Amanda+K.+and+Biju+P.+3-5

**Geometry 3-5**

**Standard 1:**  Analyze characteristics and properties of two-dimensional geometric shapes and develop mathematical arguments about geometric shapes. **Expectations:** 1. Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe these attributes. - We learned about different types of triangles and quadrilaterals. We also said whether these shapes had reflection symmetry, rotational symmetry, or whether they were asymmetrical (no symmetry).

- We identified different 3D such as prisms, pyramids, and cylinders. We discussed their different characteristis such as faces, parallel bases, surface areas and volumes. In order to help us better understand these concepts we created our own and played with nets, along with playing with wooden 3D blocks, and hollow plastic 3D shapes that we filled with filler product. By using and playing with nets and blocks students will have a better grasp of the concets.  2. Classify two- and three- dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids. - We classified: Triangles: acute, obtuse, right, isosceles, equilateral, and scalene Quadrilaterals: parallelogram, rectangle, rhombus, kite, square and trapezoid

1) Polyhedra: a 3D solid with ALL flat faces such as: 2) Non-Polyhedra: a 3D solid that does not contain all flat surfaces such as:
 * -** We classified: 3D shapes: two main categories 1) Polyhedras 2) Non-Polyhedras
 * Pyramids: a solid with one polygonal face which is known as the base and a point not located in the plane of the polygon.
 * Prisms: a 3D solid with two parallel, congruent faces that are connected by rectangular faces.
 * Cylnder: a 3D solid with two circular, parallel, congruent faces.
 * Cone: a 3D solid that contains a circular region that is connected to a point not located in the plane of the circular region.

3. Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes. - A quadrilateral has 360 degrees because a triangle has 180 degrees. This can be seen when you divide a quadrilateral into two parts, creating two triangles. 4. Explore congruence and similarity

- In class we experimented with the difference between using equal in a statement versus using congruent. We then decided that as educators, congruent was probably that better choice to use, but in all actuality either one work. We also investigated ideas of similarity using the rubber band stretchers.

5. Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions. - We do this everyday in our daily class discussions. In order to support any conjecture that is made in class, logical arguments must be made to support that conjecture otherwise it is usually thrown out. Although sometimes this can be time consuming in the end we normally end up with a correct conjecture that we can use. ** Standard 2: ** Specify locations and describe spatial relationships using coordinate geometry and other representational systems.


 * Expectations: ** <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> 1. Describe location and movement using common language and geometric vocabulary.

<span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">- We worked with describing location and movement by using a variety of different mathematical programs in class such as: Exploredraw ( we moved the turtle to different locations to create different shapes), Scratch ( we told the sprite where to and how to move to create shapes), and sketchpad ( to create shapes and discover the said shapes symmetry, rotational and reflectional). <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> 2. Make and use coordinate systems to specify locations and to describe paths. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">- By using Scratch we were able to create scripts that told the sprite exactly what path to travel along in order to reach a specific location while forming a particular shape. <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> 3. Find the distance between points along horizontal and vertical lines of a coordinate system.

<span style="color: #0075ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: center;">** Standard 3: ** Apply transformations and use symmetry to analyze mathematical situations. <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">**Expectations:** <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> 1. Predict and describe the results of sliding, flipping, and turning two-dimensional shapes. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> - We dealt with this expectation in doing Project 1 on Geometers Sketchpad. We experimented with reflecting(flipping) and rotating(turning) a number of different triangles

<span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">2. Describe a motion or a series of motions that will show that two shapes are congruent. - We have seen this through flipping, rotating and sliding shapes. If a shape undergoes anyone of those transformations and lands directly on top of another shape, both of the shapes are congruent.

<span style="color: #11b611; font-family: 'Comic Sans MS',cursive; font-size: 120%;">3. Identify and describe line and rotational symmetry in two- and three- dimensional shapes and designs.

- First we defined line symmetry as when a shape has a line that divides that shape into two equal halves that mirror each other, and then we defined that a shape has rotational symmetry if you can turn it on its center of rotation less than 360 degrees and it lands exactly on itself. Then we were given a number of different two dimensional quadrilaterals and triangles and were asked to classify each of them as having line symmetry, rotational symmetry, or whether they were asymmetrical (no symmetry). After this was done it was realized that if a shape had more than one line of symmetry, then it also had rotational symmetry.

**<span style="color: #0075ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Standard 4: ** <span style="color: #0075ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 135%; text-align: center;">Use visualization, spatial reasoning, and geometric modeling to solve problems. <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 192%; text-align: center;">**Expectations:** <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">1. Build and draw geometric objects. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">- We did this in two different programs, one on our calculator and one on the computer. On our calculator there is a program called ExploreDraw, in which you direct a turtle around in order to draw any shape of your choice. On the computer we had a program called Scratch in which you directed a cat, or an object of your choice around, just like the turtle on your calculator. By using these programs it will help students have a better understanding of concepts we are trying to teach them and they will grasp the ideas faster. <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">2. Create and describe mental images of objects, patterns, and paths. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">- In order to draw shapes on either ExploreDraw or Scratch it was very important that you understood the exact movements you needed your object to make. This forced us to picture the objects we were making mentally, as well as recognize the paths and patterns of these different paths. <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">3. Identify and build a three-dimensional object from two-dimensional representations of that object. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> - We did this in class when we were experimenting with nets. A net is a 2-D pattern that can be folded to form a 3-D figure. We attempted making prisms, cylinders, cones, and pyramids while in class. <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">

4. Identify and build a two-dimensional representation of a three-dimensional object.

<span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">- For this expectation we were given an object and were asked to create a net of the object. By looking at the 3D solid we had to reason what arrangements of "squares" would form the proper net to create the surface area of the 3D object. <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> 5. Use geometric models to solve problems in other areas of mathematics, such as number and measurement.

6. Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">- When we were learning about surface area and volume we talked about how it could relate to everyday life. We can use the concept of surface area when we need to buy new carpet or flooring for a room in our homes and when we need to buy packing material to ship objects through the mail.

<span style="color: #21c4ab; display: block; font-family: 'Comic Sans MS',cursive; font-size: 220%; text-align: center;">**Measurement 3-5**

<span style="color: #0075ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">**Standard 1:** <span style="color: #0075ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: center;">Understand measurable attributes of objects and the units, systems, and processes of measurement. <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">**Expectations:** <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">1. Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> - We've done this in the most basic form so far by understanding that the appropriate way to measure angle size is in degrees by using angle rulers.

- We found the surface area of 3D solids by coming up with the formula 2(l x w) + 2(l x h) + 2(w x h), where "l" is the length, "w" is the width, and "h" is the height

- We came up with a formua to find the volume of a rectangular 3D solid which is l x w x h <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">2. Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> - In class we all looked at a rectangle and we were asked to find the area of that rectangle. Two people came up with two different answers. The units were not specified so they were both talking about the same amount of area, so they were both actually correct. <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">3. Carry out simple unit conversions, such as from centimeters to meters, within a system of measurement.

4. Understand that measurements are approximations and understand how differences in units affect precision.

- When using pi to determine any measurements our answers will always be approximations and not exact answers because pi contains such a large decimal place. In order to help get our answers as close to the "real" answer as posible it is acceptable to leave the symbol for pi in the answer to help prevent rounding errors.

5. Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way.

- We dealt with this in Project 2 with the "Blob". We were asked to trace around the blob and turn it into a rectangle. Upon doing this we were asked to find the changes if any in the perimeter and the area. We found that the perimeter stayed the same while the area did change upon the transformation.

<span style="color: #0075ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">**Standard 2:** <span style="color: #0075ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: center;">Apply appropriate techniques, tools, and formulas to determine measurements. <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">**Expectations:** <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">1. Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes.

- In project #2 we focused on this idea with the "blob". To determine the perimeter of the irregular shape we can measure a string around the shape. To determine the are of the irregular shape we could create a rectangle around the shape that we know the area of and then subtract the area that is not covered by the irregular in order to figure out the area.

2. Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">- So far in the course we've only dealt with the angle size area of this expectation, understanding what an angles is (interior as well as exterior) and how to figure out its measure using definitions, formulas, as well as other methods (ie. the triangles inside the other shapes). <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">3. Select and use benchmarks to estimate measurements. 4. Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms.

<span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">We came up with area formulas for all three of these shapes in class. Rectangle: A= l x w Triangle: (1/2) x b x h Parallelogram: b x h <span style="color: #11b611; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> 5. Develop strategies to determine the surface areas and volumes of rectangular solids. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;"> In class we came up with formulas to find the surface area and the volume of rectangular solids. SA= 2(l x w) + 2(w x h) + 2(h x l) V= length x width height <span style="color: #800080; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: left;">Mostly good identification of the big ideas, the connections among standards and the whole development of these ideas was not necessarily articulated. More evidence needs to be made for why these ideas are important or significant. <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 120%; text-align: left;">