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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​Access the Illustrative Mathematics Project website. Open the Content Standards page. Open the Grades 6-8 Expressions and Equations and Ratios and Proportional Reasoning pages and the Grade 8 Functions page. Solve the tasks associated with the three domains.
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