CompassLearning Odyssey Math Toolkit

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1 CompassLearning Odyssey Math Toolkit 2008 CompassLearning 203 Colorado St. Austin, TX 78701

2 The Odyssey Math Toolkit The Odyssey Math Toolkit contains tools or virtual manipulatives accessible to students at all levels of CompassLearning Odyssey Mathematics K-8. The tools support the teaching and learning of mathematics, providing opportunities for students to practice and apply skills. All twelve virtual manipulatives can be used with lessons or as standalone tools for support and investigation of mathematical concepts. The tools are accessible from the student desktop or from within lessons designated by the teacher, and do not reside within a single course. This enables a student access and use of appropriate tools, unrestricted by the level of the lesson they are working. The tools are designed to span the grade levels as well as the math strands. The use of virtual tools helps students transition concepts from the concrete to the abstract as they develop mathematical understanding. The virtual tools in the Odyssey Math Toolkit represent the most common tools used in classrooms today. The tools asset in mathematics instruction by: helping students see connections among objects, symbols, language, and ideas; assisting students in thinking flexibly about mathematics, providing opportunities to use creativity to solve new mathematics problems and explore mathematics with less anxiety; and providing an ideal environment for students to explore, test, build, think, talk, connect, and reason with mathematical concepts. Rationale and Research for the Odyssey Math Toolkit CompassLearning understands the importance of scientifically-based research in both the development and implementation of its instructional programs. In the development of curriculum, CompassLearning s Odyssey curriculum is based on the research and recommendations of the national professional organizations, federal advisory panels, and independent groups such as the Instructional Research Group in Long Beach, CA. In mathematics the use of manipulatives has long been found to support students in understanding of math concepts ( Butler, Miller, Crehan, Babbitt, & Pierce, 2003; Cass, Cates, Smith & Jackson, 2003). They can be a valuable method of introducing new concepts and linking them to prior knowledge for both primary and secondary students, particularly those who struggle with mathematics (Gagnon & Maccini, 2001). Virtual manipulatives, such as those found in the Odyssey Math Toolkit, which mimic the attributes of concrete manipulatives, can be just as effective in supporting the development of math concepts (Clements, 1996). The Odyssey web-based tools and activities are an effective addition to any mathematics curriculum. The Odyssey tools were designed to provide visual representations of math concepts. Analyzing these visual representations support understanding of more abstract, symbolic concepts ( Butler, Miller, Crehan, Babbitt, & Pierce, 2003; Stylianou, 2002); the ability to translate from one form of representation to another is an important factor in problem-solving (Gagatsis & Shiakalli, 2004). The Odyssey representations are both dynamic and interactive to aid students in seeing underlying patterns and recognizing critical elements, which is important for grasping math concepts (Ahmed, Clark-Jeavons, & Oldknow, 2004; Arcavi, 2003 ; Sloutsky & Yarlas, 2000). CompassLearning, Inc Page 2 of 27

3 The Odyssey Math Toolkit complements the web-based lessons by providing opportunities for students to practice or apply procedures. While a textbook can provide only a fixed set of problems, Odyssey Mathematics allows each student to apply and solve as many problems as they need to in order to develop understanding of a strategy or skill. While the activities provide feedback on the correctness of student responses, the manipulative tools within the toolkit allow students to apply reasoning and communication skills in solving problems. Activities such as these can help students in developing automaticity in skills (Cummings & Elkins, 1999) and in developing strategies for recalling basic facts and solving problems (Atkinson, Derry, Renkl, & Wortham, 2000; Kalyaga, Chandler, Tuovinen, & Sweller, 2001; Ward & Sweller, 1990). Virtual Manipulatives The Odyssey Math Toolkit integrates accessible, innovative tools or virtual manipulatives into instruction to develop conceptual understanding as well as to be available for independent investigation. These tools reside in the Odyssey Manager and are available from the student desktop or from within a lesson. There is an embedded tutorial for each of these tools that is located under the help icon. The tools include: Algebra Tiles Allow students to use pre-set expressions to create their own algebraic expressions and use algebra tiles to represent values. Base Ten Blocks Allow students to use ones, tens, and hundreds blocks to represents numbers and complete operations. Calculator Allows students to use a full function calculator. Coordinate Graphing Tool Allows students to plots lines, linear inequalities, points, and other special relationships on the coordinate plane. The student can pan around the coordinate plane, change the scale, magnify the viewing window, and rotate lines and linear inequalities. Counters Allow students to use counters to represent numbers and operations. Data Representation Tool Allows students to enter data and create various types of graphs and charts such as bar charts, line graphs, circle charts, histograms, stemand-leaf plots, and box-and-whisker plots. The tool also calculates the mean, median, mode, and range of data sets. Fraction Tool Allows students to use circle or bar modes to model, compare, add, or subtract fractions. Geoboard Tool Allows students to make polygons using simulated rubber bands on a peg board. The student can measure their created shapes to find lengths and angle measures and the tool calculates the area and perimeter of the shapes as well. CompassLearning, Inc Page 3 of 27

4 Number Line Tool Allows students to plot points, rays, and inequalities on a number line, as well as perform addition and subtraction operations on two or three numbers on a number line. The number line can be set to work with decimal, integer, or whole number values and the tool calculates comparisons and distances between points plotted on the number line. Probability Tool Allows students to investigate experimental probability with spinners, coins, number cubes, and marbles. There are options for two spinners, two coins, two number cubes, and various marble combinations with or without replacement. Solid Shaper Tool Allows students to see, color, and dilate both two-dimensional and three-dimensional figures and shapes. The tool also reveals the number of faces, edges, and vertices in the figures and shapes. Transformation Tool Allows students to place various plane figures on the coordinate plane and then rotate, dilate, reflect, or translate them showing both the original figure and the transformed image. Multiple transformations, a history panel showing previous transforms, a ruler, and a protractor are special features of this tool. Professional Development CompassLearning recognizes professional development as an essential component in the implementation of curriculum to meet the needs of students and to guide them on the path toward student achievement. CompassLearning offers on-going professional development that enables effective integration of its programs. Based on research in the fields of education, adult learning, staff development, and technology, our professional development offerings focus on teacher and student results and increase student achievement by leveraging the schools investments. Professional development programs are designed to support all aspects of program implementation including awareness sessions for administrators, teachers, and parents; software training; classroom management strategies; and technology and curriculum integration strategies. Courses can be based on CompassLearning s current offerings or can be customized for the district to align to specific district interventions. CompassLearning has over thirty-eight years of experience providing training for teachers and understands the importance of continuous, targeted professional development for effective program integration. Odyssey professional development sessions are led by CompassLearning Education Consultants who work with educators onsite to create and customize training to meet the unique professional development needs of the school or district personnel. The Education Consultants (ECs) for CompassLearning have been successful educators, consultants, and managers and are among the most qualified in the educational software industry. More than half of them hold masters degrees and have substantial experience in the field of education; almost ninety percent hold current teaching credentials. Because each school district has different needs, abilities, and resources, CompassLearning Implementation Plans are developed in cooperation with each school district. Prior to the installation, a planning meeting takes place between district officials and the CompassLearning professional development team to create a schedule and training structure that meets the district s needs. CompassLearning, Inc Page 4 of 27

5 CompassLearning This guide was designed to support an introductory preview of the CompassLearning Odyssey Math Toolkit using trial student user names and passwords. This Preview Guide provides only a cursory glance at portions of the CompassLearning total solution. To begin the preview, go to: Before logging in, please check the system requirements by clicking on System Requirements at the bottom of the login screen. Click your browser s back button to return to the login screen. Check your system for the required plug ins. Click Check System. Note: All plug ins are free downloads. CompassLearning, Inc Page 5 of 27

6 For the purposes of this preview we accessed the Odyssey Math Toolkit from the student desktop. The Odyssey toolkit menu is also available to students from within an instructional lesson. This capability is controlled by the teacher and can be turned off or on as needed. Teachers also have the ability to project the Odyssey Math Toolkit using a projector or interactive whiteboards for collaborative learning; students to demonstrate problem solving skills, and students to use concrete examples at their seats to solve problems. CompassLearning, Inc Page 6 of 27

7 Preview as a student Basic Navigation for Students from the Launch Pad Log into CompassLearning Odyssey as a student [use student user name(s) and password(s)], to see the Student Launch Pad. From the launch pad students may proceed to the Math Toolkit icon on the left side. This will bring up the toolkit menu. Note: The toolkit icons change and are age appropriate for the student, but the tool icon menu remains the same. Primary level icon Intermediate level icon Middle school level icon Odyssey Math Toolkit Algebra Tiles work by the concept that every rectangle has a length, width, and area. The length and the width are the lengths of the sides of the rectangle in some unit. The area is how many squares of that unit it takes to cover the rectangle. The Algebra Tiles allow students to manipulate and represent the multiplication of monomial and binomial expressions. To activate the Algebra Tiles, click on the icon in the menu box. There are 3 Preset Expressions provided as practice or an Expression can be entered by the student. Using the X- axis and the Y-axis, place the algebra tile in the work space. CompassLearning, Inc Page 7 of 27

8 Drag a tile to the left or bottom axes to make it a factor of a product you are representing. Tiles can be rotated by moving the mouse over the corner of a tile. A round black dot will appear that can be used to rotate the tile. To resize a tile, drag the slide next to the x or y. To delete a tile, drag it to the waste basket. A red rectangle will display around the area representing the resulting product. Add tiles to the workspace that will fill the product and place them inside of the red rectangle. Using the first Preset Expression, find the product of (x-1) and (x+1). Example: Click on the tiles x, -1, x and +1. You will need to rotate the x tile for it to fit. To rotate, move your mouse over the tile until a black dot appears. Click on the dot. Arrange the tiles on the x-axis and the y- axis. Fill in the red outlined box to solve the problem. Using the FOIL method, add tiles to the workspace for each of the factors of the product. x * x = x 2 Click on the x 2 tile and drag it into the red outlined workspace. - 1 * x = - x Click on the x tile and drag it on top of the x 2 tile. CompassLearning, Inc Page 8 of 27

9 x * + 1 = x Click on the x tile, rotate it and drag it next to the x 2 tile. - 1 * + 1 = - 1 Click on the - 1 and drag it next to the - x tile. When complete, click the button. If you are correct, you will receive positive feedback. Incorrect answers will need to be fixed. Base Ten Blocks help students conceptualize our standard counting system. In the Math Toolkit, the base ten blocks provide a hands-on, interactive learning tool for students to practice skills with place value. Students simply click and drag the building blocks of numbers to explore math concepts. To activate Base Ten Blocks, click on the icon in the menu box. Clicking on the help icon gives a features overview or a guided tour. Placing blocks in the work area allows students to represent place value. Using the tools section students are able select, group, split, and rotate blocks. Viewing place value in standard, expanded, or word form is available in the notation panel. Selecting an operation allows students to represent, add, or subtract blocks. CompassLearning, Inc Page 9 of 27

10 Example: Printing the work area is available by selecting the printer icon at the top menu. Select the radio button next to Represent in the operations panel. Click on the yellow hundreds block to create a block in the hundreds column. Click the yellow block in each place value to create additional blocks in the hundreds, tens, and ones place. Note the value in the notation panel and the place value in the operation panel. To delete a block click on the block and then select the delete/eraser button in the tool panel. Next select the radio button next to Add in the operations panel. When you select the add option the work space is divided into two rows to represent two addends. Click on the first yellow block in each place value to create blocks in the top row of the work space. The notation panel shows the number. Click on the second yellow block in each place value to create blocks in the second row. The tool panel allows you to split, group or move blocks. Note that the notation panel automatically shows the sum. Click on the Show Result button to view the addition problem. Click Clear All to start another problem. Next select the radio button next to Subtract in the operations panel. When you select the add option the work space is divided into two rows to represent the minuend and subtrahend. Click on the first yellow block in each place value to create blocks in the top row of the work space. The notation panel shows the number. CompassLearning, Inc Page 10 of 27

11 Click on the orange block in each place value to create blocks in the second row. The notation panel now reflects the difference in the two represented numbers. The tool panel allows you to split, group or move blocks. Click on the Show Result button to view the subtraction problem. Click Clear All to start another problem. The Calculator tool operates much like a normal calculator and is available for students to perform calculations. To turn on the Calculator, click on the icon in the menu box. Use the mouse to select keys on the calculator. To move the calculator, click and hold the mouse and move the calculator to its new location. To close the calculator, click on the icon. Example: Use the Pythagorean Theorem (c 2 = a 2 + b 2 ) and the calculator to find the missing side of each triangle. Round each to the nearest tenth. 1. a = 2 b = 7 c = 53 CompassLearning, Inc Page 11 of 27

12 7.3 Coordinate Graphing provides students with a tool for graphing and exploring functions. Coordinate graphing is a visual method for showing relationships between numbers. The relationships are shown on a coordinate grid. A coordinate grid has two perpendicular lines, or axes, labeled like number lines. The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the x-axis and y-axis intersect is called the origin. To activate the Coordinate Graphing tool select the icon in the menu box. lines, magnify, and pan the grid. Clicking on the help icon allows students to receive a feature overview or a guided tour. Features a coordinate plane area to display plotted points, lines, equations, and inequalities. Provides various tools in the tools panel to plot points, rotate, change scales, connect Allows input values to be placed in the data table to graph ordered pairs, lines, and inequalities. Equations and inequalities can be entered in the equation panel. Displays all of the graphed objects in different colors on the coordinate plane and an equation window displays the points or equations. Shows the position of the curser. Example: Click in the blank box for Equation 1 and type y = 2x + 4. Click the Plot button after entering the equation. The equation y = 2x + 4 now appears on the coordinate plane as well as in the equation window. If you choose to delete click on the line and then the delete/eraser tool. CompassLearning, Inc Page 12 of 27

13 Click on the Add icon in the tool panel to plot a point. Drag the curser to where you would like to plot the point. It automatically fills in the data table. Repeat the process with the add tool or enter the coordinates in the Data Table to plot another point on the coordinate plane. It will change colors. To connect the points select the Connect tool in the tool panel then, click on the two points you want to connect. A line will connect the points and the linear equation for the line will be in the Equation 2 box. Continue to explore the tools and change the scale of the grid by clicking on the numeric scale button. Click on the hand/pan button to move around the grid. Select Clear All and start creating new data by clicking on the Equation 1 panel and entering an inequality this time. Counters are an engaging way to introduce many different math concepts. Young students can start off with counting, or work on simple addition and subtraction problems; older students can practice multiplication and division. Students can also use math counters to illustrate story problems. These counters can be used to study and analyze data-sets using multiple graphic representations. To activate the Counters, click on the icon in the menu box. Students can have a feature overview or a guided tour by clicking on the help icon. CompassLearning, Inc Page 13 of 27

14 Available tools in the tool panel include a selection tool, counters, delete/erase, a ten frame, a bucket, and empty the bucket icons. The Operations panel permits students to select if they would like to represent the number or counters, add or subtract. The notation panel allows the total represented by the number word or numeral to be shown. Example: Select the Represent radio button to represent numbers using counters on the work space and hidden numbers using the bucket. Click on the counters icon and then on the work space to add counters. The notation panel will reflect the total number in the work space. Click on the delete icon and then on any counters that you wish to remove. The notation panel will reflect the new total. Select Clear All to empty the work space. Click on the ten frame icon and then anywhere in the work space to add it. Click on the counter icon and then in the ten frame cells to add counters. The counters in the ten frame are identified with a star. Next click on the bucket icon to add to the work space. Click on the counter icon and then on the bucket to add counters into the bucket. The bucket changes color to indicate the presence of counters in the bucket, but they are hidden from view. The notation panel represents the total number of counters in the work space, including those in the bucket. Click on the empty bucket icon to reveal the hidden counters. CompassLearning, Inc Page 14 of 27

15 The notation panel can show the total in word or number form. Select Clear All and click on the radio button next to Add. The work space will divide into two areas. Click on the counters or ten frame and counters to add to each side of the work space. The counters will be different colors to reflect the addends and the notation panel will reflect the sum. Click on the Show Result button to show the addition problem. Select Clear All and then click on the radio button next to Subtract. The work space will once again be divided into two parts. Click on the counter icon or the ten frame and then counters to reflect the minuend and the subtrahend parts of the problem. Students can hide the notation panel to check their understanding and then click on show result to see the subtraction problem. Data Representation provides a tool that illustrates various aspects of data representation. Students use the tool to illustrate how information can be organized in many different ways to make it easy for us to read and understand. Graphs and charts are great because they communicate information visually. For this reason, graphs are often used in newspapers, magazines, and businesses around the world. To activate the Data Representation tool, click on the icon in the menu box. Info panel shows range, median, mean, and mode. Print capability allows work space to be printed. Students can have a features overview or a guided tour by clicking on the help Choose from line, bar, histogram, circle, stem-and-leaf, or box-and-whisker data representations. Provides data table to enter data for graphing. icon. CompassLearning, Inc Page 15 of 27

16 Example: Default graph is line chart. Type a name for the graph Favorite Fruits. In the Data Table change the label name to Fruit. Change the value name to Votes. Fill in the Data Table with Apples, Bananas, Oranges, Pears and the # of votes. Click on Plot to see line chart. Chart information is located in the Info Panel. By selecting another type of graph from the pull down menu, the fruit data is automatically transferred to another graph. Select Bar Chart to view the fruit information in another type of graph. Now select Circle Chart to view the data in a different way. Roll over the circle chart to see the % of each section. Select Clear All to clear the workspace and create another graph. Select Histogram and enter name such as Favorite Football Teams or Class Test Scores. Change value name in the data table and type in data. Click Plot. The Frequency Panel shows how many votes or students where in the ranges. The graph represents the ranges. The Info Panel information shows Range, Median, Mean, and Mode. CompassLearning, Inc Page 16 of 27

17 To view this same data in a Box-and Whisker Plot or Stem-and-Leaf Plot select it from the pull down menu. Select Clear All to enter new data in any data representation. To print the workspace, select the print icon at the top of the chart. Fractions are better understood when seen. This tool allows students to practice, compare, and solve problems using visual representations of fractions as part of a whole in either circle or bar form. To activate Fractions, select the icon from the menu box. Students can select to take a guided tour or feature overview by clicking on the help icon. The Fractions workspace allows the student to model, compare, add and subtract fractions. in either a circle or bar format. Students can choose to illustrate fractions Students select the number of divisions (denominator) and the amount to be shaded (numerator). When adding or subtracting the tool shows how to find the least common multiple to add or subtract like denominators. Students can print the workspace by selecting the print icon. Example: The default when opening the tool is Model and 1 Fraction using a circle. Click on 2 Fractions and select the bar icon or circle icon at the top right. Use the up and down arrows to choose how many divisions will be in each fraction (denominator). CompassLearning, Inc Page 17 of 27

18 Type in the numerator of each fraction to illustrate shading of each fraction. Click on Equalize Fractions button to bring up the window that demonstrates how to multiply the numerator and the denominator in each fraction to find the least common denominator. Now select Compare from the pull down menu and once again choose either the circle or bar format. Use the up and down arrows to choose how many divisions you want in each fraction. Click on the Compare button to see if the fractions are equal to, greater than or less than. Try comparing various fractions. Click Clear to reset the workplace. Select Add from the pull down menu. Once again use the up and down arrows to choose the number of divisions for each fraction. Click on the numerator of each fraction and type in a number. Click on the Sum button. If your fractions have different denominators you will get a message window. Click OK. A workspace will show the student how to multiply the numerator and denominator to be able to add. To subtract fractions, select Subtract from the pull down menu. Follow the same process as before to set up your fractions and solve the problem. Clear the area and solve another problem or exit. CompassLearning, Inc Page 18 of 27

19 Geoboard is a virtual board covered by a lattice of pegs around which students can span virtual rubber bands to form segments and polygons. This provides a great manipulative tool to explore basic shapes and concepts in plane geometry such as perimeter and area. To activate the Geoboard, click on the icon in the menu box. Students can select to take a guided tour or feature overview by clicking on the help icon. Work area allows students to create shapes using simulated bands. The tools area allows students to select colored bands, activate the ruler and protractor and erase. The measurements panel calculates the area and perimeter of a selected shape on the work area. Students can reset or elect to print the work area with the top tool bar. Example: In the tool panel select the band icon and then a color. Click on the work area to attach the band to a peg. Click on another point of the band and while holding down the mouse button, stretch the band to a second peg. Continue to click on the band and hold down the mouse button to create a triangle, square, rectangle or another shape. Click any number of times to alter the shape. The shape can also be altered by deleting a point. Select a point to highlight and then click on the delete/erase icon in the tool panel. CompassLearning, Inc Page 19 of 27

20 To measure length with the ruler, click on the ruler and then rotate using the rotating buttons on the ruler. Click on the X to close the ruler. To measure the angles with the protractor, click on the protractor and rotate once again using the rotate buttons on the tool. Click on the X to close the protractor. To calculate the area and perimeter, click on the shape to highlight it and then on the calculate button. The area in square units and the perimeter in units will calculate in the measurements panel. Clear the area and create another shape or exit the tool. Number Line allows the student hands-on practice in grasping and making lasting connections in plotting points, rays, and inequalities, as well as to perform addition and subtraction operations on two or three numbers. Students work with decimal, integer, or whole number values and can calculate comparisons and distances between points plotted on the number line. To activate the Number Line tool, click on the icon in the menu box. Students can select to take a guided tour or feature overview by clicking on the help icon. The number line can be set in intervals for integers, decimals, or whole numbers. CompassLearning, Inc Page 20 of 27

21 Activity options include plotting points, showing inequalities or operations. Distance button calculates the distance between points. Compare button allows the student to view the relationship between the plotted points and the number line. The rays button draws rays from the point of origin to the plotted point. To print click on the printer icon. Example: In the work area, select plot points and integers. Plot points A, B, and C at various points on the number line by clicking on the point and dragging to the number line. Click on Show Rays and the rays will display the distance from the point of origin. Click on Distance to show the distance between the plotted points. Click on Compare to show the comparison of points. Now select Operations from the pull down menu. Integers are already selected. Now the student can show the operation of addition or subtraction with two or three numbers. Fill in the equation boxes, choose + or and click on the arrow again to show the rays which demonstrate the operation. Select Clear to compute another operation. CompassLearning, Inc Page 21 of 27

22 Now select Decimals from the pull down menu and the number line will change. Fill in the equation boxes once again and click on the arrow to show the rays to illustrate the operation taking place. The student can do the same operations with whole numbers by selecting that option from the pull down menu. or Exit. Next select Inequalities from the pull down menu. Select either Integers, Decimals or Whole Numbers to change the number line. In the equation box select the inequality symbol of less than or equal to, less than, greater than or equal to, or greater than. Type the number in the equation. Click on the Plot button to illustrate the inequality on the number line. Click Clear to illustrate another inequality Probability helps students figure out the likelihood of something happening. The probability of the occurrence of an event can be expressed as a fraction or a decimal from 0 to 1. In any probability problem, it is very important to identify all the different outcomes that could occur and the visual representation of the probability tool helps with understanding. To activate the Probability tool, click on the icon in the menu box. Students can select to take a guided tour or feature overview by clicking on the help icon. Students can choose between spinners, marbles, number cubes, and coins. The properties panel displays the controls of the experiment such as what color marbles, how many sections on the spinner, and how many spins, flips or draws. The Graph button displays the results in a bar graph format. The Result Table displays the results of an experiment in terms of the relative frequency of each event and the expected probability. CompassLearning, Inc Page 22 of 27

23 As with the other tools in the Math Toolkit, students can print out the work area. Example: With the Spinner chosen click on the number of sections for the spinner and multiple spins in the properties panel. Using the up and down arrows select how many spins in the experiment. Click on Spin button to animate spins. The result table will show the results of the spins. Click on Graph to show the results of the experiment in a bar graph. Click the reset button at the top to do another experiment with the spinner. Next select Coins and choose the number of coins and the number of flips for the probability experiment. Click on the Flip button to animate the experiment and view the results of the event frequency and probability in the table. To see the bar graph of the coin experiment, click on Graph. Click the reset button to clear the area and conduct another coin flipping experiment or move on to another probability tool. Next select Number Cubes from the pull down menu. In the properties panel select one or two cubes and the number of tosses for the experiment. Click on the Toss button to animate tossing the number cubes. The Result Table automatically reports the event frequency and the probability. If there CompassLearning, Inc Page 23 of 27

24 are more events a green scroll bar will appear on the right side of the table to move up and down to see all the results. Like the other probability tools, the bar graph can be shown by clicking on Graph. Select Marbles from the pull down menu. In the properties panel select the number and colors of the marbles, the number of draws and if the marble is to be replaced after each draw. Click on the Draw to animate the marbles being drawn out of the bag. Try the experiment with different variables and then exit back to the tool menu. Solid Shaper allows the student to learn about various 2D and 3D geometric shapes and solids along with their properties. Manipulating and coloring each shape is used to explore the number of faces, edges, and vertices. Students can visualize the relationship between the number of faces, vertices, and edges. To activate the Solid Shaper, click on the icon in the menu box. Students can select to take a guided tour or feature overview by clicking on the help icon. Navigate between a variety of 2D and 3D shapes in the shapes panel. Choose shape, colors for faces, dilation factor. The properties of the geometric shape are displayed in the properties panel. Students can move and rotate shapes. Example: In the 2D shapes select a shape such as trapezoid so it will appear in the work area. Select a color by clicking on the color square of your choice. The properties of the 2D shape will be reflected in the panel with the edges and vertices. Slide the bar in the dilation panel to enlarge the figure. CompassLearning, Inc Page 24 of 27

25 To rotate the figure, move the mouse over one of the vertices till a hand appears and move the figure around. Experiment with several shapes. Click on 3D shapes and select a shape such as cube. The properties of the 3D shape will be reflected in the panel with faces, edges and vertices. Select colors by clicking on a face of the shape and then on the color square of your choice. You can enlarge the figure by sliding the dilation bar and the changes will be reflected in the dimension panel. Rotate the figure by moving the mouse over the figure until the hand appears. By making the faces various colors students can understand the properties of the geometric figure. By clicking on the transparent button, the student can view all edges, faces and vertices in the shape. Experiment with other shapes or exit. Transformation enables students to change various geometric shapes using rotations, reflections, translations or enlargements - and combinations of these transformations. Students can visualize what geometrical and mathematical effects these changes have on the symmetries and other properties of the shapes. To activate the Transformation Tool, click on the icon in the menu box. Students can select to take a guided tour or feature overview by clicking on the help icon. The shapes panel allows the choice of a shape to work with on the work space. The transformation panel has a translate feature to move the shape in a horizontal (x) or vertical (y) direction, a dilation factor to increase or decrease size, a rotate feature, and a horizontal or vertical reflection button. On the tool panel, a ruler, protractor and eraser are available. CompassLearning, Inc Page 25 of 27

26 The history panel will display a history of the transformations on the image. Example: Select a shape for the work area. Type in numbers in the X and Y transformation boxes and click on the Show button. The image is translated by the numbers entered and is shown in a lighter shade to differentiate it from the original. The history panel reflects the translations performed. To delete a step, click on the trash can. To delete the image click on the eraser icon in the tools panel. Select another shape to put on the work space. The shape can be moved by clicking on the shape and moving it. (This is not a transformation.) Move the slider button to change the dilation of the figure and a new shape will appear. Click on the ruler or the protractor tool to measure a side or angle. The ruler and the protractor can be moved and rotated as needed. Try several shapes and dilations. Note that the history panel reflects the dilations. Click the reset button in the top toolbar to clear the work area. Select another shape for the work space. Using the up and down arrows choose a rotate degree to create another figure. Choose the horizontal reflect button to show the reflection of the shape. The figures are different shades to reflect the differences. The history panel shows the rotations and reflections. Continue to select shapes and show reflections and rotations. Just like all the tools students can print their work area. CompassLearning, Inc Page 26 of 27

27 Summary The Odyssey Math Toolkit provides students and teachers with easily accessible, handson tools for exploration, discovery, practice, and application. In support of state and national standards and professional development recommendations, the Math Toolkit provides access from any grade level and any place in or out of the Odyssey math curriculum for unprecedented access to encourage, motivate, and entice students to learn more about mathematics. CompassLearning, Inc Page 27 of 27

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