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
Lesson 2. Setting up a formula
Lesson 3. Setting up a formula
Lesson 4. Setting up a formula
Lesson 5. Setting up a formula by trial and error
Lesson 6: Arithmetic sequence
Lesson 7: Setting up a formula
Lesson 8: Setting up a formula
Lesson 9: Setting up a formula
Lesson 10: Setting up a formula
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
Lesson 12. Problems
Lesson 13. Problems
Lesson 14. Problems
Lesson 15. Problems
Lesson 16: Problems
Lesson 17: Solving ratio and proportion problems with the use of diagrams; Part 2; Part 3
Lesson 18: Similar triangles; Part 2; Part 3
3. Use mathematics to represent and analyze quantitative relationships between dependent and independent variables in real- world problems.
Lesson 19. Dependent and independent variables; Part 2; Part 3; Part 4
Lesson 20. Analyzing quantitative relationships
Lesson 21. Analyzing quantitative relationships
Lesson 22. Analyzing quantitative relationships
Lesson 23. Analyzing quantitative relationships
Linear and Quadratic Equations and Inequalities
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.
Lesson 24. Equivalent expressions for equalities and inequalities Part 1, Part 2, Part 3, Part 4
Lesson 25. Explaining the meaning of symbolic expressions Part 1, Part 2, Part 3, Part 4 Part 5
Lesson 26. Solving linear equations and representing them on graphs Part 1, Part 2, Part 3, Part 4 Part 5 Part 6
Lesson 27. Solving linear inequalities and representing them on graphs Part 1, Part 2, Part 3, Part 4 Part 5
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).
Lesson 28. Creating algebraic expressions
Lesson 29. Creating algebraic expressions
Lesson 30. Creating algebraic expressions
Lesson 31. Creating algebraic expressions
Lesson 32. Creating algebraic expressions
Lesson 33. Creating algebraic expressions
6. Use mathematics to solve real-world problems using numerical and algebraic expressions and equations.
Lesson 34. Problems
Lesson 35. Problems
Lesson 36. Problems
Lesson 37. Problem
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
Lesson 39. Quadratic Functions Part 1 Part 2 Part 3 Part 4 Part 5 Part 6
Lesson 40. Solving Quadratic Equations by Factoring and Completing the Square Part 1 Part 2 Part 3 Part 4 Part 5 Part 6
Lesson 41. Multiplying, Dividing, and Factoring Polynomials Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 Part 7
8. Interpret graphs of linear and quadratic equations and inequalities, including solutions to systems of equations.
Lesson 42. Graphs of Linear Inequalities in Two Variables Part 1 Part 2 Part 3 Part 4
Lesson 43. Graphs of Quadratic Inequalities in Two Variables Part 1 Part 2 Part 3 Part 4
Lesson 44. Solving Systems of Linear Equations Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 Part 7 Part 8
Assessment
CSET Math Subtest II Algebra and Functions Questions: 10-12
Good multiple choice items: Work through problems that deal with the algebra and functions domain.
NY Grade 6 State Test Questions
NY Grade 7 State Test Questions
NY Grade 8 State Test Questions
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.