mathematics standard 4.4 spatial sense and geometry
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Mathematics Standard 4.4Spatial Sense and Geometry
Five goalsfor preschool students to..become mathematical problem solvers thatcommunicate mathematically;reason mathematically;make mathematical connections; anduse mathematical representations to model and interpret practical situations
Five goals.in actionProblem solving?Communicating?Reasoning?Connecting?Representing?
New Jerseys Revised Preschool Math Standards4.1: 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.
Content StrandBig IdeaNumber 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.
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 away4.4.1: 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. 4.4.1: 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).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).
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 were 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?
Im a Cylinder!
My shape is round, my side is 1, can you guess my name?
Im a Circle!
I have no flat faces. I have no straight edges, and I have just only one curved face.
What am I?
Im a Sphere!
I have 3 sides and they are all straight. I have also 3 cornersCan you guess my name?
Im a Triangle!
I have one curved face, my only one flat face is a circle, and I have one vertex(corner).
What am I?
Im a Cone!
Im 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! Im a Square!
I have 4 straight edges.2 of my edges are longand 2 are shorter. Butdont forget, I also have4 corners.
Now guess, what am I ?Im a Rectangle!
Im 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 Teachers 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 needto organize and interpret their world through amathematical lens. It is the teachers job to keep thelens in focusthe actions of learning and teachingare inseparable.
ResourcesThe 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
Todays workshop is all about New Math Standards 4.4: Spatial Sense and Geometry what preschoolers should know and be able to do.
To define content of Standard 4.4, giving teachers a deeper understanding of geometric concepts and spatial sense.
To explore classroom materials and create short activities that demonstrate high quality interactions as they are align to Standards 4.4.
*What you say:
These are the 5 goals or process skills we want our preschoolers to be actively engaged during math and through out their day; these goals are interwoven throughout each of the Standards.
***Transition to the next .****You will read each process skill, define it and give an example ( provided below) *** Problem Solving: finding a solution or an answer to a question
Example: It looks like you have used shapes and what made you draw some figures while others you used the real shapes?
Communicating: Sharing thoughts, ideas, and feelings with others through gestures, facial expressions, drawings, writing, and speaking.
Example: It looks like you have used shapes to make columns (rows), what made you draw some figures while others you used the real shapes?
Reasoning: Thinking through a question or a problem to arrive at an answer.
Example: Can you tell me what you have done with of the shapes/colors?
(mathematical reasoning is a key process in learning and developing mathematical knowledge in all areas of mathematics, including number and operations, classification, patterning, measurement, and geometry)
Connecting: Linking new learning to previous experience.
Example: I can see that you have sorted all the shapes that look the same by color, can you remember something else we did in discovery that we sorted by shape or color?
Representing: Showing ones thoughts or ideas in a variety of ways using a variety of tools.
Example: I can see that you have used shapes and have drawn some shapes on your work, can you tell me more about your work?
Reasoning, communicating, and representing lend themselves, specially, to data analysis.****Take a minute and show audience the Standards, the teachers practice and the learning outcomes.***You will read/say:
Each part of the Standard. Each of the Standard have Preschool Numbers and indicators, we will be discussing these ahead.The learning outcomes for each of the standards are targeted for the end of the 4 year old experience.Also emphasize the words begins to, explaining to participants that we are helping young children explore and expand their understanding of math content.
Standard 1 is about number sense ------------------------------------------------------------------- Common Core Domain Alignment with/ Counting and Cardinality -childrens understanding of numbers and quantities.
Standard 2 is about number sense ------------------------------------------------------------------- Common Core Domain Alignment with/ Counting and Cardinality -childrens understanding of number relationships and operations.
Standard 3 is about conceptualize measurable attribute -----------------------------Common Core Domain Alignment with/ Measurement and Data Childrens ability to .-compare, -order; and -begin to measure. Standard 4 is about spatial and geometric sense -----------------------------------------------Common Core Domain Alignment with/ Geometry-childrens ability to identify and use shapes; and -childrens understanding of position in space. ****This is a handout**
You will say:In a high-quality preschool classroom, preschoolers are intentionally introduced to and engage in the big ideas or (common core goals.)
This is an example of Big Ideas. There are many other Big Ideas.
Each of the Big ideas are embedded throughout the preschool Standards/Strands.
Data analysis runs through the teaching practices for each of the 4 strands.
*Geometry is all about shapes and spaces, and shapes properties.Geometry is about manipulating, comparing, and discussing 2D and 3D shapes.