TIPM3Second and Third Grade Geometry

November 3, 2010

Mathematical PracticesMathematical Practices1. 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 PracticesMathematical Practices1. 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.

GeometryGeometryReason 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 Van Hiele Levels of Geometric ThoughtGeometric Thought

Level 0: Visualization

DescriptionSee geometric shapes as a whole; does not focus on their particular attribute

ExampleA student would identify a square but would be unable to articulate that it has four congruent sides with right angles.

Teacher ActivityReinforce this level by encouraging students to group shapes according to their similarities

Shape SortShape SortWork 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 SortShape SortWork 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?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 SortShape Sortvan 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 SortingAttribute Block SortingDescribe AttributesVenn 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 Secret Sort What’s My Rule?

Shapes with right angles

van Hiele Levels of van Hiele Levels of Geometric ThoughtGeometric Thought

Level 1: Analysis

DescriptionRecognize that each shape has different properties; identify the shape by that property.

ExampleA 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 Property Lists for QuadrilateralsQuadrilaterals

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 van Hiele Levels of Geometric ThoughtGeometric Thought

Level 2: Informal Deduction

DescriptionSee the interrelationships between figures

ExampleGiven the definition of a rectangle as a quadrilateral with right angles, a student could identify a square as a rectangle.

Teacher ActivityCreate 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.

LunchLunch

3- Dimensional Geometry3- Dimensional Geometry

3-D Line Plot

Sets of Nets

BreakBreak

3-D Line Plot

Sets of Nets

MoneyMoney2.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?

MoneyMoneyMoney Bags

Making Cents of Dollars

Roll to a Quarter

Roll From a Dollar

Money in the Bank

ReflectionReflectionTwo 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.