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

•Supporting Teachers. Serving Students

Algebra Practice

with a Geometry Connection

Bob Battinich

Pacent Learning Solutions


The Problem

Students entering Geometry are not retaining Geometry concepts taught in General Math courses from grades 3rd – 7th.


Equity

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


Focus Geometry Concepts

Basic Angle Relationships

1) Supplementary Angles

2) Complementary Angles

3) Vertical Angles

4) Triangle Sum Theorem



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.



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.



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).



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.



6MG 2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.



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.



7th Grade Standards

Nothing

8th Grade Standards

Nothing

Grade Level Students2 years without any Angle Relationships



Geometry 5th Grade



Geometry 6th Grade


Question

Where can we embed the practice of Algebra concepts in a Geometric context to keep basic angle relationships fresh in students minds.


Algebra Concepts

Algebra Units/Strands1) One Variable Equations

2) Linear Equations

3) Systems of Equations

4) Operations with Polynomials

5) Quadratic Equations

6) Rational Expressions


Supplementary Angles

One Variable Equations

(3x)°(4x + 5)° 12x + 20x2

Quadratic Equations

(4x + 5) + (3x) = 180A1 4.0*, A1 5.0*

x2 + 12x + 20 = 180A1 14.0*


Complementary Angles

(4x)°

(7x + 2)°


x2

4x + 30

Quadratic Equations

(4x) + (7x + 2) = 90A1 4.0*, A1 5.0*

(x2) + (4x + 30) = 90A1 14.0*


Vertical Angles

Systems of Equations

60°3x – y

120°3x + 3y

(5x – 6)°(3x + 8)°


5x – 6 = 3x + 8 A1 4.0*, A1 5.0*

3x + 3y = 1203x – y = 60

A1 9.0*

Quadratic Equations

(x2)° (2x + 24)°

x2 = 2x + 24A1 14.0*


Triangle Sum Theorem

Quadratic Equations

503x

x2

(3x – 5)°(2x)°

(4x – 4)°


(2x) + (3x – 5) + (4x – 4) = 180A1 4.0*, A1 5.0*

(x2) + (3x) + (50) = 180A1 14.0*


1 Variable Equations

Linear Equations

Systems PolynomialsQuadratic Equations

Rational Expressions

Supp x xComp x xVert x x xTST x x


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.


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.


Area and Perimeter

3MG 1.3* Find the perimeter of a polygon with integer sides.


Area and Perimeter

4MG 1.4 Understand 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.


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.


Area and Perimeter

6AF 3.1 Use 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).


Area and Perimeter

6AF3.2 Express in symbolic form simple relationships arising from geometry.


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.


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.



Geometry 7th Grade


Area and Perimeter

Simplifying Algebraic Expressions

3x2x

15

5x8

Combining Like Terms

42x

3x + 5Distributive Property

8

2x + 1

23x – 7

2x + 15 + 3x + 8 + 5x 4(3x + 5)8(2x + 1) – 2(3x – 7)


Area and Perimeter


4

2x + 3

3xP = 45m 6

x + 4

A = 30m2

4 + (2x + 3) + (3x) = 45 = 306(x 4)2


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 = 7 62


Area and Perimeter

Systems of Equations


Area and Perimeter

Operations with Polynomials

2x2 – 9

3x2 – 2x + 4

x2 + 5x

Addition

2x – 5

3x – 4

Multiplication

2x + 5

3x – 4

x2x – 3


Area and Perimeter

Quadratic Equations

x2 + 2x + 8 = 23 x(x – 4) = 45

x

x + 4

A = 45m28

x2

P = 23m2x


Area and Perimeter


2

3x 12x 25

2

2

x x 20x 16

2

2 2

3x 12 x x 20Area

x 25 x 16

45x

2

1x

2

35x 2 2

1 4 3Perimeter

x 5x 5x


1 Variable Equations

Linear Equations

Systems PolynomialsQuadratic Equations


Supp x xComp x x

Vertical x x xTST x xArea x x x x x

Perimeter x x x x


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Curriculum & Presentations

2010 CMC-South


Contacts

Bob Battinich– (916) 296-3958– [email protected]

Documents

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