Danville District #118 Mathematics Transitional Algebra (PARCC Framework version) Curriculum and Scope and Sequence
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1 The eight Mathematical Practices will be incorporated throughout the course: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. The Mathematics Standard Modeling will be incorporated throughout the course. The Number & Quantity Standards listed below will be incorporated throughout the course. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. (N-Q.1) Define appropriate quantities for the purpose of descriptive modeling. (N-Q.2) Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. (N-Q.3) 1
2 Unit One Rational and irrational numbers 2 weeks Know that there are numbers that are not rational, and The student will be able to: Inquiry Centers approximate them by rational numbers. (8.NS.A) Know that numbers that are not rational are called Identify functions from Problem-Based Learning irrational. Understand informally that every number graphs, data sets, verbal has a decimal expansion; for rational numbers show scenarios that the decimal expansion repeats eventually, and Identify the characteristics of engagement activities convert a decimal expansion which repeats eventually a function, including domain (see Teacher-Created into a rational number.(8.ns.a1) Classify polynomials based on highest degree and Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. (8.NS.A2) Work with radicals and integer exponents.(8.ee.a) Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that is irrational. (8.EE.A2) number of terms Evaluate functions for given values Write functions based on given criteria - Pizzazz book 1 AGS Algebra 2
3 Unit Two Pythagorean Theorem 3 weeks Common Core Standards Objectives Actions Resources The student will be able to: Inquiry Centers Understand and apply the Pythagorean Theorem.(8.G.B) Solve multi-step linear Problem-Based Learning Explain a proof of the Pythagorean Theorem and its equations converse. (8.G.B6) Solve quadratic equations Apply the Pythagorean Theorem to determine Solve linear inequalities engagement activities unknown side lengths in right triangles in real-worl (see Teacher-Created and mathematical problems in two and three dimensions. (8.G.B7) Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (8.G.B8) - Pizzazz book 1 AGS Algebra 3
4 4
5 Unit Three Functions 2 weeks The student will be able to: Inquiry Centers Define, evaluate, and compare functions. (8.F.A) Understand that a function is a rule that assigns to each Perform operations on Problem-Based Learning input exactly one output. The graph of a function is the set polynomials of ordered pairs consisting of an input and the Completely factor corresponding output. (8.F.A1) polynomials engagement activities Compare properties of two functions each represented in (see Teacher-Created a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (8.F.A2) Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. (8.F.A3) Use functions to model relationships between quantities. (8.F.B) Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. (8.F.B5) - Pizzazz book 1 AGS Algebra 5
6 6
7 Unit Four Introduction to linearity 3 weeks Common Core Standards Objectives Actions Resources The student will be able to: Inquiry Centers Understand the connections between proportional Represent and interpret the relationships, lines, and linear equations. (8.EE.B) equation of a line Problem-Based Learning Graph proportional relationships, interpreting the unit graphically, verbally, rate as the slope of the graph. Compare two different numerically, algebraically in proportional relationships represented in different the appropriate form based ways. (8.EE.B5) on the given information Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. (8.EE.B6) Use functions to model relationships between quantities. (8.F.B) Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. (8.F.B4) Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. (8.F.B5) Determine the equation of a line given a variety of information Apply properties of linear graphs to statistics engagement activities (see Teacher-Created - Pizzazz book 1 AGS Algebra 7
8 Unit Five Patterns of association in bivariate data 4 weeks Investigate patterns of association in bivariate data The student will be able to: Inquiry Centers (8.SP.A) Construct and interpret scatter plots for bivariate Solve a system of linear Problem-Based Learning measurement data to investigate patterns of association equations algebraically and between two quantities. Describe patterns such as graphically clustering, outliers, positive or negative association, Solve a system of linear engagement activities linear association, and nonlinear association. inequalities graphically (see Teacher-Created (8.SP.A.1) Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. (8.SP.A.2) Use the equations of a linear model to solve problems in the text of bivariate measurement data, interpreting the slope and the intercept (8.SP.A.3) Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on a two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe the possible association between the two variables. - Pizzazz book 1 AGS Algebra 8
9 (8.SP.A.4) Unit Six Nonlinear functions 3 weeks Define, evaluate and compare functions. (8.F.A) The student will be able to: Inquiry Centers Give ples of functions that are non linear (8.F.A.3) Solve a system of linear Problem-Based Learning Use functions to model relationships between equations algebraically and quantities (8.F.B) graphically Describe quantitatively the functional relationship Solve a system of linear engagement activities between two quantities by analyzing a graph. inequalities graphically (see Teacher-Created Sketch a graph the exhibits the qualitative features of a function that has been described verbally (8.F.B.5) - Pizzazz book 1 AGS Algebra 9
10 Unit Seven Solving linear equations 3 weeks Analyze and solve linear equations and pairs of The student will be able to: Inquiry Centers simultaneous linear equations (8.EE.C) Solve linear equations in one variable. (8.EE.C.7) Solve a system of linear Problem-Based Learning Give ples of linear equations in one variable equations algebraically and with one solution, infinitely many solutions, or graphically nom solution.. Show which of these possibilities Solve a system of linear engagement activities is the case by successively transforming the given inequalities graphically (see Teacher-Created equation into simpler forms, until an equivalent equation of the form x=a, a=a or a=b results. (8.EE.C.7.a) Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. (8.EE.C.7.b) - Pizzazz book 1 10
11 AGS Algebra Unit Eight systems of linear equations 4 weeks Analyze and solve linear equations and pairs of The student will be able to: Inquiry Centers simultaneous linear equations (8.EE.C) Analyze and solve pairs of simultaneous Solve a system of linear Problem-Based Learning equations(8.ee.c.8) equations algebraically and Understand that solutions to a system of two linear graphically equations in two variables corresponds to points of Solve a system of linear engagement activities intersection of their graphs, because points of inequalities graphically (see Teacher-Created intersection satisfy both equations simultaneously (8.EE.C.8.a) Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations (8.EE.C.8.b) Solve real-world and mathematical problems leading to two linear equations in two variables. (8.EE.C.8.c) - Pizzazz book 1 11
12 AGS Algebra Unit Nine Exponents and scientific notation 3 weeks Work with radicals and integer exponents. (8.EE.A) The student will be able to: Inquiry Centers Know and apply the properties of integer exponents to generate equivalent numerical expressions. (8.EE.A1) Solve a system of linear Problem-Based Learning Use numbers expressed in the form of a single digit equations algebraically and times an integer power of 10 to estimate very large or graphically very small quantities, and to express how many times Solve a system of linear as much one is than the other. (8.EE.A3) inequalities graphically Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. (8.EE.A4) engagement activities (see Teacher-Created - Pizzazz 12
13 book 1 AGS Algebra 13
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