this powerpoint is from day 5 of math week. it covers… 1. assessment 2. the math of unit 5 3. the...

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This PowerPoint is from Day 5 of Math Week. It covers…1. Assessment2. The Math of Unit 53. The math of part 5 of Unit 4

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High School MathThe Standards Based Way

Day 5

Nicole Spiller

West Georgia RESA

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Problem of the Day In the figure below, point Q is fixed and point P starts at 4

and moves left along the x-axis. As P moves left along the x axis toward O, the area of POQ changes. Use the information given to complete the table below to show how the area of POQ changes as P goes from the position shown to the origin O.x-coordinate of P Area of POQ

4 3  2 1 0 

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Housekeeping

• Breaks

• Cell Phones

• Restrooms

• Parking Lot

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Activator

• Word Splash

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Essential Question/Enduring Understandings

• What math is in Unit Six?

• What math is in part five of Unit Four?

• How does assessment impact what students should know and be able to do?

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Assessment

• What is assessment?

• What is the difference between assessment and grading?

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Thoughts on Grading

• The Case against the zero

• Grading: Are grade an accurate reflection of student learning?

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Thoughts on Assessment

• Open Ended Items

• Will this be on the test?

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Assessment

• For Learning– Usually Formative

– Usually detailed, specific, and descriptive feedback

– Checks learning to determine what to do next

– Designed to assist student and teacher

• Of Learning– Usually Summative

– Usually compares student learning to other students

– Checks what has been learned to date

– Doesn’t need to involve student

Both are important!!! We must have a balance!

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Assessment for Learning

1. Students are involved so a shared language and understanding is developed.

2. Students receive specific, descriptive feedback about the learning, during the learning.

3. Students collect, organize, and communicate evidence of their learning to others.

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Assessment for Learning

4. Teachers adjust instruction in response to ongoing assessment information received from students and selves.

5. A safe learning environment invites further risk taking, mistake making, goal setting, and support for learning.

GMSA Conference Assessment for Learning 2/3/2005

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Video GameA Learning Task

• Distance formula introduced

• The relationship between the Pythagorean theorem and the distance formula

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Part five of Unit Four

• 3 Game Tasks– Fairness– Yahtzee– Application

• Culminating Task

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Unit 6 – Coordinate Geometry

• Pre Requisites:– Plotting points in all quadrants– Scatter plots– Lines and systems of lines, including finding

equations of lines, finding slopes of lines, and finding the slope of a line perpendicular to a given line.

– Pythagorean Theorem

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Overview of Unit 6

• This unit investigates the properties of geometric figures on the coordinate plane. Students develop and use the formulas for the distance between two points, the distance between a point and a line, and the midpoint of segments. Focusing students’ attention on a coordinate grid as a reference for locations and descriptions of geometric figures strengthens their recognitions of algebraic and geometric connections.

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Essential Question/Enduring Understandings

• Algebraic formulas can be used to find measures of distance on the coordinate plane.

• The coordinate plane allows precise communication about graphical representations.

• The coordinate plane permits use of algebraic methods to obtain geometric results.

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Key Standards

MM1G1: Students will investigate properties of geometric figures in the coordinate plane.Determine the distance between two points.Determine the distance between a point and a line.Determine the midpoint of a segment.Understand the distance formula as an application of the Pythagorean Theorem.Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

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Related Standards

• MM1G2: Students will understand and use the language of mathematical argument and justification.Use conjecture, inductive reasoning, deductive reasoning, counterexample, and indirect proof as appropriate.Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

• MM1G3: Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

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Related Standards

• MM1P1: Students will solve problems (using appropriate technology)

• MM1P2: Students will reason and evaluate mathematical arguments

• MM1P3: Students will communicate mathematically• MM1P4: Students will make connections among

mathematical ideas and to other disciplines• MM1P5: Students will represent mathematics in multiple

ways

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Concepts/Skills to Maintain

• Plotting points in all quadrants• Making scatter plots• Finding slopes and equations of lines• Finding equation of a line perpendicular to a

given line• Pythagorean Theorem• Properties of special quadrilaterals

–

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Tasks• Task 1 and 2: Distance and mid point formulas

• Tasks 3 and 4:Applications in the coordinate plane

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New YorkA Learning Task

• Key Points:– Introduction of the mid point formula

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Quadrilaterals Revisited A Learning Task

• Key Points:– Distance and mid point formulas in the

coordinate plane– Use the coordinate plane to verify conjectures

related to triangles and quadrilaterals

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Euler’s VillageA Learning Task

• Key Points:– Investigate properties of geometric figures in

coordinate plane

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Surveillance of the VillageA Culminating Task

• This task incorporates all of the material learned in this unit in an applied setting.

• It may be appropriate for students to work on this task throughout the unit with periodic deadlines

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End of Day 5