Kirsten+&+Jenns'++Page

Note: Both Kirsten and Jenn work on this wiki page together and all the work is equally contributed ||
 * ~ Geometry Standards for Grades Pre-K-2
 * Standard #1 |||||| * **Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships ** ||
 * Expectations |||||| # recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;
 * 1) describe attributes and parts of two- and three-dimensional shapes;
 * 2) investigate and predict the results of putting together and taking apart two- and three-dimensional shapes ||
 * How we applied it in class |||||| # Defined types of triangles and defined a polygon, worked with quadrilaterals, used patty paper to show reflection, brought in shapes that had reflection/rotation symmetry, made posters about symmetry. In determining which shapes have reflection, rotation, and/or both we were able to make conjectures about what properties were needed in order to have both rotation and reflectional symmetry
 * 1) defined line segment, side, made bigger terms into smaller terms (i.e.: polygon=shape), defined types of quadrilaterals and triangles, 3D shapes have a volume
 * 2) Talked about isosceles triangles and how to make different triangles, discussed how if all 4 sides are congruent in a quad. then at the angles will also be (either 2 separate sets or all the same), found angles of reflection and rotation( using estimation with patty paper or a protractor), used GSP to play with shapes, we used patty paper to trace each side of a triangle; we then were able to draw a straight line which is 180 degrees; this showed us that all the interior angles of a triangle equal 180 degrees (or a straight line), sorted shapes, "name my rule" game; in the "name my rule" game we were able to make predictions based off of the material we learned in class. Either having memorized the shapes definition or looking back in our notes we were able to guess which "rules" were able to be applied to a certain shape and also which shapes couldn't be applied to the certain shape because it didn't follow the rule. We developed nets ( a 2D outline of an unfolded 3D shape), and found out that there are many different possible nets to one 3D shape. ||
 * How it is useful |||||| This is useful so that we can classify various shapes, even if they are irregular. This will help especially in the younger grades to develop a general knowledge. To construct new shapes/ find their area or angles. To classify the shapes we can test if they have rotational or reflectional symmetry (a shape has rotational symmetry if you can turn it around its center of rotation less than 360 degrees and it lands exactly on top of itself again) (a shape has reflection symmetry if it has a line of symmetry) (a line of symmetry is a line that divides a shape in 2 equal halves that mirror each other). We can also classify different shapes by the number of sides they have, for example a three sided polygon would be a triangle and a four sided polygon would be a quadrilateral. ||
 * Other mathematical connections |||| Connects to many other areas, all different shapes, also helps to know for future learning. Can be connected to symmetry and angles because you need to have a basic understanding of the shape in question first. Connects to measurement because you need to know the measurements to find other things about the shape (ex: you need to know length and width to fine area) ||  ||


 * Standard ** #2 ** || * **Specify locations and describe spatial relationships using coordinate geometry and other representational systems ** ||
 * Expectations || # describe, name, and interpret relative positions in space and apply ideas about relative position;
 * 1) describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance
 * 2) find and name locations with simple relationships such as "near to" and in coordinate systems such as maps. ||
 * How we applied it in class || # We used scratch to help us see which direction our sprite would move to draw a shape and what directions we needed to put in to make him create the correct angle measure. Using scratch we predicted what shape would be created using the given steps. We used reflection mirrors to draw and move original shapes to a new position, there were very useful in sliding.
 * 1) Using the white board we discussed exactly how our sprite would move, especially focusing on exterior angles
 * 2) We used geo-boards to create shapes and to determine what type of shape we had just made, i,e. an isosceles triangles or an equilateral triangle. We were able to use one of the functions of the geo-boards that measures all the the sides and angles of a shape. That enabled us to prove that the shape we created fit our class definition for the given shape. Geo-boards can be considered a coordinate grid for plotting shapes. ||
 * How this is useful

|| In order to used scratch to make a list of commands (to make a shape), you need an understanding of both exterior angles and interior angles, otherwise your shape will not be computed correctly. You also have to have knowledge of which direction to turn (meaning using the exterior angle measurement and not the interior angle measurement). Using geo-boards we learned how sliding, rotation, and reflecting a shape effect the shape in very different ways. The program is helpful in developing the concepts behind these different movements with shapes. ||

Somewhat touching on irregular shapes. Irregular polygons can have symmetry too, rotational or reflection, but, for sure, a regular polygon will have both types of symmetry because all of its sides and angles will be congruent. We made posters with lists of shapes in each symmetry. (patty paper was useful for much of this because you can easily demonstrate the turn needed to complete a rotation) ||
 * Standard **#3** || * **Apply transformations and use symmetry to analyze mathematical situations ** ||
 * Expectations || # recognize and apply slides, flips, and turns;
 * 1) recognize and create shapes that have symmetry ||
 * How we applied it in class || # We talked about the types of symmetry, defined reflection symmetry, defined rotation symmetry, defined line of symmetry We found that if the shape was moving around the center point and fit perfectly on top of itself before completing a 360-degree turn then it had rotational symmetry, If we were able to fold the shape at the line of symmetry and the two halves of the shape mirrored each other perfectly then we knew it had reflectional symmetry. If the shape did not fit either category, then it was asymmetric
 * 1) We found angles of rotation, talked about asymmetrical, reflection symmetry, and rotational symmetry, talked mainly about regular polygons. we made a poster that had several different triangles and quadrilaterals on it placed in the right category
 * How this is useful || Many shapes have symmetry, and recognizing these similarities will help us develop new relationships between shapes. Useful for finding interior/ exterior angles in the future. It is useful in creating other shapes that have symmetry. Once you understand the concepts, it is easier to make a shape that has symmetry. The more properties known, the more connections that can be drawn between that shape and other shapes, useful to compare symmetry, and to know about angle measurements ( Angle of rotation, exterior, interior angles) ||
 * Other mathematical connections || Measurement of degrees, finding angles, congruency. The exterior angle and the angle of rotation are the same measurement. Knowing about the differences between a flip, turn and slide is important for later concepts about shapes and angles. Understanding how to accomplish each shows understanding about both symmetry and angles. ||


 * Standard **#4** || * **Use visualization, spatial reasoning, and geometric modeling to solve problems ** ||
 * Expectations || # create mental images of geometric shapes using spatial memory and spatial visualization;
 * 1) recognize and represent shapes from different perspectives; relate ideas in geometry to ideas in number and measurement;
 * 2) recognize geometric shapes and structures in the environment and specify their location ||
 * How we applied it in class || # used sketchpad to manipulate shapes which can help one to mentally manipulate shapes, by making nets one must mentally imagine what the shape looks like
 * 1) we found areas of one shape using other shapes (i,e: a trapezoid by making it into a rectangle), we saw how many different nets you can use to make one 3d shape (i.e. a cube)
 * 2) we talked about how bridges/ swing sets are made of triangles because they are sturdy shapes, we played the guess my shape game with 3d shapes ||
 * How this is useful

|| To mentally be able to manipulate the shapes. To see comparisons to other shapes. It is important for students to be able to mentally manipulate shapes because sometimes there won't be a pencil and paper ready, or they won't have graph paper or measuring tools, so they need to be able to mentally manipulate the shape to solve the problem. When students can picture what might be, later they can try to prove this concept using things they know. this is helpful so that they can think out the process and know WHY instead of just knowing what the rule is. ||
 * Other mathematical connections || Using reasoning is handy not only in math class but in many real life activities as well. like was mentioned above, a student in our class used visualization when her husband was building a swing set and needed the area of a triangle. Manipulating shapes, numbers, and formulas will be useful in future math classes because they knowledge will only build on these basics. A real life situation we thought of was if you are buying a couch and know the dimensions of your room, when you see a couch you like you can compare those dimensions and see how it would fit into your room.

We discussed 3-D shapes and their nets. A net is a 2-D pattern that will turn into a 3-D shape. This takes mental visualization to see what the net of a 3D shape would be. Or, the reverse, to see what a net will become. ||

** ...................................................................................... Measurement Standards for Grades Pre-K-2**

2. compare and order objects according to those attributes 3. understand how to measure using nonstandard and standard units 4. select and appropriate unit and tool for the attribute being measured || b= base h= height To find the area of a triangle we used this formula: (bxh) / 2 To find the area of a trapezoid we used this formula: (b1 + b2) height / 2 To find circumference of a shape use: diameter x pi To find diameter of a shape use: circumference x pi To find the radius you simply divide the diameter by 2 To find the diameter you simply multiply the radius by 2
 * ** Standard #1 ** || * **Understand measurable attributes of objects and the units, systems, and processes of measurement.** ||
 * Expectations || 1. recognize the attributes of length, volume, weight, area, and time
 * How we applied this in class || In class we learned the different formulas to find the areas of different shapes, the circumference of different objects, the radi of different shapes, and the perimeter of different shapes. We cut out shapes and manipulated them to see how they related to other shapes in order to find area formulas for each of them.

We classified shapes in a chart according to : polyhedra and non polyhedra. (we also sub categorized them into prisms, pyramids ect. ect.)

We measured in nonstandard units: using patty paper and string We measured in standard units: protractor, compass, ruler

We developed volume of a box as length x width x height. We used wooden blocks to figure out how to maximize and minimize surface area. ||
 * How this is useful || It is useful in many real life scenarios. For example when building anything from a table to building a house. It is good to know other ways to measure in case you don't carry around a protractor in your purse. True, these expectations are also useful for estimation and spatial visualization skills. ||
 * Other mathematical connections || It is important to know the differences between volume, area ect. When solving future problems, knowing the difference will help you know how to find the correct answer. ||

2. 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; 3. use tools to measure; 4. develop common referents for measures to make comparisons and estimates ||
 * **Standard #2** || * ==Apply appropriate techniques, tools, and formulas to determine measurements== ||
 * Expectations || 1. Measure with multiple copies of units of the same size, such as paper clips laid end to end;
 * How we applied this in class || Using materials such as a meter stick to measure the length of a room is useful to gives students a hands on experience with math and measurements. By learning how to measure with a meter stick students will learn different types of measurements (centimeters, millimeters, inches, etc.) and which types of measurements are appropriate to use for measuring items or rooms of different sizes.

the mystery man activity- we were able to enlarge a shape to twice (and then 3 times) its original size by using a rubber bands attached to our pencil and then tracing.

We used patty paper to make a compass by using the base line as the 180 degree angle. Then we folded the paper in half to form two 90 degree angles. We folding each of those halves in half, making 45 degree angle marks. This means we have a mark at 0, 45, 90, 135, and 180 degrees. Continuing with this process we can make more and more increments. You can also use a angle ruler, or protractor. ||
 * How this is useful || Students can use their own methods of measuring. For example, using their hands as a unit of measurement (ex: my desk is 4 hands high). In this way they can see how depending on the units used to measure, the number of units will change, what may be only 4 hands high, is 28 paper clips high.

Students also must learn which measurements are best for the situation. You would not use centimeters to measure the length of a huge room, that would be impractical. ||
 * Other mathematical connections || Determining the measurements yourself relates to reasoning. This relates to symmetry because if you know the measurements you can find out if a shape is symmetrical or not. It also ties in to finding out the area, volume ect because you need measurements to find out those formulas. ||

Nice work, good connections to the big ideas of class activities that are appropriate for this grade band. Especially in measurement and spatial visualization between and among 2D and 3D shapes.