Amanda+B.+&+Myranda+J.+Pre+K-2+Page

=Geometry Standard for Grades Pre-K-2 = = =

-Describe attributes and parts of two and three dimensional shapes. -Investigate and predict the results of putting together and taking apart two and three dimensional shapes . || 1.) Having shapes shown on the overhead for a few seconds and retrieving what shape we saw in that short of time by drawing it on our own papers. 2.) Geometers sketchpad: Building triangles and then reflecting and rotating them and then naming the shape that is created. 3.) Shape sorting: As a group, sorting paper shapes by different properties, including the number of sides, number of vertices, whethere they are symmetric or assymmetric, whether the shape has parallel lines, whether it is a "right shape" (having a 90 degree angle), whether the shape is concave or convex, whether it is regular or irregular, and whether the shape has obtuse angles vs. acute angles. 4.) "Name my rule": As a group, one member made a group of shapes with a rule in mind, and the other members had to guess the rule of the shapes. 5.) Venn diagrams; with these diagrams, shapes are more easily grouped together or apart. We can compare the attributes of the shapes within the diagrams and see whether they connect or not.
 * Standard 1: || Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathemetical arguments about geometric relationships. ||
 * Expectations: || -Recognize, name, build, draw, compare, and sort two and three dimensional shapes.
 * Applied in class: || * 1/12/10 - Finding the characteristics and properties that make up the geometric shape of a triangle. Making two lists: All triangles & some Triangles . Finding what belongs to list and determing the right answer.
 * Giving shapes a definition as a class.
 * Activities:

-Along with the above activities in class, we found that the 'exception' shapes are often concave. These shapes have a vertex that goes toward the center of the shape, creating an angle that measures greater than 180 degrees. - As a class we investigated why the sum of the angles of a triangle are 180 degrees. We cut each angle off of a triangle and put them together, they created a straight line, 180 degrees. -Finding the sume of the angles in a quadrilateral to be 360 degrees. This method involved splitting a quad into triangles by dividing through opposite angles. -Finding a way to create an equilateral tirangle using circles. Drawing the triangle within the 3 circles to create and equilateral triangle to investigate the congruent sides. -When making triangles with polystrips, we were able to take the sides apart and find the relationship between the three sides, being that the sum of the two shorter sides must be greater than the longest side. We used the polystrips and also used a calculator program for Random Integars to see whether we could create triangles with any side lengths. We developed the triangle inequality theorum from this: A+B>C. Shorter sides being A and B, longest side being C. -With quadrilaterals, we used polystrips and were also able to take these shapes apart and find the relationship between the four sides. We used polystrips and a calculator program for Random integars to find whether we could create quadrilaterals with any given sides. We found that the sum of the three shortest sides A,B,C, must be greater than the longest side, D. A+B+C>D.

- We come to a realization that 2-D shapes = base X height, 3-D shapes = length X width X height - A 2-D shape is flat, 3-D shapes are solids that are either hollow or filled. -Recognizing the differences: 3-D 2-D || STANDARD 1: VERY NICE DESCRIPTIONS OF ACTIVITIES AND DISCUSSIONS WE DID IN CLASS TO ADDRESS THESE EXPECTATIONS. GOOD TO NAME SPECIFIC PROPERTIES AND CHARACTERISTICS OF SHAPES TO EXEMPLIFY YOUR POINTS HERE. USEFULNESS OF TASKS AND CONNECTIONS TO OTHER MATHEMATICAL IDEAS MISSING.
 * Comparing two and three dimensional shapes:

-Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance -Find and name locations with simple relationships such as "near to" and in coordinate systems such as maps. || -In class we used tools like Scratch and Sketchpad on the computer to help us navigate the space and direction of shapes. By using these applications we were able to come up with assumptions about shapes and their position of angle.  -We understood that from the original shape's spot to the 3rd final movement, there was basically a point of rotation. We could look at it as not only being reflected twice but being rotated at a certain degree.  - Though this is not the exact same from our writing assignment we can still see in it using different shapes. -One of the red triangles were reflected to make the green triangle and then the green triangle was reflected to make another red triangle. -The red triangles are the two shapes that are basically being rotated at a certain degree a point. (The point is where all those lines meet)    || STANDARD 2: I DON'T SEE HOW EXAMINING SYMMETRY IS ADDRESSED SPECIFICALLY BY THESE EXPECTATIONS. THIS STANDARD IS MORE ABOUT THE LOCATIONS OF SHAPES IN SPACE, SO ARE YOU REFERRING TO COLLECTIONS OF SHAPES IN RELATIONSHIP TO EACH OTHER IN TERMS OF WHERE THEY ARE LOCATED ON THE PAPER? OR LOCATIONS OF POINTS IN RELATION TO THEIR REFLECTIONS AND ROTATED IMAGES? *PATTY PAPER, NOT PADDY PAPER. GOOD SPECIFICATIONS OF USEFULNESS OF USING TECHNOLOGY TO ADDRESS THIS STANDARD.
 * ** Standard2: ** || Specify locations and describe spatial relationships using coordinate geometry and other representational systems ||
 * Expectations: || <span style="color: #4871ea; font-family: 'Comic Sans MS',cursive;">-Describe, name and interpret relative positions in space and apply ideas about relative position
 * Applied in class: || <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">-In class we used relative position and shapes by doing the class activity with poster paper and dividing shapes into: Assymmetric, rotational, and reflectional. We used paddy paper to trace the shapes and determine if it can rotate, have a line a symmetry, or if it was a irregular shape. Once depending that we put them in certain areas. Interpreting a shapes characteristics gives you a better understanding and easier to find relationships between certain shapes.
 * On our 3rd writing assignment we were asked to reflect a shape from one line then reflect that same shape from another line.

- Recognize and create shapes that have symmetry. || - Turning 2D shapes at their centerpoint to investigate their reflection symmetry and if they have it. -Folding 2D shapes into congruent parts to see if they mirror eachother, investigating their reflectional symmetry and whether they have it. -In class, we used paddy paper to help us figure out if a shape is rotational or reflectional. First, we would trace the shape onto the paddy paper and from there we could determine whether it had complete rotational or reflective. In reflectional we were able to fold it in half down the middle and determine whether it mirrored itself or if it was irregular. To determine whether it was rotational or not we would place the shape over the paddy paper and turn the shape until it matched up to the traced shape, if it did we knew it had some sort of rotational symmetry, if it did not match up until 360 degree turn we knew it was not rotational. -Finding the sum of the interior angles of a 2D shapes by splitting the shape into triangles connecting vertex at center without going outside of the shape.
 * Standard3: || <span style="color: #f07738; font-family: 'Comic Sans MS',cursive;">Apply transformations and use symmetry to analyze mathematical situations. ||
 * Expectations: || <span style="color: #4871ea; font-family: 'Comic Sans MS',cursive;">-Recognize and apply slides, flips and turns
 * Applied in class: || <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">Project 1: Geometers sketchpad: Building triangles and then reflecting and rotating them and then naming the shape that is created.

- We came to the conclusion that any triangle that copies it exact self and is rotated can become a quadrilateral. -Here we can see that the original triangle was isosceles and we duplicated it and rotated it, put them together and resulted in a quad. o Finding the symmetry in 3D shapes. How they compare. We used blue plastic 3D shapes and filled one we thought was similar to another, where their bases are congruent and symmetric, and filled the other shape, giving us a way to compare the symmetries the two different 3D shapes by comparing their fillings. <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 11pt;">The use of the word similar here is not being used correctly. Examining symmetry of 3D shapes might involve finding lines of symmetry or angles of rotation. || <span style="font-family: 'Comic Sans MS',cursive;">STANDARD 3: SAY MORE ABOUT HOW THE GEOMETER'S SKETCHPAD PROJECT ADDRESSED THIS STANDARD. THE DESCRIPTION OF HOW WE APPLIED IDEAS OF TRANSFORMATIONS IN CLASS IS GOOD.
 * In one part of the Geometer's Sketchpad we had triangles that would eventually create quadrilaterals.

-Recognize and represent shapes from different perspectives; Relate ideas in geometry to ideas in number and measurement -Recognize geometric shapes and structure in the enviroment and specify their location. || <span style="color: #008000; font-family: 'Comic Sans MS',cursive;"> o Drawing nets of 3D shapes that give us the opportunity to help find and visualize the area and volume of the shapes. · Looking at drawings of 3D shapes from different sides to get their different perspectives. · Finding how the sides of the 3D shapes nets compare to the volume and area. From this we created formulas to find the volumes of these 3D shapes. We used the 'cubes' that create the nets to measure the 3D shapes. || =**<span style="color: #de6e8d; font-family: 'Comic Sans MS',cursive;">Measurement Standards for Grades Pre-K-2 **= -Understand how to measure using nonstandard and standard units -Select an appropriate unit and tool for the attribute being measured || <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">- In class we had flat plastic circles where we used a string to wrap around the circle to get an estimate size of its diameter and circumference. - We also saw the string used in Project 2, while looking at "the blob". By tracing the shape with a string we can create other shapes and compare area and notice similarities and differences. -For example, we used a cone and a cylinder. We filled the cone with filling and once it was full, we put that filling in the cylinder. We repeated this until the cylinder was full. This was a way of finding the volume formula of the cone. Since the cone was 1/3 of the cylinder we were able to use the cylinders formula and using 1/3 instead. -Along with the above we found that a shape like a cone compares to a cylinder with a congruent base and congruent height. A sphere works in the same way: The sphere filled the cylinder 2/3 full, the shapes both having congruent diameter and height. While a pyramid with a square base filled the cube 1/3 full, while the cube and pyramid both having congruent square base and height. ||
 * Standard 4: || <span style="color: #f07738; font-family: 'Comic Sans MS',cursive;">Use visualization, spatial reasoning, and geometric modeling to solve problems ||
 * Expectations: || <span style="color: #4871ea; font-family: 'Comic Sans MS',cursive;">-Create mental images of geometric shapes using spatial memory and spatial visualization
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">Applied in class: || * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">Going home and looking in magazines for rotational, reflectional, and asymmetrical shapes.
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">Relates to finding examples of geometric shapes in our enviroment. Example: Stop sign = Octagon[[image:http://www.exchange3d.com/cubecart/images/uploads/aff186/Stop_Sign.jpg width="86" height="70" caption="http://www.exchange3d.com/cubecart/images/uploads/aff186/Stop_Sign.jpg"]]
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">While using the Scratch during class we had to come up with alternative ways to find out how to make a shape. We used angle measurements and knowing the amount of sides on each shape to help us come up with a final product.
 * Standard 1: || <span style="color: #f07738; font-family: 'Comic Sans MS',cursive;">Understand measurable attributes of objects and the units, systems, and processes of measurement ||
 * Expectations: || <span style="color: #4871ea; font-family: 'Comic Sans MS',cursive;">-Recognize the attributes of length, volume, weight, area and time; compare and order objects according to these attributes
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">Applied in class: || * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">A process of measurement using nonstandard units is using a string to measure a shape.
 * Using hollow solids and using filling to fill them up and compare the volume of other solids through the nonstandard unit of the filling.

-Use repetition of a single unit to measure something larger than the unit -Use tools to measure; develop common referents for measures to make comparisons and estimates. || <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">- Used a technique with rubber band as a tool. The rubber band was tied in a knot equally and split in half. Took one end of the rubber band and held it at a point and a pencil at the other point. Making the knot trace over the shape, we carefully went over the shape to get a enlarged version of the shape. To get it even more enlarged, use more than one rubber band. - When using Mystery Man shape we noticed that the original smaller triangle can fit in the enlarged shape, X amount of times, just copying itself. -If the band was a k-band (k being the number of bands/knots), the scale factor of the new shape is k. The original perimeter(P) increases by k; P*K. The area(A) of the original shape increases by K-squared; A*K-squared.
 * Standard 2: || <span style="color: #f07738; font-family: 'Comic Sans MS',cursive;">Apply appropriate techniques, tools, and formulas to determine measurements ||
 * Expectations: || <span style="color: #4871ea; font-family: 'Comic Sans MS',cursive;">-Measure with multiple copies of units of the same size
 * <span style="font-family: 'Comic Sans MS',cursive;">Applied in class: || * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">Mystery Man Activity - given a random shape and asked to enlarge it.

<span style="font-family: Helvetica,cursive;">--In an in class activity we used hollowed solid shapes and used filling to find the similarity between the other solid hollowed shapes. With this we were able to use multiple copies of a smaller volumed shape and use that filling to compare to a larger volumed shape. (ex. cone & cylinder) By using multiple copies of the filling in the cone we were able to see how many times bigger the cylinder's volume is from the cone. -When first filling the cone and then put the filling into the empty cylinder, we could predict it was 1/3 filled. We tested that by refilling the cone and dumping the filling into the cylinder until it was completely full. -Along with the above we found that a shape like a cone compares to a cylinder with a congruent base and congruent height. A sphere works in the same way: The sphere was 2/3 the area of a cylinder with the congruent diameter and height. While a pyramid with a square base is 1/3 the volume of a cube with congruent square base and height. The comparison here between 2D and 3D activities is not necessarily correct. If you're interested in 3D shapes that are similar they would be enlarged copies of the same thing. For example, a bouncy ball is similar to a kickball (same shape, different size). || <span style="font-family: 'Comic Sans MS',cursive;">

GENERAL COMMENTS:

~ **<span style="font-family: 'Comic Sans MS',cursive;">MAJOR CONCEPTS DEVELOPED IN THE COURSE **<span style="font-family: 'Comic Sans MS',cursive;">~ THE MAJORITY OF EXPLANATIONS HERE SEEM TO CONNECT TO SYMMETRY. OTHER IDEAS SUCH AS RELATIONSHIPS BETWEEN SPECIAL TYPES OF SHAPES (TRIANGLES, QUADRILATERALS) AND THE DEVELOPMENT OF ANGLE AND ANGLE MEASURE SEEM TO BE UNDERREPRESENTED. WHAT ABOUT VENN DIAGRAMS? <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">Generally good identification of the major ideas including both 2D and 3D shapes. <span style="font-family: 'Comic Sans MS',cursive;"> ~ **<span style="font-family: 'Comic Sans MS',cursive;">IMPORTANCE AND CONNECTIONS **<span style="font-family: 'Comic Sans MS',cursive;">~ THE DESCRIPTION IN STANDARD 2 MAKES CONNECTIONS TO THE USEFULNESS OF THE ACTIVITIES AND HOW THE IDEAS WERE DEVELOPED. MOST STANDARDS ARE LACKING IN THE USEFULNESS OF THE CONCEPT AND CONNECTIONS TO OTHER MATHEMATICAL IDEAS. FOR EACH STANDARD, TRY TO FOCUS ON ONE MAJOR MATHEMATICAL CONNECTION. FOR INSTANCE, HOW ARE THESE GEOMETRIC IDEAS RELATED TO MEASUREMENT STANDARDS? WHAT CONNECTIONS ARE THERE TO REASONING AND PROOF? ARE THERE ANY PARALLELS BETWEEN THE TYPES OF ACTIVITIES AND REASONING DONE IN GEOMETRY TO HOW IDEAS AND CONCEPTS ARE DEVELOPED IN NUMBER AND OPERATIONS? ALGEBRA? <span style="color: #800080; font-family: 'Comic Sans MS',cursive;">The connections within standards and expectations are absent; not much if any discussion on usefulness or importance of concepts.