Theresa+and+Megan's+page+for+Pre-K+-+2nd+grade

There are four goals for the geometry standard and two goals for the measurement standard :
 * __Pre-K - 2nd Grade__**


 * __Geometry__**

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

1. recognize, name, build, draw, compare and sort two and three dimensional shapes.
 * triangles are shapes that have 3 sides
 * quadrilaterals are shapes that have 4 sides
 * along with knowing the difference between quadrilaterals and polygons, the students might want to know they difference between squares vs. rhombus and rectangles vs. parallelograms if there is any type of comparison.
 * ex, a square is a special kind of rectangle
 * ex, squares and rectangles both must have 90 degree angle measures, but they don't both have to have congruent sides
 * we began studying polygons in class first by naming attributes (ex, what do ALL triangles have or what do SOME triangles have)
 * we then formed a more concrete definition (such as, a triangle is a polygon with three sides)
 * we used materials such as polystrips, and programs such as Sketchpad and Scratch to build these shapes

2. describe attributes and parts of two and three dimensional shapes.
 * how many sides does the shape have?
 * how many angles does the shape have?
 * does it have line segments, lines, rays?
 * what attributes can you measure within the shape? (angles, sides)
 * sorting shapes by their different sizes to identify what kind of triangle it is (types of triangles: isosceles, acute, scalene, equilateral, right, obtuse)

3. investigate and predict the results of putting together and taking apart two and three dimensional shapes. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
 * example: in class we took a piece of paper and folded it to make a square, leaving a rectangle as an access piece. Folding the big square, we were able to make 5 different shapes by folding and folding (folding a trapezoid into a triangle or square, whatever it makes and so on) in the end we had 6 different shapes and we were able to predict and execute that when pieced together it made the beginning square.

1. describe, name and interpret relative positions in space and apply ideas about relative position.
 * this idea came into play when we discussed transformations (rotations, reflections and translations)
 * we discussed the idea of orientation, which we decided was the position of a shape in space
 * we determined that orientation only changes when a shape is flipped. it does not change when a shape is slided

2. describe, name and interpret direction and distance in navigating space and apply ideas about direction and distance.
 * transformations (reflections, rotations, translations)
 * these are all isometries (they create a congruent shape, but with a different orientation)
 * dialations (not isometries), stretch or shrink a shape
 * in class we used rubber bands to demonstrate how a shape can be enlarged by a scale factor, but the general shape and the angle measures are preserved

3. find and name locations with simple relationships such as "near to" and in coordinate systems such as maps. Apply transformations and use symmetry to analyze mathematical situations

1. recognize and apply slides, flips and turns.
 * Slides- A shape that slides over either the y-axis or x-axis.
 * Flips- Shape that is reflected over a line of symmetry and has direct reflection of 90 degrees.
 * Turns or translation- stays the same shape and size but has a different orientation.
 * in class we traced a shape onto patty paper, placed the transparent patty paper over a set of axis and moved the shape around, so we could see how the shape can slide, flip, rotate or turn (while still preserving its shape)

2. recognize and create shapes that have symmetry.
 * shapes that have rotation symmetry, reflection symmetry or no symmetry
 * rotation symmetry - the shape can be rotated in any direction and will still be symmetric
 * reflection symmetry - the shape can be folded in half, and all the sides/angles will match up
 * in class we sorted shapes into these three categories (rotation symmetry, reflection symmetry and no symmetry)
 * shapes such a squares and equilateral triangles have rotation and reflection symmetry
 * shapes such as rhombi and rectangles have reflection symmetry (you can fold the shape in half and the sides will match up)

Use visualization, spatial reasoning, and geometric modeling to solve problems

1. create mental images of geometric shapes using spatial memory and spatial visualization.
 * we used tangrams to show how you can take apart shapes and arrange them differently to create "new" shapes
 * two triangles can be put together to create a parallelogram

2. recognize and represent shapes from different perspectives.
 * we are just starting to get into this, but the idea of 3D shapes can fit into this category What about the nets?
 * there are different ways to view a 3D shape (from the top, from the bottom or from the side)

3. relate ideas in geometry to ideas in number and measurement.

4. recognize geometric shapes and structures in the environment and specify their location
 * ex: Computers are a rectangular shape. Wheels on your car are circle. Pyramids are triangles.

__**Measurement**__

Understand measurable attributes of objects and the units, systems, and processes of measurement

1. recognize the attributes of length, volume, weight, area and time.
 * length is the attribute used when measuring how long something is What about using the poly strips and finding out about the sum of the sides on a triangle and quadrilateral?
 * in class we used length to measure sides of polygons
 * the units involved in length include inches, centimeters, feet, miles
 * area is the idea of "covering" something
 * in class we said that if you can use a piece of paper to cover the surface of something, you can determine its area, because you are covering it What about area rules we developed?

2. compare and order objects according to these attributes.
 * Venn Diagram
 * a way to categorize shapes
 * if the circles intersect, the shape can have one of the attributes, or both of them
 * ex. a triangle can be a right triangle, an isosceles triangle, or a right isosceles triangle (the Venn Diagram for this relationship would be intersecting circles)
 * disjoint relationships are ones that have nothing in common (ex, a rectangle and a triangle are not related and would each have their own, separate circles)

3. understand how to measure using nonstandard and standard units.
 * a degree is used to measure angles
 * a degree can be defined as a "wedge" or a "piece"
 * to measure how big the angle is, you must see how many wedges fit in the space between the two lines (where the angle is located)
 * in class we folder patty paper into wedges and tried to determine how many wedges fit into the space between two lines

4. select an appropriate unit and tool for the attribute being measured. Apply appropriate techniques, tools, and formulas to determine measurements
 * length is the attribute we are measuring (the //length// of a side, table, piece of paper, etc.)
 * the //unit// of measurement is specific, such as inches, centimeters, feet, etc,
 * when measuring length for example, we use something such a ruler to determine how long something is
 * in class we used rulers to measure side lengths
 * we used protractors and angle rules to measure angles

1. measure with multiple copies of units of the same size, such as paper clips laid end to end.
 * using a pencil to measure side of a book
 * ex, in class we used an 8.5 x 11 piece of paper to cover the surface of a table to determine area

2. use repetition of a single unit to measure something larger than the unit, for instance, measuring the length or a room with a single meter stick.

3. use tools to measure.
 * we used angles rulers are protractors to predict where the angles are
 * when trying to figure our a right triangle (90 degrees) we knew that a book was the 90 degrees so we used that.
 * when looking at degrees we used patty paper to figure out how we could figure out how many "units" were in a degree.
 * using polystrips to physically see triangles or quadrilaterals and the "movements" of the angles (the many angles we might get from a rhombus). We can see if the given measurements truly make a Triangle or quad that we are looking for.

4. develop common referents for measures to make comparisons and estimates.
 * we knew that quadrilaterals and a angle measurement of 360 degrees. when we split the shape in half it added up to 180 degrees
 * we also used this idea of 180 degrees in other polygons
 * we figured out how many triangles could be made inside of the polygon and since we already knew that each triangle has a sum of 180 degrees, we could determine what the interior angle measurement was for that polygon