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Pre-K–2 Expectations: Grades 9–12 Expectations: What is it? A website for teachers or alternative educators (homeschool) that provides free, printable math work sheets in all areas and for all grade levels in mathematics. =__ Pattern Blocks __= = By: Racheal Haines = //Pattern Blocks// can be used for all types of math lessons such as adding and subtracting, multiplication and division, fractions, geometry, plane tiling, and symmetry. The shapes available for //Pattern Blocks// are a triangle, a square, a parallelogram, a rhombus, a trapezoid, and a hexagon. Students are able to be rotated these shapes in any direction. The shapes can be changed to an assortment of colors. They can be superimposed on each other or themselves. They can be made bigger or smaller. Lastly, they can be cloned. NLVM provides an array of activities where a student can experiment with most of the mathematical concepts listed above. **2.9.K.A:** Identify and describe common 2-dimensional shapes **2.9.K.B:** Identify and draw lines of **symmetry**, with adult assistance **2.9.1.A:** Name, describe and draw/build 2-dimensional shapes **2.9.1.B:** Identify and draw lines of symmetry K-2 grades Expectations : Using //Pattern Blocks// in Geometry, a teacher could ask his or her students to identify, draw/build, compare, and, sort two-dimensional shapes. The shapes could consist of a triangle, a square, a parallelogram, a rhombus, a trapezoid, and a hexagon. //Pattern Blocks// can also help students recognize the symmetry between shapes. Depending on the grade, students could identify and draw the line of symmetry.
 * JAMIE HANSEN DOUTS**
 * What does this manipulative do/show? :** The Great Circle manipulative is a virtual globe that can be used in place of a physical globe, but ideally would be explored in conjunction with a physcial globe of the world. With the Great Circle manipulative, students click on any highlighted city on the globe then click on a second city to see the Great Circle route. The Great Circle route is shown in green and a straight-line path on the Mercator (flat map of the world) is shown in red at the bottom of the manipulative, and also on the globe at the top. And in the upper left hand corner in green, the great circle distance is shown in miles. For Example, I clicked on Bombay India and Tokyo, Japan to see the Great Circle path and its distance of 4,196 miles. By rotating the virtual globe, it should be clear how much shorter the green great circle route is, but this observation has even more impact if students have access to a physical globe. The manipulative suggests that students replicate the virtual Great Circle with the classroom globe and a piece of string. The students would stretch a piece of string from one city to city. The stretched string is automatically part of a great circle. From this kind of exercise, students should be able to recognize that great circle distances are always the shortest and that a great circle is what we would get by slicing a plane through the center of the sphere and the two cities on the surface.
 * How does it connect to NCTM standards?:** This manipulative connects to upper elementary to high school levels. It utilizes NCTM pre-K through 12 Standards and Expectations regarding measurement, data and analysis, geometry, process standards and possibly crossover to numbers and operations and algebra with older students.
 * pose questions and gather data about themselves and their surroundings;
 * sort and classify objects according to their attributes and organize data about the objects;
 * represent data using concrete objects, pictures, and graphs.
 * What are your thoughts on this resource?:** I think that this manipulative is excellent. It is user friendly for teachers and students alike. This manipulative is ideal for the teacher to demonstrate that a straight line is not always the shortest way to reach a point. This gives students the chance to explore and learn on their own in a guided direction. The Great Circle manipulative can be used for many different grade levels since it is a generally open manipulative.
 * understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each;
 * know the characteristics of well-designed studies, including the role of randomization in surveys and experiments;
 * understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable;
 * understand histograms, parallel box plots, and scatterplots and use them to display data;
 * compute basic statistics and understand the distinction between a statistic and a parameter.
 * FREE MATH WORKSHEETS K-12**
 * Where can they be found?** []
 * How could it connect to teaching that supports NCTM standards?**
 * NCTM Standard: K-12,** covers all areas of mathematics
 * What are your thoughts on this resource?** I think this site is very useful. It provides worksheets for all areas in mathematics //and// has a variety of games, flashcard, and enrichment activities (even holiday themed math activities). These additional activities could be helpful when students finish early with in-class work, to have as extra credit or to keep on hand for substitute teachers.
 * What does the manipulative do/show? **
 * How does it connect to NCTM Standards? **
 * NCTM Standards: K-2 grades**
 * Geometry Standards: **

**2.8.2.C:** Recognize, describe, extend, create, and replicate a variety of patterns including attribute, activity, number, and geometric patterns.
 * Algebra Standards: **
 * 2.8.PK.C:** Recognize and replicate number and geometric patterns
 * 2.8.1.C:** Recognize, describe, extend, replicate and transfer number and geometric patterns
 * 2.1.2.C:** Use drawings or models to show the concept of a fraction as part of a whole; use whole numbers and simple fractions (halves, thirds, and fourths) to represent quantities

In general, the website is very simple and easy to negate which is wonderful for young students. There are an array of activities provide for //Pattern Block// which is great because of all the areas of mathematics they are used in. This game allows for simple use as just allowing the students to explore two-dimensional shapes or it can be made complex by the activities provide. For example, one activity is to figuring out what shape would be considered half a unit of another shape. One of the big features or lack of features in the //Pattern Blocks// section is that during the activities there is no feedback provided to the user. The activities ask the player to do certain tasks with the shapes once he or she completes the request there is no feedback whether it is wrong or the right. For this reason, I would not use this resource as an independent activity for my students. I might allow them to just experiment with the shapes independently but I would not allow them to practice the activities provided. I would use the activities as a whole class introduction to a certain concept where //Pattern Blocks// can be used.
 * K-2 grades Expectations: **Using //Pattern Blocks// for Algebra, a teacher could ask his or her students to recognize, replicate numbers and geometric patterns. They can also help students describe, extend, and create certain geometric patterns. //Pattern Blocks// are very popular tool for representing fractions. They can be used as models or as a tool to help students understanding.
 * What are your thoughts on the resource? **

=__ POINT OUT THE VIEW __= =By: Racheal Haines= Where can it be found? [] What is it? //POINT OUT THE VIEW// is a game that represents the concept of Spatial Visualization. The concept shows connections between the three-dimensional world and the two-dimensional world. The game has four characters standing around a two-dimensional grid made up of forty-blocks with a three-dimensional “building” made of cubes on top of it. Each character has a different view of the “building”; the view could be of front, back, right or left of the building. The player must represent each character’s view by selecting certain boxes on a chart. The chart represents the two-dimensional grid it contains forty boxes. There are ten levels in the game that go from easy to hard. There are two features that help the player figure out each character’s views; one is the two-dimensional grid the “building” stands on. It allows the player to count how many spaces the figure is from the end of the grid. The player can use that information to choose the correct boxes in the chart. The second feature is a hint button; it shows a location of a certain cube within a character’s view on the chart. A cube in the figure and its corresponding box in the chart will flash at the same time. If the player selects the correct views for each character then he or she can move on to the next “building.” The “building” will look different and all the character will have a different view of it. How could it connect to teaching that supports NCTM standards? NCTM Standard: 3-5 grades Geometry Standards: Identify and draw a two-dimensional representation of a three-dimensional object. What are your thoughts on this resource? I loved POINT OUT THE VIEW!!! PBS always puts out quality children’s products whether it is a show or website. Children’s learning is always a first priority for them and I really think they did a great job on this game. I was having trouble understanding the concept of Spatial Visualization; I could grasp how to transform the view of a three-dimensional figure into a two-dimensional drawing. After I played POINT OUT THE VIEW a couple times I finally understood the concept. The game made it fun so it took the pressure away of getting the correct answer. I could just absorb how the process of transforming a three-dimensional figure into a two-dimensional drawing was done. I would definitely use POINT OUT THE VIEW in my future classroom. It is easy to use and proves great feedback so student would be able to work on it independently. I would use the game as a center to practice mastery of math concepts or as a review game after the Spatial Visualization lesson. POINT OUT THE VIEW helps students’ future learning by sharpening their problem solving skills. The game gives the player certain tools but does not explain how to use them, for example the grid that the three-dimensional figure lays on is a tool but is does not explain in the directions. This makes the student use their problem solving skills to figure out how the game works. In life, there aren't always directions for everything a person may encounter so these skills are important.

Caitlynn Engle

**Ladybug Leaf**

**What does this manipulative do/show? :** The Ladybug Leaf manipulative allows for students to follow a pattern of tracing different objects such as the perimeter of a stop sign (8-sided figure) along with a speed limit sign (4-sided figure). It also could allow students to learn ways in which line segments are connected in order to create different geometric shapes, if instruction is given by the teacher. The students have the ability to use their creativity to design any two dimensional shape. Also, this manipulative can be used to allow students to create a program for the ladybug to follow in which they create the path and are able to visual the spatial process of the line segments. **How does it connect to NCTM standards?:** This manipulative connects to the Pre-K to grade 2 mathematical standard “recognize, name, build, draw, compare, and sort two- and three-dimensional shapes”. One way a teacher could use this manipulative as stated above was to build two-dimensional shapes. The teacher can then have the student identify their shape and compare theirs to classmates. Another standard from the Pre-K to grade two age ranges is to “create mental images of geometric shapes using spatial memory and spatial visualization.” This standard expresses the purpose of this manipulative in regards to a students visualizing where line segments should be drawn and connected through mental images.

**What are your thoughts on this resource?:** I think that this manipulative is excellent. The teachers have just as much control as the students in either specifying what needs to be done, or just by having the students practice their own ideas. It can be used for many different grade levels since it is a flexible manipulative. Teachers can make this manipulative harder by setting standards in which the students must follow such as, hiding the ladybug under the leaf with as less than 6 moves. Students must be able to visualize in their heads a way in which this goal can be met.

**Shapezoid (other manipulative)**

**Where can it be found?:** []

**What is it?:** The purpose of this game is to complete missions by shooting the specific shape that you are assigned too at the beginning of the mission. There are squares, triangles and circles flying around through space and the student must shoot the correct shape, or else the target bounces off and no points are received. After too may incorrect shots are fired at the wrong shapes, the game is over.

**How could it connect to teaching that supports NCTM standards?:** Shapezoid could relate to the Pre-K to grade 2 standard “recognize, name, build, draw, compare, and sort two- and three-dimensional shapes”. The students will have to be able to recognize the difference between circles, triangles and squares, in order to complete the mission. **What are your thoughts on this resource?:** I think that this resource is great for students in the younger grades. It allows them to recognize common shapes, yet still have fun in the process. Many students would enjoy the fact that it is a game, but yet they are learning at the same time. If I get a job teaching young students, this manipulative will be a great tool to use in helping students learn basic shapes.

**Pentominoes (Jessica Jarlsberg)** Today I analyzed and evaluated the Pentominoes manipulative. The purpose of the Pentominoes manipulative is to allow students to manipulate the twelve different figures, which are made up of five squares each. With this virtual manipulative students are able to create different sized rectangles, build different types of congruent figures, make stairs, and work with perimeters. This manipulative is simple to use; you just have to click on the Pentomino that you would like to use and it will appear on the screen. You can then rotate it, clone it and zoom in or out. Directions and sample questions are provided on the side of the website to facilitate students discovery and exploration. This manipulative correlates to the NCTM standard that states “students should use visualization, spatial reasoning, and geometric modeling to solve problems. Pre-K–2 Expectations: In pre-K through grade 2 all students should relate ideas in geometry to ideas in number and measurement." After using this manipulative I found it not only to be beneficial, but challenging and enjoyable. The rectangles were extremely difficult to build because you had to move the different shaped Pentominoes until they fit evenly together to form a rectangle. Students who enjoy the game Tetras will enjoy working with this manipulative and the Pentominoes. This manipulative is also beneficial because it assists the students in acquiring knowledge of perimeter. The students are able to put different Pentomino pieces together and calculate the perimeter based off of the number of squares along the edge of the figure. This manipulative could also be used to teach students about area because students could count the number of 1x1 squares that the whole shape contains. In conclusion, I would use this virtual manipulative in my future classroom when working with Pentominoes because they facilitate learning with different aspects of Geometry.
 * **What does the manipulative show/do?**
 * **How does it connect to NCTM Standards?**
 * **What are your thoughts on the resource?**

**Bitesize (Jessica Jarlsberg)** Today I was also able to analyze and evaluate the Angles manipulative on the website BiteSize. This website has many manipulative games and activities to help elementary students learn math concepts. The manipulative activity I chose was regarding angles and it allowed students to identify accurate measures of angles. This website can be found at [|__http://www.bbc.co.uk/schools/ks2bitesize/maths/shape_space/angles/play.shtml__]. This activity asks students to pick the appropriate angle listed at the bottom of the screen that correctly answers the question being asked. Each question is different, but they all revolve around choosing the correct angle to stick onto a circle grid that has a water squirter on top. The aim is to choose the correct angle that will allow the water to hit the dog or other objects sitting on the outside of the circle. If you chose the wrong angle, the water will still quirt and you will see how far away you were from the object you were aiming at. The questions become more challenging as you continue through the activity. This activity correlates to the NCTM standard that states students should “analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. Pre-K–2 Expectations: In pre-K through grade 2 all students should describe attributes and parts of two- and three-dimensional shapes.” This activity is integrative because the students are engaging with angles in a game, but also testing their knowledge at the same time. This could be used for students who have just learned about different angle measures and need extra practice identifying the measure of angles. I found this activity exciting and different. It would benefit students at all levels, but the lower elementary levels would most likely find the most enjoyment in it because it is limited. I would use this activity in my future classroom to facilitate children's learning of angles and other math concepts. It is a great way for students to practice identifying angles and could be used as a center or even as review for a test on angles.
 * **What does the manipulative show/do?**
 * **How does it connect to NCTM Standards?**
 * **What are your thoughts on the resource?**

Danielle Bennett 4/11/11

Congruent Triangles allows you to construct two triangles from various combinations of sides and angles. You can choose to work with any one of four different combinations: side, side, side (SSS); side, angle, side (SAS); angle, side, angle (ASA); or side, side, angle (SSA).

**SSS**: You are given three red segments and three blue segments, with each blue segment matching a red segment. Each segment can be dragged and rotated until a triangle is formed in one color. Repeat the process with the segments of the other color. Now you have a red triangle and a blue triangle, both with matching side lengths. Drag and rotate the triangles to get matching sides together. If the triangles are congruent, when you have matched sides the colors will switch, ending in a green triangle.

**SAS**: You are given two red segments and a red angle, and three matching blue pieces. Drag and rotate the red angle so its vertex is on top of one end point of the red segment and one side of the angle lies along the segment. Then place one end of the other red segment on the vertex of the red angle and rotate the segment until it lies along the other side of the angle. When the segment coincides with the side of the angle, you get a solid red triangular region with the two given sides and included angle. Repeat the process to get a blue triangle. Drag and rotate the triangles to get matching sides together. If the triangles are congruent, when you have matched sides the colors will switch, ending in a green triangle.

**ASA**: You are given two red angles and a red segment, and three matching blue pieces. Drag and rotate a red angle so its vertex is on top of an end point of the red segment and one side of the angle lies along the segment. Then place the second red angle at the other end of the segment and rotate the angle until it lies along the segment, so that the free ends of the angles are on the same side of the red segment. You get a solid red triangular region with the two given angles and included side. Repeat the process to get a blue triangle. (Follow the last step as the previous two)

**SSA**: You are given two red segments and a red angle, and three matching blue pieces, but in this case the angle is not included between the given sides. Place the red angle at one end of a red segment with one side of the angle along the segment. Then attach the other red segment to the end of the segment opposite the attached angle. The angle determines the line along which the third side must lie. Rotate the free end of your second segment until the free end is on the line. You will get a solid red triangular region with the given sides and angle. Repeat the process to get a blue triangle, but your goal is to rotate the third blue side so that your blue triangle is NOT CONGRUENT to the red triangle. If your triangles are congruent, you get a message inviting you to Click and start over, to construct two noncongruent triangles, each having the given sides and the given angle opposite one of the sides.

This manipulative connects to the NCTM standards.  It is appropriate for grades Pre K- 2 and can be incorporated into math lessons. Students in the younger grades can use this tool during a station that may be set up around the room, or the class may want to take a trip to the computer lab during a math lesson to have this hand on experience while also incorporating technology. I found this to be useful in understanding congruent triangles. There are many more combinations for each of the 4 types once you have completed one congruent triangle successfully. There was plenty of practice opportunity. The only thing I found to be frustrating was that if you were not sure of the answer, or what to do there was nothing to click on to reveal the answer or drop a hint. The person using the tool would have to clearly understand what was being asked. Overall I think it is great hands on experience and would be enjoyable for young students.
 * Pre-K–2 Expectations**: In pre-K through grade 2 all students should–
 * recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;
 * describe attributes and parts of two- and three-dimensional shapes;
 * investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.


 * Review of another resource ** :

[]

This website is from a school district and it consists of many things to help with understanding Geometry. The first page that appears is an overview of all polygons, polyhedra, and other geometric terminology. At the top you are able to click on links to worksheets that can be printed out for practice with naming and quizzing your knowledge. Also available, are links to quizzes for polygons, lines, and solids that can be taken right on the computer.

As mentioned above, this connects with NCTM standards. It is appropriate for grades Pre K- 2 and can be incorporated into math lessons. Students in the younger grades can use this tool during a station that may be set up around the room, or the class may want to take a trip to the computer lab during a math lesson to have this hand on experience while also incorporating technology. The teacher can also print the worksheets out to use in class. I feel this resource can be very useful to a student no matter what grade they are in. This would be beneficial for those who need extra practice or if you want to incorporate some worksheets into a lesson. I like that there are quizzes and worksheets that can be printed out and that it is accessible to anyone. It is easy to navigate and clear to understand. Overall it is great for teachers and students.
 * Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships**
 * Pre-K–2 Expectations**: In pre-K through grade 2 all students should–
 * recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;
 * describe attributes and parts of two- and three-dimensional shapes;
 * investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.

~//**WEB ANALYSIS ASSIGNMENT**//~ //(Alicia Snook)//

**WHERE IT CAN BE FOUND:** [|www.hubbardscupboard.org]

**WHAT IT IS**: This site is great for teaching children in kindergarten and also as a refresher for those struggling in the upper grades. There is a tab called Math Tubs and it contains hands on activities and manipulatives for students to use that focus on a variety of math concepts. Students can work independently, developing skills such as number recognition, sorting skills, patterning skills and set recognition. **HOW IT CONNECTS TO TEACHING THAT SUPPORTS NCTM STANDARDS:** As far as Geometry goes, students will be able to identify and describe the attributes of the shapes by matching and comparing them. Students will also count by 10’s and compare values of whole numbers up to 20. There is practice of one-to-one correspondence when it comes to rolling and counting. With this activity, students will use concrete objects to determine if something is less, more or equal to the other amount. **2.8.K.A:** Use concrete objects to demonstrate understanding of equal and not equal. **2.1.K.B:** Represent equivalent forms of the same number through the use of pictures and concrete objects (including penny, nickel, and dime), up to 20. **2.1.K.A:** Demonstrate the relationship between numbers and quantities, including rote counting, one-to-one correspondence, and counting by tens, and comparing values of whole numbers up to 20. **OPINION:** I feel that the Math Tub idea is a great tool to have in the classroom because it not only allows the child to work at their own pace but it also allows them to explore until they figure out the correct answer. Math Tubs can have material at any level. It can be used as a review or even a pre assessment tool to see what the students already know. Also, these topics in the Math Tubs will aid in the mastery of future learning. Children must learn the basics such as counting, sorting, classifying and recognition in order to excel in the higher grade levels. The math tubs also allow students to engage in independent learning, which is also something that they will need for future success. The technique of hands on learning is a great way to get students involved in their education.

**__SPACE BLOCKS__:** **DESCRIPTION:** This virtual manipulative allows the students to add, rotate and connect blocks to create the activity assigned on the right column. Students count the exposed faces and determine what happens to the surface area when another block is added to the figure. Students can see if the surface area is maximized or minimized by the addition or subtraction of blocks to the figure. There are also activities that allow students to determine the correct net for the figure shown. **CONNECTION TO NCTM STANDARDS:** 

Grades 6–8 Expectations: In grades 6–8 all students should: use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume. Students will use the blocks provided to build a structure with a specific surface area. **OPINION:** Space blocks is an interactive site that permits students to engage in hands on learning by moving or manipulating the blocks to change the surface area. It also helps the students visualize breaking down an object and how it folds out into a net. This site is easy to use and provides the students problems to figure out. However, there is only seven problems provided so there is not much variety for the students to work with. Surface area is a tough idea to grasp for some students so I feel that this activity would help those struggling, visualize the problem better by physically moving the blocks into their own positions.

Stephanie Carbaugh**Geoboard--Circular****What does the manipulative do/show?**** This manipulative is a great resource for students in grades 6-8. It helps students understand angle and degree measurements using a geoboard. Students are able to do various activities to understand angles. They are able to do various activities such as constructing central angles and finding the angles of a triangle. **How does it connect to the NCTM Standards?

This manipulative connects to the NCTM Standard for Geometry. The standards is for grades 6-8 and says:

**


 * //understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;//

It helps students understand the central angles of a figure and they are able to compare different shapes and how the angles correspond. //What are your thoughts on the resource?// I found this resource to be very helpful for students but also found a few things that I did not like about it. The first thing I didn't like about the resource was the lack of instructions. I feel as though as a teacher I would need to go through it numerous times to make sure the students had a firm understanding. I think that it could have a little more directions for the student so they can work on this resource at home as well. The other thing that I did not like about this resource was that for the activities that it gives for the student it does not give them an answer. The student would not be able to make sure if they were right if they were working on this resource at home.

Math Playground: Measuring AnglesWhere can it be found? http://www.mathplayground.com/measuringangles.html **What is it?**** This game helps children get familiar with using a protractor. The game starts by telling students the rules and informing them that there is only a 1 degree margin of error. Once the game starts the students have to move the protractor around until the line on the figure is lined up with the protractor. Then they have to look at the protractor and determine the angle. Once they type in what they think the angle measurement is they are able to check their answers. ****How could it connect to teaching that supports NCTM Standards?** understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. This relates to the standards because the students are expected to understand how to use a protractor when measuring angles. **What are your thoughts on the resource?**** I found this resource to be very user friendly and beneficial for students. I find it difficult sometimes to know exactly where to place the protractor and which numbers to look at. This game can be incorporated into the classroom at any given time. It could be used through a SMART board software so that all the students would be given the opportunity to practice. **

Rachel Olszewski Platonic Solids-Slicing


 * In this manipulative, students have the option of choosing between a tetrahedron, cube, octahedron, dodecahedron, or an icosahedron that they will make a slice through. They can make the cross-sectional slice bigger or smaller, and can rotate the solid as well. On the right hand side, the students can see the 2-D view of the slice, and on the left they can see it in 3-D. They also have the option of viewing the entire solid, or just simply seeing the part that is being sliced through. This manipulative shows the students the different shapes that can be found in the platonic solid by slicing it in different ways, and visualize the intersections.**


 * This manipulative is directly connected to this NCTM standard for Geometry:**


 * In grades 6–8 all students should– **
 * precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties **


 * This is connected to it because the program has students understand the relationship between the platonic solids and the two-dimensional shapes that make up the solid. Also, they would be able to use this to see the intersections that are possible when slicing a solid. **
 * I think that this resource would be difficult to use in all grade levels, it can really only be used for older children. Also, it can be a little confusing at first, but with the correct guidance I think it could be something interesting for them to see because otherwise, it would be hard to visualize. Other than using this as a visualization tool, and something for the students to see one time, I am not sure how else it could be incorporated in to a lesson. **

Solid Figure Factory
 * [] **
 * The “Solid Figure Factory” is a game in which the student would have to match the solid figure that is given with the picture of the actual solid figure. If the student chooses the correct solid figure, then the machine creates a real-world object that is that actual figure. For example, when the student correctly chooses a cone, then the machine will spit out a birthday hat. If the student chooses the wrong solid, then they will get a “try again” message.**
 * This game would fall under the standard:**
 * Pre-K–2 Expectations for Geometry: **
 * recognize, name, build, draw, compare, and sort two- and three-dimensional shapes **


 * This game allows students to see examples of different solids, as well as matching the correct names to the pictures. With assistance, they would also be able to compare the different parts of each of the solids. **


 * Because this game could be a little redundant, I think that this would be a good review game for students to do before a test. I think that it is valuable in a review aspect, but it would not be meaningful for students to learn solely from this game. Also, after exploring the website, **
 * [], it seemed like this website was rich in other resources! **

**__Tight Weave__ - Chandler Wilson** **__IXL Third Grade Math Practice__ - Chandler Wilson**
 * What does the manipulative do/show?** This manipulative allows students to see a repeating pattern and how its works. The carpet (or square) starts off with a certain percent of purple space that is then slowly covered in gold squares. Each step takes part of the purple squares and makes it gold. This makes it where the students could conclude that eventually the entire space would be covered in gold.
 * How does it connect to NCTM Standards?** The NCTM standards state that a student learning geometry should be able to "recognize, describe and generalize patterns using sequences and series to predict long-term outcomes," this manipulative would allow the students to do that because before seeing the next step they could try to come to a conclusion of what percent will be gold. Also it fits the standard that says "identify and/or extend a pattern as an arithmetic or geometric sequence."
 * What are your thoughts on the resource?** I think that Tight Weave is an interesting resource. But I would not recommend it for a teacher to use as an assignment. They don't really have to put much thought into it if they just click for the next step to come up. The teacher could use it in the classroom as part of a lesson and before clicking ahead to the next step have the students try to work it out. I think that its pretty interesting how they got the gold squares to cover certain percentages of the purple ones but it doesn't require much effort.
 * Where it can be found:** []
 * What is it?** The IXL website is an interactive site that provides review problems, or practice problems for different grade levels. I chose the third grade math practice page. It provides review problems for 20 different topics. Some of these topics include Geometry, Properties, Place Value, Equations, Estimation, Logical Reasoning, Money, Time, Graphs and so many more. It provides little quiz like segments for each section. It can time the child as they work and tell them right away if they got one wrong and what the correct answer would be.
 * How could it connect to teaching that supports NCTM standards?** The site as a whole would relate to so many of the NCTM standards. But since we have been talking about geometry, I decided to focus on that grouping. I think that it definitely goes with the standards that state the student should be able to "identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes." It also helps them to "investigate, describe, and reason about the results of subdividing, combining, and transforming shapes." There are also a few others that it can attribute to but it all depends on which sections you are focusing on.
 * What are your thoughts on this resource?** I believe that this website is an awesome resource for any classroom. It has all different age ranges and different lessons. The teacher could use it to match up with all the different lessons their class is studying. I really focused on the geometry ones for the third grade level and I found that they even applied to what we have been learning. It provides a great review to the class material and teachers can have the students submit scores to them on the review problems if they wanted. I thought it was a great resource and would definitely use it in my own classroom.

Kristin Zerbe - Fractals - Polygonal What does the manipulative show?
 * I have the geometry manipulative called polygonal fractals. This manipulative creates a polygon depending on the number of vertices you choose, and also the probability fraction. You can choose between three and fifteen vertices, and the probability fraction can be from zero to one. The probability fraction of one puts together tight clusters of points to form the polygon. The probability fraction of zero creates a group of points that do not have a specific shape, and are spread out throughout the whole grid. There are many options when you use this manipulative. First, you can pick the number of sides you want your polygon to be, then you pick the probability fraction, and then you can hit the play button and the polygon will start to form. If you hit the pause button during the making of the polygon, you can change the color of the shape to see the transformation of the shape as it continues to grow. If you hit the stop button, the formation of the shape will stop and it will clear the shape from the screen. **

How does it connect to NCTM Standards?
 * This manipulative meets the standard “analyze characteristics and properties of two and three dimensional geometric shapes and develop mathematical arguments about geometric relationships” set by the National Council of Teachers of Mathematics. Specifically, it meets the standard set for pre-k through second grade, which states that they will be able to “recognize, name, build, draw, compare and sort two and three dimensional shapes” and “describe attributes and parts of two and three dimensional shapes.” This manipulative can help the children identify and name polygons by using the number of sides the polygon has. It helps the children build the shapes visually, even though they aren’t physically doing it, by watching the website create the shape. Also, by the website creating the shape for them, they will be able to describe the shape in a different way than if they would have a solid object in front of them. **

What are your thoughts on this resource?
 * Personally, I think this resource was a little confusing, especially if younger kids would try to use it. I had a hard time understanding the probability fraction, and to be honest, I still am a little confused. I tried to research it online, and read the teacher/parent help page, but it doesn’t give a very clear explanation. I do like the fact that you can change the number of vertices from three to fifteen because I think that is a good way for the students to become comfortable naming the polygons. I also like the fact that you can pause the creation of the polygon in the middle of the process, and change the color of the points to see the contrast. Overall, I felt that this resource is not the best option for an elementary school classroom, and that there have to be better options for the children to learn about polygons. **

Kristin Zerbe - (other resource) Geometry Board Where can it be found? What is it?
 * The manipulative that I found online is just simply called “Geometry Board.” It can be found at []. It is basically an online form of the geo-board that we use in the classroom. It is a free resource that teachers could let their students use to teach them about different shapes and polygons. The students can get on, and the first thing they can do is choose the “elastic” button, which gives them a virtual rubber band for them to hook onto the board. They can drag the rubber band to any point on the board, and then drag the other end of the rubber band to another point. They can continue to click on points of the rubber band that are located on pegs, and drag them to different pegs on the board. This allows the students to be creative and create as many shapes as they can while using this board. They can create multiple shapes at one time as well. If they create a shape, and want to create another shape, they just have to click on the “elastic” button again, and another rubber band will be put on the geo-board. They can also color in a shape by clicking on the rubber band, and choosing a color on the left hand side of the board. This will make it easier for them to see the different shapes on the board. They can also click the “measure” button on the right side of the board, and it will give them the area and perimeter of the shape. **

How could could it connect to teaching that supports NCTM standards?
 * This manipulative meets the standard “analyze characteristics and properties of two and three dimensional geometric shapes and develop mathematical arguments about geometric relationships” set by the National Council of Teachers of Mathematics. More specifically, it meets the standards set for the age group of pre-k through second grade which says that they will be able to “recognize, name, build, draw, compare and sort two and three dimensional shapes” and “describe attributes and parts of two and three dimensional shapes.” They will be able to build the shapes using the geo-board and name the shapes by counting the number of sides it has. They can also compare the shape they built to another shape that they can build on the same board. They will be able to practice making the shapes, and comparing them to other shapes that they have seen before, or compare them to shapes that they can build themselves. Another standard this manipulative meets is the standard “apply transformations and use symmetry to analyze mathematical situations.” For the pre-k through second grade, the standard says that they should be able to “recognize and create shapes that have symmetry.” The students will be able to do this using the geo-board. They will be able to create symmetrical figures, and the pegs on the geo-board will help them count the spaces in between the sides of the shape. **

What are your thoughts on this resource?
 * In my opinion, this resource would be a great tool to use in the classroom. First of all, it is free for anyone to use. Secondly, it is a very easy resource to understand and I feel that it would be easy for elementary-age children to understand as well. The children can create different shapes, with many different sides, and they can even create more than one shape at a time. They can color the shapes different colors, so that it is easy to see all of the shapes on the board at one time. They will be able to recognize and name shapes that they create, and the more they practice, the better they will get at recognizing them. Overall, it is just a very creative resource to use in the classroom that can give each child a chance to be creative, and learn about shapes and polygons at the same time. **

//Jeannie Sweder- Tangrams// What does the manipulative show?

Tangrams are composed of 7 shapes; 5 triangles, 1 square and 1 parallelogram, which the student must then rotate and move around to create a predetermined image using only those 7 shapes. The site shows the 7 different pieces and allows you to choose the picture you would like to create. It shows a dark shadow on the work area where the pieces should cover and it allows for you to flip and rotate the shapes as needed. How does it connect to NCTM standards?

PreK-2 Standards (geometry):

· recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;

· investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.

· create mental images of geometric shapes using spatial memory and spatial visualization;

· recognize and represent shapes from different perspectives

Grade 3-5 Standards (geometry):

· investigate, describe, and reason about the results of subdividing, combining, and transforming shapes What are your thoughts on the resource?

I personally enjoy this learning activity because I think that not only does it teach a student shapes but it also challenges them to think of the different ways to piece them together to make a larger shape. For instance, the student would be challenged to decide if the square would be used or if the two triangles would be placed together to be used as a square. This is because if they choose to use the two triangles over the square, they need to make sure that one, or both, of the triangles will not need to be used in another spot so it also teaches them problem solving and to think ahead. I enjoy playing with this activity and actually have a tangrams app on my ipod that I play which because I find them challenging even at my age. //Tangrams// Where can it be found?

[]

What is it?

This link is allows teachers to print off the square block of all 7 tangram pieces together, which then would be handed out to each student from them to cut apart and have their own set of tangrams. Along with the set of tangram pieces are puzzles that the student must solve such as common shapes and even the face of a man. This would allow for the students to not only practice using scissors safely but also the actually see the shape and have it to keep in front of them. How could it connect to teaching that supports NCTM standards?

This could connect to the teaching standards as it enables students to recognize shapes and rotate or flip the shapes by hand. It encourages the student to imagine the picture in their mind and then create it directly in front of them using the shapes they themselves cut. The students can then also see how combining shapes can create a larger shape or even a completely different shape, such as combining two triangles to make a square or two triangles and a square of equal size to make a trapezoid. What are your thoughts on this resource?

I do enjoy this site a little more than the online sites as it allows for the actual hands on use of tangrams and for the students to create the images on their own work space. I also like that the students would have to cut the tangram pieces out which helps them to recognize shapes and inscribes the characteristics of the certain shape in their mind for future use. The idea of the students being able to experiment with the pieces also makes me feel as though this activity is useful since they can slide and flip as they please without the nonsense of arrows and clicking to slow down their fast moving minds.

Platonic Solids- Duals (Jessica Mummau)

[]

What does the manipulative do/show? (a description)

NLVM’s manipulative shows what a Platonic Solid- Dual is. By examining the manipulative, you can learn that the 5 platonic solids can all fit another platonic solid within the first. This manipulative shows that for it to be a platonic solid- dual, the inner solid’s vertices must touch the outer solid’s faces. They are the center points of the outer solid’s faces. The manipulative allows you to have the shapes filled or a wire frame in order to see the outer solid, inner solid, or both together. You can rotate the solid to get different perspectives and color the whole solids to differentiate between them. How does it connect to NCTM Standards? (be specific)** It is connected to the NCTM standard for the grades 3-5 expectations. These two specific areas can be applied to this concept;

This manipulative combines shapes to make solids. These solids are then classified as being platonic. To find the dual to the platonic solid, the students must also understand the concepts of the second standard, which is to be able to analyze attributes of two and three dimensional shapes and develop vocabulary. **What are your thoughts on the resource? (your opinion)** I think that this resource is a good way to show the students what a platonic solid- dual is. The colors make it easy to demonstrate which part of the shape is the dual and which is the original platonic solid. **IXL** **(Jessica Mummau)** **Where can it be found?** []
 * investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;
 * identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;

**What is it?** IXL is a website that has math lessons for all ages and math subjects. It is very organized. It lists out the grade levels, and then the skills that the students should learn in that grade. When you click on a skill, it will give you questions to answer and submit and then you receive a score at the end. If you keep doing the skills, it will gradually increase in difficulty. **How could it connect to teaching that supports NCTM standards?** It clearly lists skills and benchmarks that should be met for the grade levels and subjects. There is a link on the site specifically for state standards. It has a program that follows the student’s scores on the activities and will chart and graph it for you to show you the proficiency along with the standards. All of the activities on the website were designed to go along with the state standards. **What are your thoughts on this resource?** I think that it is very organized and specific. It gives you the grade level, topic, and section of what you are doing. Something that I really liked about the questions is that if you get it wrong, it will not only tell you that it is wrong, but it has the option to look at an explanation on how to correctly do the problem.

**Web Analysis Assignment** (Molly Eckert) **What does this manipulative do/show? ** <span style="font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 10pt;">For young students, this manipulative allows the virtual experience of pouring liquid from one container to another of a similar shape, reinforcing an experiential learning of the constancy of volume. <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">How could it connect to teaching that support NCTM standards? <span style="font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 10pt;">Grades 6–8 Expectations <span style="font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 10pt;">: In grades 6–8 all students should · <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties · <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects · <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship. **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">What are your thoughts of the resource? ** <span style="font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 10pt;">I liked the idea of “How High” but I thought this section was a little tricky to do. It seems to be more of a guessing game. Something that I would have added would be an explanation of the correct answer if the student answering wrong. I believe that students will get more out of the lesson if they understand where they went wrong. I did like that the students were able to choose what bases they wanted to measure out, some being more difficult than others.

<span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 10pt; text-align: center;">**BrainPOP** (Molly Eckert) **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Where can it be found? ** <span style="font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 10pt;">[]

**<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">What is it? ** <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">This is a fun website that was f <span style="font-family: 'Times New Roman','serif';">ounded in 1999, BrainPOP creates animated, curriculum-based content that engages students, supports educators, <span style="font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 10pt;"> <span style="font-family: 'Times New Roman','serif';">and bolsters achievement. Ideal for both group and one-on-one settings, BrainPOP is used in numerous ways, from introducing a new lesson or topic to illustrating complex subject matter to reviewing before a test. This link is specifically for geometry and measurements. There are about 20 different activities that students can explore and learn more about this subject. ** <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">How could it connect to teaching that support NCTM standards? ** <span style="font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 10pt;">This site has a specific link that teaches children different triangles and figures. <span style="font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 10pt;">Grades 3–5 Expectations: In grades 3–5 all students should · <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes; <span style="font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 10pt 1in; text-indent: -0.25in;">classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids; · <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">investigate, describe, and reason about the results of subdividing, combining, and transforming shapes; · <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">explore congruence and similarity; · <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.

** <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">What are your thoughts on this resource? **  <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">I really think that this would be fun for a wide range of students. There are not only activities that would help students learn but there are quizzes, movies, and it’s also animated. They also have a standards link which explains the standard and also gives you different activities that the students could use.

**Elizabeth Chever** Geoboard-Coordinate is a very helpful applet and virtual manipulative to learn x and y coordinates with your students. Students can create shapes on this virtual geoboard, just like in real life, and describe where the shape is by saying and understanding coordinates. Two students can pair up and use two computers to play a game just like "Battleship"! The students create any shape on the geoboard (both having the same size geoboard) and give out the coordinates on their created points of their figures, and play a game just like "Battleship", based on the locations of both of their shapes. Standards for grades 3-5 for this applet include: All of these standards fit in with this particular applet and help in locating and describing different shapes. This is good practice for spacial relationships. This is a creative way of practicing coordinates with your students. Not only can they create their own figures and describe the place using coordinates, but students can also play a game with a partner practicing the coordinates and having fun learning. I can see myself using these hands on virtual manipulatives in the future, as this is great practice for learning material.
 * What does the manipulative do/show? (a description)**
 * How does it connect to NCTM standards?**
 * **"**make and use coordinate systems to specify locations and to describe paths"
 * "create and describe mental images of objects, patterns, and paths"
 * "describe location and movement using common language and geometric vocabulary"
 * What are your thoughts on the resource?**

This geometry math lesson for the early grades, kindergarden through second grade, helps the students identify and describe different shapes. These shapes include a triangle, square, rhombus, trapezoid, and hexagon. The lesson is sectioned off with manipulatives, technology, paper/pencil activities, and literacy connections. The teacher uses manipulatives of the different shapes to introduce to the students and ask them to describe what it looks like. Next, the teacher can use the "Describe the Shape" paper to identify the different shapes listed there and then the children can use a computer applet to show which shape matches up with the name. Since the pattern block applet no longer exists on this website, the applet from our class can be used in place. ([]). Lastly, students can use grid paper to create and name the shapes the teacher gives out, and then create pictures using those shapes to tell a story. There are many elementary geometry books that can be used in the classroom as well. The PreK-Grade 2 NCTM geometry standards support this lesson. Particularly, the standard "recognize, name, build, draw, compare, and sort two- and three-dimensional shapes" fits perfectly into this lesson, as well as "create mental images of geometric shapes using spatial memory and spatial visualization". These two standards are the main and only standards that support and fit perfectly into this certain geometry lesson. Young children will enjoy this creative lesson by using manipulatives, technology, pictures, and literacy connections. I really like how there is a variety of practice on learning about the different shapes. Students use math by being creative and imaginative in creating a story by making pictures of the required shapes. However, I also wish the pattern block applet would work and be updated on this website, but the pattern block applet on the website we used in class works just as well too for this lesson. This is a great introduction to geometry and incorportating some of the important shapes.
 * My Resource:**
 * Link:** []
 * What is it?**
 * How could it connect to teaching that supports NCTM standards?**
 * What are your thoughts on this resource?**

** Erin McCaughan: ** ** What does the manipulative do/show? (a descriptive) ** <span style="color: #000000; font-family: Calibri; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">You can move manipulative in all different directions to see the faces, edges or vertices of the platonic solid. This website allows you to select a color and click on a face, an edge or a vertex. Whatever color you selected that color will fill the faces. The edges will be colored white and the vertices will be colored with a black dot. Then on the side it counts up the edges, vertices and faces for you. For example a tetrahedron has 6 edges, 4 vertices and 3 faces. After you are done one shape you can move on and try out different platonic solids. ** How does it connect to NCTM standards? (be specific) ** <span style="color: #000000; font-family: Calibri; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">Relates to NCTM standards because students K-3 need to be able to analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships. As far as three-dimensional geometric shapes they need to be able to describe attributes and parts of shapes such as identify faces, edges, vertices. This website shows the difference between a face, edge and vertex. They also need to develop vocabulary and concepts related to two- and three- dimensional geometric shapes. Three- dimensional shapes: cone, cube, cylinder, edge, face, prism, pyramid, sphere, and vertices. The website gives examples of tetrahedron, cube, octahedron, dodecahedron, icosahedrons, and tetrahedron. It shows the image and tells you the correct name for the shape. It also shows the edges, faces, and vertices of the figure. ** What are your thoughts on the resource? (your opinion) ** <span style="color: #000000; font-family: Calibri; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">I really enjoyed this resource. I think that it was helpful clicking the faces, edges and vertices and moving the figure around to be able to see the whole object visually. ** Where can you find it? **  My own website that I found is: []. ** What is it? ** <span style="color: #000000; font-family: Calibri; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">The website gives many different worksheets for English and Math. For math it is broken down into categories such as number sense, geometry, measurement, etc. It is also separated into grade categories. The website also offers online games for math that covers many different standards. The website provides a tutor in case you need help with a math problem. ** How could it connect to teaching that supports NCTM standards? ** <span style="color: #000000; font-family: Calibri; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">It could relate to NCTM standards in many ways. I looked specifically at the geometry standards for children Pre- K- 2. The website relates to these standards because one of the worksheets helps you recognize and name two- dimensional shapes. Another worksheet has real life objects that students have to identify what shape the object is. For example ice-cream is in a cone, circle, cube, sphere? There are also many other worksheets that meet NCTM standards. ** What are your thoughts on this resource? ** <span style="color: #000000; font-family: Calibri; font-size: 10pt; line-height: 115%; margin: 0in 0in 10pt;">I would definitely use this resource in my own classroom. It provides a lot of good worksheets for all ages. I like that the worksheets relate the concepts to real life objects and uses words and pictures. The games on the website are interactive and would be easy for elementary students to use.

The Attribute Train begins with a series of primary colored shapes with different numbers on them. Strung together like cars on a train, the player has to figure out the pattern of the existing cars and then select numbered shapes from the “shape bank” to complete the train. The train can also be completed through trial and error until the pattern is revealed. __ ** Algebra ** __
 * __Attribute Train-__ (Jackieraye Barr) **
 * What does the manipulative do/show?**
 * How does it connect to NCTM Standards?**
 * ** Pre-K–2 Expectations ** : Using Attribute Train, a teacher could have students classify shapes, colors and numbers. Also he or she could have students recognize, describe patterns of sequences of shapes or simple numeric patterns and translate from one representation to another. Children will analyze how the repeating patterns are generated.
 * ** Grades 3–5 Expectations ** :Ask the children to verbalize to describe the geometric and numeric patterns they solve in the Attribution Train
 * ** Grades 6–8 Expectations ** :Continue to have children verbalize the geometric and numeric patterns of the Attribute Train and to compare and contrast different types of patterns.
 * ** Grades 9–12 Expectations ** : Attribute Train may no longer be appropriate

__ **Geometry Standard** __ Attribute Train is fun, challenging, is basic enough for young kids, helps to promote verbalization of pattern, and crosses over into the art world, which I could use in art class to teach patterning in wallpaper prints, weaving, architecture, beading etc.
 * ** Pre-K–2 Expectations ** : Attribute Train helps children to recognize, name, draw, compare and sort two dimensional shapes such as triangles, squares and circles, and to identify the attributes of each shape. Attribute Train helps children to create mental images of geometric shapes, to recognize shapes.
 * ** Grades 3–5 Expectations ** : Children would be able to identify, compare and analyze the attributes of two-dimensional shapes and use vocabulary to describe the attributes, to classify the shapes by class, and to explore their similarities. Attribute Train helps children to create mental images of geometric shapes, to recognize shapes.
 * ** Grades 6–8 Expectations ** :Attribute Trains could be used to inspire geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.
 * ** Grades 9–12 Expectations: ** Not applicable
 * What are your thoughts on the resource?**

= __**Make a Roman Mosaic Online-**__ ** (Jackieraye Barr) ** =
 * Where can it be found?** []


 * What is it?** 10 colors of tiles, solid ones and split into two triangles. Combine them on a grid to create roman tile patterns, then save your pattern to use online. There are also links to Greek Key and Maze patterns, all historical in reference.

I played with this resource for a long time because it interests me. I love the nearly endless possibilities to create new patterns or mimic ancient ones. I’d like to think that the resource crosses subjects: Math, Social Studies, English and Art.
 * How could it connect to teaching that supports NCTM standards?** I could use this in my art education classes to help my students makes connections to what they learned in Math classes. I think the module may be too historically complex to have children under ten understand the Roman Empire, and some of the patterns are quite intricate. This resource I think would be best suited to middle school aged kids. Most children would be able to create their own mental images have the ability to classify and understand how numerous geometrical shapes fit together. The children would also be able to verbally describe patterns by this age and to apply those patterns to their own designs.
 * What are your thoughts on this resource?**


 * __Triominoes__ - Lauren Wiltrout**
 * What does the manipulative do/show:** Triominoes are basically triangles with different colors in each corner. The users job is to put the triangles together so that the colors match up. However sometimes the colors do not match up right away so one must rotate or reflect the image to make it work. Once the colors are matched up the students can make the triangles into anything they want.
 * How does it connect to NCTM Standards:** As described in the NCTM standards, Triominoes help students learn about the transforming of shapes. By rotating and reflecting the triangles Triominoes acts as the perfect resource for transforming shapes. This resource applies to grades 3 and up.
 * What are your thoughts on the resource:** Triominoes is a very good resource that students can use to explore transformations on their own. It also allows the students to explore their creative side while also learning about math. This would be a wonderful resource for the classroom or as a homework assignment. The students could be assigned the task of making any shape they like online while exploring the different transformations one must use to make their shape work. However though the resource is a good one, it is also a simple one. This particular resource would not take most students too long to master and perhaps even get bored with.


 * __Home School Math__ - Lauren Wiltrout**
 * Where can it be found:** This resource can be found of the internet at [].
 * What is it:** Home School Math is an online resource for math that has different games and quizzes to help students understand whatever they are learning. The link listed above will take you to the Geometry page where I have sampled many of the games. It includes such games as memory, where you have to match the different polygons. It also includes a tangram game, which is actually pretty challenging. Overall it is a resource that students can access at home or in the computer lab at school to help them fine-tune their math skills and basic understanding of what they are learning.
 * How could it connect to teaching that supports NCTM standards:** This resource connects with NCTM standards in so many ways. The first thing listed in the standards is being able to recognize, compare and sort three-dimensional shapes. As stated above Home School Math has an abundance of games dedicated to recognizing and comparing different polygons. It also has such helpful sources as, properties of a kite, which is a page dedicated entirely to the creating and understanding of what a kite is. This allows the students to understand and describe the attributes if different shapes, which is just what NCTM is looking for. NCTM also talks about the putting together and taking apart of different shapes. Home School Math has something called Polygon Playground, a place where students can go and create there own polygons and put them together and take them apart so they can see which ones go together and which do not. Due to the amount of math covered on this site Home School Math can be used from Pre-K all the way through 12th grade.
 * What are your thoughts on this resource:** In my opinion Home School Math is an amazing resource that can be used in the classroom or as a homework assignment for kids to explore. It would be a really fun pre-assessment for students understanding of Geometry, as well a good tool to use once the students begin to learn more about Geometry.


 * (Lauren Byerly) First Resource: Geoboard from** [|**http://nlvm.usu.edu/en/nav/category_g_3_t_3.html**]


 * Description:** the online geoboard allows students in grades pre-kindergarten to second grade make different shapes. There are virtual rubber bands in the left hand corner that the students can place on the geoboard and stretch to make different shapes and patterns. In doing so the students can make multiple shapes and compare them to one another on the geoboard. You can also use the online geoboard to form shapes and learn symmetry and congruency.
 * How it connects to NCTM math standards for geometry:** this virtual manipulative would allow students in pre-kindergarten to second grade make different shapes on the geoboard. The children should then be able to identify the shape they made by name. If they make more than one shape, they should be able to distinguish between the two of them and note different features, similarities, or differences of each. Also, as they stretch the bands or manipulate shapes on the board, they should be able to investigate some results of putting together and taking apart the shapes.
 * Opinion:** I think the directions given on the right hand side of the geoboard are focused more towards older kids, so I think it would be more beneficial for the younger kids to have a geoboard with fewer options to click on around it. I think that these extras could be a possible distraction to the younger kids and they may have trouble understanding what they should be learning/doing using the geoboard if they aren’t familiar with all of the other options they have to click on. However I thought the rubber bands were a great option to use on the geoboard and would really allow the children to explore various shapes on their own.


 * (Lauren Byerly)** **Second Resource: Online game –“Count On It” from** [|**http://www.gpbkids.org/countonit/**]


 * Description:** Count on it is an online game that allows children in grades kindergarten to grade three to play various levels of geometry matching games. At the kindergarten level children are given shapes to match up to their name. An example would be a box that says circle on top, and the kids have to find the picture of a circle to put in that box. There are five levels of this where the boxes get rearranged to make sure the child understands matching rather than memorizing. In grade one, more complex shapes are given. Both two-dimensional and three-dimensional shapes such as prisms and cones are used in the first grade game. It has the same format of matching as the kindergarten game has. In the second grade level, children are shown nine different pictures of angles. Their task gives them instructions such as, find all the right angles, and they need to click on the ones that are right angles. There are five levels of this game that mix up the angles and ask for right, acute, and obtuse angles. At the third grade level, it is again a matching game with different two-dimensional and three-dimensional shapes. However, the shapes get more complex with this grade level. So they are asked to find shapes such as a rhombus, scalene triangle, rectangular prism, etc. With each game they play, the shapes are changed to give some variety.
 * How it connects to the NCTM math standards for geometry:** This resource can be connected to the NCTM math standards for geometry for children in pre-kindergarten to grade 2 because it allows children to name, compare, and sort different shapes that they are shown within their grade level on the online game. Also, because they need sort the shapes, they are able to demonstrate their use of knowledge about the shape and its attributes.
 * Opinion:** This online game would be a fun and easy way to get students involved and interested in learning about shapes and angles in geometry. I think the tasks are simple enough for each grade level that all students would be able to participate. One thing I really liked about the website was that it gave an option to check your answers. So, if you had some wrong, you were able to go back and fix them before moving on to a new level. However, I did not like that it doesn’t show which ones you got wrong. I think it would be easier for the children to rearrange their shapes correctly if they were aware of which were incorrect. For older children, I don’t think this would be necessary, but younger children need more guidance. I think that no matter what this game would still require some assistance from the teacher, and it would be more effective if the teacher were going around the room helping those who had questions, and making sure that the children were applying their knowledge and skills rather than just guessing throughout the game. My only other comment about the game was that I think the second grade and third grade level should have incorporated shapes as well as angles. I just thought it was odd that only one grade level dealt with strictly angles, and then in the next grade level it went back to just shapes again.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**COBWEB PLOT** (Debra Beighley)

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Cob Web Plot, also known as Verhulst diagram is a graph that can be used to visualize successive iterations of a function y=f(x). The diagram is so-named because of its straight-line segments “anchored” to the function y=x and y=f (x) and because it can resemble a spider web. It is a basic tool to help you visualize what happens when you repeatedly apply a function to a value. The cobweb plot manipulative allows students to change the variable and observe patterns of a graphing simulation. Through the use of this manipulative you can change the curve being used; there are two kinds, “tent” and “logistic.” You can also change the initial value- (x value) and you can change the speed of the plotting. It is much easier to observe the plotting if you slow down the plotter. The cobweb plot does connect to the NCTM Standards:

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: normal;">Grades 6–8 Expectations: In grades 6–8 all students should–

 * ======<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: normal;">draw geometric objects with specified properties, such as side lengths or angle measures; ======
 * ======<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: normal;">use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume; ======
 * ======<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: normal;">use visual tools such as networks to represent and solve problems; ======
 * ======<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: normal;">use geometric models to represent and explain numerical and algebraic relationships; ======
 * ======<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: normal;">recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life. ======

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<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: normal; margin-left: 0.5in;">The cobweb manipulative can be used to supplement any lesson and can give your students a visual representation of the concept. Also, today technology is the way of life and children enjoy being able to use and demonstrate their knowledge through hands-on technology. This type of technology will allow students to experiment and enjoy learning. ======

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<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: normal; margin-left: 0.5in;">My thoughts on this resource is mixed. If you don’t know anything about cobweb plotting, this site will not interest you and will probably not benefit you. This manipulative resource does not clearly or fully explain what a cobweb plot is or even how to properly use the manipulative. This site does not provide much detail on how to actually use the manipulative and no explanation on what it actually is. I personally never heard of or seen a cob web plot before, so I was confused and frustrated. It did not teach me anything. I felt that this resource was more directed towards maybe 8th or 9th grade and is not practical for elementary use. ====== <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%; line-height: normal;">__h**ttp://www.discoveryeducation.com/. [|Discovery Education]**__

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">** Discovery Education ** is a resource that provides engaging digital resources to teachers and students, permitting educators to be more effective and increasing student achievement in all content areas. This website provides students with math-help and will generate <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">answers to specific math questions and problems, as entered by the student at any particular moment. The math answers are generated and displayed real-time, at the moment a student types in their math problem and clicks "solve." Webmath also shows the student how to arrive at the answer. In addition, this website provides teachers with a lesson plan library that covers all math concepts, including geometry. Webmath is geared towards k-12. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">This resource definitely supports the NCTM Math Standards and would be a great resource/tool for any teacher. Not only does it include the homework help, but provides manipulative to use to help reintegrate math concepts and provide students with practice problems. The website is user-friendly and is composed of many math "fill-in-forms" into which you can type the math problem you're working on. Linked to these forms is a powerful set of math-solvers, which will instantly analyze your problem, and when possible, provide you with a step-by-step solution. The homework help will eliminate frustration and make learning fun. In addition, this website offers Nutshell Math Plus which will provide explanations to your math textbook (over 70 textbooks and 75,000 problems) problems. As future teachers we can set up a free account that will allow us to set up our class, assign explanations and quizzes to individual students, groups or classes, view reports to track student activity and progress, and 24/7 homework help. This is a wonderful site and you must check it out! I absolutely love it!

Turtle Geometry (Alexandra Woolford) Turtle Geometry allows the student to create a “plan” for moving a turtle within a given area. The turtle doesn’t move until a series of “moves” are in order and the student hits “play.” “Moves” to choose from include: moving forward 1-5 spaces, rotate 15-90 degrees counterclockwise or clockwise, and change the color of the movement line. Students can choose different backgrounds: blank, maze, drawing, and rocks. The blank and drawing backgrounds can be used to design or trace your own shapes or the drawing given. The maze and rocks backgrounds can be used to create a plan that accurately gets the turtle through the maze or avoids the rocks. Turtle Geometry applies the to the Grades 3-5 Geometry Expectations of Applying Transformations: “predict and describe the results of sliding, flipping and turning two-dimensional shapes.” By designing a plan for the turtle’s path, students must predict the amount of units it must move and the amount of degrees of rotation. Students can figure these measurements out through trial and error and then once they become familiar with the measurement of one unit, they can guess what “move” should come next in their plan. Overall this is a useful manipulative. I think it’s most helpful with identifying rotations by degrees and direction. At first I found it difficult to predict how many spaces the turtle needs to move because the playing area has no grid or indication of what equals one unit. Once I became familiar with the distance after hitting play a few times, I was better able to predict how far the turtle needs to travel to get where I want. I think this tool would be appropriate for grades 4 and younger because it reinforces simple geometric concepts and is easy to use. I’m not sure if grades 5 or older would enjoy it though because of how simple and easy it would be for them.
 * What does the manipulative do/show?
 * How does it connect to NCTM Standards?
 * What are your thoughts on the resource?

Billy Bug (Alexandra Woolford) Positive Coordinate Plane: http://www.oswego.org/ocsd-web/games/BillyBug/bugcoord.html Positive and Negative Coordinate Plane: http://www.oswego.org/ocsd-web/games/BillyBug2/bug2.html


 * Billy Bug is a cute and well-designed flash game to help reinforce locating coordinates on the coordinate plane. A random point (x,y) shows up at the top of the screen and this is where the “Grub” is located. The player must move a little bug around the gridded coordinate plane to the point where the grub is located. The bug moves in one direction and one unit at a time by pushing buttons on a D-pad. As you can see, there are two versions of the same game; they are the same except that the second one includes the negative coordinates, which is a little more advanced. The game is also timed so that students are challenged to get faster and better at identifying coordinates.
 * I can imagine using this game in early algebra- possibly anywhere from 5-8th grade. This game could also be used with coordinate geometry or any subject that requires graphing with coordinates. In relation to the NCTM standards and expectations, this game would apply to the “use of mathematical models to represent and understand quantitative relationships” because by graphing points on the coordinate plane, students will have to understand the basics of positive and negative coordinates, and the x and y-axis.
 * This free online game is well designed and very easy to play. When I was learning about (x,y) coordinates I know I had the hardest time realizing and remembering what came first in the ordered pair, x or y. Therefore I think this game would be very helpful to a student like me, who learns best through visual activities.

Isometric Geoboard (Kiersten Cunningham) Multiplication Models and multiple digit problems (Kiersten Cunningham)
 * Today I had the opportunity to analyze the isometric geoboard. The purpose of the isomestric geoboard is to illustrate three dimensional shapes such as when we created cubes on the isometric geoboard paper in order to illustrate the right front corner of a building from which we learned in chapter 8 of our //Teaching Elementary Mathematics// textbook.
 * This connects with the NCTM standards in that it allows students from pre-k until 12th grade to analyze characteristics and properties of three dimensional geometric shapes and develop mathematical arguments about geometric relationships. This standard falls under the geometry standard for grades pre-k to 12th.
 * My thoughts on this resource are that it is very safe to use with children of all ages relative to the physical geoboards and rubber bands that may be used to harm one another in a regular math classroom. It is also a much easier way to compose a three dimensional figure on the computer rather than on a piece of paper where the students may feel overwhelmed due to the amount of erasing that they will encounter when composing a three dimensional figure.
 * Today I had the opportunity to analyze the multiplication models and multiple digit problems on Johnnie's math page. This specific multiplication section can be found at the URL: []. The purpose of this multiplication section is to provide students with interactive multiplication activities that teach children their multiplication tables such as the six factor tree activity which teaches the children multiples of six.
 * This connects to the NCTM standards in that it allows students in grades 3-5 who are just learning multiplication or continuing to develop their multiplication skills to understand numbers, ways of representing numbers, relationships among numbers, and the number systems when learning multiplication. This standard falls under the multiplication standard for grades 3-5.
 * My thoughts on this resource are that it is very helpful because it allows students to recieve one on one time and get specific instruction on how to learn multiplication without the stress of being embarrassed because they asked for extra help. It is also helpful because it allows the students to get a lot of extra practice that they might not recieve in the class which will allow them to sharpen their multiplication skills.

** --- ** ** Polyominoes ** By: Tyler Petrouskie Polyominoes are “one of the simplest and most basic of the virtual manipulatives.” Basically, this online resource allows children to manipulate squares by turning them, changing their color, and connecting them to other squares. This could be useful because it allows young students create patterns and become more familiar with squares. I also noticed that you can manually group the squares into 10’s and 100’s so you could use this resource as a makeshift replacement for manipulatives like longs and flats. However, the intended goal can be much more complex and involves making polyominoes. I would explain polyominoes to you, but I think Mr. Rachor did a good job of that during his demonstration of his awesome math game skills in class.
 * Description: **

 Pre-K–2: · recognize, name, build, draw, compare, and sort two- and three-dimensional shapes Grades: 3-5: · make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions. Grades 9–12: · analyze properties and determine attributes of two- and three-dimensional objects
 * NCTM Standards: **

**// Use visualization, spatial reasoning, and geometric modeling to solve problems //** Grades 3–5: · build and draw geometric objects Grades 6-8: · use geometric models to represent and explain numerical and algebraic relationships Grades 9–12: · use geometric models to gain insights into, and answer questions in, other areas of mathematics Overall, I am not too impressed with this particular virtual manipulative. I admit that it can be somewhat useful of you were teaching mathematics, but I would much rather use some sort of hands-on manipulative to work with my students. Plus, since this resource only uses squares it wouldn’t be very hard to find/make a real hands-on manipulative to replace it. I don’t believe that I would use this virtual manipulative in my classroom simply because it seems like a waste of computer lab time to do something that can easily be replaced by something else that you could create and use in the regular classroom.
 * Opinion: **

** CoolMath.com ** <span style="color: black; display: block; font-family: Times New Roman; text-align: center; text-indent: 0.5in;">http://www.coolmath.com This site is covers a lot of information and is full of some very good resources. There are links to other parts of the site are devoted to explaining all kinds of math problems in further detail from basic shapes to algebra and trigonometry. They site then branches off a few different ways. One sister site is coolmath4kids.com which lists a variety of topics for them to choose from, then once you pick the topic it gives you a lesson, ways to practice, and a couple game that they have on their site that relate to the topic. Another one of the sister sites is completely devoted to all of their games. It is called coolmath-games.com and has all sorts of games, some more educational than others. I looked at a few of the games and found a few that would be good games for reinforcing fractions and geometry, but I also found a few that wouldn’t be classroom worthy.
 * Description: **

This is a large site so if you looked hard enough you would probably be able to say that is covers nearly all of the NCTM standards throughout its many lessons and games, but I’ll write down a few standards that match the games I played. //Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships// Pre-K–2 Expectations: · recognize, name, build, draw, compare, and sort two- and three-dimensional shapes Grades 3-5: · make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions Grades 6-8: · create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship. Grades 9-12: · explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them;  Grades 3-5: · understand that the measure of the likelihood of an event can be represented by a number from 0 to 1. Grades 6-8: · understand and use appropriate terminology to describe complementary and mutually exclusive events I think this site would be useful and not very hard to integrate into a classroom. It’s an easy way that younger kids could study their math and also have a little fun in the process. I could see it being very useful with a student that is gifted in math to ensure that they don’t lose interest if they are ahead of the rest of the class. If they use this site they could browse some topics that the class didn’t cover yet, or just reinforce what they already know with fun games. -
 * NCTM Standards: **
 * Opinion: **

The Golden Triangle Katie Davis

What does the manipulative do/ show? This manipulative allows you to visualize The Golden Rectangle. The Golden Rectangle occurs when a square section is removed and the remainder is another golden rectangle. When each golden rectangle is formed they have the same proportions as the first rectangle. This process can continue infinitely. The manipulative allows you to see each step individually, all steps together, and you can pause at specific points in the plotting process.

How does it connect to NCTM Standards? This manipulative directly connects to the standards for geometric math in grades 6-8. Below are the NCTM standards that correspond with the manipulative. <span style="display: block; line-height: 16pt; margin: 0in 0in 14pt 0.5in; text-align: justify; text-indent: -0.25in;"> · Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling; <span style="display: block; line-height: 16pt; margin-bottom: 14pt; text-align: justify; text-indent: -0.25in;"> · Examine the congruence, similarity, and line or rotational symmetry of objects using transformations. <span style="display: block; font-family: 'Times New Roman'; line-height: 16pt; margin-bottom: 14pt; text-align: justify;">This is connected because they students will be able to describe how the rectangles are scaled and have the same proportions. Also they will examine the similarity between the rectangles after they transform them. What are your thoughts on the resource? I think that this is a very useful resource for students when they are learning about what the golden triangle is. The concept of The Golden Triangle can be confusing if you are just reading about it. Being able to visually see how it works would greatly help many students who are more visual learners. However, if the student has no prior knowledge of what The Golden Triangle is this could be a very confusing resource to use.

Where can it be found? http://www.primaryresources.co.uk/online/simpleshapesort.swf What is it? At this website you will find an interactive sorting game for shapes. You must sort a few shapes into two different categories. They involve concepts such as number of sides, angle classification, and shape naming. How could it connect to teaching that supports NCTM standards? This activity directly connects to the standards for geometric math from pre-kindergarten to grade 2. Below are the NCTM standards that correspond with the activity. · Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes; · Describe attributes and parts of two- and three-dimensional shapes

In this activity the students must recognize, name, compare and sort two-dimensional shapes. They must also describe attributes of two-dimensional shapes.

What are your thoughts on this resource? I think that this resource is very useful. The students are engaged and learning more about shapes. The only downfall to this activity is that it does not tell the students when they sort a shape incorrectly. They tell the students when they correctly sort, but do not tell them their errors. This activity would be useful if an adult was working with the student one on one and could observe their answers to make sure that they are grasping the concepts.

- Pythagorean Puzzles; Kate Rhue

** What does the manipulative do/show? ** The Pythagorean Puzzles demonstrate that the square on the hypotenuses of a right triangle is equal to the sum of the squares on the other two sides. This is the Pythagorean theorem in a triangle that shows that c2 = a2 + b2. Students must arrange the labeled squares and triangles so that they do not overlap and that they match the area labeled on the side of the white square.

** How does it connect to the NCTM Standards? ** As described in the NCTM Standards, students should understand and be able to create and critique inductive and deductive arguments that concern geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship. This involves grades 6-8 expectations. This manipulative helps students understand the Pythagorean relationship in a different way then using the concept of c2 = a2 + b2. It uses the shapes to demonstrate how the Pythagorean theorem works.

** What are your thoughts on the resource? ** I think this is a great resource to help students understand the process of the Pythagorean theorem in a different way then just adding the sides of the triangle and using c2 = a2 + b2.. It is an active online activity that can help students understand why and how the Pythagorean theorem works. Some students may struggle with flipping the triangles and squares to the correct rotation to fit in the white square. Some students may struggle with figuring out the first puzzle, but after using that as a practice, the rest should come a bit easier. I think this would be a better activity if it were used hands-on in the classroom rather then an online activity.

__ Pythagorean Theorem Game __

** Where can it be found? ** This resource can be found on the internet; __ http://www.crctlessons.com/Pythagorean-Theorem.html __ ** What is it? ** An online lessons that prepares 8th grade students for the CRCT. It is a fun learning process for 8th grade students and teachers. This link takes you to the Pythagorean theorem page where there are two video lessons that talk about the theorem. There is also a page to take a test on the subject and a game web page to play a game activity. Overall it is a great resource for a student to prepare for the CRCT and to help understand the main concepts of the Pythagorean theorem.

** How could it connect to teaching that supports NCTM standards? ** The NCTM Standards connect by helping to demonstrate geometric ideas of how the Pythagorean theorem works and how it works with different manipulatives. These games, quizzes, and videos allow students to learn how to create arguments and view the Pythagorean relationship in multiple ways. The game allows students to have fun applying math in real-life situations.

** What are your thoughts on this resource? ** I think this resource is overall a good help for students who are struggling with the Pythagorean theorem or just want to review and study the concepts. It also helps in all other subjects related to 8th grade math and is a very helpful way for students to learn through an online resource.

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**//Shelby Blevins – Fractals – Iterative//**

**What does the manipulative do/show?** <span style="display: block; font-family: 'Times New Roman'; line-height: 19pt; text-align: justify; text-indent: 0.5in;">The manipulative shows the development of iterative fractals by applying a certain process repeatedly. As time passes, the image becomes more detailed and complex. The manipulative is not very interactive. You have the choice of which fractal you would like to watch develop, but you cannot control the growth. You may only pause and play the “growth” process and change colors so that you can better visualize the “growth” that is occurring.

**How does it connect to NCTM standards?** <span style="color: #262626; display: block; font-family: 'Times New Roman'; line-height: 19pt; text-align: justify; text-indent: 0.5in;">Iterative fractals relate to the NCTM PreK-2nd Grade standard “understand patterns, relations and functions: recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.” It also relates to the standard for 3rd-5th grade “describe, extend, and make generalizations about geometric and numeric patterns.” The children would be able to observe the reproductive patterns of different shapes and visually experience the “growth” of each fractal in order to better understand patterns.

**What are your thoughts on the resource?** <span style="display: block; font-family: 'Times New Roman'; line-height: 19pt; text-align: justify; text-indent: 0.5in;">I think that this manipulative would be hard to relate to elementary math. It’s a difficult concept to understand, even in its simplest form. I feel as though using this manipulative would have no great value in the elementary school other than it being a interesting thing to show the children in your class.

**Resource**: []

**What is it?** <span style="display: block; font-family: 'Times New Roman'; line-height: 19pt; text-align: justify; text-indent: 0.5in;">This website explains in simpler terms what iterative fractals are and how they are made. The website has an animation of a simple fractal which would facilitate basic understanding of the concept in an elementary classroom. It shows simpler versions of the fractal than those in the manipulative page. It also shows some examples of really complex fractals, as well as fractals that can be found all around us in nature, which could provide some interesting tidbits for your lesson on fractals.

**How could it connect to teaching that supports NCTM standards?** This resource could connect to teaching that supports the NCTM standards in that it better demonstrates the constant growing pattern than the NLVM manipulative. It puts things in plain terms and demonstrates the growth of several fractals slowly and simply so that the children can understand and see the patterns that are occurring.

**What are your thoughts on this resource?** I would use bits and pieces from this resource in my lesson on iterative fractals in the elementary school setting. In general, it is a very difficult and complex concept to discuss and teach, and I feel as though this resource puts things a little simpler than the manipulative.

-Gaby Glenn <span style="display: block; font-family: Calibri; line-height: 19pt; margin: 0in 0in 10pt; text-align: justify;"> Ladybug Mazes <span style="display: block; font-family: Calibri; line-height: 19pt; margin: 0in 0in 10pt; text-align: justify;"> What does this manipulative show? This manipulative shows students how to comprehend moving around a maze using specific turn by turn directions. They must create the directions themselves. <span style="display: block; font-family: Calibri; line-height: 19pt; margin: 0in 0in 10pt; text-align: justify;"> How does it connect to the NCTM standards? It connects to the NCTM standards because students should be able to “describe, name, and interpret relative positions in space and apply ideas about relative position; describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance; and find and name locations with simple relationships such as "near to" and in coordinate systems such as maps.” <span style="display: block; font-family: Calibri; line-height: 19pt; margin: 0in 0in 10pt; text-align: justify;"> What are your thoughts on the resource? I think that this will help students figure out distance and navigating space, but I do not believe that it will help a child learn anything. It doesn’t teach the child how to determine the distance or how to navigate it is assumed that the child will have already mastered it.

<span style="display: block; font-family: Calibri; line-height: 19pt; margin: 0in 0in 10pt; text-align: justify;"> Math 24 Game <span style="display: block; font-family: 'Times New Roman'; line-height: 19pt; margin: 0in 0in 10pt; text-align: justify;"> Where can it be found? [] <span style="display: block; font-family: Calibri; line-height: 19pt; margin: 0in 0in 10pt; text-align: justify;"> What is it? This is a math website that builds on a child’s basic math skills as well as problem solving skills that can help them practice what they are being taught in the classroom. <span style="display: block; font-family: Calibri; line-height: 19pt; margin: 0in 0in 10pt; text-align: justify;"> How could it connect to teaching that supports NCTM standards? The site would connect to NCTM standards because it “develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers; connect number words and numerals to the quantities they represent, using various physical models and representations; and understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.” <span style="display: block; font-family: Calibri; line-height: 19pt; margin: 0in 0in 10pt; text-align: justify;"> What are your thoughts on this resource? I think this resource is helpful for not only students in grades prekindergarten through 2 but for all grades. It reinforces all the skills that are needed to be successful in math, while also being a fun thing for students to do.