THE SAME OR NOT THE SAME…THAT IS THE QUESTION? MATH ALLIANCE TEACHING ALL LEARNERS January 11, 2011 Beth SchefelkerJudy Winn Melissa Hedges

LEARNING INTENTIONS AND SUCCESS CRITERIA We are learning to develop an understanding about the relationship between rigid motion and congruency. We will know when we are successful when we can apply rigid motion to understand shapes from a different perspective to prove congruency.

CAN YOU FIND ALL POSSIBLE ARRANGEMENTS? Work with a partner. Select five color tiles of the same color. Join the five color tiles so that each square must have at least one whole side of a square must touch another whole side of another square.

FINDING ARRANGEMENTS Using the five tiles find all of the unique arrangements that can be made with the tiles. Something to think about… How many unique arrangements do you think there are? How do you know when you have found them all?

PENTOMINOES A pentomino is a shape formed by joining 5 squares as if cut from a square grid.

TRANSFORMATIONS Translations - Slides Flips Turns/Rotations

Describing Figures Coordinate Systems Spatial Relationships and Transformations Geometry Subskills

DELORES: TWISTS AND TURNS CASE 24 What struggles did the teacher note as students worked on the pentominoes? Children are trying to decide which figures in a set are unique and which are copies? Explain the connection between this task and the meaning of congruence. What ideas about congruence are highlighted in this case?

SOMETHING TO THINK ABOUT…. Many textbooks and worksheets prematurely require students to manipulate figures visually and as they name and describe the transformations…students need to use materials which allow them to feel the movement. (Bamberger, Oberdorf, and Schultz-Ferrell, 2010, p. 96)

FEEDBACK ON BINDERS BIG IDEA #1: LESSON ANALYSIS Looked carefully at the way the lessons were set up and presented, noting aspects such as.. Nature of examples provided Questions provided Vocabulary Opportunities for explorations Format of the lesson

FEEDBACK ON BINDERS BIG IDEA #1 PART C: LESSON ANALYSIS For the next two Big Ideas Use understandings gained about the Big Idea to analyze and critique how the mathematics is developed in your textbook materials. Keep in mind the focus for the big ideas is on the mathematics being taught. NOTE: This is not related to features of the text and lesson. We are looking for evidence that your critiques are primarily guided by the mathematics

FEEDBACK ON BINDERS BIG IDEA #1 PART C: DIFFERENTIATION Differentiation suggestions as provide by the textbook or in your suggestions: Considered suggestions offered by the textbook to support students with barriers (i.e. language and visual-spatial) Considered the structure of the following features: Introductions Questions Students explorations Small group activities

FEEDBACK ON BINDERS BIG IDEA #1 PART C: DIFFERENTIATION Important Findings You Noted: Sometimes the suggestions for differentiation didnt connect to the Big Idea of the mathematics in the lesson!

FEEDBACK ON BINDERS BIG IDEA I: FEATURES OF POLYGONS Differentiation section for the next two Big Ideas Focus even more on relating differentiation to conceptual understanding Go beyond accommodations to provide access

HOMEWORK FOR Part A: In the case we read in class, Delores: Twists and Turns (Case 24, p ), there are three rows of figures created with the square tiles (one after line 149 and two after line 177). For each row: Using grid paper, cut out 10 identical copies of the first shape. Describe the transformation(s) - slides, flips, and turns - that relate the first figure in each row to each of the other figures in that row. Part B: Read Case 25, Ellie: Making Shapes with Triangles (p ) and be ready to discuss it in class on January 25.