Topic: Expressions, Equations and Functions Days: 13 Key Learning: Expressions, equations, tables and graphs are used to model realworld situations. Unit Essential Question(s): How do you write and evaluate algebraic expressions? How can algebraic expressions and equations represent actual situations? Evaluate expressions M11.A.2.2.1, M11.A.3.1.1, 2.1.8.E, 2.1.8.B, 2.2.8.A Write expressions, equations, inequalities M11.D.1.1.1, 2.8.8.C Represent functions as rules, tables, graphs M11.D.1.1.1, M11.D.1.1.2, M11.D.1.1.3, M11.D. 2.1.2, 2.8.8.B, 2.5.8.B, 2.11.8.C, M8.D.1.1.1, M8.D. 1.1.3 How do you evaluate expressions? How do you write expressions from (ET) verbal models? (A) How do you write equations and inequalities from verbal models? (ET) What is a function and how can it be represented with an equation, a table of values and a graph? (ET) PEMDAS (Order of Operations), verbal model, unit rate,, function, range, domain, input, output substitution, power, base, exponent Additional Information: Attached Document(s):
Topic: Expressions, Equations and Functions Concept: Evaluate expressions PEMDAS (Order of Operations) - substitution - power - base - exponent - Days: 13 Concept: Write expressions, equations, inequalities verbal model - unit rate - - - Concept: Represent functions as rules, tables, graphs function - range - function domain range input output domain - input - output -
Topic: Properties of real numbers Days: 20 Key Learning: Our real number system is infinite and can be represented in multiple ways. How can we represent numbers in multiple ways using operations and symbols? Unit Essential Question(s): Graph and compare. Operations Simplify. M11.A.1.1.1, M11.A.1.3.1, M11.A.1.3.2, M11.A. M11.A.2.1.1, 2.4.8.D, 2.1.8.F M11.D.2.2.1 3.2.1, 2.1.8.C, 2.2.8.C, 2.4.8.B, 2.1.8.A, 2.2.8.B What are the different types of numbers and how do you find the absolute value of these numbers? (ET) How do you add and subtract rational numbers? (A) When do you use the distributive property and how do you use it? (A) What are the properties that we use in multiplying and adding numbers? (A) What are like terms and how do you combine them? (A) How do you multiply and divide rationals? (A) How do you evaluate square roots and compare them with other number types? (ET) integers, rational number, irrational numbers, opposites, absolute value additive identity, additive inverse, multiplicative identity, multiplicative inverse, reciprocal distributive property, coefficient, constant, term, like terms Additional Information: Attached Document(s):
Topic: Properties of real numbers Concept: Graph and compare. integers - rational number - irrational numbers - opposites - absolute value - Days: 20 Concept: Operations additive identity - additive inverse - multiplicative identity - multiplicative inverse - reciprocal - Concept: Simplify. distributive property - coefficient - constant - term - like terms -
Topic: Solving Equations Days: 17 Key Learning: To solve equations, you perform inverse operations to both sides of the equation to isolate a variable. Unit Essential Question(s): How do you solve equations? Solving equations M11.D.2.1.3, M11.A.2.1.1, M8.D.2.1.1 M11.D.2.1.3 Literal equations What steps are used to solve equations with a variable on one side? (A) How do equation solving steps help us rewrite equations and formulas? (ET) What process do you use when representing a word problem as an equation? (A) How can you apply equations to solve real life problems? (ET) What steps are used to solve equations with variables on both sides? (A) How do you solve equations which contain fractions? (A) Inverse Operations, equivalent equations, Identity, complementary and supplementary angles, corresponding, vertical and adjacent angles, alternate interior and alternate exterior angles literal equation Additional Information: Include angle types in this unit. Attached Document(s):
Topic: Solving Equations Concept: Solving equations Inverse Operations - equivalent equations - Identity - complementary and supplementary angles - corresponding, vertical and adjacent angles - alternate interior and alternate exterior angles - Days: 17 Concept: Literal equations literal equation -
Topic: Solving Proportions Days: 15 Key Learning: Proportions are a powerful tool for problem solving. How can real life problems be modeled and solved using proportions? Unit Essential Question(s): Ratios and Proportions M11.A.2.1.3, M11.A.2.1.1, 2.1.8.D, 2.2.8.D, 2.2.8.E, 2.2.8.F Solving Problems with Proportions 2.1.8.D, 2.8.11.D, 2.4.11.E, M11.A.2.1.1, M11.A. 2.1.3 What is a proportion? (A) How do we use proportions to solve rate problems? (ET) How do you create an equation from a proportion? (A) How can you solve percent problems using proportions? (ET) How can you find the percent of change? (ET) How can proportions be used to solve problems involving similar triangles? (ET) How can proportions be used to solve scale problems? (ET) cross product similar triangles Additional Information: Commission and sales tax must be included with the percent EQ. Attached Document(s):
Topic: Solving Proportions Concept: Ratios and Proportions cross product - Days: 15 Concept: Solving Problems with Proportions similar triangles -
Topic: Graphing Linear Functions Days: 15 Key Learning: The graph of a linear functions shows the relationship between two variables. Unit Essential Question(s): What information do you need to graph a linear function? Graph using a table. Graph using intercepts Slope and rate of change M11.D.4.1.1, M11.D.2.1.2 M11.D.2.1.2 M11.D.3.1.1, M11.D.3.2.1 What are the parts of a coordinate How do you use intercepts to graph a What is slope and how do you find it? plane? (A) linear function? (ET) (A) How do you graph a linear equation using a table? (A) How do you graph equations which contain only one variable? (A) What is "Rate of Change" and how do you find it? (ET) quadrant, axis, origin, ordered pair, x-intercept, y-intercept, Standard form rise, run, slope, rate of change linear function Graph using slope intercept form M11.D.3.2.3, M11.D.2.1.2 Function Notation 2.8.11.Q What are "m" and "b" and how do you How do you use and interpret function use them to graph linear functions? (A) notation? (A) What is true about the equations of lines that are parallel? (A) slope-intercept form Additional Information: Attached Document(s):
Topic: Graphing Linear Functions Concept: Graph using a table. quadrant - axis - origin - ordered pair - linear function - Days: 15 Concept: Graph using intercepts x-intercept - y-intercept - Standard form - Concept: Slope and rate of change rise - run - slope - rate of change - Concept: Graph using slope intercept form slope-intercept form -
Topic: Writing linear functions Days: 17 Key Learning: Equations can be written to fit data and used to make predictions about the data. Unit Essential Question(s): How do you write the equation of a line? write linear equation M11.D.3.1.1, M11.D.3.2.1, M11.D.3.2.2, M11.D. 3.2.3, M11.D.4.1.1, M11.D.2.1.3 parallel and perpendicular lines M11.C.3.1.2, M11.D.3.2.3, M11.D.3.2.2, M11.D. 3.2.1, M11.D.4.1.1, M11.D.2.1.3 scatter plots and linear regression M11.D.2.1.3, M11.D.3.2.1, M11.D.3.2.2 How do you use slope and y-intercept to write the equation of a line? (A) How do you write the equation of a line given two points on a line? (A) How do you write the equation of a line given the slope and a point on the line? (A) How do you use slope to find the equation of a parallel or perpendicular line? (A) How do you find the equation of a line of best fit and make a prediction on the line of best fit? (ET) How do you use a graphing calculator to create a scatterplot and calculate the linear regression equation? (ET) parallel, perpendicular scatter plot, positive correlation, negative correlation, no correlation, line of best fit, trend line, linear regression Additional Information: Attached Document(s):
Topic: Writing linear functions Concept: write linear equation - Days: 17 Concept: parallel and perpendicular lines parallel - perpendicular - Concept: scatter plots and linear regression scatter plot - positive correlation - negative correlation - no correlation - line of best fit - trend line - linear regression -
Topic: Inequalities Days: 14 Key Learning: Linear inequalities and absolute value equations and inequalities have unique graphs. How are solutions to linear inequalities and absolute value equations and inequalities represented? Unit Essential Question(s): Inequalities in one variables M11.D.2.1.1 Absolute value equations and inequalities M11.D.2.1.1 Inequalities in two variables M11.D.2.1.2 How do you graph the solution to an How do you solve absolute value How do you graph a linear inequality inequality? (A) equations? (ET) in two variable? (ET) How do you solve an inequality? (Key Question: What happens when you multiply or divide by a negative?) (A) How do you solve and graph the solution to compound inequalities? (ET) How do you solve and graph the solutions to absolute value inequalities? (ET) How do you determine algebraically and graphically if an ordered pair is a solution? (ET) compound inequality absolute deviation linear inequality in two variables, boundary line, boundary line Additional Information: Attached Document(s):
Topic: Inequalities Concept: Inequalities in one variables compound inequality - Days: 14 Concept: Absolute value equations and inequalities absolute deviation - Concept: Inequalities in two variables linear inequality in two variables - boundary line - boundary line -
Topic: Laws of Exponents Days: 20 Key Learning: Several properties of exponents can be used to simplify expressions containing positive, negative and zero exponents. Why do we need to know how to simplify exponential expressions? Unit Essential Question(s): products and quotients M11.A.2.2.1, M11.A.2.2.2 zero and negative exponents M11.A.2.2.1, M11.A.2.2.2 scientific notation M11.A.1.1.2, M11.A.2.2.1 How can you convert between exponential expressions and expanded notation? (A) How do you simplify expressions containing zero and negative exponents? (A) How can you convert between scientific and standard notation? (A) What is meant by "simplifying a power to a power", "simplifying a product of powers", and "simplifying a power of a product"? (A) What is meant by "simplifying a power to a power", "simplifying a product of powers", and "simplifying a power of a product"? (ET) What is meant by "simplifying a Quotient of Powers"? (A) What is meant by "simplifying a Quotient of Powers"? (ET) How do you simplify expressions containing zero and negative exponents? (ET) How can you compute with numbers in scientific notation? (ET) power, exponent, base Additional Information: Attached Document(s):
Topic: Laws of Exponents Concept: products and quotients power - exponent - base - Days: 20
Topic: Polynomials Subject Area(s): Days: 25 Key Learning: Operations can be performed on polynomials. Equations can be written using polynomials to allow us to solve problems. How can we perform operations on polynomials and how can the operations help us solve problems? Unit Essential Question(s): Sums, Differences and Products M11.D.2.2.1 Factoring M11.A.1.2.1, M11.D.2.2.2 Solve quadratic equations M11.D.2.1.5 How can polynomials be classified and What patterns can be used to find How do you use the Zero-Product identified? (A) some products quickly? (ET) Property? (A) How do you add and subtract polynomials? (A) How can sums or differences of polynomials be used to solve problems? (ET) How can multiplication with polynomials be performed? (A) How can area problems be solved using products of polynomials? (ET) How do you factor polynomials of the form x2 + bx + c? (A) How do you factor polynomials of the form ax2 + bx + c? (A) How do you use special products to factor special polynomials? (ET) How can terms be grouped to facilitate factoring? (ET) How can complete factoring be used to solve polynomial equations? (ET) How can you create and solve a polynomial equation that models area and vertical motion? (ET) binomial, trinomial, polynomial, FOIL root, zero of a function, perfect square degree, leading coefficient, monomial trinomial Additional Information: Methods for multiplying polynomials can include: 1. distributive property 2. columns 3. FOIL 4. table Attached Document(s):
Topic: Polynomials Subject Area(s): Concept: Sums, Differences and Products binomial - trinomial - polynomial - degree - leading coefficient - monomial - Days: 25 Concept: Factoring FOIL - Concept: Solve quadratic equations root - zero of a function - perfect square trinomial -
Topic: Radicals Subject Area(s): Days: 21 Grade(s): Key Learning: Radical expressions can be simplified. Graphs of radical equations can be compared and applied to real life situations. How can radical equations and their graphs be used to model real life problems? Unit Essential Question(s): Graphs of radical functions M11.D.2.1.2 Simplify radical expressions M11.A.1.1.3, M11.A.1.1.1 Operations on radical expressions M11.A.2.2.1 How do you graph the parent square How do you add and subtract radical root function? (A) expressions? (A) How do operations performed on the parent square root function change its graph? (ET) How do you use the Product Property of Radicals to simplify a radical expression? (A) How do you multiply radical expressions? (A) How do you use the Quotient Property of Radicals to simplify radical expressions? (A) How do you rationalize the denominator of a radical expression? (A) How do you multiply radical expressions? (A) What makes radical terms "like terms"? (ET) radical expression, radical function, square root function, parent square root function simplest form of a radical expression, rationalizing the denominator, conjugates Page 1 of 2
Topic: Radicals Subject Area(s): Days: 21 Grade(s): Solve radical equations M11.D.2.1.5 Pythagorean Theorem and related formulas M11.C.3.1.1, M11.C.1.4.1, 2.10.11.B How do you solve a radical equation? (A) How can radical equations be used to solve real life problems? (ET) Why can radical equations have extraneous solutions? (ET) How can you find the distance between 2 points in the coordinate plane? (A) How can you find the midpoint of a line segment given coordinates of its endpoints? (A) How can the Distance and Midpoint formulas be used to solve real life problems? (ET) radical equation, extraneous solution hypotenuse, legs of a right triangle,, midpoint, midpoint formula, distance formula Additional Information: Attached Document(s): Page 2 of 2
Topic: Radicals Subject Area(s): Days: 21 Grade(s): Concept: Graphs of radical functions radical expression - radical function - square root function - parent square root function - Concept: Simplify radical expressions simplest form of a radical expression - rationalizing the denominator - conjugates - Concept: Solve radical equations radical equation - extraneous solution - Concept: Pythagorean Theorem and related formulas hypotenuse - legs of a right triangle - - Pythagorean Theorem midpoint - midpoint formula - distance formula -
Topic: PSSA Prep Days: 7 Key Learning: Formulas and shortcuts can be used to solve problems. What formulas and shortcuts are helpful for solving problems? Unit Essential Question(s): Formulas M8.A.2.2.2, M8.B.2.3.1, M8.B.2.3.2, 2.5.8.B, 2.3.8.B, 2.9.8.C, M8.B.2.1.1, M8.B.2.1.3, M8.B. 2.1.2, 2.3.8.A, 2.3.8.E, M8.B.1.1.4 Pythagorean Theorem M8.C.1.2.1, 2.5.8.B, 2.10.8.A Mental Math with Percents M8.A.3.2.1 How are formulas for area, perimeter What is the Pythagorean Theorem? (A) How can shortcuts be used to find and surface area used? (ET) percents of numbers? (ET) How are formulas used with angle measures? (ET) How are temperature conversions made? (ET) How can the Pythagorean Theorem be used to solve problems? (ET) area, perimeter, surface area, simple interest, rate, regular polygon, irregular polygon, volume Pythagorean Theorem, hypotenuse, leg, square root Additional Information: Attached Document(s):
Topic: PSSA Prep Concept: Formulas area - perimeter - surface area - simple interest - rate - regular polygon - irregular polygon - volume - Days: 7 Concept: Pythagorean Theorem Pythagorean Theorem - hypotenuse - leg - square root -
Topic: Data and Statistics Days: 10 Key Learning: Data can be analyzed and used to make decisions Unit Essential Question(s): What can we do with data? Box and Whisker Plots 2.6.8.A, 2.6.8.E, M8.E.1.1.3, M8.E.4.1.2 Scatterplots 2.6.8.C, M8.E.4.1.1, M8.E.4.1.2 Use of Different Graph Types 2.4.8.F, 2.5.8.A, M8.E.1.1.1, M8.E.1.1.2, M8.E.4.1.2 How is a Box and Whisker Plot made? What is a scatterplot? (A) When is it best to use different graph (A) types? (A) What are quartiles and the IQR and what do they show? (ET) What do the types of correlation look like and what do they mean? (A) How can we make predictions using data in a scatterplot? (ET) When is it best to use different graph types? (ET) box and whisker plot, quartiles, interquartile range (IQR), upper quartile, lower quartile, median scatterplot, correlation, line of best fit circle graph, line graph Additional Information: Students should recognize strong versus weak correlation. Review of multiple bar graphs, stem-and-leaf plots and histograms is provided in "Class Starters" in the PSSA Prep SmartBoard file Attached Document(s):
Topic: Data and Statistics Concept: Box and Whisker Plots box and whisker plot - quartiles - inter-quartile range (IQR) - upper quartile - lower quartile - median - Days: 10 Concept: Scatterplots scatterplot - correlation - line of best fit - Concept: Use of Different Graph Types circle graph - line graph -
Topic: Probability Days: 10 Key Learning: Probability can be used to compare and contrast, and to make predictions and inferences. Unit Essential Question(s): How can probabilty be used to make predictions? Simple Experimental and Theoretical Probability 2.7.8.D, 2.7.8.E, M8.E.3.1.1, 2.7.8.B, 2.7.8.C Compound Events M8.E.3.2.1, 2.7.8.B, 2.7.8.E, 2.7.8.D What is experimental probability and How can the total number of outcomes (A) how do you find it? (A) be found for compound events? (A) How can you use experimental probability to make predictions? (ET) What is theoretical probability and how do you find it? (A) How can you use theoretical probability to make predictions? (ET) How do you find the probability of compound events? (ET) How do you find the probability of independent and dependent events? (ET) experimental probability, theoretical probability, outcomes, sample space compound events, independent events, dependent events, tree diagram Additional Information: Permutations and combinations are found using lists and tree diagrams, not factorial formulas. Attached Document(s):
Topic: Probability Concept: Simple Experimental and Theoretical Probability experimental probability - theoretical probability - outcomes - sample space - Days: 10 Concept: Compound Events compound events - independent events - dependent events - tree diagram -