Jeni+M.+&+Melissa+P.+~+Pre-K-2

 ​ Geometry and Measurement Standards for: Pre-K ~ 2nd Grades Geometry Standard #1 ~ Analyze characteristics and properties of two and three dimensional geometric shapes and develop mathematical arguments about geometric relationships. Expectations ~ How we Applied it in Class ~ > We defined a polyhedra as a prism or pyramid shape. We defined non-polyhedra shapes as cylinders, cones, and spheres. > We defined a polyhedra as a prism or pyramid shape. We defined non-polyhedra shapes as cylinders, cones, and spheres.
 * recognize, name, build, draw, compare, and sort two- and three- dimensional shapes:
 * 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.
 * We sorted shapes into different categories using the Guess My Rule Cards in our course pack. We played Guess My Rule with our groups and the players had to guess how the rule holder was sorting the cards, ex. acute vs. obtuse or equilateral vs. scalene.
 * We defined line segments, and the angles and sides of the triangle.
 * We took a triangle apart to show in fact that the angles easily made up 180 degrees.
 * When doing rotational and reflectional symmetry we showed how a shape could be divided into two equal halves and put back together by using the line of symmetry. When we folded a shape at the line of symmetry we could see that the two halves mirrored each other. In class we drew shapes and were able to guess if they had rotational or reflectional symmetry.
 * We played another Guess My Shape game using the 3-D wooden shapes at our tables. One person had a shape n their head and the others had to ask questions like: "Does your shape roll?" If the answer was yes then that would eliminate all the shapes tha cannot roll.
 * We also played a game similar to Guess My Shape, the teacher shows a quick image on the projector and then the students try to figure out what shape it was with only using the quick image that they saw.
 * We sorted two dimensional shapes that were precut into recognizable shapes, such as obtuse vs. acute shapes.
 * We defined line segment, the sides of a triangle, and simplified word terms.
 * We sorted two dimensional shapes that were precut into recognizable shapes, such as obtuse vs. acute shapes.
 * We discussed the idea that if you took a circle and cut it into congruent wedges then you could form a soccer field design or also a basic rectangle shape. This will be similar, however, will not be an accurate rectangle because the lines will always have some sort of curve in it from the simple curved line of the circle. The more wedges you have from your circle will make the soccer field appear more rectangle though but it won't be a true rectangle. An example is to follow:

Start thinking about teaching Geometry to children. We are to ask some children of this age group to draw a picture of what they think each shape looks like. I used a few of my Pre-Kindrgarten students to tell me what a triangle, square, circle and a line were. Here are some results:

Together the children came up with the conjecture that Triangles all have three equal sides, squares have four equal sides, a circle means that it doesn't have any equal sides like a triangle and square, and a line is just straight. It is great that you actually engaged young students in conversations about geometry. What a great experience. Now, as a teacher, one of the challenges will be in knowing the more advanced conceptions and definitions of these objects, how do you help students to develop more robust conceptions of these ideas and prepare them for more formal study. Using several manipulatives might be a good key here (including blocks and even technology).

Geometry Standard #2 ~ Specify locations and describe spatial relationships using coordinate geometry and other representational systems. Expectations ~ How We Applied it in Class~
 * describe, name, and interpret relative positions in space and apply ideas about relative positions.
 * 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.
 * Sketchpad to construct shapes, not just draw them.
 * <span style="font-family: Arial,Helvetica,sans-serif;">We explored angle degrees in Geo-board (on our TI-73) to create different polygons.
 * By using Logo light and Scratch we developed some of these ideas because it helped to show the relationships between certain shape.
 * We worked in table groups to form a page of symmetry. We needed to take quadrilaterals and triangles and put them in their appropriate groups: reflectional symmetry, rotational symmetry, asymmetrical.

<span style="color: #f91ac0; font-family: 'Comic Sans MS',cursive;">Geometry Standard #3 ~ Apply transformations and use symmetry to analyze mathematical situations <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">Expectations ~ How We Applied it in Class ~
 * recognize and apply slides, flips, and turns.
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">recognize and create shapes that have symmetry.
 * We made a list of shapes that were symmetrical and asymmetrical.
 * We use patty paper to create shapes that have symmetry as well as for showing the flips and turns of shapes.
 * We found items at home that were symmetrical and asymmetrical and brought them to class to show others.
 * <span style="font-family: Arial,Helvetica,sans-serif;">We used two rubber bands knotted together to show how a shape can be redrawn to a larger size for shapes.
 * We took alpha shapes and figured out which ones had symmetry and then figured out what type of symmetry.
 * We enlarged the Mystery man by using a double knoted rubber band. We used a finger to hold one rubber band in place then we put a pencil in the other rubber band and drew a slightly larger one. You could continue making larger Mystery men by adding more rubber bands.
 * Patty paper is also helpful to determine if you really can fold a shape and have line symmetry, if you needed a more percise drawing geometry sketchpad would be helpful and show the lines of reflection and measurments.

<span style="color: #f91ac0; font-family: 'Comic Sans MS',cursive;">Geometry Standard #4 ~ Use visualization, spatial reasoning and geometric modeling to solve problems <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">Expectations~ How We Applied it in Class~ <span style="color: #008000; font-family: 'Comic Sans MS',cursive;"> <span style="color: #f91ac0; font-family: 'Comic Sans MS',cursive;">
 * <span style="color: #008000; 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;">recognize and represent shapes from different perspectives.
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">relate ideas in geometry to ideas in number and measurement.
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">recognize geometric shapes and structures in the environmental specify their location.
 * We drew shapes in our groups on large sheets of paper to show visualization and also allow other groups to view and correct if need be.
 * We found items at home that were geometric and brought them to class to make a list.
 * The phythagorean theorem helped develop the idea of relating ideas in geometry to ideas in number and measurements
 * We were introduced to sketchpad. Sketchpad helped us learn how to construct a shape and not just drawing the shape.
 * We were introduced to Scratch and Explorer draw to learn about finding the exterior angles of a shape.
 * <span style="font-family: Arial,Helvetica,sans-serif;">We used an angle ruler in class to show an accurate measuring of angles.
 * <span style="font-family: Arial,Helvetica,sans-serif;">We explored NETS in class and made a two dimensional shape that could be folded into a 3 dimensional shape for: prisms, cylinders, cones and pyramids.
 * <span style="font-family: Arial,Helvetica,sans-serif;">We filled 3D shapes with " fillers" (small bites of plastic) to compare the volume of each shape.
 * We discussed 3-D shapes and their nets. A net is a 2-D pattern that will turn into a 3-D shape. Below are some examples of some nets that we needed to construct to make a 3-D shape.



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Measurement Standard #1 ~ Understand measurable attributes of objects and the units, system, and processes of measurement <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">Expectations~ How We Applied it in Class~
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">recognize the attributes of length, volume, weight, area, and time.
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">compare and order objects according to these attributes.
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">understand how to measure using nonstandard and standard units.
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">select an appropriate unit and tool for the attribute being measured.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Getting into shapes, we have developed how to find the volume of each shape. Such as length x width x height by playing with unifix cubes and wooden blocks.
 * <span style="font-family: Arial,Helvetica,sans-serif;">We found the formula for finding the surface area to be: sa=2(lw)+2(wh)+2(hl). <span style="color: #800080; font-family: 'Times New Roman',Times,serif;">this kind of symbolic rule might not be appropriate for this grade level. understanding the total areas of all the surfaces is a more important concept here.
 * <span style="font-family: Arial,Helvetica,sans-serif;">We had a chart in the front of the room where we were able to classify shapes on the chart into groups of polyhedras and non-polyhedras, we also had sub categories to place the shapes in such as pyramids, prisms, etc.
 * ======<span style="font-family: Arial,Helvetica,sans-serif;">In class we determined the formulas to find out the areas of different shapes, the perimeter of different shapes, the circumference of different objects, and the radius of different shapes, We cut out shapes and used them to see how they related to other shapes in order to find area formulas for each of them. ======
 * ======<span style="font-family: Arial,Helvetica,sans-serif;">We determined that the volume of a shape is its length x width x height, in which we found the area of wooden blocks with.In class we measured circular objects with string to get the diameter and circumference. The volume in a cone, pyramid or sphere shapes can be compared to the volume in a cylinder shape by pouring their volumes, separately, in the empty cylinder. This measurement shows a student a nonstandard unit of measurement.The unit used for filler was tiny recycled tire pieces poured into shapes to fill them up, and emptied into a larger shape (cube) as a tool to compare volume sizes. ======

<span style="color: #f91ac0; font-family: 'Comic Sans MS',cursive;"> Measurement Standard #2 ~ Apply appropriate techniques, tools, and formulas to determine measurements <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">Expectations~ We measured volume with multiple tire pieces of the same size to fill empty shapes, (i.e., cubes, cylinders, cones, pyramids, spheres.)
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">measure with multiple copies of units of the same size, such as paper clips laid end to end.
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meter stick.
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">use tools to measure.
 * <span style="color: #008000; font-family: 'Comic Sans MS',cursive;">develop common referents for measures to make comparisons and estimates.
 * We used patty paper to make a compass by using the base line as the 180 degree angle. We make a dot in the center of the line to help us just where the folding will occur from. Then we folded the paper in half to form two 90 degree angles. On each 90 degree angle we folded it in half still basing this the fold mark off the center of the 180 degree line. That will make our 45 degree angle and 135 degree angle. Continue with this process. [OTHER STANDARD UNITS TO MEASURE ANGLES? (E.G., ANGLE RULER)]
 * In class we took empty shapes, such as cubes, cylinders, cones, shperes, and measured the volume of them by filling them with special filling that we had.
 * We also talked about having a pizza be the base for a 360 degree object. Each degree would be a different slice of that pizza.


 * MAJOR CONCEPT****S** <span style="color: #800080; font-family: 'Times New Roman',Times,serif;">Good identification of major concepts; some might not be explicitly important for this grade band but most were right on.
 * DEVELOPMENT, IMPORTANCE, AND CONNECTIONS OF CONCEPTS** <span style="color: #800080; font-family: 'Times New Roman',Times,serif;">In most cases the development of the ideas were well stated, but sometimes the importance of studying these ideas was not as evident.
 * CONNECTIONS TO PSSM** <span style="color: #800080; font-family: 'Times New Roman',Times,serif;">Very good use of examples to illustrate the connections to the standards.