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Patterns and Functional Relationships

 

1. Represent patterns, including relations and functions, through tables, graphs, verbal rules, or symbolic rules.

 

Lesson 1. Setting up a formula

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Lesson 2. Setting up a formula

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Lesson 3. Setting up a formula

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Lesson 4. Setting up a formula

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Lesson 5. Setting up a formula by trial and error

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Lesson 6: Arithmetic sequence

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Lesson 7: Setting up a formula

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Lesson 8: Setting up a formula

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Lesson 9: Setting up a formula

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Lesson 10: Setting up a formula

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2. Use proportional reasoning such as ratios, equivalent fractions, and similar triangles, to solve numerical, algebraic, and geometric problems.

 

Lesson 11. Ratios and proportions - Introduction

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Lesson 12. Problems

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Lesson 13. Problems

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Lesson 14. Problems

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Lesson 15. Problems

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Lesson 16: Problems

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Lesson 17: Solving ratio and proportion problems with the use of diagrams; Part 2;  Part 3

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Lesson 18: Similar triangles;  Part 2;  Part 3

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3. Use mathematics to represent and analyze quantitative relationships between dependent and independent variables in real- world problems.

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Lesson 19. Dependent and independent variables;  Part 2;  Part 3;  Part 4

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Lesson 20. Analyzing quantitative relationships

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Lesson 21. Analyzing quantitative relationships

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Lesson 22. Analyzing quantitative relationships

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Lesson 23. Analyzing quantitative relationships

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Linear and Quadratic Equations and Inequalities

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4. Find equivalent expressions for equalities and inequalities, explain the meaning of symbolic expressions (e.g., relating an expression to a situation and vice versa), find the solutions, and represent them on graphs.

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Lesson 24. Equivalent expressions for equalities and inequalities  Part 1, Part 2, Part 3, Part 4

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Lesson 25. Explaining the meaning of symbolic expressions  Part 1, Part 2, Part 3, Part 4  Part 5

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Lesson 26. Solving linear equations and representing them on graphs  Part 1, Part 2, Part 3, Part 4  Part 5  Part 6

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Lesson 27. Solving linear inequalities and representing them on graphs  Part 1, Part 2, Part 3, Part 4  Part 5

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5. Recognize and create equivalent algebraic expressions (e.g., 2(a+3) = 2a + 6), and represent geometric problems algebraically (e.g., the area of a triangle).

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Lesson 28. Creating algebraic expressions

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Lesson 29. Creating algebraic expressions

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Lesson 30. Creating algebraic expressions

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Lesson 31. Creating algebraic expressions

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Lesson 32. Creating algebraic expressions

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Lesson 33. Creating algebraic expressions

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6. Use mathematics to solve real-world problems using numerical and algebraic expressions and equations.

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Lesson 34. Problems

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Lesson 35. Problems

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Lesson 36. Problems

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Lesson 37. Problem

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7. Have a basic understanding of linear equations and their properties (e.g., slope, perpendicularity); the multiplication, division, and factoring of polynomials; and graphing and solving quadratic equations through factoring and completing the square.

 

Lesson 38. Linear Functions  Part 1   Part 2   Part 3   Part 4   Part 5   Part 6   Part 7  Part 8

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Lesson 39. Quadratic Functions Part 1   Part 2   Part 3   Part 4   Part 5   Part 6

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Lesson 40. Solving Quadratic Equations by Factoring and Completing the Square  Part 1   Part 2   Part 3   Part 4   Part 5   Part 6

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Lesson 41. Multiplying, Dividing, and Factoring Polynomials  Part 1   Part 2   Part 3   Part 4   Part 5   Part 6  Part 7

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8. Interpret graphs of linear and quadratic equations and inequalities, including solutions to systems of equations.

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Lesson 42. Graphs of Linear Inequalities in Two Variables   Part 1   Part 2   Part 3   Part 4   

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Lesson 43. Graphs of Quadratic Inequalities in Two Variables  Part 1   Part 2   Part 3   Part 4   

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Lesson 44. Solving Systems of Linear Equations  Part 1   Part 2   Part 3   Part 4   Part 5   Part 6   Part 7  Part 8

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Assessment

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CSET Math Subtest II Algebra and Functions Questions: 10-12

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Good multiple choice items: Work through problems that deal with the algebra and functions domain.

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​NY Grade 6 State Test Questions

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NY Grade 7 State Test Questions

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NY Grade 8 State Test Questions

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Good constructed response items: 

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  • Access the Mathematics Assessment Project website. Work through problems from the Grades 6 & 7 Tests for Middle School that deal with the algebra and functions domain. You may also access the summative tasks page if you want to solve more problems.  

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