1. Supporting Teachers. Serving Students Algebra Practice with a Geometry Connection Bob Battinich Pacent Learning Solutions

2. Supporting Teachers. Serving Students The Problem Students entering Geometry are not retaining Geometry concepts taught in General Math courses from grades 3 rd – 7 th.

3. Supporting Teachers. Serving Students Equity Students who repeat Algebra 1, either in 9 th or 10 th grade, are 2+ years removed from Geometry concepts taught in General Math curriculum.

4. Supporting Teachers. Serving Students Focus Geometry Concepts Basic Angle Relationships 1) Supplementary Angles 2) Complementary Angles 3) Vertical Angles 4) Triangle Sum Theorem

5. Supporting Teachers. Serving Students Basic Angle Relationships 3MG 2.4 Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle.

6. Supporting Teachers. Serving Students Basic Angle Relationships 4MG 3.5 Know the definitions of a right angle, an acute angle, and an obtuse angle. Understand that 90°, 180°, 270°, and 360° are associated, respectively with ¼, ½, ¾, and full turns.

7. Supporting Teachers. Serving Students Basic Angle Relationships 5MG 2.1* Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software).

8. Supporting Teachers. Serving Students Basic Angle Relationships 5MG 2.2* Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems.

9. Supporting Teachers. Serving Students Basic Angle Relationships 6MG 2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

10. Supporting Teachers. Serving Students Basic Angle Relationships 6MG 2.2* Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.

11. Supporting Teachers. Serving Students Basic Angle Relationships 7 th Grade Standards Nothing 8 th Grade Standards Nothing Grade Level Students 2 years without any Angle Relationships

12. Supporting Teachers. Serving Students Basic Angle Relationships Geometry 5 th Grade

13. Supporting Teachers. Serving Students Basic Angle Relationships Geometry 6 th Grade

14. Supporting Teachers. Serving Students Question Where can we embed the practice of Algebra concepts in a Geometric context to keep basic angle relationships fresh in students minds.

15. Supporting Teachers. Serving Students Algebra Concepts Algebra Units/Strands 1) One Variable Equations 2) Linear Equations 3) Systems of Equations 4) Operations with Polynomials 5) Quadratic Equations 6) Rational Expressions

16. Supporting Teachers. Serving Students Supplementary Angles One Variable Equations (3x)° (4x + 5)° 12x + 20 x2x2 Quadratic Equations (4x + 5) + (3x) = 180 A1 4.0*, A1 5.0* x 2 + 12x + 20 = 180 A1 14.0*

17. Supporting Teachers. Serving Students Complementary Angles (4x)° (7x + 2)° One Variable Equations x2x2 4x + 30 Quadratic Equations (4x) + (7x + 2) = 90 A1 4.0*, A1 5.0* (x 2 ) + (4x + 30) = 90 A1 14.0*

18. Supporting Teachers. Serving Students Vertical Angles Systems of Equations 60° 3x – y 120° 3x + 3y (5x – 6)° (3x + 8)° One Variable Equations 5x – 6 = 3x + 8 A1 4.0*, A1 5.0* 3x + 3y = 120 3x – y = 60 A1 9.0* Quadratic Equations (x 2 )° (2x + 24)° x 2 = 2x + 24 A1 14.0*

19. Supporting Teachers. Serving Students Triangle Sum Theorem Quadratic Equations 50 3x x2x2 (3x – 5)° (2x)° (4x – 4)° One Variable Equations (2x) + (3x – 5) + (4x – 4) = 180 A1 4.0*, A1 5.0* (x 2 ) + (3x) + (50) = 180 A1 14.0*

20. Supporting Teachers. Serving Students 1 Variable Equations Linear Equations SystemsPolynomials Quadratic Equations Rational Expressions Supp xx Comp xx Vert xxx TST xx

21. Supporting Teachers. Serving Students How about Area and Perimeter? Where can we embed the practice of Algebra concepts in a Geometric context to keep basic area and perimeter concepts fresh in students mind.

22. Supporting Teachers. Serving Students Area and Perimeter 3MG 1.2*Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them.

23. Supporting Teachers. Serving Students Area and Perimeter 3MG 1.3*Find the perimeter of a polygon with integer sides.

24. Supporting Teachers. Serving Students Area and Perimeter 4MG 1.4Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.

25. Supporting Teachers. Serving Students Area and Perimeter 5MG 1.1*Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle.

26. Supporting Teachers. Serving Students Area and Perimeter 6AF 3.1Use variables in expressions describing geometric quantities (e.g., P=2w + 2I, A = ½ bh, C = πd — the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).

27. Supporting Teachers. Serving Students Area and Perimeter 6AF3.2 Express in symbolic form simple relationships arising from geometry.

28. Supporting Teachers. Serving Students Area and Perimeter 7MG 2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

29. Supporting Teachers. Serving Students Area and Perimeter 7MG 2.2 Estimate and compute the area of more complex or irregular two- and three- dimensional figures by breaking the figures down into more basic geometric objects.

30. Supporting Teachers. Serving Students Basic Angle Relationships Geometry 7 th Grade

31. Supporting Teachers. Serving Students Area and Perimeter Simplifying Algebraic Expressions 3x 2x 15 5x 8 Combining Like Terms 4 2x 3x + 5 Distributive Property 8 2x + 1 2 3x – 7 2x + 15 + 3x + 8 + 5x 4(3x + 5) 8(2x + 1) – 2(3x – 7)

32. Supporting Teachers. Serving Students Area and Perimeter One Variable Equations 4 2x + 3 3x P = 45m 6 x + 4 A = 30m 2 4 + (2x + 3) + (3x) = 45 = 30

33. Supporting Teachers. Serving Students Area and Perimeter Linear Equations Find the area of the polygon created by the given linear equations. a. y = 2x + 3 b. y = -3 c. 3x + 2y = 6 Area =

34. Supporting Teachers. Serving Students Area and Perimeter Systems of Equations

35. Supporting Teachers. Serving Students Area and Perimeter Operations with Polynomials 2x 2 – 9 3x 2 – 2x + 4 x 2 + 5x Addition 2x – 5 3x – 4 Multiplication 2x + 5 3x – 4 x 2x – 3

36. Supporting Teachers. Serving Students Area and Perimeter Quadratic Equations x 2 + 2x + 8 = 23 x(x – 4) = 45 x x + 4 A = 45m 2 8 x2x2 P = 23m 2x

37. Supporting Teachers. Serving Students Area and Perimeter Rational Expressions

38. Supporting Teachers. Serving Students 1 Variable Equations Linear Equations SystemsPolynomials Quadratic Equations Rational Expressions Supp xx Comp xx Vertical xxx TST xx Area xxxxx Perimeter xxxx

39. Supporting Teachers. Serving Students Softcopy of Material Visit www.pacent.orgwww.pacent.org Curriculum & Presentations 2010 CMC-South

40. Supporting Teachers. Serving Students Contacts Bob Battinich – (916) 296-3958 – bob@pacent.org