Last updated: 7/14/2016

Mat230 Geometry CCLS - Module 4 - Connecting Algebra and Geometry through Coordinates (25 days - 7 weeks)

Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
 (1) G-GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
 (1) A-REI.12 Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. (1) A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Lesson 5 - 8

4-8 Triangles and Coordinate Proof

6-2 Parallelograms

6-3 Tests for Parallelograms

6-4 Rectangles

6-5 Rhombi and Squares

6-6 Trapezoids and Kites

Slope

Parallel

Perpendicular

Distance

Bisect

Directed Line Segment

1a,b; 4; 5; 7b-c

 (1) G-GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Lesson 5 - 8

3-3 Slopes of Lines

3-4 Equations of Lines

ADDITIONAL CONTENT: Include Partitioning a Directed Line Segment

Slope

Parallel

Perpendicular

1a-b, f; 4g; 5; 6c; 7a

 (1) G-GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Lesson 12 - 15

10-8 Equations of Circles

Bisect

2, 3a-c, 4a-f, 6a-b

 (1) G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
 (1) G-MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). (1) G-MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

Lesson 1 - 4

Lesson 9 - 11

1-6 Two-Dimensional Figures

11-1 Areas of Parallelograms and Triangles (include Perimeter)

Distance

1d-e,