Transcript K-2 Geometry Power Point 2 22 14

Geometry
Grades K-2
Goals:
 Build an understanding of the mathematical
concepts within the Geometry Domain
 Analyze how concepts of Geometry progress
through the grades
 Discuss the van Hiele levels of geometric thought
 Explore Geometry Stations and Resources to Take
Back to Your Classroom
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Progression of Geometry
Kindergarten
Major Clusters
Counting and Cardinality
 Know number names and the count sequence.
 Count to tell the number of objects.
 Compare numbers.
Operations and Algebraic Thinking
 Understand addition as putting together and
Supporting/Additional Clusters
Measurement and Data
 Describe and compare measurable attributes.
 Classify objects and count the number of
objects in categories.
Geometry
 Identify and describe shapes.
adding to, and understand subtraction as taking 
Analyze, compare, create, and compose
apart and taking from.
shapes.
Number and Operations in Base Ten
 Work with numbers 11–19 to gain foundations
for place value.
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Progression of Geometry
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Progression of Geometry
Second Grade
Major Clusters
Operations and Algebraic Thinking
 Represent and solve problems involving addition
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
and subtraction.
Add and subtract within 20.
Work with equal groups of objects to gain
foundations for multiplication.
Supporting/Additional Clusters
Measurement and Data
 Work with time and money.
 Represent and interpret data.
Geometry
 Reason with shapes and their attributes.
Number and Operations in Base Ten
 Understand place value.
 Use place value understanding and properties of
operations to add and subtract.
Measurement and Data
 Measure and estimate lengths in standard units.
 Relate addition and subtraction to length.
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Kindergarten
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes,
cones, cylinders, and spheres).
1. Describe objects in the environment using names of shapes, and describe the
relative positions of these objects using terms such as above, below, beside, in
front of, behind, and next to.
2. Correctly name shapes regardless of their orientations or overall size.
3. Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional
(“solid”).
Analyze, compare, create, and compose shapes.
4. Analyze and compare two- and three-dimensional shapes, in different sizes and
orientations, using informal language to describe their similarities, differences,
parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g.,
having sides of equal length).
5. Model shapes in the world by building shapes from components (e.g., sticks and
clay balls) and drawing shapes.
6. Compose simple shapes to form larger shapes. For example, “Can you join these two
triangles with full sides touching to make a rectangle?”
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First Grade
Reason with shapes and their attributes.
1. Distinguish between defining attributes (e.g., triangles are closed and three-sided)
versus non-defining attributes (e.g., color, orientation, overall size) ; build and
draw shapes to possess defining attributes.
2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular
prisms, right circular cones, and right circular cylinders) to create a composite
shape, and compose new shapes from the composite shape.1
3. Partition circles and rectangles into two and four equal shares, describe the shares
using the words halves, fourths, and quarters, and use the phrases half of, fourth
of, and quarter of. Describe the whole as two of, or four of the shares. Understand
for these examples that decomposing into more equal shares creates smaller
shares.
_________________
1 Students do not need to learn formal names such as “right rectangular prism.”
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Second Grade
Reason with shapes and their attributes.
1. Recognize and draw shapes having specified attributes, such as a given
number of angles or a given number of equal faces.1 Identify triangles,
quadrilaterals, pentagons, hexagons, and cubes.
2. Partition a rectangle into rows and columns of same-size squares and count
to find the total number of them.
3. Partition circles and rectangles into two, three, or four equal shares,
describe the shares using the words halves, thirds, half of, a third of, etc.,
and describe the whole as two halves, three thirds, four fourths. Recognize
that equal shares of identical wholes need not have the same shape.
_________________
1 Sizes are compared directly or visually, not compared by measuring.
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Progression of Geometry
• Read and make note of the the main concepts
of grades K, 1, and 2
• Identify how the concept changes and
increases in rigor and understanding for the
student
• What connections can you make to other
domains/concepts?
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Van Hiele Levels
•Pierre van Hiele and Dina van Hiele-Geldof
•Created a 5 level hierarchy of ways of understanding
spatial ideas
•Each level describes the THINKING PROCESS used in
geometric contexts.
•0-Visualization
•1-Analysis
•2-Informal Deduction
•3-Deduction
•4-Rigor
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Level 0: Visualization
• The objects of thought at Level 0 are shapes and
what they “look like”.
• The appearance of the shape defines it
• A square is a square “because it looks like a
square”
• Turn it…and it’s a diamond
• Sorting will be based on…pointy, fat, dented in, or
“looks like a house”
• The products of thought at level 0 are classes or
groupings of shapes that seem to be “alike.”
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Level 1: Analysis
• The objects of thought at level 1 are classes of shapes
rather than individual shapes.
• Students are able to consider all shapes within a class
rather than a single shape.
• They can think about what makes a rectangle a
rectangle (four sides, opposite sides parallel, opposite
sides of the same length, four right angles, congruent
diagonals, etc.)
• The irrelevant feathers (size, color, orientation) fade
into the background.
• The products of thought at level 1 are the properties of
shapes.
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Level 2: Informal Deduction
• The objects of thought at level 2 are the properties of shapes.
• Students are able to develop relationships between and
among properties of geometric objects
• Able to reason…”If all four angles are right angles, the shape
must be a rectangle. If it is a square, all angles are right
angles. If it is a square, it must be a rectangle.”
• Begin to focus on logical arguments about the properties
• Engage in “if-then” reasoning
• The products of thought at level 2 are relationships
among properties of geometric objects.
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Deduction and Rigor
• Level 3: Deduction
• The objects of thought at level 3 are relationships
among properties of geometric objects
• The products are deductive axiomatic systems of
geometry
• Level 4: Rigor
• The objects of thought at level 4 are deductive
axiomatic systems for geometry
• The products of thought at level 4 are comparisons and
contrasts among different axiomatic systems of
geometry
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Mason Article
• As you read…
• What stuck out or interested you?
• What implications do the van Hiele levels have
on your planning and teaching?
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van Hiele Videos
• As you watch consider:
1) What types of questions is Dr. Mason
posing to the students?
2) On what van Hiele level do you think
student is functioning?
• 3) What evidence in the video suggests
that level?
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van Hiele Videos
• Video 1
http://coedpages.uncc.edu/abpolly/5301/coursedoc
s/van-hielle-vids/927.MPG
• Video 2
http://coedpages.uncc.edu/abpolly/5301/coursedoc
s/van-hielle-vids/928.MPG
• Video 3
http://coedpages.uncc.edu/abpolly/5301/coursedoc
s/van-hielle-vids/930.MPG
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K-5 Math Teaching Resources Website
• http://www.k-5mathteachingresources.com
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Let’s Play the Barrier Game!
Play with your partner
What are the strengths of this strategy?
What experiences would they need before using
this type of game?
Brainstorm 5 more ways to use this strategy?
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Online Resources
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Great Video Library!
http://www.engageny.org
Games for concept practice
http://www.sheppardsoftware.com/
Lessons and activities
http://illuminations.nctm.org/
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Time To Explore!
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Find a partner.
Explore the Geometry tasks for K-2
Record “Things I Want to Remember”
Ask questions
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Not quite…
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