CCGPS Mathematics Unit-by-Unit Grade Level Webinar First Grade Unit 3: Understanding Shapes and Fractions September 5, 2012 Session will be begin at 3:15 pm While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

CCGPS Mathematics Unit-by-Unit Grade Level Webinar Grade One Unit 3: Understanding Shapes and Fractions September 5, 2012 Turtle Toms– Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Expectations and clearing up confusion This webinar focuses on CCGPS content specific to Unit 3, Grade One. For information about CCGPS across a single grade span, please access the list of recorded GPB sessions on Georgiastandards.org. For information on the Standards for Mathematical Practice, please access the list of recorded Blackboard sessions from Fall 2011 on GeorgiaStandards.org. CCGPS is taught and assessed from and beyond. A list of resources will be provided at the end of this webinar and these documents are posted on the K-5 wiki.

Expectations and clearing up confusion The intent of this webinar is to bring awareness to:  the types of tasks contained in the unit.  your conceptual understanding of the mathematics in this unit.  approaches to tasks which provide deeper learning situations for your students. We will not be working through each task during this webinar.

Welcome! Thank you for taking the time to join us in this discussion of Unit 3. At the end of today’s session you should have at least 3 takeaways:  The big idea of Unit 3  Something to think about… food for thought  How can I support student understanding?  What is my conceptual understanding of the material in this unit?  a list of resources and support available for CCGPS mathematics

Please provide feedback at the end of today’s session.  Feedback helps us all to become better teachers and learners.  Feedback helps as we develop the remaining unit-by-unit webinars.  Please visit to share your feedback. After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. Turtle Gunn Toms– Elementary Mathematics Specialist

Activate your Brain What is a “regular” shape? Which of these are regular? Bonus for the curious :

Activate your Brain What is a rectangular shape? Which of these are rectangles? Bonus for the curious:

Misconceptions It is important to realize that inevitably students will develop misconceptions… Askew and Wiliam 1995; Leinwand, 2010; NCTM, 1995; Shulman, 1996

Activate your Brain What is a “regular” shape? Which of these are regular?

Activate your Brain What is a “regular” shape?

Activate your Brain What is a “regular” shape?

Misconception – Invented Rule?

Square

Misconception- Invented Rule? Which ones are trapezoids?

Misconceptions

Shape properties- failure to identify examples of shapes that are not identical to their own mental image or prototype. Shape orientation- Shapes are not recognized unless in “usual” orientation. Language-based- – Level 1- corners, pointy, diamond, – Higher levels- angle, rectangular, rhombus, kite, congruency

Misconceptions Therefore it is important to have strategies for identifying, remedying, as well as for avoiding misconceptions. Leinwand, 2010; Swan 2001; NBPTS, 1998; NCTM, 1995; Shulman, 1986;

Misconceptions What vocabulary have we used in our discussion of misconceptions today?

Misconceptions Size of share is directly related to number of shares. Fourths are larger in size than halves, because 4 is a greater number than 2.

Misconceptions Be careful in your use of language here and everywhere. Larger and smaller are indicators of size, not quantity, and so can be confused by students. Use greater than and less than, or more and fewer, when discussing number and quantity.

What’s the big idea? Students describe their physical world using geometric ideas and vocabulary. They can describe, create, and categorize shapes based on likenesses and differences. Students possess spatial thinking. Students can partition shapes into equal parts of a whole.

What’s the big idea? Understanding geometric likenesses and differences. Describing the physical world using geometric ideas and vocabulary. Understanding of equal size, quantity, or value.

What’s the other big idea? Standards for Mathematical Practice What might this look like in the classroom? Wiki- Inside math- Illustrative Mathematics- Edutopia- Teaching channel- Math Solutions-

Activate your Brain

What’s the big idea? Enduring Understandings Essential Questions Common Misconceptions Strategies for Teaching and Learning Overview Standards

Coherence and Focus – Unit 3 What are students coming with from Unit 2? A developing understanding of number sequence, number and quantity, and some beginning ideas about addition and subtraction.

Coherence and Focus- Unit 3 Where does this understanding lead students? Look in your unit and find the Enduring Understandings.

Coherence and Focus – Unit 3 View across grade bands K-6 th  Understanding the fundamental properties of geometric figures  Understanding angles and angle measure  Geometric measurement- area, perimeter, volume  Coordinate plane as a way to visualize and mathematize geometric ideas.  Fraction understanding, operations with fractions. 8 th -12 th  Everything!

Navigating Unit Three The only way to gain deep understanding is to work through each task. No one else can understand for you. Make note of where, when, and what the big ideas are. Make note of where, when, and what the pitfalls might be. Look for additional tools/ideas you want to use Determine any changes which might need to be made to make this work for your students. Share, ask, and collaborate on the wiki.

Revision-ish Unit 3 We have reposted Unit 3, with the alignment issues corrected. It can be found in LV and on GSO. Labeling of fractions (1/2, etc…)- not a requirement, ultimately your call. Watch your language. MD. 4 not overtly addressed, however, it is on the map. Page 19 of the 1 st grade GLO- Cluster 1 and K.G.1 doesn’t need to be there forever, is included as a nod to the transition standard, positional words.

Questions from the Wiki Labeling of fractions Why is unit 3 suddenly about fractions? Why are operations and algebraic thinking put all the way at Unit 5?

What’s the big idea? Understanding geometric likenesses and differences. Describing the physical world using geometric ideas and vocabulary. Partitioning shapes into equal shares.

Examples & Explanations Standards addressed in Unit 3 CCGPS.1.G.1: Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes.

Examples & Explanations Standards addressed in Unit 3 CCGPS.1.G.2 : Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

Basic Understandings for Teachers Polygon- a plane figure bounded by three or more straight sides Square-a polygon with four equal sides, 4 right angles Triangle- a polygon with exactly three sides Rectangle- Two pairs of parallel sides, and 4 right angles Hexagon- a polygon with exactly six sides. Trapezoid- a quadrilateral with at least one pair of parallel sides.

Basic Understandings for Teachers Circle- a 2D figure that consists of all points equidistant from its center. “Perfectly round” Closed polygon- a two-dimensional figure in which exactly two sides meet at every vertex, and no sides cross each other

Basic Understandings for Teachers Prism- a 3D shape with 2 identical (congruent) parallel bases that are polygons, with corresponding sides of the bases connected with rectangles (right prisms) if connected with polygons they are oblique prisms. Cube- a right prism whose faces are all squares Right rectangular prism- See prism, and have the parallel bases be rectangles. Right indicates that the elements of the prism are perpendicular to the bases.

Basic Understandings for Teachers Cone- a 3D shape with one base that is a circle (or other curved shape) connected to a single point, the apex, which lies in a plane outside the plane of the base, creating a curved surface. Cylinder- a 3D shape with two identical parallel bases that are circles (or other curved shapes) connected by a curved surface. Sphere-a 3D shape which has all points on its surface a fixed distance from a point called its center. “perfectly round ball”

Examples & Explanations Standards addressed in Unit 3 CCGPS.1.G.3 : Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Examples & Explanations Standards addressed in Unit 3 CCGPS.1.MD.4 : Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than another.

Examples & Explanations Resources which work with Unit 3: Blocks Clay Sketches Collages Constructions Thinking… Modeling

Examples and Explanations What understandings do students need in order to think geometrically? Exposure to and use of geometric vocabulary Exposure to shapes of different sizes and orientations, both regular and irregular Non-examples Hands-on grappling with shapes, shape construction, shape decomposition and composition, shape partitioning

Examples & Explanations Geometric Thinking Look for likenesses and differences. Expansiveness of thought Understanding of properties at an appropriate developmental level Reasoning and articulating thought both verbally and in journals

Examples & Explanations

Where is it going?

Examples & Explanations

h/geometry/ h/geometry/

How to develop all of these? Hold number talks regularly, expand them to include geometric ideas that support development of understanding. Not sure about the geometry yourself? VandeWalle, “Teaching Student-Centered Mathematics- K-3” Clements and Sarama- “Learning and Teaching Early Math”

Just remember:

Examples & Explanations Standards: Illustrative Mathematics- MD.4 SEDL- Tools: Tools for the Common Core: standards/ On the wiki: Discussion threads Unpacked standards from other states. Proceed with caution.

Assessment

Formative- tasting while you cook. Summative- the completed dish.

Navigating Unit Three The only way to gain deep understanding is to work through each task. No one else can understand for you. Make note of where, when, and what the big ideas are. Make note of where, when, and what the pitfalls might be. Look for additional tools/ideas you want to use Determine any changes which might need to be made to make this work for your students. Share, ask, and collaborate on the wiki.

Resource List The following list is provided as a sample of available resources and is for informational purposes only. It is your responsibility to investigate them to determine their value and appropriateness for your district. GaDOE does not endorse or recommend the purchase of or use of any particular resource.

Have you visited the wiki yet?

Very First Grade Wiki- 5.wikispaces.com/ 5.wikispaces.com/ Inside math- Edutopia- Teaching channel- Blogs/websites   

Resources Books  Van De Walle and Lovin, Teaching Student- Centered Mathematics, K-3  Clements and Sarama, Learning and Teaching Early Math  Parrish, Number Talks  Shumway, Number Sense Routines  Wedekind, Math Exchanges

Resources Common Core Resources  SEDL videos - Core/Pages/Math.aspx or Core/Pages/Math.aspxhttp://secc.sedl.org/common_core_videos/  Illustrative Mathematics -  Dana Center's CCSS Toolbox -  Arizona DOE - practices/mathematics-standards/ practices/mathematics-standards/  Inside Mathematics-  Common Core Standards -  Tools for the Common Core Standards -  Phil Daro talks about the Common Core Mathematics Standards -

Resources Professional Learning Resources  Inside Mathematics-  Edutopia –  Teaching Channel -  Annenberg Learner - Assessment Resources  MARS -  MAP -  PARCC -

As you start your day tomorrow…

Thank You! Please visit to provide us with your feedback! Turtle Gunn Toms Program Specialist (K-5) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Join the listserve! Follow on Twitter! (yep, I’m tweeting math resources in a very informal manner)