NKCES Summer Workshop
Robin Hill
Kentucky Department of Education
Mathematics Consultant
June 1, 2012
Targets for this session
Classroom Teacher
• I can use Scale City resources to effectively
assist students with understanding
proportional relationships.
Teacher Leader
• I can use resources to customize the Scale City
PD modules to lead PD on proportional
reasoning in my school or my district.
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http://www.ket.org/scalecity/
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National Educational Telecommunications
Association (NETA) Award
INSTRUCTIONAL MEDIA Award
KET / Lexington Kentucky
Scale City: The Road to Proportional
Reasoning (Instructional Content)
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PD Modules for Scale City
• Module 1: Preparing To Teach Proportional
Reasoning
• Module 2: Using Scale City To Teach
Proportional Reasoning
• Module 3: Introduction to Scale City Learning
Modules
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Reflecting on teaching proportional
reasoning
Take a few minutes to answer the following
questions:
• What does proportional reasoning mean to you?
• What is the place of proportional reasoning in the
Common Core Mathematics Standards for grades
six through eight?
• How might you engage students in learning about
proportional reasoning so that it is enjoyable as
well as understandable?
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Activity from Dr. Sandy Atkins
http://www.creatingahas.com/
Complexity of Effective Intervention presented
at the Association of State Supervisors of
Mathematics Conference, 2012
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Module 1: Preparing To Teach
Proportional Reasoning
Focuses on eight skills students should master before
exploring Scale City:
– Division of whole numbers (links to CCSSM – KCAS)
– Simplifying fractions (videos and flash quiz)
– Developing an understanding of proportional relationships
(video)
– Multiplying mixed numbers (video)
– Dividing fractions (video)
– Understanding percent (video)
– Ordering decimals (videos and flash quiz)
– Metric measurement (videos)
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Resource Samples in packet
• http://tdcms.ket.org/scalecity/pdf/AnIntroduc
tiontoScaleCity.pdf Linda Sheffield
• http://tdcms.ket.org/scalecity/pdf/ScaleCityVocabulary.pdf
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Module 1 – page 3
http://www.teachersdomain.org/resource/scl10.plr.module1/
Scale City PD - Module 1, page 3
For video link click here.
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Module 1 – page 4
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Module 1 – page 7
Simplifying fractions
• Read the fourth grade standard for extending
understanding of fraction equivalence and ordering
from the Number and Operations – Fractions domain
in the Common Core Mathematics Standards.
• Number and Operations--Fractions
• Think about how the standards in the previous section
on multiplication and division relate to simplifying
fractions and determining whether two fractions are
equivalent. Also, consider how this relates to the
standard above on extending understanding of fraction
equivalence.
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Module 1 – page 7
Simplifying Fractions
Click here for video on the left to watch Harper
simplify the fraction 500/1000. Before viewing,
think about how you would like to have Harper
simplify this fraction. Consider the following
questions:
•Do you think that Harper has a conceptual
understanding of what it means to simplify a
fraction? Why or why not?
•What does Harper understand about simplifying
fractions? What would you do to strengthen this
understanding on a concrete level as suggested by
the standard above?
•The fractions that Harper is working with are all
equivalent to ½. What questions might you ask to
extend her understanding to other equivalent
fractions?
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Module 1 – page 10
Developing an understanding of
proportional relationships: Part 3 of 3
A proportion is a relationship of equality between two
ratios. Think about how finding equivalent ratios and
solving a proportion are similar to finding equivalent
fractions. What do you want students to know about
how they are alike and how they are different?
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Module 2: Using Scale City To Teach
Proportional Reasoning
Teaching Module 2 includes the following:
• The math explored in all eight Scale City
modules
• Brief descriptions of the video “fieldtrips”
featured in the Scale City modules
• Step-by-step explorations of each module’s
interactive simulation and the final quiz
• A look at the additional resources included in
Scale City
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Module 2: Includes Virtual Mini
Fieldtrips
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Page 2 Dinosaur World
Page 3 Louisville Slugger Museum
Page 4 World of Mural Painting
Page 5 Miniature Land
Page 6 World Chicken Festival
Page 7 Sky-Vue Drive-in
Page 8 Belle of Louisville
Page 9 Kentucky Horse Park
Page 10 Scale City Quiz
Page 11 Teacher’s Diner in Scale City
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Includes Virtual Mini Fieldtrips
Cave City, Kentucky
London, Kentucky
Louisville, Kentucky
Winchester, Kentucky
Kentucky Murals
Maysville, Kentucky
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Belle of Louisville / Music Video
http://www.ket.org/scalecity/flvplayer.html?file
=belle_of_louisville&hiLo=med
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Module 3: Introduction to Scale
City Learning Modules
Teaching Module 3 is a brief introduction to
some of the resources from the following Scale
City learning modules, along with more
opportunities to observe students’
mathematical reasoning.
• Dinosaur World
• World of Mural Painting
• Miniature Land
• Kentucky Horse Park
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One-dimensional scaling: Size-O-Rama
Dinosaur World introduces students to one-dimensional
scaling. If this is your students’ first experience with
proportional reasoning, we recommend that you start
with this learning module. Module 3 – pages 3 – 7.
• Let’s review the sixth and seventh grade Common Core
Standards on proportional reasoning, percent, and
scale drawings.
• Click here for video
• Resource:
http://tdcms.ket.org/scalecity/pdf/Dino_HO3.pdf
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Two-dimensional Scaling: Area
• Explore the sections of the World of Mural
Painting module for the students. Recall the
virtual mini field trip on murals then check out
the artist’s description of how he uses math in
his work and the written interactive guide at
the Scale City mural web page. You can also
watch the demonstration of the Mural Math
interactive found in Teaching Module 2.
Module 3 – pages 8 – 10
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Three-dimensional Scaling:
In Miniature Land, the video takes you on a tour
of two miniature collections. Watch the video,
paying particular attention to the Math Alerts.
Note that the miniatures in the video are built
using different scales. In the interactive,
students begin by scaling up the dimensions of a
tiny house to a larger version using a ratio of
1:10. Module 3 – pages 11 – 13
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Scaling up volume by a factor of 10
• Click here to watch Laura as she determines
the volume of a box that has used a scale
factor of 10 to scale up a cubic centimeter.
– What might you do to help her continue to build
these concepts?
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Time, Distance, and Speed
Let’s review the eighth grade Common Core
Standards specific to expressions, equations,
and functions.
– Eighth Grade Expressions, Equations and
Functions
– The Kentucky Horse Park video and online activity
explore the mathematics of direct and inverse
proportions as they relate to time, distance, and
speed.
– More information and a suggested lesson plan are
available at the Scale City Teacher’s Diner.
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Mathematical relationships among
rate, time, and distance
Direct and inverse proportions
Click here to view video
Module 3 – pages 14 – 15
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http://www.ket.org/scalecity/
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Additional Resources
• Phil Daro speaks, http://vimeo.com/30924981
• Hexagons of the standards progression for ratios and
proportional relationships
http://turnonccmath.com/
• http://commoncoretools.me/tools/
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The Common Core State Standards in Mathematics
K
1
2
3
4
5
6
7
8
Statistics and
Probability
Measurement and Data
Ratios and
Proportional
Relationships
CC
9
10
11
12
Statistics and Probability
F
Functions
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Algebra
Functions
Operations and Algebraic Thinking
Number and Quantity
Expressions and
Equations
Geometry
Geometry
Click on any red domain for more details.
Click on the upper left corner for the next stream through the standards.
Modeling
© Copyright 2011 Institute for Mathematics and Education
Standards Progression Documents
• Ratios and Proportional Relationships
http://commoncoretools.files.wordpress.com/
2012/02/ccss_progression_rp_67_2011_11_1
2_corrected.pdf
• Expressions and Equations
http://commoncoretools.files.wordpress.com/
2011/05/expressions_and_equations.pdf
• Functions
http://commoncoretools.files.wordpress.com/
2011/05/functions.pdf
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Revisit Targets
Classroom Teacher
I can use Scale City resources to effectively
assist students with understanding
proportional relationships.
Teacher Leader
I can use resources to customize the Scale City
PD modules to lead PD on proportional
reasoning in my school or my district.
June 1 2012
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Next Steps
• I plan to use these resources in my classroom
by …
• I plan to utilize these resources in my
school/district by …
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KET – Award-winning project
PD Evaluation and Certificate opportunity
When you have completed all three modules,
please let KET know what you think about this
self-paced professional development by taking
the survey. Module 3 – page 16
For PD certificate of participation, contact:
Mary Duncan
KET Education Division
800-432-0951
mduncan@ket.org
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Robin.hill@education.ky.gov
502-564-2106
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