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Mathematics Standard 4.4 Spatial Sense and Geometry
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Mathematics Standard 4.4 Spatial Sense and Geometry.

Jan 17, 2016

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Page 1: Mathematics Standard 4.4 Spatial Sense and Geometry.

Mathematics Standard 4.4Spatial Sense and

Geometry

Page 2: Mathematics Standard 4.4 Spatial Sense and Geometry.

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

Page 3: Mathematics Standard 4.4 Spatial Sense and Geometry.

Five goals….in action

Problem solving?

Communicating?

Reasoning?

Connecting?

Representing?

Page 4: Mathematics Standard 4.4 Spatial Sense and Geometry.

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.

Page 5: Mathematics Standard 4.4 Spatial Sense and Geometry.

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.

Page 6: Mathematics Standard 4.4 Spatial Sense and Geometry.

Geometry

Page 7: Mathematics Standard 4.4 Spatial Sense and Geometry.

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)

Page 9: Mathematics Standard 4.4 Spatial Sense and Geometry.

3 Dimensional Shapes – 3D

Page 10: Mathematics Standard 4.4 Spatial Sense and Geometry.

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

Page 11: Mathematics Standard 4.4 Spatial Sense and Geometry.

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

Page 12: Mathematics Standard 4.4 Spatial Sense and Geometry.

Visualization recall and represent what was seen visually

Page 13: Mathematics Standard 4.4 Spatial Sense and Geometry.

Visualization see from different orientations

Page 14: Mathematics Standard 4.4 Spatial Sense and Geometry.

Visualization seeing block creations from different

perspectives

Page 15: Mathematics Standard 4.4 Spatial Sense and Geometry.

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).

Page 16: Mathematics Standard 4.4 Spatial Sense and Geometry.

4.4.1: Respond to and use positional words

Page 17: Mathematics Standard 4.4 Spatial Sense and Geometry.

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.

Page 18: Mathematics Standard 4.4 Spatial Sense and Geometry.

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

Page 19: Mathematics Standard 4.4 Spatial Sense and Geometry.

I have one curved face, I have 2 flat circular faces.

What am I?

I’m a Cylinder!

Page 20: Mathematics Standard 4.4 Spatial Sense and Geometry.

My shape is round, my side is 1, can you guess my name?

I’m a Circle!

Page 21: Mathematics Standard 4.4 Spatial Sense and Geometry.

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!

Page 22: Mathematics Standard 4.4 Spatial Sense and Geometry.

I have 3 sides and they are all straight. I have also 3 corners

Can you guess my name?

I’m a Triangle!

Page 23: Mathematics Standard 4.4 Spatial Sense and Geometry.

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!

Page 24: Mathematics Standard 4.4 Spatial Sense and Geometry.

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 ?

Page 25: Mathematics Standard 4.4 Spatial Sense and Geometry.

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!

Page 26: Mathematics Standard 4.4 Spatial Sense and Geometry.

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!

Page 27: Mathematics Standard 4.4 Spatial Sense and Geometry.

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?

Page 28: Mathematics Standard 4.4 Spatial Sense and Geometry.

4.4.3: Manipulate, compare and discuss the attributes of 2D & 3D

shapes.

Page 29: Mathematics Standard 4.4 Spatial Sense and Geometry.

The Teacher’s Role in Promoting Understanding of Number and

Counting

• Throughout the day

• Through high-quality teacher-child interactions

• Throughout the environment

Page 30: Mathematics Standard 4.4 Spatial Sense and Geometry.

Throughout the Environment

Page 31: Mathematics Standard 4.4 Spatial Sense and Geometry.

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.

Page 32: Mathematics Standard 4.4 Spatial Sense and Geometry.

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