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1 Curriculum Map for Algebra I Pre-Algebra Review: 5 days (review Chapter) ( , , , ) Targeted NJ Core Curriculum Content Standards: A-SSE.A.1a, N-RN.B.3, A-CED.A.1, A-REI.D.10, A-REI.B.3, N-Q.A.3, N-Q.A.2 Enduring Understandings: Students will understand how to apply the rules of algebra to manipulate variables. Students will understand how to keep an equation balanced and how to solve for an unknown to solve for a solution. Students will understand the similarities and differences in solving inequalities versus equations. Essential Questions: How can we write an unknown as an algebraic expression? How can we evaluate algebraic expressions? How can we use the properties of algebra to simplify expressions? How can we isolate an unknown quantity? How can we apply the concept of equations to real world applications involving percents? Compare and contrast inequalities with equations? Why do we need to shade a region for an inequality? What does the line represent in the inequality? Concepts What students will know 1. understand how unknown items can be written using variables 2. understand how to use expressions to evaluate specific instances 3. understand the properties of real numbers Core Content/Objectives Skills What students will be able to do 1. Write an expression using addition, subtraction, multiplication, and/or division 2. Translate words into an expression 3. Write Rules to describe a pattern 4. Simplify a numerical expression with multiple operations 5. Evaluate algebraic expressions with multiple operations Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Due to the review of this chapter, use the book activities and extensions to give added dimension. Use graphing calculator to explore tables. Specifically use the extension on 3.4 Instructional Actions Assessment How learning will be assessed Test Daily Homework 1

2 4. understand the importance of order of operations 5. understand how algebraic expressions can be manipulated 6. understand how data can be represented in different forms such as tables, graphs, and equations 7. understand how the math concepts apply to modeling problems 8. Understand the operations needed to isolate an unknown in an equation 9. Apply the concept of an equation to modeling problems 10. Apply the concept of an equation to proportions and percents 11. To apply the procedures of equations to inequalities 12. Understand the distinction between and equation and an inequality 13. Interpret and write an inequality in different forms 6. Evaluate real world expressions 7. Simplify Square root expressions 8. Estimate a square root 9. Classify Real numbers 10. Compare, graph and order Real numbers 11. Identify Properties of real numbers 12. Use properties for mental calculations. 13. Write Equivalent expressions using different properties 14. Understand counterexamples of properties 15. Add and subtract positive and negative real numbers (including whole, decimals, and fractions) without a calculator 16. multiply and divide real numbers (including whole, decimal, and fractions without a calculator) 17. Simplify square root expressions 18. Simplify expressions using the distributive property 19. Rewrite fractional expressions 20. Use the multiplication property of Use the distributive property for mental math 22. Combine like terms 23. Classify equations as true or false statements 2

3 24. Identify solutions of an equation 25. Solve multi step equations involving distributive property, fractions, and decimals 26. Use equations to model word problems 27. Solve equations with variables on both sides 28. Use equations to model word problems 29. Identify equations with no solution or infinite solutions 30. Use proportions or percent equation to find the percent, part, or whole (base) 31. Find the percent decrease, increase, error given a word problem 32. Solve multi step inequalities(distributive property, variables on both sides, combine like terms) 33. Understand solutions to inequalities. 34.Write and solve multi step inequalities 35. Solve inequalities with no solution and infinite solutions Resources/Technology: Graphing Calculator, possibly videos to guide review, ELMO 3

4 Ch1-2 Modeling: 6 days (review Chapter): (1.9, 2.5, 2.6, 2.7, 2.8, 2.10 (percent error) Targeted NJ Core Curriculum Content Standards: A-REI.D.10, A- CED.A.2, A-CED.A.4, A-REI.A.1, N-Q-A.1, A-REI.B.3, A-CED.A.1, N-Q.A.2 Enduring Understandings: Students will understand how to keep an equation balanced and how to solve for an unknown to solve for a solution. Students will understand how multiple models can be used to interpret a real-world situation. Students will use proportional relationships to solve for unknown values. Students will use real world models to create and solve proportions. Essential Questions: How can we isolate an unknown quantity? How can we apply the concept of equations to real world applications involving proportions and percents? How can we use tables, graphs, and equations to model a real world situation? Concepts What students will know 1. understand how data can be represented in different forms such as tables, graphs, and equations 2. understand how the math concepts apply to modeling problems 3. Apply the concept of an equation to modeling problems 4. Apply the concept of an equation to proportions and percents Core Content/Objectives Skills What students will be able to do 1. Write an equation from a word problem 2. Use mental math, tables and estimation to find solutions 3. Identify if an order pair is a solution 4. Using Tables, equations, and graphs as multiple representations of data 5. Solve a literal equation/formula for certain variable 6. Understand the solution of a literal equation in a real world example 7. Substitute values and connect to real world meaning Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Due to this chapter being a review, use the activities and extensions in the book as motivation for the unit. Spend an entire day using modeling activity Instructional Actions Assessment How learning will be assessed Test Daily Homework 4

5 8. Use ratios to compare unit rates, convert units, convert rates, and convert between systems 9. Use cross products to solve MULTIstep proportions 10. Use proportions to solve word problems 11. Use proportions and similar figures to find the length of a side 12. Use similarity to solve word problems 13.Interpret scale drawings 14. Interpret scale models 15. Use proportions or percent equation to find the percent, part, or whole (base) 16.Solve word problems using simple interest formula 17. Find the percent decrease, increase, error given a word problem 18. Find minimum and maximum dimensions 19. Find the greatest possible percent error Resources/Technology: Graphing Calculator, possibly videos to guide review, ELMO 5

6 Ch 3: 7 days (review Chapter): Pair 3.5 & 3.8 together before 3.6 & 3.7 Targeted NJ Core Curriculum Content Standards: A-REI.B.3, A-CED.A.1, A-SSE.A.1b Enduring Understandings: Students will understand the similarities and differences in solving inequalities versus equations. Students will interpret the meaning of the solutions to absolute value equations and inequalities. Essential Questions: Compare and contrast inequalities with equations? Why do we need to shade a region for an inequality? What does the line represent in the inequality? What does the absolute value equation represent and how are they related to inequalities? Core Content/Objectives Concepts What students will know 1. To apply the procedures of equations to inequalities 2. Understand the distinction between and equation and an inequality 3. Interpret and write an inequality in different forms 4. Understand the connection of equations and inequalities to absolute value problems Skills What students will be able to do 1. Solve multi step inequalities(distributive property, variables on both sides, combine like terms) 2. Understand solutions to inequalities 3. Write and solve multi step inequalities 4. Solve inequalities with no solution and infinite solutions 5. Write a compound inequality from a verbal expression 6. Solve a compound inequality involving and/or 7. express solutions using interval notation 8. Solve an absolute value equation Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Due to this chapter being a review, use the activities and extensions in the book as motivation for the unit. Specifically use the extension on 3.4 Spend at least one day dedicated to modeling problems Instructional Actions Assessment How learning will be assessed Test Daily Homework 6

7 and inequality 9. Solve an absolute value equation and inequality word problem 10. Solve absolute value equation with no solution Resources/Technology: Graphing Calculator, possibly videos to guide review, ELMO 7

8 Ch 4: 12 days (semi-review Chapter) ***try to complete before end of MP1 Targeted NJ Core Curriculum Content Standards: F-IF.B.4, A-REI.D.10, F-IF.B.5, N-Q.A.2, F-IF.A.1, F-IF.A.3 Enduring Understandings: The students will understand the concept of a function and how we can represent functions graphically, in a table, and by a rule. Essential Questions: What is a function? What distinguishes a linear function from non-linear functions? How can we write a rule for a relation? How does a linear function relate to an arithmetic sequence? Concepts What students will know 1. Understand the key features of graph or table and use it to describe the nature of the function 2. Understand the difference between a linear and non-linear function 3. Understand how to apply the evaluation of an expression to graphing a function 4. Understand the concept of a function and what makes a relation not a function Core Content/Objectives Skills What students will be able to do 1.Analyze graphs 2. Match tables and graphs 3. Sketch graphs 4. Understand and apply dependent variable, independent variable, input and output 5. Represent Geometric Relationships using tables words, equations and graphs 6. Represent linear functions using multiple representations 7. Understand the difference between linear and nonlinear functions shown by multiple representations 8. write rule to describe a nonlinear Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Use the 4.3 activity/extension Use the 4.4 activity/extension Spend at least one day dedicated to modeling problems Instructional Actions Assessment How learning will be assessed Test Quiz Daily Homework 8

9 5. Apply the concepts of linear function to an arithmetic sequence 6. Apply functions and graphing to modeling problems function 9. Interpret the rule of a function based on an equation 10.Graph a real world function and its reasonable solutions 11.Identify and understand the difference between continuous and discrete graphs 12. Graph nonlinear functions based on an equation 13. Write a function based on a real world situation 14. Evaluate a real world function 15. Write a non-linear function from a real world situation 16. Identify functions using mapping diagrams 17. Identify functions using the vertical line test 18. Evaluate a function using function notation 19. Find the range of a function giving a domain set 20. Identify a reasonable domain and range based on a word problem 21. Extend a sequence 22. Identify an arithmetic sequence 23. write a recursive formula 24. Write an explicit formula based on a word problem 25. Write an explicit formula from a 9

10 recursive formula 26. Write a recursive formula from an explicit formula Resources/Technology: Graphing Calculator, possibly videos to guide review, ELMO 10

11 Ch 5: 21 days (save 5.7 for statistics unit) ***(try to complete before Xmas Break) Targeted NJ Core Curriculum Content Standards: F-LE.A.1b, A-CED.A.2, F-IF.C.7a, F-LE.A.2, G-GPE.B.5, F-BF.B.3 Enduring Understandings: The students will understand the meaning of slope and the relationship it has in creating a line. The students will grasp the concept of a line and be able to represent it graphically and algebraically through an equation in multiple forms. Essential Questions: How is the rate of change related to slope? What are the advantages of the different forms of an equation of a line? How can we write an equation of a line given two points or a point and it s slope? How can we write a line that is either perpendicular or parallel to another line? What does the absolute value function look like and how can we translate it? How is this related to point slope form? Concepts What students will know 1. Understand the relationship between the rate of change and slope 2. Understand how the slope and another point on a line enables you to graph and find an equation 3. Understand the connection between the different forms of a line 4. Understand the connection between the slope formula and point slope form of a line Core Content/Objectives Skills What students will be able to do 1. Find the rate of change using a table 2. Find the slope using a graph 3. Find the slope using two points 4. Find the slope of horizontal and vertical lines 5. Identify a direct variation 6. Write a direct variation equation 7. Graph a direct variation 8. Write a direct variation from a table 9. Identify the slope and the y intercept 10. write an equation in slope intercept form 11. Write an equation from a graph 12. write an equation from two points Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections 5.8 Extension Activity Spend parts of lessons and an entire day completing modeling problems Instructional Actions Assessment How learning will be assessed Test Quiz Daily Homework 11

12 5. To understand and apply the relationship between parallel and perpendicular lines 6. To apply linear models to real world situations 7. To understand the connection between the translations of the absolute value curve and point slope form 8. To understand the translations apply to all functions 13.Graph a linear equation 14. Model a function 15. Write an equation in point slope form 16. Graph using point slope form 17. Use two points to write an equation 18.Use a table to write an equation 19. Find the x and y intercepts 20.Graph a line using the intercepts 21. Graph horizontal and vertical lines 22. Transform to standard form 23. Use standard for as a model and understand solutions 24. Write an equation of a line parallel to 25.Classify a line as a parallel to or perpendicular to 26. Write an equation of a perpendicular line 27. Solve real world problems involving parallel and perpendicular lines 28. Graph an absolute value function by shifting the parent function 29. Describe the translation that occurs 30. Graph a step function Resources/Technology: 12

13 Graphing Calculator, ELMO 13

14 Ch6: 11 days (try to complete before mid-term) Targeted NJ Core Curriculum Content Standards: A-REI.C.5, A-REI.C.6, A-REI.D.12 Enduring Understandings: The students will understand how to solve a system of equations and inequalities by finding the intersection or overlapping areas. Essential Questions: What does the solution of a system look graphically? How can we find the solution algebraically? How will the solutions of a system of inequalities differ from a system of linear equations? Concepts What students will know 1. Understand the graphical interpretation of a solution of a system 2. Apply the graphical interpretation to understand the infinite and no solution scenarios 3. To understand the algebraic laws that support solving systems algebraically 4. To understand why the shading and solid/dotted lines exist for a Core Content/Objectives Skills What students will be able to do 1. Solve a system of equations by graphing 2. Write a system of equations based on a real world situation 3. Graph systems with one, infinite, or no solution 4. Solve a system using substitution 5. Write a system of equations based on a real world situation, use substitution to solve 6. Use substitution to solve systems with infinite and no solution 7. Solve a system using elimination 8. Solving systems with infinite or no Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Spend parts of lessons and an entire day completing modeling problems Instructional Actions Assessment How learning will be assessed Test Quiz Daily Homework 14

15 linear inequality 5. To apply the concept of solving a system to a system of inequalities 6. To apply the concept of a system of equations and inequalities to real world situations solution 9.Using systems to solve real world situations 10. Determine which method is most appropriate 11. Understanding break even, constraints,and viable solutions 12. Identify whether an ordered pair as a solution to a linear inequality 13. Graph a linear inequality 14. Graph a linear inequality to solve a word problem 15. Graph a system of inequalities 16. Write a system based on the graph of inequalities 17. Use a system of linear inequalities to solve a real world problem Resources/Technology: Graphing Calculator, ELMO 15

16 Ch7: 12 days (try to complete before President s Day) Targeted NJ Core Curriculum Content Standards: N-RN.A.1, F-IF.C.7e, F-IF.C.8b, F-BF.A.2 Enduring Understandings: The students will understand the laws of exponents and be able to apply them to simplify and solve problems involving them. Essential Questions: How can we simplify an expression using the law of exponents? Compare and contrast an exponential equation to a linear equation? What does the graph of an exponential look like and how can we change it s appearance? How are geometric sequences related to exponential functions? Concepts What students will know 1. Understand the rules of exponents 2. To understand how to graph exponential functions using tables and calculator 3. To understand the connection between a system of linear equations and a system involving a linear and exponential equation 4. Understand the relationship between the exponential function and a geometric sequence Core Content/Objectives Skills What students will be able to do 1. Simplify expressions with zero and negative exponents 2. Evaluate expressions with zero and negative exponents 3. Use an exponential expression provided in a real world problem and find a solution 4. Multiply powers with same bases 5. Multiply algebraic expressions 6. Multiply with scientific notation 7. Simplify expressions with rational exponents 8. Simplify an exponent raised to a power Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Use problems and activities from book involving modeling problems Instructional Actions Assessment How learning will be assessed Test Quiz Daily Homework 16

17 5. To model real life situations using exponential functions 9. Simplify power to a power where further multiplication is necessary 10. Raising scientific notation to a power 11. Simplify exponents using division 12. Dividing numbers in scientific notation 13. Raise a quotient to a power 14. Simplify more difficult exponential expressions involving all the rules 15. Identify linear and exponential functions from a table 16. Evaluate an exponential function using function notation 17. Graph an exponential function 18. Graph an exponential model 19. Find the solution to a system of exponential and linear using a graphing calculator 20. Use exponential equations to model real world situations 21. Solve compound interest problems 22. Model Exponential decay and growth 23. Identify geometric sequences 24. Find the recursive and explicit formulas 25.Use sequences to solve real world problems 26. Write geometric sequences as 17

18 functions Resources/Technology: Graphing Calculator, ELMO 18

19 Chapter 8: 12 days Targeted NJ Core Curriculum Content Standards: A-APR.A.1, A-SSE.A.1a Enduring Understandings: The students need to understand how the inverse operations of multiplying and factoring are related in simplifying and expanding expressions, and the importance of these methods in other areas of math. Essential Questions: How can we rewrite an expression as a product or vice versa? Why is re-writing an expression important? Concepts What students will know 1. To understand how the algebraic rules for simplifying an algebraic expression into a product of its parts 2. To understand how to expand a polynomial using rules of multiplication and the distributive property Core Content/Objectives Skills What students will be able to do 1. Find the degree of a monomial 2.Add and subtract monomials 3. Classify polynomials 4. Multiply a monomial by a trinomial 5. Find the GCF of an expression 6. Factor out a GCF 7. Use factoring to solve real world problem 8. Multiple a binomial by a binomial 9. Multiply a binomial by a trinomial 10. Use multiplication to solve more difficult word problems 11. Use multiplication to square binomials 12. Apply squaring a binomial to a Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Use problems and activities from book involving modeling problems Spend at least one day reviewing all types of problems Instructional Actions Assessment How learning will be assessed Test Quiz Daily Homework 19

20 real world situation 13. Factor trinomials when a = Factor trinomials when a does not = 1 15.Apply factoring to area problems 16. Factor perfect square trinomials 17. Factor difference of two perfect squares 18. Factor completely (GCF the difference of two 19. Factor a cubic polynomial by grouping- 4 terms 20. Use factor by grouping to find the dimensions of a rectangular prism Resources/Technology: Graphing Calculator, ELMO 20

21 Targeted NJ Core Curriculum Content Standards: F-IF.C.7a, A-REI.B.4a, A-REI.B.4b Chapter 9: 15 days (**complete before PARCC) Enduring Understandings: Students will understand the distinguishing features of a quadratic model, and how to find these features graphically and algebraically. Essential Questions: What does the graph of the quadratic function look like and how can we find the key features of the graph? How can we solve a quadratic equation? What is the difference between a quadratic equation versus linear and exponential models? How is vertex form related to point slope form and translations? Concepts What students will know 1. Understand the differences between linear, quadratic, and exponential functions 2. Relate the vertex form of a quadratic to the translations of the absolute value function and to point slope form of a line 3. Apply the methods to find all important features of a quadratic graph Core Content/Objectives Skills What students will be able to do 1.Identify a vertex of a parabola as a max/min 2. Graph a quadratic using a table with vertex (0,0) 1.Find vertex using formula 2. identify axis of symmetry 3.graph parabola (Use table to identify points) 1 Solve a quadratic by graphing 2.Solve a quadratic using square roots 3.Determine reasonable solutions 1 Use the zero product property to Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Use problems and activities from book involving modeling problems, especially the activities in 9.2 and 9.4 Instructional Actions Assessment How learning will be assessed Test Quiz Daily Homework 21

22 4. Understand the advantages of the different methods of solving a quadratic 5. Apply the quadratic knowledge to real world modeling problems understand solutions 2.Solve quadratic by factoring 3. Solve quadratics not in standard form by factoring 4.Use factoring to solve real world problems 1 Find c value to complete the square 2.Solve a quadratic by completing the square 3. Find the vertex by completing the square 4. Complete the square when a does not equal 1 1.Use the quadratic formula to solve a quadratic 2. Solve world problems using the quadratic formula and discuss how solutions translate in real world problems 3.Identify the appropriate method used to solve a quadratic 4. Use the determinant to predict characteristics of solutions Resources/Technology: Graphing Calculator, ELMO 22

23 Targeted NJ Core Curriculum Content Standards: G-SRT.C.8, A-REI.A.2, F-IF.C.7.b, A-CED.A.2 Chapter 10: 9 days (skip 10.6) Enduring Understandings: Students will understand the distinguishing features of a radical model, and how to find these features graphically and algebraically. Essential Questions: How are radical expressions represented? What are the characteristics of square root functions? How can you solve a radical equation? Concepts What students will know 1. Solve problems using the Pythagorean Theorem 2. Identify right triangles 3. Simplify radical expressions involving products and quotients 4. Simplify sums and differences of radical expressions 5. Simplify products and quotients of radical expressions 6.Solve equations containing radicals 7. Identify extraneous solutions 8. Graph square root functions 9. Translate graphs of square root functions Core Content/Objectives Skills What students will be able to do 1. Find the length of a hypotenuse 2. Find the length of a leg 3. Identifying right triangles given 3 side lengths 4. Simplify a radical by removing perfect square factors 5. Simplify a radical by removing variable factors 6. Multiply 2 radical expressions 7. Simplifying fractions within radicals 8. Rationalizing denominators 9.Combine like radicals 10.Multiply radical expressions 11. Rationalize a denominator using Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Use problems and activities from book involving modeling problems, especially the activities in 10.1 Instructional Actions Assessment How learning will be assessed Test Quiz Daily Homework 23

24 conjugates 12. Solving by isolating a radical 13 Using a radical equation 14 Solving with a radical on both sides 15. Identifying extraneous solutions 16 Finding domain of a square root function 17. Graphing a square root function Resources/Technology: Graphing Calculator, ELMO 24

25 Chapter 12: 16 days (cover only and include 5.7 and 9.7) Targeted NJ Core Curriculum Content Standards: Enduring Understandings: The students will understand how to analyze a given data set using graphs, tables, the measures of center and spread, and regression analysis. Essential Questions: What type of model fits the scatter plot the best? How can we make the data more visual? What are the advantages of the different types of graphs? What are advantages and disadvantages of the different measures of center and spread? What do the measures of center and spread tell us about the data? Concepts What students will know 1. Understand an appropriate model for a scatter plot 2. Apply different visual graphs and tables to a set of data 3. Interpret the measures of center and the measures of spread Core Content/Objectives Skills What students will be able to do 1. Make a scatter plot and describe its correlation 2. Write the equation of a trending line based on a real world scenario 3. Use graphing calculator to find line of best fit 4. Identify whether relationships are causal 5 Choose a model by graphing 6 Choose a model using different ratios 7. Model real world data 8. Make a frequency table 9.Make a histogram Activities/Strategies Learning Activities/ Differentiation Interdisciplinary Connections Complete the residual activity in book due to PARCC test content! Complete extension activity with 12.3 on standard deviation using calculator Must complete extension activity 12.5 involving 2 way frequency tables Instructional Actions Assessment How learning will be assessed Test Quiz Daily Homework 25

26 10.Interpret Histogram 11. Create a cumulative frequency table 12. Summarize a data set 13 Create a box and whisker plot 14 Interpret a box and whisker plot 15. Find percentile rank 16 Find measure of central tendency 17. Find a data value 18. Find the range 19. Find measure of central tendency and ranges 20. Compare measure of central tendency 21 Classify Data 22. Identify types of data 23. Choose a sample method 24. Understand bias surveys 25. Determine bias in a sample Resources/Technology: Graphing Calculator, ELMO 26

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