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East Bernstadt Independent Mathematics Pacing/Curriculum Mapping Document Algebra 1 Unit/ Linear and Exponential Relationships – Instructional Days 31 - 90 Time Standard(s) *Several 8th grade standards overlap the Algebra 1 high school standards, but both are listed. 8.F.4 – construct a function to model a linear relationship between two quantities, identifying and interpreting the rate of change as slope and the y-intercept as the initial value of the function. 8.F.5 – graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different way. 8.F.2 – compare the properties of two functions. 8.F.3 – interpret the equation y = mx + b. 8.F.6 – use similar triangles to explain why the slope if the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx and y = mx + b. 8.EE.8 – analyze and solve pairs of simultaneous linear equations. N.RN.1 – explain how the definition of the meaning rational exponents follows from extending the properties of integer exponents to those values. N.RN.2 – rewrite expressions involving radicals and rational exponents using the properties of exponents. A.REI.5 – prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A.REI.6 – solve systems of linear equations exactly and approximately. A.REI.10 – understand that the graph of an equation is the set of all of its solutions. A.REI.11 – explain why the x-coordinate of the intersection point is the solution and use technology to graph the system. A.REI.12 – graph the solutions to a linear inequality in two variables. F.IF.1 – understand the domain and range of a function. F.IF.2 – use function notation, evaluate functions for inputs, and interpret statements that use function notation. F.IF.3 – recognize that sequences are functions, recursive or explicit. F.IF.4 – interpret key features of graphs and tables of functions. F.IF.5 – relate the domain of a function to its graph. F.IF.6 – calculate and interpret the average rate of change of a function over a specified interval. F.IF.7 – graph funtions expressed symbolically and show key features of the graph. F.IF.9 – compare properties of two functions each represented in different ways. F.BF.1 – write a function that describes a relationship between two quantities. F.BF.2 – write arithmetic and geometric sequences both recursively and explicitly. F.BF.3 – identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x+k). F.LE.1 – distinguish between situations that can be modeled with linear and exponential functions. F.LE.2 – construct linear and exponential functions. F.LE.3 – observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or as a polynomial function. Learning Target(s) Knowledge, Reasoning, Skill, Product) Formative Assessment (match target to I can… assessment) 1. Write equations from proportional relationships. 2. Determine whether a relationship between two CBM week 7 - #1-4 quantities is proportional and/or a linear function. CBM week 8 - #1-5 3. Compare properties of two functions represented in CBM week 9 - #6-7 different ways by interpreting the slope and y-intercept CBM week 10 - #6-8 in terms of context. CBM week 11 - #9-13 4. Use similar triangles to explain slope in the coordinate CBM week 12 - #9-13 plane. CBM week 13 - #9-15 5. Extend properties of exponents to rational exponents. CBM week 14 - #16-17 6. Analyze and solve linear equations and pairs of CBM week 15 - #16-17 East Bernstadt Independent Mathematics Pacing/Curriculum Mapping Document Algebra 1 simultaneous linear equations. 7. Solve systems of linear equations. 8. Represent and solve equations and inequalities graphically. 9. Define, evaluate, and compare functions. 10. Understand the concept of a function and use function notation. 11. Use functions to model relationships between quantities. 12. Interpret functions that arise in applications in terms of context. 13. Analyze functions using different representations. 14. Build a function that models a relationship between two quantities. 15. Build new functions from existing functions. 16. Construct and compare linear, quadratic, and exponential models and solve problems. 17. Interpret expressions for functions in terms of the situation they model. Vocabulary Rate of change Constant of proportionality Equivalent ratios Function Linear Nonlinear Slope y-intercept system of linear equations linear inequality solution exponential growth decay regression quadratic polynomial Resources Go Math – Algebra 1 Chapters 5-11 ThinkCentral Study Island National Library of Virtual Manipulatives (NLVM) CBM week 16 - #9-17 Unit 2 test – Linear and Exponential Relationships Instructional Strategies Reciprocal Teaching Collaborative Grouping Questioning Discussion Kagan Structures Technology SmartBoard ThinkCentral Interactive Study Island NLVM Summative Assessment Unit Assessment – Algebra 1 Unit 2 Linear and Exponential Relationships TEST Small Group / Learning Centers Small groups Hands-on activity - Match Game – Function/equation/graph East Bernstadt Independent Mathematics Pacing/Curriculum Mapping Document Algebra 1 Reciprocal Learning groups – real-world problems Program Review Extended response – writing evidence Art – poster – Company A vs. Company B, Profit vs. cost0 Unit/ Time Name of Unit or Theme- 4 Weeks; Aug. ___ - Aug. ______ Writing Standard(s) Concepts/Skills (label introduce, review, mastery) Week 1 Learning Target(s) Knowledge, Reasoning, Skill, Product) Formative Assessment (match target to assessment) Instructional Strategies Vocabulary Resources Technology Portfolio Connection East Bernstadt Independent Mathematics Conferencing- Learning Centers Pacing/Curriculum Mapping Document Algebra 1