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__GEOMETRY STANDARDS__

Analyze characteristics and properties of two-and three dimensional geometric shapes and develop mathematical arguments about geometric relationships. We talked about angles of shapes and how to measure them. Angles are made by two line segemts meeting each other at a point called the vertex. Line segments can go on over forever and the angle would still be the same; the line segment's measure would be different. We have discussed triangles and quadrilaterals which are all polygons. A polygon is a simple colsed curve with straight sides. Need to CLEARLY identify concepts. "We talked about angles" just doesn't give me much information. What did we talk about? How does that connect to this expectation? What did we do? What does "gone over" mean???
 * identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;

TRIANGLE: A polygon that has three sides and three interior angles. Interior sum of all angles in a triange is 180 degrees. ANGLE: formed by two line segments (rays) at a shared endpoint, called the vertex. POLYGON: a simple closed curve with straight lines. QUADRILATERAL: Polygon with 4 sides and 4 angles. KITE: a quadrilateral​ with 2 pairs of congruent adjacent sides. SQUARE: a parallelogram with all sides and angles congruent. A rhombus with all angles congruent. RECTANGLE: a parallelogram with 2 / 4 right congruent angles. RHOMBUS: a parallelogram with 4 congruent sides. TRAPEZOID: a quad with one set of parallel sides. PARALLELOGRAM: a quad that has 2 sets of parallel sides. All of the these defintions were created by our class How? We examined lots of triangles, for example, and made a list of attributes that all triangles have and that just some triangles have. From the list of what all have, we began to form our definition of what is a triangle. From the list of attributes that just some triangles have, we defined special triangles, such as right triangles, obtuse triangles, etc. and were done as simple as possible but has enough information for any person to understand. How did we come up with these definitions? Did we only describe triangles in general? In our first project we created a shape by using the directions that we were given. From that shape we could transform shapes by grabbing an endpoint or side and moving the mouse creating a bigger or smaller shape. Think about your project. Did you combine or transform any shapes there? If so, how were they combined/transformed? Think about some homework problems that we've discussed. Haven't we developed any logical arguments in those responses? No new comments to address these questions. Angle, Vertex, Radius -We can describe movement by using a coordinate system or synthetically by reflecting, rotating, or translating a shape. what did we do in class that had us examining these ideas? Why are they important? Do they connect to other ideas?? Need to answer these questions for all entries.
 * classify two- and three-dimensional shapes such as triangles and pyramids;
 * investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;
 * make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.
 * Specify locations and describe spatial relationships using coordinate geometry and other representational systems.**
 * describe location and movement using common language and geometric vocabulary;

We use coordinate systems for transformation (isometries), the sub groups of transformations are: translations, rotations, and reflections. And what did we find out? - We used (x,y) to find locations in the coordinate systems. in plain quadrant 1, the coordinates are (+x,+y), in the second segment quadrant, the coordinates are (-x, +y). In the third quadrant, the coordinates are (-x,-y). In the fourth quadrant, the coordinates are (+x,-y). These are the coordinates you have to use to figure out where given coordinates are located on the coordinate PLANE. Did we try to find distances??
 * make and use coordinate systems to specify locations and to describe paths;​
 * find the distance between points along horizontal and vertical lines of a coordinate system.


 * Apply transformations and use symmetry to analyze situations.**

- Slides: Slides are done around the x and y coordinates or synthetically on the plane using rulers and compasses. Sliding can only happen when you use addition or subtraction in the coordinates. Both coordinates have to be added or subtracted by the same number for the slide to work properly. If you multiply or divide the coordinates you have diametrics not sure what this is; perhaps you meant "dilations" which means you stretch the shape width or length wise.
 * predict and describe the results of sliding, flipping, and turning two-dimensional shapes;​

-Flipping: When you flip a shape over the x or y axis, the shape has to be congruent to the original shape. This means that the shape has to be the same distance from the line of reflection. All points of the original shape have to be measured to the line of reflection and transferred into the desired coordinate plain. Flips can be done over all four of the axis areas.

-Turning: slides-translation flipping-reflection turning-rotation you can use these ideas to to find if a shape is congruent or not congruent You can use patty paper, mira, ruler, protractor, or angle ruler to see if a shape is congruent to another shape. line symmetry is when you can fold a shape over a line and the shape will be the same on both sides. rotational symmetry is where you can rotate and a polygon a certain amount of degrees and the polygon will look the same as the starting position. How did we identify these symmetries? What shapes had these symmetries? What kind of shapes did we examine? still no response.
 * describe a motion or a series of motions that will show that two shapes are congruent;
 * identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs.


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

We used the geoboard application on our calculators. and? We also used sketch pad on the computers. and? We used scratch the cat to find out angles, exterior angles the most. How?
 * build and draw geometric objects;

patterns could be tiles in the ceilings, area to perimeter patterns, notice that there are distinct angles in rooms By folding up nets(2-D) on each side we can make a 3-D figure When we look at a 3-D figure such as buildings on the calculator we can figure out what it looks like as a 2-D figure. We can use a certain shape to create a biggers shape to figure out formulas for area and perimeter. Buildings are made with triangular structures to help support the building and preventing it from falling over. Most roads are perpendicular to each other which creates a 90 degree angle. Corners of classrooms.
 * create and describe mental images of objects, patterns, and paths;
 * identify and build a three-dimensional object from two-dimensional representations of that object;
 * identify and build a two-dimensional representation of a three dimensional object;
 * use geometric models to solve problems in other areas of mathematics, such as number and measurement;
 * recognize geometric ideas and relationships and apply themto other disciplines and to problems that arise in the classroom or in everyday life.


 * __MEASUREMENT STANDARDS__

Understand measureable attributes of objects and the units, systems, and processes of measurement**

length is how long a side is, measured in inches, centimeters, any type of unit. Size of an angle is measured in a little wedge called a degree and they're 360 in a single turn.
 * understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute;

We can use angle rulers or protractors to measure the degrees of angles. Use rulers to measure side lengths such as inches, feet, or centimeters. 12 inches=1 foot, 3 feet=1 yard, 10 millimeters=centimeters, 30 centimeters=1 foot Approxmations are ok in math class not really, we normally like to be exact, but there not ok in building a house, they have to be precise. Centimeters are more precise than inches, inches are more precise than feet, etc. Area and perimeter will change in a dilation or a isometry. Dilation- making the shape bigger. Isometry-shape staying the same.Shape will change with a scale factor.
 * understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems;
 * carry out simple unit conversions, such as from centimeters to meters, within a system of measurement;
 * understand that measurements are approximations and understand how differences in units affect precision;
 * explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way.


 * Apply appropriate techniques, tools, and formulas to determine measurement.**

For irregular shapes.... perimeter-you can just measure around the outside of the shape by using a ruler or string. area-using squares around parts of the shape that have sharpe edges and using our knowlege to figure where we could put an edge of the shape in a different area to create a whole square. Area is measured in square units and it covers something. Length we can use a ruler, measured in inches, centimeters, feet. Volume is measured in cubic units and it fills something. Weight is how heavy or light something is, such as ounces and pounds. Temperture is how hot or cold something is, in farenheit and celcius. angles is measured by degrees, with angle rulers or protractors. Other than rulers to measure things, you can use pieces of paper, foot steps, pencils, desks, basically anything that you can use to measure. Area of a rectangle-b x h triangles-1/2 b x h parallelogram-b x h Trapezoids: (B1+B2)h/2 or 1/2(B1+B2)h These are some rules but how did we develop them? SA- can be found by counting squares on a net Volume-L x W x H same here. What was the fundamental idea for thinking about volume?
 * develop strategies for estimating the perimeters, areas, and volumes of irregular shapes;
 * select and apply appropriate standard units and tools to measure length, are, volume, weight, time, temperature, and the size of angles;
 * select and use benchmarks to estimate measurements;
 * develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms;
 * develop strategies to determine the surface areas and volumes of rectangular solids.