Coordinate Algebra and Analytic Geometry Resource Revision Highlights

Coordinate Algebra and Analytic GeometryResource Revision

Highlights

Revision Teams at work Summer 2013

Resource Revision Team’s TasksJennifer Greer

Floyd County Schoolsjgreer@floydboe.net

Evaluating newly submitted tasks Assessing the need for additional

tasks Assessing the order of current units

and tasks Editing of current units and tasks Creating additional tasks to address

gaps, if necessary

Coordinate Algebra/Acc CA Comprehensive Course Overview Located on the 9-12 math section of

www.georgiastandards.org

Designed to provide clarification of CCGPS Mathematics Standards

Organized to link together many sources of information pertinent to CCGPS Coordinate Algebra/Accelerated Coordinate Algebra

Begin at www.georgiastandards.org

Direct Link to Page

Select the CCGPS ELA/Math Tab

Direct Link to Page

Select the Mathematics option under Browse CCGPS

Direct Link to Page

Select the 9-12 option in the Mathematics

section

Direct Link to Page

Expand the Coordinate Algebra Course

Direct Link to Page

Select the Comprehensive Course Overview

Expande Coordinate Algebra

Direct Link to Page

Cover Page of CCO

Direct Link to Page

Table of Contents Outlines the

Major areas of Focus for the Course

Fully Interactive when viewed via internet

Hover over a section and select to access the section quickly

Flipbooks

Bold words will provide access to the Common Core Flipbooks

The Flipbooks offer clarification Very Large File (slow loading)

Direct link to HS Flipbook

Content Domain Flipbook Resources

Active links to standard resources

Sample Standards Page from Flip Book

Other Sections of Interest

•Unit Descriptions•Webinar Information• Assessment Resources and Instructional Support Resources• Internet Resources• Curriculum Map

GADOE Assessment and Instructional Support Sites

GADOE Instructional Support Sites

Next: Becca Wing

External Instructional Support Sites

Ms. Becca WingMath Teacher

Charles R Drew High Schoolrebecca.wing@clayton.k12.ga.us

Overview of Changes Within the Frameworks

Updates to Unit Frameworks

Task Table

Outlines the tasks by type, content and standard.

Provides suggested times

Hyperlinks to PDFs and Word Docs

Purpose of Tasks- Give teachers resources to structure Problem-Based-Learning

- Check out Dan Meyer, Robert Kaplinksy’s websites under Internet Resources in Comprehensive Course Overview

- Teachers do not have to use all tasks in a given unit, but find those that they think will best aid their students in mastering the standards

Dan Meyer http://blog.mrmeyer.com/?p=10285

Robert Kaplinsky http://robertkaplinsky.com/

Task Focus Areas for Units 1-3Unit 1 Tasks primarily address: Unit Conversion, Creating Linear Equations to model scenarios, and Describing Patterns

Unit 2 Tasks primarily address: Modeling situations with linear equations and inequalities, and Systems of equations and inequalities

Unit 3 Tasks primarily address:Modeling situations with linear or exponential functions, Exploring function notation and transformations, and Understanding sequences as functions

Next: David Scott

David Scott :Math TeacherChamblee Charter High School

 david_m_scott@fc.dekalb.k12.ga.us

Task Examples

CTE TasksAchieve CCSS- CTE Classroom Tasks

Designed to demonstrate how the Common Core and Career and Technical Education knowledge and skills can be integrated. The tasks provide teachers with realistic applications that combine mathematics and CTE content.

- CTE Tasks may require teachers to present some contextual information -Advantage: situations are not contrived

- As with all tasks, teachers NEED to work these through beforehand!

- Examples on next 2 slides…

Task Reminders It is OK to teach prerequisite skills. It is CRUCIAL for teachers to work tasks

out beforehand for best student results. Remember: Time consuming & Prep

necessary … but BIG Payoff: Real World

Application, Student Interdependent Work, Question/Problem Based Learning

Select the tasks that work best for you. The GOAL: Develop inquisitive young

minds: Encourage extension questions.

To get pre-task worksheet

on scaled diagrams visit:

scottmath.weebly.com

MARS FAL Designed by the Shell Center

http://map.mathshell.org/materials/index.php Intended as student-driven, teacher-

facilitated lessons that build conceptual understanding

Next: Dana Ray

COORDINATE ALGEBRA UNITS 4, 5 AND 6 UPDATES

Dana Raydana.ray@carrollcountyschools.co

mBowdon High School

Unit 4 Task primarily address:

Representing data using dot plots, box plots, scatter plots and frequency graphs

Interpret differences in shape, center, and spread in the context of data sets accounting for outliers

Understand correlation as the degree of fit between two variables

Find a linear function (model) for a scatter plot Use residuals to informally assess the fit of a

function

Represent & Interpret Data

TASK Math Class Basketball Star Representing Data 1:

Using Frequency Graphs (FAL)

BMI Calculations (CTE) Representing Data 2:

Using Box Plots (FAL) Public Opinion and

Leisure Time

BASIC CONTENT ADDRESSED Represent data using

dot plots, box plots and histograms

Compare and interpret center, shape and spread of two or more data sets

Use frequencies and relative frequencies to compare data sets

The Basketball Star Task

• More user friendly• Questions were

changed and rearranged to help students explore and interpret dot plots, box plots and histograms

BMI Calculations (CTE)Career and Technical Education TaskTASK COVERSHEET WITH STANDARDS ADDRESSED THE TASK WORKSHEET

BMI Calculations (CTE)POSSIBLE SOLUTIONS EXTENSION ACTIVITY

Public Opinion and Leisure Time Task

Combined Public Opinion and Leisure Time Task together

Expanded Leisure Time task by adding questions for the students to answer about the frequency table and conditional frequency table

Deleted Jana’s relative frequency table about basketball

Relationships Between Data & Finding Linear Models

TASK If the Shoe Fits! Spaghetti Regression Devising a Measure

for Correlation (FAL) TV/Test Grades Equal Salaries for

Equal Work

BASIC CONTENT ADDRESSED

Represent and interpret data on a scatter plot

Understand correlation as the degree of fit between two variables

Finding a line of best fit or regression line for the data

Assess the fit of a function by plotting and analyzing residuals

Unit 5 Task primarily address:

Describe and compare translations, reflections and rotations

Find general rules to describe transformations in the coordinate plane

Use a combination of transformations on 2D shapes

Explain and generalize transformations that maintain congruence

Describe & Compare Transformations

TASK Introduction to

Reflections, Rotations, and Translations

Exploring Reflections and Rotations

Mirrored Mappings Coordinating

Translations

BASIC CONTENT ADDRESSED Describe properties of

translations, reflections and rotations

Compare reflections and rotations

Understand reflections in the coordinate plane

Translate objects and use rules to map an input with an output

Introduction to Reflections, Rotations, and Translations Task More user friendly Questions and steps were

rearranged to help students explore and describe reflections, translations and rotations in a coordinate plane.

Generalize Transformations

TASK Transformations in

the Coordinate Plane Representing and

Combining Transformations (FAL)

Transforming Shapes (Culminating Task)

BASIC CONTENT ADDRESSED

Find general rules to describe transformations in the coordinate plane.

Recognize and visualize transformations of 2D shapes

Combine transformations Explain and generalize

transformations that maintain congruence

Transforming Shapes (Culminating Task)

More user friendly More questions added at the end for students to describe

a transformation(s) that will give the desired result on the image.

Unit 6 Partition a line segment Determine slope and equations of parallel

and perpendicular lines Use slope and distance formula to prove

simple geometric theorems in the coordinate plane

Equations of Parallel and Perpendicular Lines

TASK New York City Slopes of Special

Pairs of Lines Euler’s Village

BASIC CONTENT ADDRESSED

Partition a line segment into a given ratio

Determine slopes of parallel and perpendicular lines

Write equations of parallel and perpendicular lines given an equation of a line and a point not on that line

Geometric Properties on the Coordinate Plane

TASK Geometric Properties

in the Plane Equations of Parallel &

Perpendicular Lines (FAL)

Square (Short Cycle Task)

Surveillance of the Village (Culminating Task)

BASIC CONTENT ADDRESSED

Use slope and distance formula to prove simple geometric theorems algebraically

Find perimeter and area of polygons in a coordinate plane

Use equations of parallel and perpendicular lines to form geometric figures

Square (Short Cycle Task) This short task focuses on

using the distance formula and slope formula to determine if the points graphed will form the sides of a square.

Next: Tamaiko Chappell

ANALYTIC GEOMETRY RESOURCE REVISION

TEAMTamaiko Chappell- Lanier HS, Gwinnett County

tamaiko_chappell@gwinnett.k12.ga.usJoseph League- Harrison HS, Cobb County

Marilyn Munford- Sandy Creek HS, Fayette Countymunford.marilyn@mail.fcboe.org

Sheila Sumner- Early County HS, Early County

Units restructured to include FAL’s and CTE Tasks

A variety of tasks are included- tasks with scaffolds, as well as extension tasks

Tasks that were previously included were only checked for errors or structure- tried not to delete anything

Additional tasks were added to fill gaps where necessary

Overview of Our Work

Although the language of mathematical argument and justification is not explicitly expressed in the standards themselves, it is embedded in the Standards for Mathematical Practice (3. Construct viable arguments and critique the reasoning of others.).

New culminating task, Geometry Gardens added- students create a new neighborhood/subdivision that includes similar figures, congruent triangles and triangle inequality

Unit 1 (Similarity, Congruence and Proofs) Highlights

CTE Tasks : Access Ramp- students design an access ramp that is compliant with the Americans with Disabilities Act requirements using trigonometric ratios; Range of Motion- students track a physical therapy patient’s range of motion in his arm

“Hypsometer Activity” included as a Culminating Task

Unit 2 (Right Triangle Trigonometry) Highlights

CTE Task: Grain Storage- students are tasked with designing a wheat storage unit based on the capacity of the current facility

FAL’s: Evaluating Statements about Enlargements- helps you identify and assist students who have trouble computing area, perimeter and volume of shapes AND recognize the relationships between perimeter, area and volume after scaling

Unit 3 (Circles and Volumes) Highlights

Units 4 and 6 were mainly checked for structural errors

Unit 4- Students are introduced to complex numbers

Unit 6- Students explore circles and parabolas as conic sections; the Essential Questions are a great resource for perspective for this unit

Unit 7- Students explore basic probability; Enduring Understandings and Vocabulary are a great resource for perspective for this unit

Unit 4 (Extending the Number System)

Unit 6 (Modeling Geometry)Unit 7 (Applications of Probability)

LOTS and LOTS of tasks in this unit! A concept map for using the quadratic

formula was added FAL: Forming Quadratics- identify and

assist students who have difficulty understanding how the factored form of the function can help identify its roots, how completing the square can help identify the maximum/minimum point of the graph, how the standard form can help identify the y-intercept of the graph

Unit 5 (Quadratic Functions) Highlights

Next: Jennifer Greer

Final Thoughts? All update webinars and Unit webinars are

available for Coordinate Alg/Acc CA at https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx

All Unit webinars are available for Analytic Geometry/Acc AG at https://www.georgiastandards.org/Common-Core/Pages/Math.aspx

This presentation will be posted on the 9-10 Wiki Space

https://ccgpsmathematics9-10.wikispaces.com/

DOE Math TeamSandi WoodallMathematics Program CoordinatorPhone: 404-463-1736Email: swoodall@doe.k12.ga.us

Brooke Kline Program Specialist (6-12) 404-657-9064bkline@doe.k12.ga.usJames Pratt Program Specialist (6-12) 404-651-7272jpratt@doe.k12.ga.usTurtle Gunn Program Specialist (K-5)404-656-2608tgunn@doe.k12.ga.us