Mathematics Standard 4.4Spatial 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

Five goals….in action

Problem solving?

Communicating?

Reasoning?

Connecting?

Representing?

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.

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.

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)

2 Dimensional Shapes – 2D

Triangle Square

Circle

Rectangle

Octagon

3 Dimensional Shapes – 3D

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

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

Visualization recall and represent what was seen visually

Visualization see from different orientations

Visualization seeing block creations from different

perspectives

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).

4.4.1: Respond to and use positional words

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.

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

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

What am I?

I’m a Cylinder!

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

I’m a Circle!

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!

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

Can you guess my name?

I’m a Triangle!

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!

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 ?

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!

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!

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?

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

shapes.

The Teacher’s Role in Promoting Understanding of Number and

Counting

• Throughout the day

• Through high-quality teacher-child interactions

• Throughout the environment

Throughout the Environment

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.

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