Pre-Algebra Pacing Guide 2019-2020

Syllabus / Class Procedures

Unit 0:  Growth Mindset

Math is about learning not performing.

Math is about making sense.

Math is filled with conjectures, creativity, and uncertainty.

Mistakes are beautiful things.

Assessment :

Unit 0

Unit 1:  Numbers

Classify real numbers 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 number 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 400 or it if is not a perfect square root, locate it as an irrational number between two consecutive positive integers.

Assessment:

PA.N.1.4, PA.N.1.5

Unit 2:  Expressions, Equations, and Inequalities

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.

Illustrate, write and solve mathematical and real-world problems using linear equations with one variable with one solution, infinitely many solutions, or no solutions.  Interpret solutions in the original context.

Represent, write, solve and graph problems leading to linear inequalities with one variable in the form of px + q > r and px + q < r, where p, q, and r are rational numbers.

Represent real-world situations using equations and inequalities involving one variable.

Assessments:

 PA.A.3.1, PA.A.3.2

PA.A.4.1

PA.A.4.2, PA.A.4.3

Unit 3:  Linear Equations and Functions

Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determine the value of the dependent variable.

Use linear functions to represent and explain real-world and mathematical situations.

Identify a function as linear if it can be expressed in the form of y = mx + b or if its graph is a straight line.

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 graphical properties of linear functions including slope and intercepts.  Know that the slope equals the rate of change, an that the y-intercept is zero when the function represents a proportional relationship.

Predict the effect on the graph of a linear function when the slope of y-intercept changes.  Use appropriate tools to examine these effects.

Solve problems involving linear functions and interpret results in the original context. 

Collect, display and interpret data using scatterplots.  Use the shape of the scatterplot to informally estimate a line of best fit.  Use appropriate titles, labels and units.

Assessments:

PA.A.1.1, PA.A.1.2, PA.A1.3,

PA.A.2.1, PA.A2.2

PA.A.2.3, PA.A.2.4

PA.A.2.5, PA.D.1.3

Unit 4:  Exponents

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 number expressed in scientific notation, expressing the answer in scientific notation.

Assessment:

PA.N.1.1, PA.N.1.2, PA.N.1.3

Dec 16 - 20

Assessment:

Semester Test: Units 1 - 4

Unit 5:  Pythagorean Theorem

Informally justify the Pythagorean Theorem using measurements, diagrams, or dynamic software and use the Pythagorean Theorem to solve problems in two ant three dimensions involving right triangles.

Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane.

Assessment:

PA.GM.1.1, PA.GM.1.2

Unit 6:  Surface Area and Volume

Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate measurements such as square cm.

Calculate the surface area of a cylinder, in terms of pi, using decomposition or nets.  Use appropriate measurements such as square cm.

Develop and use the formulas V = lwh and V = Bh to determine the volume of rectangular prisms.  Justify why base area (B) and height (h) are multiplied to find the volume of a rectangular prism.  Use appropriate measurements such as cubic cm.

Develop and use the formulas  V = pi (r^2)h and V = Bh to determine the volume of right cylinders, in terms of pi and using approximations for pi.  Justify why base are (B) and height (h) are multiplied to fine the volume of a right cylinder.  Use appropriate measurements such as cubic cm.

Assessment:

PA.GM.2.1, PA.GM.2.2,PA.GM.2.3, PA.GM.2.4

Unit 7:  Measurements of Central Tendency

Describe the impact that inserting or deleting a data pint has on the mean an 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.

Assessment:

PA.D.1.1. PA.D.1.2

Unit 8: Probability

Calculate experimental probabilities and represent them as percents, fractions, an decimals between 0 and 1 inclusive,.  Use experimental probabilities to make predictions when actual probabilities are unknown.

Determine how samples are chose (random, limited, biased) to draw and support conclusions about generalizing a sample to a population.

Compare and contrast dependent and independent events.

Assessment:

PA.D.2.1, PA.D.2.2, PA.D.2.3

Mar 9 - 12

Mar 13 - 20

Mar 23 -231

April 1 - 26

Assessment:

State Test