1. Mathematics Standard 4.4 Spatial Sense and Geometry

2. Five goals…for preschool students to.. become mathematical problem solvers that communicate mathematically; reason mathematically; make mathematical connections; and use mathematical representations to model and interpret practical situations

3. Five goals….in action Problem solving? Communicating? Reasoning? Connecting? Representing?

4. New Jersey’s Revised Preschool Math Standards 4.1: Children begin to demonstrate an understanding of number and counting. 4.2: Children demonstrate an initial understanding of numerical operations. 4.3: Children begin to conceptualize measurable attributes of objects. 4.4: Children develop spatial and geometric sense.

5. BIG Ideas Content StrandBig Idea Number and OperationsNumber names allow us to tell how many are in a set. MeasurementComparisons can show which is bigger, but they have to be fair. GeometryTwo shapes can be combined to make another shape. AlgebraA single collection of objects can always be sorted in more than one way. Data AnalysisCollecting and organizing data makes it easier to answer questions.

6. Geometry

7. Four Important Geometry Concepts: Shape (two and three dimensional shapes) Space (positional words) Transformations (moving shapes by sliding, flipping them over, turning and combining them) Visualization (recall and represent what was seen visually)

8. 2 Dimensional Shapes – 2D Triangle Square Circle Rectangle Octagon

9. 3 Dimensional Shapes – 3D

10. on top of the box next to the box inside the box on the table in-front or behind the box around the box close to/farther away 4.4.1: Respond to and use positional words

11. Transformations moving shapes by sliding, flipping them over, turning and combining them

12. Visualization recall and represent what was seen visually

13. Visualization see from different orientations

14. Visualization seeing block creations from different perspectives

15. 4.4: Children develop spatial and geometric sense. 4.4.1: Respond to and use positional words (e.g., in, under, between, down, behind). 4.4.1: Respond to and use positional words (e.g., in, under, between, down, behind). 4.4.2: Use accurate terms to name and describe some two-dimensional shapes and begin to use accurate terms to name and describe some three-dimensional shapes (e.g., circle, square, triangle, sphere, cylinder, cube, side point, angle). 4.4.2: Use accurate terms to name and describe some two-dimensional shapes and begin to use accurate terms to name and describe some three-dimensional shapes (e.g., circle, square, triangle, sphere, cylinder, cube, side point, angle). b. three-dimensional shapes by building with blocks and with other materials having height, width, and depth (e.g., unit blocks, hollow blocks, attribute blocks, boxes, empty food containers, plastic pipe). b. three-dimensional shapes by building with blocks and with other materials having height, width, and depth (e.g., unit blocks, hollow blocks, attribute blocks, boxes, empty food containers, plastic pipe). 4.4.3: Manipulate, compare and discuss the attributes of: a. two-dimensional shapes (e.g., use two dimensional shapes to make designs, patterns and pictures by manipulating materials such as paper shapes, puzzle pieces, tangrams; construct shapes from materials such as straws; match identical shapes; sort shapes based on rules [something that makes them alike or different]; describe shapes by sides and/or angles; use pattern blocks to compose/decompose shapes when making and taking apart compositions of several shapes). a. two-dimensional shapes (e.g., use two dimensional shapes to make designs, patterns and pictures by manipulating materials such as paper shapes, puzzle pieces, tangrams; construct shapes from materials such as straws; match identical shapes; sort shapes based on rules [something that makes them alike or different]; describe shapes by sides and/or angles; use pattern blocks to compose/decompose shapes when making and taking apart compositions of several shapes).

16. 4.4.1: Respond to and use positional words up near under in below down far over out above

17. 4.4.2: Use accurate terms to name and describe some two-dimensional shapes and begin to use accurate terms to name and describe some three-dimensional shapes.

18. We are 2-D and 3-D shapes but we’re not the same. Think very hard, try and guess our names!

19. I have one curved face, I have 2 flat circular faces. What am I? I’m a Cylinder!

20. My shape is round, my side is 1, can you guess my name? I’m a Circle!

21. I have no flat faces. I have no straight edges, and I have just only one curved face. What am I? I’m a Sphere!

22. I have 3 sides and they are all straight. I have also 3 corners Can you guess my name? I’m a Triangle!

23. I have one curved face, my only one flat face is a circle, and I have one vertex(corner). What am I? I’m a Cone!

24. I’m a Cube! I have 6 flat square faces, I have 12 straight edges, and I have 8 corners. Can you guess my name ?

25. I have 4 sides and 4 corners, try and guess my name? They are all straight, and are all the same! I’m a Square!

26. I have 4 straight edges. 2 of my edges are long and 2 are shorter. But don’t forget, I also have 4 corners. Now guess, what am I ? I’m a Rectangle!

27. I’m a Rectangular Prism! I have 6 flat faces, my faces are all rectangles (square or oblong), I have 12 straight edges and 8 corners. Can you guess my name?

28. 4.4.3: Manipulate, compare and discuss the attributes of 2D & 3D shapes. recognize shapes build with them illustrate them describe them compose and decompose compare & sort them predict what will happen when they build with them

29. The Teacher’s Role in Promoting Understanding of Number and Counting Throughout the day Through high-quality teacher-child interactions Throughout the environment

30. Throughout the Environment

31. Teachers are the key! For students to become mathematicians they need to organize and interpret their world through a mathematical lens. It is the teacher’s job to keep the lens in focus…the actions of learning and teaching are inseparable.

32. Resources The Creative Curriculum Vol 4 Mathematics Teaching Strategies, Copley, Jones and Dighe Teaching and Learning Math: The Learning Trajectories Approach by Douglas H. Clements and Julie A. Sarama The Building Blocks of Math: Lessons from Research, featuring Dr. Doug Clements