Jenna+and+Ashley's+Page-+Pre-K+-+2nd+grade

Expectations in Prekindergarten through Grade 2
=Geometry:=

I tried to catch all of your "angels" but I'm sure I missed some.
 * EXPECTATION Standard #1: Analyze characteristics and properties of two and three dimensional geometric shapes and develop mathematical arguments about geometric relationships **
 * This is expectation #1: Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes (the main goal is to allow them to associate what shapes they already know, with the name and definition of the shape, so we have listed an example of something a pre-k to second grade student might think about when they learn a shape). Can you indicate what activity we did in class that relates to this?
 * **Base**: The face of a three- dimensional shape chosen to be the "bottom" face.
 * **Edge**: A line segment formed where two faces of a three-dimensional shape meet.
 * **Face**: A flat two-dimensional surface of a three-dimensional shape.
 * **Flat**: A flat two-dimensional surface of a three-dimensional shape.
 * **Height:** The vertical distance between the face chosen to be the base and 1.) the opposite face of a prism or cylinder, or 2.) the vertex of a cone or pyramid.
 * **Net**: A two-dimensional pattern that can be folded into a three-dimensional figure.
 * **Surface Area-** The area required to cover a three-dimensional shape.
 * **Unit Cube-** A cube whose edges are 1 unit long. It is the base unit of measurement for volume.
 * **Volume-** The amount of space occupied by, or the capacity of, a three-dimensional shape. The volume is the number of unit cubes that will fit into a three-dimensional shape.
 * __2D Shapes:__ We examined more.
 * //**Triangle**//-We looked a the triangle and said that it's definition is "a polygon with three sides." We decided that this was efficient because when you have three sides to a polygon, you will automatically have three angels angles . We didn't need to say anything about it being a closed figure with straight lines either because that is all included in the definition of a polygon. We also found out that all triangles' angels have a sum of 180 degrees and you can prove this because if you place the three angels angles together, they will form a straight line.
 * //**Rectangle**//-We discovered that rectangles have four right angels angles and they are a parallelogram. We said that the definition only needed to say that it had at least two right angels because if there is two right angels, then the other two angels will automatically become right angels.(a door)
 * //**Rhombus**//-We said that a rhombus is a parallelogram with four congruent sides. We did not find anything about the angels that should be included in the definition because there is no specification for them. A rhombus can be at a slant so the angels angles can vary, but we did observe that the opposite angels are congruent, no matter how slanted the figure. (square slanted)
 * //**Square**//- We defined a square as being a rhombus with all right angels angles . We noticed that a square has the same properties with the angels as a rectangle, meaning the definition only needed to say that there has to be at least two right angels angles because once you have two, the other two will automatically be right angels. A square can also be called a rectangle because it has four right angels and it's a parallelogram so it fits the criteria. (tiles on the floor)
 * __3D Shapes__ (what we have so far):
 * **//Polyhedra//**-Polygon extended.
 * //**Prism**//- polyhedron with Rectangular sides faces with polygon-shaped top and bottom /base.
 * //**Cylinder**//- Flat, circular tops with curved edges. A three-dimensional shape with two opposite faces that are congruent circles. The side (lateral surface) is a rectangle that is "wrapped around" the circular faces at the ends.(ex: canned food)
 * //**Pyramid**//- polyhedron with Square Bottom with four isosceles or equilateral triangles. Has a plat end and a point on the other end. (Ex:Egyptian pyramids)
 * //**Cone**//- polyhedron with Circular base and vertex opposite the base. (ex: ice-cream cone)
 * **//Cube//**- A three-dimensional shape with six identical square faces.
 * **//Oblique Prism//-** A prism whose side faces are non-rectangular parallelograms.
 * **//Rectangular Prism -// A prism with a top and bottom (base) that are congruent rectangles. **
 * **//Right Prism- A prism whose vertical faces are rectangles. The bases are congruent polygons. //**
 * **//Sphere-// A three-dimensional shape whose surface consists of all the points that are given distance from the center of the shape. **
 * Describe attributes and parts of two- and three-dimensional shapes
 * (See definitions above for descriptions) Describe how we investigated these attributes
 * Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes
 * We started with a rectangular piece of paper and cut it into a square. We then cut that into two isosceles right triangles, and then cut those into a trapezoid and an isosceles triangle. Sort of; called a tangram
 * We learned how you can figure out the name of a shape and it's characteristics based on what you know about the shape it was derived from (if you cut a square into two congruent triangles, you know that the angels be will 45, 45, and 90 because of the squares angels being cut in half and one remaining the same).
 * Spatial visualization is (Not just what you describe; this is an activity that would utilize spatial visualization; being able to visualize 3D shapes, taking them apart, putting them together, and visualizing their components such as the silhouette) where you have a "stamp" or silhouette of a 3D shape and the students have to look at the different stamps of one shape and try to figure out what shape it is. (As an activity for the students to practice spatial visualization, they could experiment with cubes and the teacher could put up a shape's stamp on the overhead and the students could use the cubes to make the object.)


 * Standard #2:** Specify locations and describe spatial relationships using coordinate geometry and other representational systems You need to list the 3 expectations.
 * Four questions regarding spatial understanding where from? :
 * //Direction// (which way?)-This would mainly apply to turns, which way is the shape now placed after you have turned it?
 * //Distance// (how far?)-This would mainly apply to reflections and slides, how far away is the Original Point from the Image Point after the shape has been reflected over the line of reflection and how far did you slide the object or shape along a plane?
 * //Location// (where?)-This would mainly apply to slides and turns, where did the object end up after you slid it along the line indication where to slide the object or shape and where did the object or shape end up after you turned it?
 * //Representation// (what objects?)-This would apply to all of them, where is the new location and relation of the new point and angels in relation to the original points and angels?


 * Standard #3:** Apply transformations and use symmetry to analyze mathematical situations
 * Recognize and apply slides, flips, an turns
 * //Slides//-When an object or shape maintains all other characteristics, it's location in space or on a grid has simply moved up, down, right, or left.
 * //Flips//-When an object or shape maintains all other characteristics, the object or shape is just flipped along a line of reflection so that the original points are the same distance away from this line as the new points. (Point A was 2 inches away from the line of reflection, then Image Point A will be two inches away from the line of reflection)
 * //Turns//-When an object or shape maintains all other characteristics, it is simply moved around in any direction in space or on a grid. (Take a square and move it around and turn it around on your desk, and you have turned the object).
 * Recognize and create shaped that have symmetry
 * //Symmetry//-when a shape is congruent to another shape (they maintain all characteristics, all corresponding sides and angels angles are congruent). This is not what symmetry means.
 * As long as you follow the rules of transformations (slides, flips, and turns) you will have two shapes that are symmetric.
 * Isometries **Dilations! (when you make the object bigger or smaller) will create a shape that is similar, but not symmetrical. When something is similar, it maintains the same ratios (you must extend or shorten (multiply or divide) all the corresponding sides by the same number to maintain the same ratio). All of the angels angles will remain congruent, however, because you are simply extending or shortening the side lengths, which will have no effect on the angel's angles' measurement.** Isometries preserve everything and produce congruent shapes.
 * We used the rubber band method to test this theory and to see how you can dilate a shape. You could do this with young children too so they can see and measure all the sides and angels to see how the sides relate to one another and how the angels stay the same.

Where did the bulleted points come from?
 * Standard #4: Use visualization, spatial reasoning, and geometric modeling to solve problems. **
 * You can use what you already know about a shape's properties in order to find the measures of other angles or sides
 * All triangles have 180 degrees so you know that if you have two angles then you can add those two up and subtract the sum from 180 degrees to find the third angle
 * Young students could see that this was true by cutting the triangle's angels apart and then placing them all along a straight line to see that they equal 180 degrees (they could associate a straight line with 180 degrees, so instead of telling them all the angels will equal 180 degrees, you could tell them that they will all fit along a straight line).
 * If you know that two sides are congruent, you could find the other side (AB is congruent to DC, and you know the measure of AB, you could find the measure of DC). How?
 * If you know the measurement of one angel angle, you could find the measurement of another if they are congruent.
 * Being able to recognize different shapes in different environments and specific locations.
 * You could use patty paper and trace the original shape to see if it congruent to the other shape
 * Students could learn how to measure objects and spatial visualize which side on the new object corresponds with that side length or angle measurement on the original shape to see if the two shapes are congruent
 * Teach the children that geometry is part of everyday life, and are seen everywhere.
 * The walls of rooms are at a 90 degree angle
 * Doors are rectangles
 * Triangles are used in building houses and other buildings because they are sturdy. We learned and investigated this when we used poly strips to test the sturdiness of a triangle compared to that of any other polygons with more than three sides.
 * Teach the basic shapes of geometry: angles why is this here instead of above? You appear to create these expectations instead of using those listed.
 * //Triangle//-polygon with three sides
 * //Acute Triangle//-Triangle with at least one angle smaller than 90 degrees
 * //Obtuse Triangle//-Triangle with one angle larger than 90 degrees
 * //Right Angle//-Triangle with one right angle
 * //Isosceles Triangle//-Triangle with only two congruent sides
 * //Equilateral Triangle//-Triangle with all congruent sides
 * //Scalene Triangle//-Triangle with no sides congruent
 * //Quadrilateral//-Polygon with four sides
 * //Kite//-Quadrilateral with two pairs of congruent adjacent sides
 * //Parallelogram//-Quadrilateral with two sets of parallel sides
 * //Square//-Rhombus with all right angles
 * //Rectangle//-Parallelogram with 2 right angles
 * //Rhombus//-Parallelogram with four congruent sides
 * //Trapezoid//-Quadrilateral with only one pair of parallel sides
 * //Reflex Angles//- Angles between 180 and 360 degrees.
 * //Vertex//- A point in an angle
 * Teach the basic language of a circle:
 * //Diameter//- any line segment from a point on a circle through the center to another point on the circle.
 * //Radius//- any line segment from the center of a circle to a point on the circle.
 * //Circumference//- the distance around the circle. (area: a measure of how many square units it takes to exactly cover the region inside the circle.)

=Measurement:=


 * Standard #1:** Understand measurable attributes of objects and the units, systems, and processes of measurement
 * Recognize the attributes of length,volume,weight, and time (i.e. length requires the measurement of a side length)
 * Allowing them to look at, touch, and play with objects will allow them to recognize these things. (Using tools such as the mira, 3D shapes, objects that they can trace, circles that they can measure, etc.)
 * Compare and order objects according to these attributes (pencil lighter than a stapler, stapler lighter than a book, etc.)
 * Understand how to measure with both nonstandard (pencil, paper, hand, pool stick, etc.) and standard (centimeter, inch, foot, etc.) units
 * We used patty paper to try to come up with a way to measure angels angles and we figured out that you could measure an angle by slices, where you take the patty paper measure out a small triangular like shape and it's called a slice. How ever many of these slices fit into an angle, that was the measure of the angle. (i.e. if three slices fit in the angle, the measure of the angle would be 3 slices).
 * Select an appropriate unit and tool for the attribute being measured (i.e. don't use a pencil to measure a sidewalk and don't use a pool stick to measure a brick)
 * By doing the exercise with the patty paper explained above, we were able to figure out how geometers came up with the measurement of degrees. A degree is a small sliver, one sliver is equal to one degree. And how ever many of these slivers fit into an angle, that's the measure of the angle in degrees.

No tools to measure? Any measurements of area?
 * Standard #2:** Apply appropriate techniques, tools, and formulas to determine measurements
 * Measure the same object using different tools and units of measurement (measure a laptop with paper clips, pencils, gummy bears, etc.) Did we do this?
 * Use the same unit of measurement over and over to see how something larger and smaller than one another compare to each other in that unit of measurement (measure a pencil with paper clips and measure a chalk board with paper clips) Did we do this?
 * Use tools to measure


 * Develop the same units used to measure different objects in order to compare measurements of big and small items

>> Any mention of Sketchpad? Geoboard?
 * Understand that measuring an angle of a shape is different than measuring a side of a shape.
 * //Angle//-the turn made by a ray, line, or line segment/the area or space created between two lines, rays, or line segments/the point where to rays, lines, or line segments come together
 * //Side//-the line segments that creates the polygon or shape
 * Measure the angle with degrees and the side with inches, centimeters, or any other form of measurement you choose
 * //Degree//-the unit used to measure an angle. It is a tiny sliver or tirangular-like shape that you use to fill in the space, turn, or point to where two angels meet and how ever many of those slivers fit inside that area, that is the measurement of your angle in degrees.
 * Once you rotate a shape, in order to get it back to where it started, you will have to turn it 360 degrees
 * The scratch program helps students learn about angles and turns; and also helps them learn the concept of exterior angles. How so?

=IMPORTANT: Teach the children to be independent reflective learners.=
 * You want your students to be able to look back on what they learned and to asses themselves in order to decide whether or not they understand the material and allow them to teach themselves based on what they already know.