Dueling Calculators
http://nlvm.usu.edu/en/nav/frames_asid_312_g_4_t_1.html?from=topic_t_1.html

“Dueling Calculators” an applet allows students to visually and numerically see the differences calculator truncating and rounding can play in mathematics. When a calculator truncates (due to the size of its viewing window), answers are not usually effected greatly. Over time, however, repeated truncation can drastically change the solutions and results we get. This applet provides a resource for students to see that change.

Escape from KNAB

http://www.escapefromknab.com/

Escape from KNAB is a program that connects real-world situations, like filling out a tax form, in a make-belief, out-of-this-world, story. Students will analyze different situations, like choosing between two job offers that have varying benefits, and decide on which conditions will allow them to make the most money to be able to afford a return flight home from the distant planet, KNAB. Students problem solving skills will be practiced as they try and earn and save money.

Pearson SuccessNet

http://www.pearsonsuccessnet.com

Pearson SuccessNet was created to assist both teacher in the classroom and for students at home. The site contains online videos that teachers can use in the classroom to introduce or explain a given concept (all secondary math concepts), while also providing students with online tutorials, videos, and practice problems that students can access from their home computer with a log-in identification. This program offers assistance to students who may need it outside the classroom, while providing technology to teachers inside the classroom. This is a pay site.

Stick or Switch
http://nlvm.usu.edu/en/nav/frames_asid_117_g_3_t_5.html?from=category_g_3_t_5.html

This program is a math version of the old game show, “Let’s Make a Deal” in which students have the choice of one of three doors, but behind only one of them is the grand prize. The object of the program is to showcase that by staying with your initial choice throughout the game (not switching your pick), you have lowered your probability of winning. The greater probability of winning is when students switch their picks after the first door is revealed. This program is centered on discovery based learning and potential for stimulating discussion on probability.

Stick or Switch
http://nlvm.usu.edu/en/nav/frames_asid_117_g_3_t_5.html?from=category_g_3_t_5.html

Description
This program is a math version of the old game show, “Let’s Make a Deal” in which students have the choice of one of three doors, but behind only one of them is the grand prize. The object of the program is to showcase that by staying with your initial choice throughout the game (not switching your pick), you have lowered your probability of winning. The greater probability of winning is when students switch their picks after the first door is revealed. This program is centered on discovery based learning and potential for stimulating discussion on probability.

Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
- Data Analysis and Probability, 6-8: Students will be able to collect and analyze data in order to formulate questions about probability.

What is the nature of the mathematics?
The main concept addressed with this program is probability. Students are working with fractions to represent probabilities: “There is a 1/3 chance of getting the grand prize by sticking with my initial choice.” Students are also analyzing data their ‘wins’ and ‘losses’ from a table that is provided by the technology in order to determine the best method, or the highest probability, for getting the grand prize.

How does learning take place?
The technology uses its own version of “Let’s Make a Deal” to show students that being aware of probabilities of events can be beneficial in situations. Students, by trial and experimentation, discover that by switching their first choice of prize to the alternate choice actually increases their chances of winning the grand prize. As students begin to make this discovering, there is a set of questions that students can answer in the “strategy” portion of the game that help bring their findings to light. This experimentation and reflection is the basis for a potential discussion on probability and how having a great probability means a more likely chance. The discussion can also build to why switching their first choice of prize to the alternate has a higher chance of probability.

What role does technology play?
This technology affords students the opportunity to communicate and collaborate with peers, as well as provides access to information and automates tasks to support student learning. The technology purpose is to serve as a jumping point for a discussion about probability, using created data from the game “Let’s Make a Deal” as a basis. Because of this, the technology provides access to information for students about probability in a “strategy” portion of the program and it keeps track of student data by automatically updating a chart that displays whether the student “won” or loss. This way the students are better informed and can focus on communication and collaboration.

How does it fit within existing school curriculum?
This program would be a beneficial supplement to be used in any probability or data analysis unit. It could be a great pre-assessment tool for teachers to see what knowledge of probability their students currently have.

How does the technology fit or interact with the social context of learning?
The technology’s biggest draw is the fact that it isn’t meant to assess or necessarily teach students about probability, but rather to promote discussion amongst peers and as a class. The technology offers a jumping point for debate: Is it better to stick with your original choice of door, or change it midway through the process? By using the technology the students can bolster their explanations and knowledge to make meaningful contributions to a discussion on probability.

What do teachers and learners need to know?
Some students may not be familiar with the game, “Let’s Make a Deal.” Therefore it might be beneficial for teachers to explain how the game works in detail before kids use the technology and become confused with the directions or objective.

Dueling Calculators
http://nlvm.usu.edu/en/nav/frames_asid_312_g_4_t_1.html?from=topic_t_1.html

Description
“Dueling Calculators” an applet allows students to visually and numerically see the differences calculator truncating and rounding can play in mathematics. When a calculator truncates (due to the size of its viewing window), answers are not usually effected greatly. Over time, however, repeated truncation can drastically change the solutions and results we get. This applet provides a resource for students to see that change.

Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Numbers and Operations, 6-8: Students will be able to understand large numbers (numbers with many digits) as they are written in calculator notation.
-Data Analysis, 6-8: Students will be able to interpret data in a table as well as in a graph and understand the connection between the two.
-Communication, 6-8: Students will able to clearly communicate their ideas using mathematical language about rounding and truncating.

What is the nature of the mathematics?
The concepts being displayed are calculator truncating, rounding, and the limitations of calculators. These concepts are displayed in the technology using two calculators, a table of created data, and a graph of the data. The students must interpret the data through discussion and collaboration with peers to gain understanding of the concepts displayed.

How does learning take place?
Learning takes place through meaningful discussion with peers. While the technology provides great data for analysis and visuals for interpretation, what the technology does not do is offer answers or conclusions for the data presented. Thus it is the students’ responsibility, through careful thinking and fruitful discussion, to use what is provided in the technology to reach conclusions about calculator truncation and rounding in general, and their effects on a data set.

What role does technology play?
The technology shows two calculators that are set side by side, one that displays nine-digits and the other that displays eight-digits. The technology allows students to set an input that is the same for each calculator, and the calculators put the input into a given function (provided by the technology), and display an output, which is truncated to the last spot in each calculator’s display. The calculators then take their truncated output and put them back into the original function as inputs. Because of truncation, the outputs for each calculator begin to change, and students have the opportunity to see the change both in numerical data displayed, as well as in a visual graph.

This technology affords peers the opportunity for communicating and collaborating with one another. The technology acts as a starting point for a discussion on the effects of rounding and calculator truncating. By interpreting the data presented in a table and on a graph provided by the technology through discussion, students are able to reach conclusions about calculator truncation and the effects rounding have on numbers.

How does it fit within existing school curriculum?
This technology would be a great beginning of the year activity. Some students nowadays are becoming too reliant on technologies, calculators especially, and are becoming weak in computational skills. By discussing the pitfalls of relying on calculators entirely and examining their limitations, students will begin to understand that complete reliance on calculators can be a detriment to their learning. It is also a fantastic introduction to some math vocabulary, like “truncate”, and provides a great visual of what it means for a calculator to truncate a number.

How does the technology fit or interact with the social context of learning?
This program can be a great tool for leading a whole-class discussion on the cautions of technologies. What is problematic about relying on technology completely? What do users have to know when using a technology? What limitations do calculators have? Teachers can even move to a discussion on rounding. How does rounding affect a set of data? This technology is designed to stimulate discussion and communication amongst students and the classroom.

What do teachers and learners need to know?
While students do not need have a particular knowledge of the functions the program provides (some may be a little abstract for early-secondary students) or how to graph the functions, students and teachers must be able to interpret the graph the technology generates and compare the two sets of data generated by the two calculators. A basic understanding of how functions work (there is an output for every input) is essential.