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. June Kentucky Department of Education2

June Kentucky Department of Education3

National Educational Telecommunications Association (NETA) Award INSTRUCTIONAL MEDIA Award KET / Lexington Kentucky Scale City: The Road to Proportional Reasoning (Instructional Content) June Kentucky Department of Education4

PD Modules for Scale City Module 1: Preparing To Teach Proportional Reasoning Module 1: Preparing To Teach Proportional Reasoning Module 2: Using Scale City To Teach Proportional Reasoning Module 2: Using Scale City To Teach Proportional Reasoning Module 3: Introduction to Scale City Learning Modules Module 3: Introduction to Scale City Learning Modules June Kentucky Department of Education5

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? June Kentucky Department of Education6

Activity from Dr. Sandy Atkins Complexity of Effective InterventionComplexity of Effective Intervention presented at the Association of State Supervisors of Mathematics Conference, 2012 June Kentucky Department of Education7

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) June Kentucky Department of Education8

Resource Samples in packet tiontoScaleCity.pdf Linda Sheffield tiontoScaleCity.pdf Vocabulary.pdf Vocabulary.pdf June Kentucky Department of Education9

Module 1 – page 3 Scale City PD - Module 1, page 3 For video link click here.here June Kentucky Department of Education10

Module 1 – page 4 June Kentucky Department of Education11

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. June Kentucky Department of Education12

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:here 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? June Kentucky Department of Education13

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? June Kentucky Department of Education14

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 Scale City June Kentucky Department of Education15

Module 2: Includes Virtual Mini Fieldtrips 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 QuizScale City Quiz Page 11 Teacher’s Diner in Scale CityTeacher’s Diner in Scale City June Kentucky Department of Education16

Includes Virtual Mini Fieldtrips Cave City, Kentucky Louisville, Kentucky Kentucky Murals Maysville, Kentucky London, Kentucky Winchester, Kentucky Lexington, Kentucky June Kentucky Department of Education17

Belle of Louisville / Music Video =belle_of_louisville&hiLo=med June Kentucky Department of Education18

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 June Kentucky Department of Education19

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.proportional reasoning, percent, and scale drawings. Click here for videohere Resource: June Kentucky Department of Education20

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 – 10World of Mural Painting muralsthe written interactive guide at the Scale City mural web page June Kentucky Department of Education21

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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.Miniature Land 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 June Kentucky Department of Education23

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.here – What might you do to help her continue to build these concepts? June Kentucky Department of Education24

Time, Distance, and Speed Let’s review the eighth grade Common Core Standards specific to expressions, equations, and functions. – Eighth Grade Expressions, Equations and FunctionsExpressions, 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. The Kentucky Horse Park – More information and a suggested lesson plan are available at the Scale City Teacher’s Diner. June Kentucky Department of Education25

Mathematical relationships among rate, time, and distance Direct and inverse proportions Click here to view videohere Module 3 – pages 14 – 15 June Kentucky Department of Education26

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Additional Resources Phil Daro speaks, Hexagons of the standards progression for ratios and proportional relationships June Kentucky Department of Education28

Modeling K The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards. Functions

Modeling K The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Number and Operations Fractions (3 – 5) Enlarge concept of number beyond whole numbers, to include fractions Use understanding of the four operations to extend arithmetic to fractions Solve word problems related to the equation ax = b (a and b fractions) © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

Modeling K The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Ratios and Proportional Relationships (6 – 8) Extend work on multiplication and division; consolidate multiplicative reasoning Lay groundwork for linear functions in Grade 8 by studying quantities that vary together Solve a wide variety of problems with ratios, rates, percents © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

Modeling K The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Functions (8) Extend and formalize understanding of quantitative relationships from Grades 3-7 Lay groundwork for more extensive work with functions in High School © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

Modeling K The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Functions (9 – 12) Interpreting Functions Building Functions Linear Quadratic and Exponential Models Trigonometric Functions © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

Standards Progression Documents Ratios and Proportional Relationships /02/ccss_progression_rp_67_2011_11_1 2_corrected.pdf /02/ccss_progression_rp_67_2011_11_1 2_corrected.pdf Expressions and Equations /05/expressions_and_equations.pdf /05/expressions_and_equations.pdf Functions /05/functions.pdf /05/functions.pdf June Kentucky Department of Education34

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 Kentucky Department of Education35

Next Steps I plan to use these resources in my classroom by … I plan to utilize these resources in my school/district by … June Kentucky Department of Education36

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 June Kentucky Department of Education37

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