3D & STEM With Tinker CAD

Transcription

1 3D & STEM With Tinker CAD by Alex Reyes Digital Maestro Magazine digitalmaestro.org

2 Table of Contents Table of Contents. 2 Wheel and Axle with TinkerCAD.. 3 The Workplane... 4 The Basic Shape... 6 Printing Separate Parts 13 Making Things Fit.. 19 Printing the Wheel and axle 21 Toy Top. 22 Figuring the Angle We Are Not Done Yet In Review Page 2 : Digital Maestro Magazine : digitalmaestro.org

3 Wheel and Axle with TinkerCAD Tinkercad is a free online application for the development of basic 3D objects. It can be used on most devices that run Windows, Mac OS X, and Chrome. Tinkercad can also be used on tablet devices like ipad and most Android OS tablets. There isn t anything to install. All you need to do is head on over to It s easy to create an account and for convenience, it also integrates with popular social media and cloud services for account creation and login. These services include Facebook, Google, Yahoo, and Microsoft. Google and Microsoft account integration is very useful for school districts that use these services for student accounts. A Tinkercad account is required because all projects are created and saved online. Go over to and create an account or use a social media option. The option to sign in with a social media provider will be available through a link below the username field. Click one of the account options and proceed to log in with the information for that account. To sign in with a social media account click the Sign In button. Page 3 : Digital Maestro Magazine : digitalmaestro.org

4 The Workplane We will create a basic design in this lesson so we can understand the Tinkercad 3D development environment and get some teaching done while we are at it. I m an educator and the purpose of this lesson is to help other educators integrate 3D modeling and printing into their lessons. This lesson has a heavy focus on education and educators, but you don t have to be an educator to learn the skills. After all, the purpose of this lesson is to teach students and if you are a student then I hope you will learn from this lesson. The lesson is designed to include lots of teachable moments and lots of opportunities for problem-solving. I haven t solved all the problems ahead of time and created a tidy lesson. Well, I did solve the problems, but I left the problems in so you could see how they were resolved. In the real world, we encounter problems during the creation process and things don t always go as we plan. This is what I left in. Students need to know that there isn t one ready-made solution but multiple solutions to problems. We will be creating a wheel and axel. Wheel and axle are simple machines. They are easy to create in Tinkercad but they present their own set of challenges. These challenges are not difficult but in learning to deal with these challenges we will learn to use the Tinkercad software. I will also be sneaking in some math and academic vocabulary along the way. Click the Create new design button. Each design is given a random name. We can change this name by clicking the project name field. Type A Basic Wheel and press enter to update the project name. The Workplace is a grid of vertical and horizontal lines. The grid lines are grouped into 10-millimeter squares. There are twenty of these squares vertically and twenty horizontally. The workspace is therefore 20 centimeters by 20 centimeters. Page 4 : Digital Maestro Magazine : digitalmaestro.org

5 This is the perfect time to have students calculate the surface area of the Workplane. The surface of the Workplane comes to 400 square centimeters. While you are at it, calculate the perimeter. To calculate the area of a square we multiple the measurements of each side. Twenty times twenty is four-hundred centimeters. This means there are 400 one centimeter squares on the Workplane. Select Inches and click the update Grid button. I think the United States is the only country that has not fully embraced the metric system. We can switch from the metric system to using the Standard system used in the United States. Click the Edit Grid button. The button can be found in the lower right corner of the Workplane. The Workplane grid is just under 8 inches on each side. Each group of squares is divided into 1/8 inch squares. The area of the Workplane is less than 64 inches square. Have students calculate the area and perimeter using both metric and standard measurement. I find it much easier to use the metric system when developing projects so I will be using this system on the Workplane. Switch back to the metric system using the same process. Click the units selector in the grid properties panel. Page 5 : Digital Maestro Magazine : digitalmaestro.org

6 The Basic Shape A panel on the right has basic shapes we will use to develop a project. The basic shapes include a cube, cylinder, pyramid, and prism. Before placing a shape on the Workplane we need to place a ruler. This ruler will help us measure the length, width, and height of our objects and project. The Ruler tool is found above the shapes panel. Click on the ruler tool. The ruler measurements begin at the corner where the rulers meet. The black circle where the rulers meet is used to move the ruler around the Workplane. The white dot with the x in the middle is used to remove the ruler. The lines in the circle next to the close button allow us to switch the measurements for the edge from the endpoint to the mid-point. The rulers use the endpoint automatically. Click the circle and move the rulers a little closer to the front of the Workplane so we have room to create. Align the edges of the rulers to the major lines. These lines are darker than the others. Move the mouse pointer onto the Workplane. The mouse pointer will take on the shape of a carpenter s square. A carpenter s square is two rulers connected to form a right angle. A right angle is an angle that measures 90 degrees. Place the ruler somewhere near the center of the Workplane. Click the cylinder shape in the shapes panel. Angles and 90 degrees are two good teachable or review moments. Capitalize on them. Page 6 : Digital Maestro Magazine : digitalmaestro.org

7 Move the mouse onto the workplane and the cylinder will move with the mouse. Move the cylinder near the corner where the rulers meet and click once to place the cylinder there. The shape will be placed on the Workplane and a lot of information related to the shape s size and position is presented around the shape. These measurements are very important because they can make our project creation much easier if we understand what they mean and their purpose. We will go over what they mean in the next few paragraphs. These measurement indicators are not complicated and using them is as simple as changing their value. The measurement to the left of the cylinder is measuring the width of the cylinder. This measurement is the cylinder s diameter since the cylinder has a circle for the base. The cylinder has a diameter of 20 millimeters or 2 centimeters. This measurement is along one of the grid lines on the Workplane. This is important to know because the next measurement looks similar but is not along one of the grid lines. The measurement on the right is for the cylinder s height. The measurement arrow is a little bit at an angle. The height of the cylinder is also 2 centimeters. Here is another teachable moment where we can review measurement, cylinder, base, diameter, height and even radius. There are some very useful shortcut keys to remember. These will also make your job easier. Make sure the cylinder is selected. Click it once if it is not selected. Press the letter F on your keyboard. This will zoom in on the cylinder. Page 7 : Digital Maestro Magazine : digitalmaestro.org

8 Here is another important shortcut key combination. Press and hold the option key on your keyboard. Press and release the minus key two or three times while holding down the option key. This will zoom away from the selected object. Pressing the plus key will zoom into a selected object. We will bring the cylinder closer to the corner. Click once on the number for the vertical ruler, or the Y-axis. The value is in green. Change the number to zero. There is another measurement for the cylinder that also measures 2 centimeters. This measurement is also the diameter of the circle or base of the cylinder. Note that all the height, width, and length measurements are highlighted in blue. There are two measurements where the rulers meet. These are highlighted in green. These measurements give us the distance of the shape from the edges where the rulers meet. In this example, the shape is 10 millimeters or 1 centimeter away from both rulers. The distance of your object from the ruler edges might be different. We can use any of these numbers to manipulate the shape. We can change its height, width, length, and distance from the rulers. The grid on the Workplane is like the X and Y coordinate system used in math. The ruler going from left to right is on the X-axis and the ruler going from bottom to top on the left side is on the Y-axis. The left edge of the shape will align to the vertical ruler or to the Y-axis. Repeat the process with the distance for the X-axis. The left and bottom edges of the shape are now aligned to the X and Y-axis. Did you notice the gradual transition from vertical and horizontal rulers to X and Y-axis? That s academic vocabulary. Page 8 : Digital Maestro Magazine : digitalmaestro.org

9 The diameter of our wheel is 2 centimeters and so is the width. Click on the height measurement and change it to 5 millimeters. The measurement of the height of the cylinder is along a different axis. In 3D space, this is called the Z-axis. Our basic wheel is done but in order for a wheel to be useful, it needs to work with other simple machines. An axle is another simple machine similar to a wheel and helps transfer the work done by the wheel. An axle is a rod that connects one or more wheels. Go back to the shapes panel and place another cylinder onto the Workplane. Make sure to place the cylinder on the Workplane so you can see both the X and Y-axis measurements. Change the X and Y measurements to 5 millimeters. This represents the diameter of our axle. We need to place the axle in the center of our wheel. This is where we need to do a little bit of math. Don t worry, it s simple math. The wheel measures 20 millimeters by 20 millimeters. The center of the wheel is at 10 millimeters. This is the distance from any of the edges toward the center. This is also the radius of the circle. The axle measures 5 millimeters in diameter and the center is at 2.5 millimeters, the radius. The center of each circle is half the distance across the circle. This is the radius of the circle. Leave the Z-axis measurement at 20 millimeters. This measurement represents the length of the axle. Page 9 : Digital Maestro Magazine : digitalmaestro.org

10 The center of each cylinder, the wheel, and the axle, needs to align with the other. The center of the circle in our axle needs to be 10 millimeters inward from the X and Y-axis. Subtract 2.5 millimeters from 10 and we get 7.5 millimeters. This is the distance the axle cylinder edge needs to be from each X and Y- axis or the edge of the rulers. The dotted red line in the illustration below shows that the edge of the axle is 7.5 millimeters from the edge of the wheel. When we get the 7.5 millimeters from the axle s edge to the ruler and add it to the 2.5 millimeters of the axle s radius we get 10 millimeters. This is where the center of our axle needs to be so it matches the center of the wheel. Click once on the wheel. Instead of creating another wheel from scratch we will use the existing wheel and make a copy. Click the duplicate icon in the button bar. Find the X and Y measurements for the axle and place 7.5 for each. Our wheel is now completed with an axle. Wheels usually come in pairs. Before we create the other wheel, we should extend the axle a little more. Click the axle s Z-axis value and change it from 20 to 40 millimeters. Page 10 : Digital Maestro Magazine : digitalmaestro.org

11 Up to this point, we have used all the measurement boxes to modify our project. We can use the mouse to make changes to the shape. It s less precise but in this example, it is very useful. Look for an icon that looks like a black water drop. Click the icon and drag up toward the top of the axle. The top of the wheel should match perfectly with the top of the axle. The copy of the wheel will become visible. We will also see a green highlighted value on the right. This value is for the distance from the bottom of the wheel to the workplane. If we want the top of the cylinder to match with the top of the axle what should this distance be? Remember that the distance measured is from the bottom of the cylinder. The axle measures 40 millimeters and the wheel has a height of 5 millimeters. We subtract 5 from 40 to get 35 millimeters. Enter this value to update the vertical distance of the wheel. It really helps when addition and subtraction are more than problems to solve on a sheet of paper. Why do we need to learn to add and subtract? To make sure the wheel and axle fit properly, of course. Printing A 3D object isn t the same as printing images on paper. Objects printed in 3D need to take gravity into consideration. This wheel and axle combination might look ready to print but when printed we see that something has gone wrong. The image below shows that the object had an issue during the fabrication process. The issue is with the wheel that is above the surface of the printing plate. The plastic filament had nothing to rest upon so strands of the plastic were pulled by gravity and did not form a proper wheel. Page 11 : Digital Maestro Magazine : digitalmaestro.org

12 The process of creating 3D models with consumer printers is called Fused filament fabrication or Fused deposition modeling. This is the process of taking filament from plastics, melting it and then layering it to form objects. If you are an educator I encourage you to print this out and show it to students after the design process. Have them discuss what went wrong. Have students discuss possible solutions. This is a great time to stop the lesson and have them find solutions on their own. Have the students present possible solutions. Print some of their solutions and see if they work. It s more important to print the ones that don t work than the ones that do. After all, if you already know the answer, then where is the challenge. Page 12 : Digital Maestro Magazine : digitalmaestro.org

13 Printing Separate Parts A solution to the problem we encountered when printing the wheel might be to print the wheel on top separately to avoid the issue with gravity. To fix this problem we need to do two things. We need to print the wheel above the surface on its own so it is resting on the 3D printer plate and we need to make a hole in the wheel to accommodate the axle after printing. Open the Basic Wheel project. We need to make a hole for the wheel so the axle fits within the hole. Most of the work we need for this is already in place. Click once on the axle. The axle will take on a transparent look. We need to merge the shapes into one. The hole will then become part of the wheel. To merge the shapes, we need to select both of them first. The axle should still be selected. Hold the Shift key on the keyboard and click once on the wheel. Holding the Shift key adds the second selection to the first. In the properties box for the shape, click the Hole option. This will use the shape of the axle to cut a hole in the wheel. Page 13 : Digital Maestro Magazine : digitalmaestro.org

14 A blue highlight appears around the selected shapes. If we were to merge the shapes now the axle hole shape will disappear and the wheel will be left floating in space. We need to duplicate the shapes so they are not part of our original wheel axle combination. Click the duplicate button in the button bar. Click and drag the copy off to the side. Click and drag any shape and they will both move. through. This is because the end of the axle or the top of the axle cylinder is aligned perfectly with the top surface of the wheel. We can close the hole in one of two ways. We can reduce the length of the axle that will be used for the hole from 40-millimeters to 37 millimeters. This will leave a 3-millimeter fill at one end of the wheel. We could also raise the wheel 2-millimeters above the 40-millimeter hole created by the axle. This would result in the same thing. The point here is that there is more than one way to come up with a solution. I like to include this step in my training with teachers and students because students have at times become accustomed to one answer being the only solution because of standardized tests. I find that teachers and students like to know that there are multiple ways of coming up with a solution. There are times when teachers and students will come up with three or more solutions to the same problem. I like to encourage this whenever possible. I often learn as much from my students as they learn from me. In this example, I will reduce the length of the axle to 37 millimeters. Click once on the Workplane to release the selected objects then select the axle hole shape. Change the value from 40 to 37. This wheel will no longer be attached to the axle and needs to be attached later with glue once printed. To make this happen we need to close one of the holes in the wheel. The hole in the wheel is currently going all the way Page 14 : Digital Maestro Magazine : digitalmaestro.org

15 If you choose to raise the height of the wheel then click once on the workplace to release the selection of the shapes and click once on the wheel. Change the distance from the surface from 35 to 38. We don t need the wheel from the original wheel and axle combination. Click once on the wheel. Select either the axle for the hole or the wheel then hold the shift key down while selecting the other. You should see a blue highlight around both objects. Click on the trashcan icon to delete the wheel shape. Click the group icon to merge the shapes. The axle used for the hole will disappear and the wheel will remain floating in 3D space. Page 15 : Digital Maestro Magazine : digitalmaestro.org

16 We still need the axle that was used to create the hole. We need to convert the axle back into a solid. Click on it once. want to print it out ahead of time and ask students to find solutions. Click once on the wheel. Around every object, there are rotation handles. Click once on the rotation handle in front of the wheel. When we click the handle, a circular protractor appears below the wheel. Click on the solid option in the shape configuration panel. Click on the rotation handle to the right of the wheel. A circular protractor appears which allows us to rotate the wheel end over end. We need to bring the wheel down to the surface before printing. Before bringing the wheel down to the surface we need to think about what is going to happen when the wheel prints. We can t see it in the shape at the moment, but the hole for the axle is on the bottom side of the wheel. We know from experience that 3D printers need to contend with gravity. This includes the hole in the wheel. We might get unwanted plastic in the hole and that could affect how the axle and wheel fit together. It would be better if the hole were facing up. We need to flip the wheel over. This is a good time to ask students to predict what will happen when the wheel is printed with the hole facing the workplane. You might Click once on the rotation handle above the wheel shape. Another circular protractor appears that allows us to rotate the wheel end over end. At the top of the protractor, we see the number zero. This is the current angular rotation of the object relative to the workplane. As we work with 3D objects and modeling we will learn that the measurements we make are often based on the view we are working with at the time. Page 16 : Digital Maestro Magazine : digitalmaestro.org

17 Here is a little mental exercise. If we were floating in space which end would be up and which end would be left or right? In reality and end can be up or down. The same is true for left and right. The work plane helps us stay grounded. The workplane is always our starting point and the rulers help us measure objects along the x and y-axis. A full rotation is 360 degrees. Half a rotation is 180 degrees. To get the hole for the wheel to rotate to the top we need to rotate the wheel 180 degrees. Find the measurement of the wheels distance from the workplane and replace the value with zero. Click once on the zero value and enter 180. The wheel will rotate 180 degrees and the hole in the wheel will be visible. The wheel and axle on the left along with the wheel on the right are almost ready to be printed. If you are doing this along with students as part of a class project, you should print this out ahead of time and ask them why the wheel doesn t fit onto the axle. This is another opportunity to stop the lesson and give students time to come up with solutions to the problem. Page 17 : Digital Maestro Magazine : digitalmaestro.org

18 The axle diameter and the hole for the axle to fit within the wheel are the same size. One needs to be able to accommodate the other. Do you change the diameter of the axle or the diameter of the wheel? Page 18 : Digital Maestro Magazine : digitalmaestro.org

19 Making Things Fit The axle we used to create a hole in the wheel made a hole the exact size of the axle s diameter. This poses a problem when trying to fit the wheel and axle together. To fit the pieces together we can reduce the diameter of the axle and this will change the axle s circumference. Circumference is calculated by multiplying Pi, 3.14, by the diameter. Multiplying 3.14 by 5 is Changing the diameter by half a millimeter will give us a smaller circumference. A diameter of 4.5 millimeters multiplied by 3.14 gives millimeters for the circumference. This is a good time for teachers to have students predict what will happen when we reduce the size of the axle by this value and if there are other values that might produce different results. Click once on the axle and change the values for X and Y to 4.5 millimeters. Whenever we make a change to one object in a project this tends to affect how other objects relate to the change. The change in the axle s diameter has changed its position relative to the center of the wheel. Before we made the change, the axle needed to be displaced 7.5 millimeters from zero along the X and Y axis. An axle with a diameter of 4.5 millimeters has a radius of 2.25 millimeters. This is what happened when we changed the diameter of the axle. The distance of the axle from the edges of the ruler remained the same and that shifted the center of the axle s position. The center of the axle is no longer aligned with the center of the wheel. The green crescent shape in the illustration represents the shift in the position of the axle relative to the edges of the rulers. The orange circle is the size of the axle after the change in diameter from 5 millimeters to 4.5 millimeters. Subtracting 2.25 millimeters, the radius of the axle, from 10 millimeters, the radius of the wheel, gives 7.75 millimeters. We need to change the distance of each axis from 7.5 to 7.75 millimeters. Changing these values will place the center of the axle back into alignment with the wheel. Page 19 : Digital Maestro Magazine : digitalmaestro.org

20 Change the corresponding values in Tinkercad. The offset axle provides another teachable opportunity. You might want to ask students what would happen if we left the axle where it was and what effect that would have on the other wheel. What would be the effect of having an offset wheel on an automobile? Could an offset wheel provide opportunities for different combinations of simple m a c h i n e s? D o s t u d e n t s t h i n k t h i s combination of simple machines with an offset axle could be useful? Have students think of possible reasons and solutions then you might want to show them a Cam. A Cam is a wheel with an offset center. Page 20 : Digital Maestro Magazine : digitalmaestro.org

21 Printing the Wheel and axle To print the project, we need to download the file and import it into our 3D printer s software. Click the Export button in the button bar. your computer. The file is very small. This is because the file is just a set of instructions with all the measurements necessary for the software to render and print the 3D object. Tinkercad offers 3 file formats. Most 3D printers will accept the STL file format. Click this button and the file will be downloaded to Open this file in your 3D printer s software and print away. Page 21 : Digital Maestro Magazine : digitalmaestro.org

22 Toy Top Printing things with a 3D printer can be fun and educational at the same time. In this lesson, we will learn how to create and print a toy top. Along the way we will learn how math and physics work to create and spin the top. The skills to create the top will in Tinkercad have already been learned when we created the wheel. This demonstrates how a skill can be used in a variety of ways. When teaching I like to layer new skills with previously learned skills. These set the foundation for students to learn skills with increased complexity. I also like to explore these skills in a variety of contexts. In this lesson, we will reinforce math concepts like radius, diameter, circumference, volume, cylinder, cone, 3D, coordinate plane, measurement, translation, and merge. We will also reinforce science concepts of mass, matter, viscosity, gravity, inertia, potential energy, kinetic energy, centrifugal force, and balance. Click on the Ruler tool to add a ruler to the workplane. Align the corners of the ruler to the main lines of the x and y-axis of the workplane. Go to the main Tinkercad page and create a new 3D design. Title the design, toy top. Page 22 : Digital Maestro Magazine : digitalmaestro.org

23 Select a cylinder from the shapes panel and place it on the workplane. Chang the x and y values for the shape to 50 millimeters. Change the distance measurements from the x and y-axis so the cylinder rests on the ruler s edges. This makes things much easier to measure and align. Above the cylinder we will attach a handle which we will use to spin the top. Place a cylinder from the shapes panel on the workplane and within the cylinder shape. Try to center the cylinder within the other cylinder as much as you can. The top will have a diameter of 5-centimeters and a height for the cylinder portion of 1- centimeter. Change the height value to 1 centimeter. The grid is segmented into 1 millimeter squares. To get a height of 1 centimeter, we need to enter a value of 10 millimeters. The color of both shapes is the same. It might be easier to work with the shapes if they each had a different color. This does not affect the color of the printed shape. The color of the shape is determined by the color of the spool placed in the printer. Note that up to this point all the skills to begin the project have been the same skills used to create the wheel. Page 23 : Digital Maestro Magazine : digitalmaestro.org

24 The Shape configuration panel should be open. If it is not, click the Shape button top open the panel. Click on the solid color button. A palette of colors will open. Select a color that contrasts with the orange color of the other cylinder. The height of the handle is 20 millimeters. Only half of the handle is available above the main cylinder. A handle of two centimeters should be enough to help us spin the top. There are two ways we can increase the length of the handle. We can raise the bottom of the handle 10 millimeters above the surface. We could also increase the height of the cylinder by another ten millimeters. In the example, both options are valid. Both of these shapes are solids when printed. Moving the handle up will not create a hole. Click the shape disclosure triangle if the panel is in the way. The handle in this top will be 2 centimeters long. Instead of raising the shape above the surface, we will lengthen the shape. Change the height from 20 millimeters to 30 millimeters. The handle doesn t have to be very thick so it will have a diameter of 1 centimeter. Change the x and y values of the shape from 20 millimeters to 10 millimeters. All the changes to the width and height of the cylinder have placed the center of the handle away from the center of the base. Aligning shapes is much easier once we have made all the necessary changes to each shape. Page 24 : Digital Maestro Magazine : digitalmaestro.org

25 To align the edges let s review how objects are aligned. The alignment measurements are from the edge of the ruler to the edge of the shape. The distance from the edge of the top s main cylinder to the center is 25 millimeters. This is the radius of the circle. The diameter is 50 millimeters. The diameter of our handle is 10 millimeters so the distance from the edge of the circle to the center is 5 millimeters. It is important to measure the distance from the center of the object to the edge of the object to get the proper measurements. If the center of the handle is to be aligned with the center of the main sphere then we need to subtract the 5-millimeter radius of the handle from the 25 millimeters radius of the main cylinder. The edge of the handle s cylinder is 20 millimeters from the edge of the tops main cylinder. Change the distance of the handle s edge from the x and y axis of the ruler to 20 millimeters. This is the top portion of our toy top. Printing this part of the top is very easy because it is like the wheel we printed in the last lesson. The bottom of the top is a different story. We learned from the wheel lesson that objects cannot be printed above a surface. What we will do is print the bottom of the top separately so we can join the pieces later. This portion of the top is almost complete. We need to make some modifications to the height of our cylinder to accommodate the printing of separate pieces. Click on the main cylinder and change the height from 10 millimeters to 5 millimeters. Page 25 : Digital Maestro Magazine : digitalmaestro.org

26 Click on the handle and change the height from 30 millimeters to 25 millimeters. This assures that the handle is still 20 millimeters long. We could leave the measurement at 25 millimeters if we want. The shapes configuration panel will show we have two shapes selected. Click the Group button. These pieces will be printed together. We will merge these pieces and move them to one side so we can work on the bottom of the top. Click on one piece so it is selected then hold the shift key on your keyboard and click on the other shape. This will select both shapes. The color of both shapes will change to one color. This is usually orange. Click and drag the grouped shapes up and to the right. You could also click and drag a selection box around both pieces. Page 26 : Digital Maestro Magazine : digitalmaestro.org

27 Get the cylinder shape from the shapes panel and place it near the corner where the rulers meet. Change the distance measurements so the edges of the cylinder meet with the edges of the ruler on the x and y-axis. diameter of the cylinder to match the size of the other yet. The height of the cone is too much for our top. The height is currently at 20 millimeters. This means that 15 millimeters of the cone is above the surface of the cylinder. Reduce the height of the cone to 10 millimeters. Change the height of the cylinder to 5 centimeters. The base of the cone is a little wide and this affects the point where the top will spin. We can make the radius narrower by changing the diameter of the cone s base. Find the cone shape in the shapes panel and place it within the cylinder we just placed on the workplane. The diameter of the base of the code is the same as that of the cylinder so aligning the cone s center and the cylinder s center is easy. Note that we have not changed the Page 27 : Digital Maestro Magazine : digitalmaestro.org

28 We are going to learn another way of changing a shapes length, width, or height. To demonstrate the difference, change the diameter of the cone s base from 20 to 10 millimeters. This changes the diameter and changes the center of the shapes position. This means we need to figure out how to center the cone. There is an easier way to resize objects so they remain centered. Change the value back to 20 millimeters. Go to the shape configuration panel for the code. Click the Shape disclosure triangle if it is not open. Find the base radius configuration. The radius of the base is 10 millimeters. Click on the number 10 and change it to 5. Press the return key on your keyboard to update the shape. The top of the cone will be more acute because we changed the radius of the base. The cone will also resize and the center of the cone will remain with the center of the cylinder. The shape was changed this way because we changed the radius and not the diameter of the base. Page 28 : Digital Maestro Magazine : digitalmaestro.org

29 Before resizing the bottom of our top, we will merge the cone and the cylinder. Select both shapes. Click the Group button. Change the diameter of our top base to 50 millimeters. When we resized the grouped shape we also changed the radius of the top s cone that will make contact with the surface when it spins. Teacher Tip: This is a good opportunity to run an experiment. Does the cone s angle affect the Top s spin? Divide the class into small groups and print different cone angles for each group. For example, a group of four can have four tops, each with a different cone and angle for the cone. Each student can spin their top and create a table to collect data. Students can create tables and gather information about the spin time for each cone angle. I will go over how to get the angle for the cone at the end of the lesson. When students are collecting information on their table they might consider why we want to spin the top multiple times and collect information about each spin. Looking at the data students might see that the time for each spin changes by either small amounts or large amounts. Collecting data on a table with ten spins students can determine a range of time that it took for the top to stop spinning. They can also get an average, mean, and mode from the data. Students can create a graph with the information. We can change the angle of the cone. Before changing the angle, we need to ungroup the objects. Select the grouped object and click the ungroup button. We can leave the cone as it is or we can change the radius to get a different angle for the cone. Page 29 : Digital Maestro Magazine : digitalmaestro.org

30 When changing the radius of the cone we might also need to change the height. In this example, I changed the radius of the cone to 3 millimeters, but much of it is still below the cylinder surface. Changing the height from 20 to 25 millimeters raises the top of the cone a little more. The two halves of the top are ready to print. Once they are printed they can be glued together. Does the diameter of the Top s body affect the duration of spin? Does the height of the cone affect the duration of spin? When the top begins to slow down and wobble, this is called precession. Figuring the Angle The cone is a three-dimensional shape, but if we look at it as a two-dimensional triangle then figuring the angle is simple. If we divide the triangle in half then we can use the radius and height to determine the angle of a right triangle. To solve for the angle, we will use some trigonometry. Up to this point the math has been simple but don t worry I will walk you through it and offer online calculators than can solve the problem for you. The image below represents a cross section of the cone. The center of the triangle has been split in half so the triangle is now two right-triangles. A right-triangle has two legs a n d a h y p o t e n u s e. W e k n o w t h e measurement of the two legs. These are the radius and height of our cone. The legs join to form the 90-degree angle of the right triangle. The opposite side is the hypotenuse. Before solving for the angle let s solve for the hypotenuse. The image below shows the labels for the legs and hypotenuse. It also shows the formula for the Pythagorean theorem. The Pythagorean theorem states that a squared plus b squared equals c squared. This product has a lot of variables students can modify to create an experiment. Does the angle of the cone affect the duration of spin? Page 30 : Digital Maestro Magazine : digitalmaestro.org

31 We will use an online calculator to solve for the hypotenuse. Use this link, solverighttriangle. The actual link is very long so I shortened the link using bit.ly. Bit.ly is a service that shortens long links by creating a custom short link for the actual lengthy link. The page provided by Google is set to solve for the hypotenuse of a right triangle. To use the calculator, we enter the values for a and b. After entering the values, the calculator returns the answer for the length of the hypotenuse, which is approximately millimeters. The two wavy lines before the number mean approximately. To solve for the angle, we will use another calculator. We are now going into the realm of trigonometry. Trigonometry uses Sine, Cosine, and Tangent to determine the values of angles in a triangle. Each is used to solve for a different angle. Each represents a ratio of the sides connected to the angle. The function we use to solve for the angle depends on the angle we need to know. There is a useful way for us to know which one to use. The phrase SOHCAHTOA tells us how to solve for the angle. The phrase consists of nine letters. We divide the letters into groups of three to understand the process. The first three letters SOH mean that if we want to solve for the Sine of an angle we need to divide the Opposite side by the Hypotenuse (sine = opposite/hypotenuse). The opposite is the triangle leg that is opposite the angle. This helps find the angle if we only know two of the measurements. In this case that would be the length of the opposite side and the length of the hypotenuse. The image below shows the angle we would solve with the Sine function. Page 31 : Digital Maestro Magazine : digitalmaestro.org

32 CAH solves for the Cosine by dividing the Adjacent side by the Hypotenuse. We can use the same image to show that if we know the length of the adjacent side and the length of the hypotenuse, we can solve for the angle. The last three letters, TOA, mean that we solve for the Tangent by dividing the Opposite leg by the Adjacent leg. The image below shows how we would use Tangent to solve for the angle in this triangle. The adjacent side is always next to the angle to be solved. Enter 25 for a and 3 for b. Select the option to solve for angle B. We are ready to calculate the angle. Before calculating, place a check mark next to the option to show an explanation. This will show the steps used to solve for the angle. Click the calculate selected button. To solve for the angle, we will use an online calculator. The calculator is provided by mathportal.org. The link to this calculator is To use the calculator, we need to select which angle we want and provide two values. We know the lengths of a and b. We also know the length of the hypotenuse but the value is only an approximation. Page 32 : Digital Maestro Magazine : digitalmaestro.org

33 The page will refresh with the answer. The answer is degrees. We can round this to about 7 degrees. The explanation shows that the angle was solved using the Tangent. The explanation goes on to show how the formula was used to solve for the angle. The second to the last step changes tan(b) to B=arctan. Arctan is the opposite of Tangent or inverse. We need to use arctan because 3 divided by 25 is.12, which is a decimal. We need a value in degrees. The function buttons available are the sin, cos, and tan buttons. These are not the ones we need. In some calculators, there is a way to calculate the arcsine, arccosine, or arctan by pressing a modifier key. With this calculator, we need to click the func button for additional functions. We will use an online calculator to see how we arrived at degrees. The Desmos website offers a free scientific calculator. Use the link to access the calculator. Click the func button. In the additional functions section, we see a row of buttons below the sin, cos, and tan buttons. These represent the inverse of sin, cos, and tan. They are the same as the arcsine, arccosine, and arctan. The calculator is a basic scientific calculator that works well for what we need to do. Page 33 : Digital Maestro Magazine : digitalmaestro.org

34 Click the inverse of tan button. The inverse tan function will appear in the formula bar. We will enter our decimal value within the parenthesis. Enter.12 from our calculation above. The calculation is immediate and we see that the angle is very much the same as the one we calculated using the other calculator. After rounding, the angle is 7-degrees. We Are Not Done Yet The angle we calculated is only half the angle. Remember that we divided the triangle in half. To get the complete angle we need to multiply by 2. The angle for the tip of our cone is Rounding to the nearest hole number we get approximately 14 degrees. In Review I really love this project because I can teach, reinforce, and provide practical applications of the math concepts I want to teach. In this project we can covered circles, cylinders, cones, radius, diameter, circumference, volume, angles, triangles, right triangles, the Pythagorean theorem, Sine, Cosine, Tangent, and how to use calculators. We also worked with fractions and decimals. We divided a fraction to get a decimal. We rounded the decimal value. We multiplied decimal values. If the students spun a variety of tops with different points then we can include data collection, creating tables, average, range, mode, median, and even a standard distribution curve if we took it that far. Students could graph their data and provide a report of their findings. Include a hypothesis and you have the making of a good science project. Page 34 : Digital Maestro Magazine : digitalmaestro.org

35 If you like this book then you might like these books too. Sphero for STEM Code Sphero and teach your students STEM concepts. Teach students to apply geometry skills like angles, shapes, and perimeter. Apply science skills of mass, motion, and acceleration. Wirecast Live Streaming Use the free version of Wirecast to live stream events over YouTube. Create studio quality video that integrates a variety of media and different camera shots. Start your own television studio with very little and stream live content at your campus. Microsoft Class Notebook With a Microsoft Office 365 account available to school districts you can create classroom notebooks. Classroom notebooks are great for distributing and collecting a variety of written exercises from students. Class Notebook uses the free OneNote app which is available for a variety of mobile devices. Page 35 : Digital Maestro Magazine : digitalmaestro.org

36 If you like this book then you might like these books too. Thinking Maps with Google Drawings Use Google Drawings to create online thinking maps. Thinking maps can be created by students or shared by teachers with students. Learn to create circle, bubble, flow, brace, and doublebubble thinking maps. Students will not only learn to use thinking maps but they will also learn the skills it takes to build the thinking maps by manipulating graphic objects in Google Drawing. Interactive Stories with Google Slides Google slides can be used to create interactive stories. In this book you will learn how to add interactive elements like buttons and links. You will also learn how to add voice over audio for students with reading difficulties. You will learn how to add animated Gifs to a presentation for something a little more interesting than simple slide in and slide out transitions. Screencast with Screencastify Screencastify is a free screen recording app for the Google browser and Chromebook. In this book you will learn how to use Screencastify to record web pages, computer desktops, and content captured with an external camera like a webcam. You will also learn how to upload your video to YouTube and share them with the world. Students can create video and share them with you and other students through Google Drive. Page 36 : Digital Maestro Magazine : digitalmaestro.org