revision teams at work summer 2013. evaluating newly submitted tasks assessing the need for...
TRANSCRIPT
Coordinate Algebra and Analytic GeometryResource Revision
Highlights
Revision Teams at work Summer 2013
Resource Revision Team’s TasksJennifer Greer
Floyd County [email protected]
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 [email protected]
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 1-3
Unit 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
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
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 Task
TASK 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
[email protected] League- Harrison HS, Cobb County
Marilyn Munford- Sandy Creek HS, Fayette [email protected]
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: [email protected]
Brooke Kline Program Specialist (6-12) [email protected] Pratt Program Specialist (6-12) [email protected] Gunn Program Specialist (K-5)[email protected]