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Mathematics Standard 4.4Spatial Sense and
Geometry
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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
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Five goals….in action
Problem solving?
Communicating?
Reasoning?
Connecting?
Representing?
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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.
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BIG Ideas
Content Strand Big Idea
Number and Operations Number names allow us to tell how many are in a set.
Measurement Comparisons can show which is bigger, but they have to be fair.
Geometry Two shapes can be combined to make another shape.
Algebra A single collection of objects can always be sorted in more than one way.
Data Analysis Collecting and organizing data makes it easier to answer questions.
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Geometry
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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)
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2 Dimensional Shapes – 2D
Triangle Square
Circle
Rectangle
Octagon
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3 Dimensional Shapes – 3D
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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
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Transformations moving shapes by sliding, flipping them over, turning and combining them
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Visualization recall and represent what was seen visually
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Visualization see from different orientations
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Visualization seeing block creations from different
perspectives
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4.4: Children develop spatial and geometric sense. 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:
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).
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4.4.1: Respond to and use positional words
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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.
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We are 2-D and 3-D shapes but we’re not the same. Think very hard, try and guess our names!
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I have one curved face, I have 2 flat circular faces.
What am I?
I’m a Cylinder!
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My shape is round, my side is 1, can you guess my name?
I’m a Circle!
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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!
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I have 3 sides and they are all straight. I have also 3 corners
Can you guess my name?
I’m a Triangle!
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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!
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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 ?
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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!
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I have 4 straight edges.2 of my edges are longand 2 are shorter. Butdon’t forget, I also have4 corners.
Now guess, what am I ?
I’m a Rectangle!
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I’m a Rectangular Prism!
I have 6 flat faces, myfaces are all rectangles(square or oblong), Ihave 12 straight edgesand 8 corners.
Can you guess my name?
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4.4.3: Manipulate, compare and discuss the attributes of 2D & 3D
shapes.
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The Teacher’s Role in Promoting Understanding of Number and
Counting
• Throughout the day
• Through high-quality teacher-child interactions
• Throughout the environment
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Throughout the Environment
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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.
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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