2 Identify, describe, and analyze linear relationships between two variables. PA.A.2.3 Identify graphical properties of linear functions, including slope and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship. PA.A.2.4 Predict the effect on the graph of a linear function when the slope or y-intercept changes. Use appropriate tools to examine these effects. PA.A.2.5 Solve problems involving linear functions and interpret results in the original context. PA.D.1.3 Collect, display, and interpret data using scatter plots. Use the shape of the scatter plot to find the informal line of best fit, make statements about the average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels, and units. |
Timing 3-4 weeks Objectives |
How can exponents and real numbers be used to solve real-world situations? |
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PA.N.1.1 Develop and apply the properties of integer exponents, including a0 = 1 (with a 0 ), to generate equivalent numerical and algebraic expressions. PA.N.1.2 Express and compare approximations of very large and very small numbers using scientific notation. PA.N.1.3 Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation. PA.N.1.4 Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers. |
Timing 2-3 weeks Objectives PA.GM.1.1 |
How can the Pythagorean Theorem be used in real-world situations? |
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PA.GM.1.1 Justify the Pythagorean theorem using measurements, diagrams, or dynamic software to solve problems in two dimensions involving right triangles. PA.GM.1.2 Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane. |
Timing 2-3 weeks Objectives |
How are two dimensional and three-dimensional objects related to each other in real-world situations? |
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PA.GM.2.1 Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units (e.g., cm2 ). PA.GM.2.2 Calculate the surface area of a cylinder, in terms of pi (π ) and using approximations for pi (π ), using decomposition or nets. Use appropriate units (e.g., cm2) PA.GM.2.3 Justify why base area (B) and height (h) in the formula V=Bh are multiplied to find the volume of a rectangular prism. Use appropriate units (e.g., cm3 ). PA.GM.2.4 Develop and use the formulas V = (𝜋 r)2h and V = Bh to determine the volume of right cylinders, in terms of (𝜋) and using approximations for pi(𝜋). Justify why base area (B) and height (h) are multiplied to find the volume of a right cylinder. Use appropriate units (e.g., cm3 ). |
Timing 2-3 weeks Objectives |
How do data points affect mean and median in real-world situations? |
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PA.D.1.1 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using technology to examine this impact. PA.D.1.2 Explain how outliers affect measures of center and spread. |
Timing 3-4 weeks Objectives |
How can probability be used in real-world situations? |
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PA.D.2.1 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. PA.D.2.2 Determine how samples are chosen (random, limited, biased) to draw and support conclusions about generalizing a sample to a population. PA.D.2.3 Compare and contrast dependent and independent events.
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Timing 2-3 weeks Objectives
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How can mathematical patterns be used to expand our understanding? |
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PA.A.1.2 Use linear functions to represent and model mathematical situations. PA.A.2.1 Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. PA.A.2.2 Identify, describe, and analyze linear relationships between two variables. PA.A.2.3 Identify graphical properties of linear functions, including slope and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship. PA.D.1.3 Collect, display, and interpret data using scatter plots. Use the shape of the scatter plot to find the informal line of best fit, make statements about the average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels, and units. |
Distance Learning Resources/ Supplemental Activities |
How can students develop and show evidence of understanding? | Multiple objectives are covered in this material. These math tasks are designed to enhance current curriculum and support distance learning. |
Introduction to the OKMath Framework