Transcript Geometry_Nov2

TIPM3
Second and Third Grade Geometry
November 3, 2010
Mathematical Practices
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
Mathematical Practices
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
Geometry
Reason with shapes and their attributes.
2.G.1. Recognize and draw shapes having specified attributes, such as a
given number of angles or a given number of equal faces. Identify
triangles, quadrilaterals, pentagons, hexagons, and cubes.
3.G.1. Understand that shapes in different categories (e.g., rhombuses,
rectangles, and others) may share attributes (e.g., having four
sides), and that the shared attributes can define a larger category
(e.g., quadrilaterals). Recognize rhombuses, rectangles, and
squares as examples of quadrilaterals, and draw examples of
quadrilaterals that do not belong to any of these subcategories.
Van Hiele Levels of
Geometric Thought
Level 0: Visualization
Description
See geometric shapes as a whole; does not focus on their particular
attribute
Example
A student would identify a square but would be unable to articulate
that it has four congruent sides with right angles.
Teacher Activity
Reinforce this level by encouraging students to group shapes
according to their similarities
Shape Sort
Work in groups of 4 with set of 2-D shapes
1.Each person selects a shape. In turn, tell one or two
things you find interesting about your shape. There are no
right or wrong answers.
2.Randomly select two shapes. Find something that is alike
about the two shapes. Find something that is different.
3.The group selects one shape at random and places it in
the middle of the table. Find all the other shapes that are
alike the target shape according to the same rule.
Shape Sort
Work in groups of 4 with set of 2-D shapes
1.Select one shape at random and place it in the middle of
the table.
2.Find all the other shapes that are alike the target shape
according to the same rule.
For example – this shape is like the target shape because it has a
curved side and a straight side. Then all the shapes put into the collection must
have a straight side and a curved side.
3. Do a second sort with the same target shape, but use a
different property.
What’s My Shape?
•One student is the leader and is given a secret-shape
folder.
•The other students are to find the shape in the folder by
asking questions to the leader to which the leader can
answer only yes or no.
•The group can eliminate shapes as they ask the questions
to narrow down the possibilities.
•They are not allowed to point to a shape and ask if that is
the one.
•Ask questions until the choices are reduced to one shape.
Shape Sort
van Hiele
•
•
This is a level 0 activity because students are
operating on shapes they see in front of them.
These shapes may “change” or have different
properties as they are rearranged or rotated.
The object of this activity is to begin to see that there are
likenesses and differences in shapes.
Attribute Block Sorting
Describe Attributes
Venn Sorting by Attribute
Secret Sort
•Create a small selection of objects of about five shapes that
fit a secret rule.
•Leave others that belong in the group in a pile. Try to find
additional pieces that belong to the same set and/or guess
the rule.
Secret Sort
What’s My Rule?
Shapes with right angles
van Hiele Levels of
Geometric Thought
Level 1: Analysis
Description
Recognize that each shape has different properties; identify the
shape by that property.
Example
A student is able to identify that a parallelogram has two pairs of
parallel sides, and that if a quadrilateral has two pairs of parallel
sides it is identified as a parallelogram.
The products of thought at level 1 are the properties of
shapes.
Property Lists for
Quadrilaterals
Work in groups of 3 or 4.
List as many properties as you can that are applicable to all
the shapes on their sheet.
•Use an index card to check right angles.
•Use rulers to compare side lengths and draw straight lines.
•Look for lines of symmetry.
•Use tracing paper for angle congruence.
•Use the words “at least” to describe how many of
something.
Does the property apply to all the shapes in the category?
van Hiele Levels of
Geometric Thought
Level 2: Informal Deduction
Description
See the interrelationships between figures
Example
Given the definition of a rectangle as a quadrilateral with right
angles, a student could identify a square as a rectangle.
Teacher Activity
Create hierarchies (i.e. organizational charts of the relationships) or
Venn diagrams of quadrilaterals to show how the attributes of one
shape imply or are related to the attributes of others.
Lunch
3- Dimensional Geometry
3-D Line Plot
Sets of Nets
Break
3-D Line Plot
Sets of Nets
Money
2.MD.8. Solve word problems involving
dollar bills, quarters, dimes, nickels,
and pennies, using $ and ¢
symbols appropriately. Example: If
you have 2 dimes and 3 pennies,
how many cents do you have?
Money
Money Bags
Making Cents of Dollars
Roll to a Quarter
Roll From a Dollar
Money in the Bank
Reflection
Two important ideas about teaching Geometry
concepts to 2nd and 3rd graders are:
1.
2.
Two important ideas about teaching money
concepts to 2nd and 3rd graders are:
1.
2.