McKenzie’s Blog

Explore Learning

Gizmo #1

Circle: Circumference and Area

Simulation Summary

In this gizmo, the students have the opportunity to manipulate the radius of a circle and then calculate the diameter, area and circumference. The exploration guide begins with allowing the user to select a radius and demonstrates that the length of the diameter is twice the length of the radius. The equation for the area of a circle is then given and advises the user to substitute 3 for pi. The user is asked to estimate the area of the circle and then advised to check their answer using the gizmo. Additionally, the user is challenged with finding the area given the diameter instead of the radius and also with using 22/7 as an estimate of pi when the radius is a multiple of 7.

 

Evaluation

This gizmo is a fun, interactive tool that can be used to teach the area and circumference of a circle. The strengths of the gizmo are that the radius can be manipulated and then the diameter can be calculated and shown visually. This gives students a good idea of the relationship between the two elements. The area and circumference can also be calculated using the radius chosen. I also like that the diameter, area and circumference calculations can be checked shown or hidden. This allows for the student to get a visual representation of the circle and radius, and then allows time for calculation. The user or teacher can show the answers to the calculations at their own leisure.

The weaknesses of this gizmo are that pi is introduced but not explained. I would have liked to see more exploration as to what pi is and how it is derived before plugging it in to equations. Additionally, the gizmo has the option to measure arc lengths, but the exploration guide gives no instruction or suggestion on how to use that feature. The guide mainly focuses on area calculations and not on circumference calculations. I suppose it would be up to the teacher to come up with the instruction to accompany the gizmo.

How would I use this in my class?

This gizmo would be useful as a visual aid for a class when introducing area and circumference. I would use it on a projection screen, or better yet, a smart board, to give the students a visual reference while we learned the equations. I don’t foresee the students using this on their own, as I think there is a lot of instruction that needs to go along with the gizmo. It seems to be a good aid in teaching the material rather than stationary examples in the book or on a worksheet. Students could pick the length of the radius and even work in groups to come up with diameter, area and circumference. The answers can be revealed to the class by the teacher, using the gizmo.

Gizmo #2

3D and Orthographic Views – Activity A

Simulation Summary

This gizmo test students skills in visualizing and building three-dimensional figures. The exploration guide begins with detailed instructions on how to use the gizmo. It explains how to place blocks on the grid, how to add blocks, how to stack blocks, and how to move the grid to view it from all angles. It follows with the goal of the gizmo (to match blocks on a 3D grid to an aerial view, a front view and a side view). The current views can be shown or hidden and the goal view can also be shown. Once the user thinks they have the correct answer, they can click the ‘check’ button. The answer will show as correct or incorrect, but a block count is also shown (in addition to a minimum block count). For an extra challenge, the user can attempt to build the figure with the least amount of blocks possible.

 

Evaluation

This gizmo is awesome. I spent quite a bit of time playing with it myself and challenging my skill from new game to new game. I can see this being a hit with the students as a very fun way to become oriented with three dimensions. I really like that even if you don’t use the minimum amount of blocks you can still get still win the game and that it is an extra challenge to use the minimum amount of blocks. The sides are color coded for easy distinction.

The weakness of this gizmo is very limited. I don’t really understand why they included the option to hide both the current view and the goal view, but it doesn’t necessarily bring down the quality of the gizmo.

How would I use this in my class?

This gizmo would be useful for all students in a lab situation where the could work individually at their own pace. It is built as a game, so they really wouldn’t realize how much they are learning while they play. I could be free to roam through the lab and help struggling students who don’t easily get the concept of viewing from each angle. The kids who take to it immediately can work ahead and be challenged with each new game. It would also be very helpful to have a master screen at the front of the lab where I could demo how to use the gizmo and go through the directions with the class.

Gizmo #3

Surface and Lateral Area of Prisms and Cylinders

Simulation Summary

With this gizmo, users can vary the dimensions of a prism or cylinder to investigate how the surface area changes. They can also use the unfolded view of the diagram to compute both lateral and surface area of the object. The unfolded view is defined by the word ‘net’ in the exploration guide. The guide describes how the 3D view and the net change as the base width and height are manipulated. The user has the choice of a base shape of a circle, rectangle or triangle.

 

Evaluation

This gizmo is an interactive tool that can be very useful in showing, not just explaining, how to break down the lateral and surface area of 3D figures. The strengths of the gizmo are that the sides of the figures are layed out in a 2D format to show the user, without turning the figure, just how much space each side takes up. This gives students a good idea of the relationship between the sides of the figures when they are layed out in the net. The lateral and surface area of each figure can be shown or hidden once the user has set the dimensions of the base figure. This allows for the student to get a visual representation of the circle, rectangle or triangle, and then allows time for calculation. The user or teacher can show the answers to the calculations at their own leisure.

The weaknesses of this gizmo are that it does not seem independent of teacher instruction, so the students would have trouble using it on their own. The concepts of lateral and surface area are not explained, but their equations are given. It is a tool for accompanying instruction from the teacher, but not a substitute.

How would I use this in my class?

This gizmo is similar to gizmo one in that I think it would be useful as a visual aid for a class used on a projection screen or smart board. I would use it as a teaching aid to show the students a visual reference while learning the concepts of surface area of 3D objects. Again, as in gizmo one, I don’t foresee the students using this on their own, as I think there is a lot of instruction that needs to go along with the gizmo. It seems to be a good aid in breaking down the components of a 3D objects in a 2D format. I would use it in congruence with equations or story problems that the class would answer either indificually or in groups. The answers to the problems presented to the class can be revealed by me as the lesson progresses.