Kelsey+S.+and+Stephanie+W.

=Geometry 6-8 =

**Standard 1**:  Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. dimensional objects using their defining properties. 2. Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects. 3. Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity and the pythagorean relationship. **Standard 2:** Specify locations and describe spatial relationships using coordinate geometry and other representational systems. 2. use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides. **Standard 3:** Apply transformations and use symmetry to analyze mathematical situations 2. examine the congruence, similarity, and line or rotational symmetry of objects using transformations **Standard 4:** use visualization, spatial reasoning, and geometric modeling to solve problems
 * Expectations** 1. Precisely describe, classify, and understand relationships among types of two- and three-
 * Have kids have a class discussion and come up with their own definition. grades 6-8 should know and have a good understanding of shapes at this age. Create a class discussion and have the class come up with what they think the definitions of each shape and the different types of shapes are. Use common properties to determine what shape it is.
 * using the program smilemath on the TI-73 calculator can help understand relationships between angles helping to guesstimate angle sizes. this can help kids see if angles are congruent, obtuse, acute, etc. it will help with an overall understanding of the relationship of angles and shapes.
 * __Guess my rule game__- We played this game using only Triangles. The game covers all three expectations. The game is played by one person thinks of a rule in their head for the group of triangles (ex: right triangles, obtuse triangles, isosceles, etc.). then you start by placing one on the table that is in the group and one that isn't. The rest of the group must ask questions of which triangles are or aren't in the group. As you place these triangles in the groups the group members must try and guess the rule of your group of triangles. This activity helps children learn the different properties of triangles. It also helps children learn that certain triangles can be put into several different groups(ex: obtuse triangle could also potentially be an isosceles triangle). It helps children define triangles as well.
 * __Quadrilateral property sort game__- This game is similar to the Guess my rule game. This time you randomly selected two of the given properties on the little slips of paper. Then you take the quadrilaterals and sort them into each group, Which you are aloud to have some that fit into neither group. Then you figure out how these groups would fit into a Venn diagram. This will help kids learn that Quads have many different properties and that there are many different types of quads.
 * Expectations** 1. use coordinate geometry to represent and examine the properties of geometric shapes
 * (We have not discussed this in class)
 * (We have not discussed this in class)
 * Expectations** 1. describe sizes, positions, and orientations of shapes under informal transformations such as slips, turns, slides and scaling
 * A program called 'Sketchpad' allows you to create different kinds of shapes. Sketchpad has tools that allow you to rotate, slide, and reflect shapes. Students can explore the program to help them learn how to create various shapes. and it
 * In class we used measuring tools to reflect, rotate, and slide various shapes. We rotated shapes around one of its own sides as well as a point not connected to the shape. Some examples of these can be found in the Course Pack on pages 126-132, as well as many others.
 * THIS FITS BOTH EXPECTATIONS 1 & 2: We used a program called sketchpad to help us form various shapes. You are able to create different shapes that are draggable and you can create your own tools.we created various triangles such as right isosceles triangles and obtuse scalene triangles. We rotated the shapes and reflected them to find out what other shapes they formed by doing this. this will help children see the various amounts of shapes that are created by putting other shapes together.
 * Expectations** 1. draw geometric objects with specific properties, such as side lengths or angle measure
 * there are a few programs we have used like scratch, explore draw and geoboard. letting the kids experiment with these programs can help kids recognize specific properties of shapes (regular/irregular). in programs like scratch and explore draw these help kids figure out how to find an exterior angle and what it is. you must find the exterior angles of shapes in order to form them in these programs. you can use the formula 360/n (n = the number of sides). the exterior angle plus the interior angle comes to form 180 degrees, which is why when you are headed straight ahead then you must turn a certain number of degrees which is the exterior angle and then the rest of the 180 that is left becomes your interior angle.

2.use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume 3. use visual tools such as networks to represent and solve problem -- this expectation is actually talking about networks as in vertex-edge graphs but I see the connections you are making here. 4. use geometric models to represent and explain numerical and algebreic relationships 5. recognizable and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science and everyday life
 * we came up with our own nets of different 3D shapes. we had to figure out a net for shapes like, cones, pyramids, prisms, etc. (fits expectation 3 as well--->)also we did activities where we were given various nets formed by cubes and we had to figure out what prism/3-dimensional shapes that it turned out to be in the end.
 * we were given nets and we had to figure out the surface area of the box.
 * we also used 3-dimensional shapes to help us discover the formulas for other 3D shapes.
 * We were shown nets of a shape and then we had to create that shape using building blocks.
 * we had to some up with a various amount of nets so the would make up the same 3D shape every time.
 * there were certain problems we were given in class and the problem gave us a certain number of cubes. we had to come up with different ways to stack/pack the cubes to help us minimize and maximize the surface area. e.g. this could help us solve problems to help us package something with using the least amount of packaging possible.(could fit in expectation 3 also)
 * in class we came up with a Venn diagram of rotational and reflection symmetry. We brought in things we found in magazines and online photos that were things we found in everyday life (e.g. picture of a house, bicycle wheel, flower, etc.) and sorted them into the Venn diagram; does it have rotational? reflection? or both? this will help kids see that shapes are all around us and they can recognize the types of symmetry better.

=Measurement 6-8 =

<span style="color: #ff0047; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%; text-align: center;">**Standard 1:** Understand measurable attributes of objects and the units, systems, and processes of measurment <span style="color: #ff0047; display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">2. understand relationships among units and convert from one unit to another within the same system <span style="color: #fd4608; display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">3. understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area and volume <span style="color: #ff0047; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 130%; text-align: center;">**Standard 2:** Apply appropriate techniques, tools and formulas to determine measurments <span style="color: #f90606; display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">1. Use common benchmarks to select appropriate methods for estimating measurements <span style="color: #ff0047; display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">2. select and apply techniques and tools to accurately find length, area, volume and angle measures to appropriate levels of precisions <span style="color: #fd4608; display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">3. develop and use formulas to determine the circumference of of circles and the area of triangle, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes <span style="color: #ff6700; display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">4. develop strategies to determine the surface area and volume of selected prisms, pyramids and cylinders <span style="color: #f90606; display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">5. solve problems involving scale factors, using ratio and proportion
 * Expectations** <span style="color: #f90606; display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">1. understand both metric and customary systems of measurment
 * (We have not discussed this in class)
 * in class we had to cut out shapes we were given and we had to come up with ways to find the areas of those shapes. people used different units to find these shapes. example: we all had the same size rectangle and some people used 4x2 or 10x5 but its because they had different size units. so what you have to do is make sure you include your units when measuring because someone could be using cubes that are 1x1cm or some students could use 1x1inches for the same shape. you need to make sure students are able to convert between units like that and make sure they understand the various units you can use to measure just one shape.
 * Using graph paper, we could count up the number of cubes in a shape to calculate the area, surface area and volume of shapes. Those cubes would be unites^2. Angle measures are found in degrees, perimeter is in unites(of any kind, inches, centimeters, etc), area is in units^2, surface area is in units^2 and volume is in units^3.
 * Expectations**
 * Using patty paper, you can estimate the measure of an angle. Using one side of the patty paper as equaling 180 degrees, you can then fold it in half, resembling 90 degrees and then fold that again to resemble 45 degrees and so on. You can then fit the patty paper to the angle and estimate what the angle measure is. You can use one of your folds as a benchmark for determining the measure. this teaches children how to estimate angle measurements. this can also teach children what a degree is. it is 1/360 of a full rotation, so it takes 360 degrees to make a full rotation. by folding the patty paper this tell the children that we would need to fold the paper 360 times in order to make an accurate measure.
 * we came up with ways to find length, area, perimeter and different measures of a shape for similar shapes. w hat was the general technique behind these methods?
 * We used graph paper with it's "cubes" to determine length, area, and volume.
 * For angle measure, we used patty paper and folded it into approximate angle measures to estimate the measure of angles if we had no angle measure tools, like a protractor, available to us.
 * In class we were given different shapes to cut out (our "pink shapes"). We were then asked to develop universal formulas for certain shapes ( like circles, triangles, rectangles, trapezoids, and parallelograms) in order to find their area. We had to find a way to determine the area of theses shapes without their measurements given, to find a formula we could use. EXAMPLE: For a parallelogram, create two right triangles, cut one off and flip it around and put it with the other triangle to form a rectangle. Find the area of the two rectangles and then add them together to find the area of the parallelogram. letting students come up with formulas will help them explore the shapes more in depth and they can figure out what the formulas are and what the really represent.
 * In class we worked with three-dimensional shapes to create formulas to find the surface area and volume of the specified shapes.
 * We created the formula for finding the surface area of a rectangular prism by using what we already know. We already know how to find the area of a rectangle, therefore, we came up with the formula for finding surface area of a rectangular prism as SA= 2(length x width) + 2(height x width) + 2(height x length).
 * we came up with different ways in class how to come up with surface area and volume. we discovered that u have to use your area formulas of a 2d shape to come up with the surface area and volume of a 3d shape. we found that to find the surface area you take the area of a all the individual sides and then add them together and that becomes your total surface. we came up with are area as Length x Width.
 * In class (with Dr. Browning) we used transparent 3D shapes and used filler to calculate volume formulas. Using the filler we compared the volumes of cones, pyramids, and sphere's to that of a cylinder. We compared how much of the filler filled the cylinder from the filler that completely filled one of the shapes. The volume formulas we created are as follows: For a cylinder: V=Area of circle x height; cone: V = 1/3 Area of circle x height; pyramid: V= 1/3 length^2 x height; sphere: V=2/3 Area of circle x diameter.
 * we played a drawing game, where we were given a shape (super sleuth man) and we had to scale it to make it bigger. we attached two rubber bands that were the same size and held one end at a point on the same page as our original shape, then we took three rubber bands of the same size and did the same thing. we came up with the conjecture that two geometric shapes are similar if all corresponding angles have the same measure and all corresponding sides are proportional. another conjecture that was formed was that if "k" is our scale factor and we have a rubberband the size of "k-band" then perimeter= (Perimeter*k) and area= (Area*k^2). students will learn to explore with the rubberbands to come up with these types of conjectures. students will also learn that similar shapes must have same size angles and proportional sides.

<span style="color: #ff0047; display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">6. solve simple problems involving rates and derived measurements for such attributes as velocity and density
 * we did not go over this in class.

GENERAL COMMENTS The pythagorean theorem is also a topic that will be covered in grades 6-8. Generally good connections to what we did in class, it would be nice to see some more on how these ideas are useful or relevant and also what connections can be formed across the standards. - SOME CONTENT AREAS SEEMED TO BE MISSING OR CONNECTIONS NOT MADE EXPLICIT WHEN ACTIVITIES OVERLAPPED BETWEEN SEVERAL STANDARDS/EXPECTATIONS. WORK TO MAKE THESE CONNECTIONS MORE EXPLICIT SO THAT YOU ARE NOT INTRODUCING REPEATED WORK, BUT RATHER CROSS REFERENCING THE SAME WORK AND EXPLAINING HOW THE IDEAS ARE CONNECTED. - CONNECTIONS AND USEFULNESS OF IDEAS NOT ALWAYS MADE EXPLICIT, BUT IN SOME CASES SOME REALLY GOOD EXPLANATIONS WERE GIVEN, AS IN THE FIRST STANDARD. - THE WAYS IN WHICH THE CONTENT WAS CONNECTED TO THE STANDARDS WAS GOOD, AGAIN, SOME IDEAS AND CONNECTIONS SEEMD TO BE MISSING. SEE REMARKS NOTED ABOVE.