Introduction to Geometry & Measurement Core Mathematics Partnership Building Mathematical Knowledge and High-Leverage Instruction for Student Success July 18, 2016 8:00-9:30 Joe

Summer Instructional Staff Dr. DeAnn Huinker, UWM Curriculum & Instruction Dr. Michael Steele, UWM Curriculum & Instruction Dr. Kevin McLeod, UWM Mathematical Sciences Dr. Henry Kepner, UWM Curriculum & Instruction Mr. Joe Giera, South Milwaukee School District Ms. Beth Schefelker, South Milwaukee School District Ms. Liz Cutter, Whitnall School District

School Districts School District of Cudahy School District of South Milwaukee Milwaukee Public Schools

Project Goals Goal 1. Deepen mathematical knowledge & understanding of content progressions aligned to the Common Core State Standards for Mathematics. Goal 2. Strengthen instruction through the use of high-leverage teaching practices to increase student success in mathematics. Goal 3. Increase teacher collaboration within and across schools in moving to common practice with the Common Core.

Geometry & Measurement Summer Institute 2016 Geometry & Measurement Focus on: Operations and Algebraic Thinking Domain Extensions to Expressions and Equations domain in Grades 6-8 Connections to NBT and NS

Learning Intentions & Success Criteria We are developing: An understanding of the big ideas of the Geometry and Geometric Measurement as outlined in the CCSSM. We will know we are successful when we can: Identify the big ideas of Geometry and Geometric Measurement. Identify a need to improve instructional practice in the domains of geometry and geometric measurement.

Emphasize here that our focus is on geometry and geometric measurement Emphasize here that our focus is on geometry and geometric measurement. (We will not look at other forms of measurement—weight, time, etc.—and we will not look at Data in the “Measurement and Data” domain.

TIMSS Data Grade 4 Whole Numbers Fractions and Proportionality Measurement Estimation and Number Sense Geometry International Mean 67 49 56 64 United States 71 51 53 Grade 8 Fractions / Number Sense Proportionality Measurement 58 45 59 42 40 48 The Trends in International Mathematics and Science. The Trends in International Mathematics and Science Study(TIMSS) provides reliable and timely data on the mathematics and science achievement of U.S. students compared to that of students in other countries.

General conclusions… As numerous studies have shown, U.S. elementary and middle school students are failing to develop an adequate understanding of geometric concepts, geometric reasoning and geometric problem solving. Furthermore, a majority are unprepared to study the more sophisticated geometric concepts and proof in high school. (Clement and Battista 1992) Read it, turn and talk- what’s one sentence that stood out for you? TCM February 1999

Additional thoughts… U.S. students seemed to do better on items that were straightforward but formal in nature and not as well on spatial visualization and problem solving. The results suggest that U.S. students need more experience with spatial visualization, solving geometric problems and three dimensional geometry.

8th Grade TIMSS 2011 Geometric Shape - Reasoning

8th Grade TIMSS 2011 Geometric Measurement - Applying

4th Grade TIMSS 1995 Geometric Measurement - Applying

4th Grade TIMSS 1995 Geometry

4th Grade TIMSS 1995 Geometry

Suggestions To improve geometry teaching significantly, teachers need tasks that help them better understand the nature of their students’ geometric reasoning, and they need to know what research says about such reasoning. Where is this quote from?? TCM February 1999

As students engage in Geometry and Measurement tasks… What are you looking for as students work, as well as, in student work samples? What are you listening for? What questions should you be asking to target the mathematical idea(s)? How will you use this information to support focused discussions?

Starting on the same page

Geometry and Geometric Measurement: Easy targets for humor When you heard this class would be ending with geometry and measurement, what were you thinking? As you talked, what were some of the ideas brought forward?

Thinking back on your own math education… If you preferred Geometry, go to the left side of the room. If you preferred Algebra/Number, go to the right side of the room. If you liked both, go to the back of the room. If you liked neither, go to the front of the room. Beth & Liz (preface with connection to when) Conversation: What do you notice about the sort?

Building Common Ground Find a partner in your group and have a short conversation about what you have in common with your feelings about Geometry. Find a partner across the room and share your feelings about Geometry.

Building the Landscape of Geometry and Geometric Measurement Brainstorm concepts and ideas you believe are related to the topic of Geometry and Geometric Measurement. In trios.. record each original idea on a sticky note. In table groups…Share and sort into categories; place onto your poster. Debrief: What are some of the categories you came up with? Onto poster paper Use sticky notes and move around

Essential Understandings of Geometry Classification of Shapes Features or properties of geometric shapes can be analyzed and described to define and refine classification schemes with growing precision. Spatial Visualization Spatial relationships and spatial structuring involves developing, attending to, and learning how to work with imagery, as well as to specify locations. Geometry is the branch of mathematics that addresses spatial sense and geometric reasoning. Take out and study. What do you notice? Try to make sense in these. Talk in groups. Did any of this come up in your posters? Transformations Transformation involves working with geometric phenomena in ways that build on spatial intuition by explaining what does and does not change when moving and altering the objects and the space that they occupy.

Essential Understandings of [Geometric] Measurement How Much Measurement specifies “how much” by assigning a number that corresponds to a certain unit to attributes such as length, area, volume, and angle. Comparing Some attributes can be compared directly, others are measured and compared indirectly, and some are computed from other measurements. Motion Motion is useful in coordinating attributes and measures of length, area, volume, and angle. One way to analyze and describe geometric objects, relationships among them, or the space they occupy is to quantify—measure or count—one or more of their attributes. Geometric measurement vs measurement These are my “how” Composing and Decomposing Building or breaking apart objects facilitate measuring them; those decompositions and compositions clarify relationships between attributes and units of measure and are the basis to derive formulas. V = B h

Stop & Jot: As a learner of math, identify your confidence level with Geometry on a scale of 1 to 5. What are you hoping to learn from this study of Geometry? As a teacher of math, identify your confidence level with Geometry on a scale of 1 to 5. What are you hoping to gain from this study of Geometry?

Starting with geometric measurement

Progressions Document: K-5 Geometric Measurement Open your K-5 Geometric Measurement Progressions document to page 2 Read the overview through the bottom of page 3. Highlight crucial ideas that help define the study of Geometric Measurement.  Check in with your shoulder partners about the crucial ideas and why you thought they were important. Chart big ideas they are listing from the progressions doc Length is continuous, it connects to, but is different from cardinality Kids have to understand what an attribute is Indirect vs. direct comparison Creating personal benchmarks Overarching concept of a unit Geometric measurement connects the 2 most critical domains of early math- geometry and number

Progressions: Geometry, 7-8, High School Read the Overview at the top of page 2 and the paragraph on Geometric Measurement at the top of page 4. Turn and Talk… Where does the work we just read about in K-5 grow as students move to the upper grades?

Learning Intentions & Success Criteria We are developing: An understanding of the big ideas of the Geometry and Geometric Measurement as outlined in the CCSSM. We will know we are successful when we can: Identify the big ideas of Geometry and Geometric Measurement. Identify a need to improve instructional practice in the domains of geometry and geometric measurement.

Core Mathematics Partnership Project Disclaimer Core Mathematics Partnership Project University of Wisconsin-Milwaukee, 2013-2016   This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors. This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.