Circle 0
http://nlvm.usu.edu/en/nav/frames_asid_122_g_3_t_1.html?open=instructions&from=topic_t_1.html

Description
The purpose of this applet is to promote addition, logic, and problem solving skills. The goal of the activity is to find sums of 21 using the integers that are given in a set of circles that are intertwined. Students who successfully can makes sums of 21 in each of the circles complete the activity.

Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Numbers and Operations, 6-8: Students will be able to compute integers fluently using addition skills.
-Problem Solving, 6-8: Students will be able to apply and reflect on strategies that help solve a mathematical problem (Circle 21).
-Reasoning and Proof, 6-8: Students will be able to make and investigate mathematical conjectures by reasoning which numbers would be best to make 21 in a given circle and then testing said conjectures.

What is the nature of the mathematics?
This program crosses multiple standards set forth by the NCTM. While on the surface the game appears to only be a simple addition game with integers, there is much more mathematics involved than at first glance. Students are practicing “logic analysis” by making examining the set of numbers that are given in order to determine the best placement for each number in a circle. Students are also using reasoning skills (“Well if I put a -3 here, then I have to put a four there.”) while solving the problem.

How does learning take place?
Learning takes place as students begin to investigate their conjecture on what three numbers it would take to make circle’s sum zero. Students are making and testing conjectures while analyzing the results to figure out the correct solution to the puzzle. With continued practice of integer addition skills the puzzle provides, students will begin to increase their computational fluency with integer computations.

What role does technology play?
This applet allows students to show and test their knowledge of adding integers while also allowing students to apply logic and reasoning skills to solve a mathematical puzzle.

This applet is a fun and challenging way for students to practice adding integers in a game/puzzle format. When students are able to make twenty-one in a circle by dragging the given numbers into a circle, the technology turns the circle a tan color, representing the students were correct in making twenty-one. When all the intertwining circles have twenty-one inside of them, the technology turns all the circles red, meaning the students have won the game. The technology also provides students with multiple “Circle 0” games, meaning students who finish one can move onto another, or if a student is stuck on one game can try a different one.

How does it fit within existing school curriculum?
This technology would work well in a secondary setting as students practice their adding of integer skills, as well as their problem solving and logic skills. This program is not designed to teach students how to add integers or think logically, and does not offer any hints on how to solve the puzzle, but it does allow student to practice all these skills in fun and engaging format. Hence the technology should be used as a supplement to an existing curriculum and unit on integer computation.

How does the technology fit or interact with the social context of learning?
The technology is designed to be done individually, however the applet could be used as a partner activity. As suggested on the “teacher page” of the applet, students could partner together and “race” against one another to see who can make zero the fastest. This would allow interaction to occur as well as motivation when completing the puzzle.

How are important differences among learners taken into account?
For students that struggle with integer addition, there are two similar applets, “Circle 21” and “Circle 99” that follow the same rules as “Circle 0”, but allow students to work with adding just whole numbers (smaller whole numbers in “Circle 21”, larger whole numbers in “Circle 99”). While students are not increasing their computational fluency by adding integers, they are still applying problem solving strategies as well as logic and reasoning skills, making the activity worthwhile.

What do teachers and learners need to know?
Because this activity involves doing a lot of computations, it is recommended that student come prepared with a paper and pencil to work out computations. The applet does not provide a calculator or any place to work through computations. Students that try to do the math mentally may open themselves up for more mistakes, so depending on the level of student the teacher should make sure that the students have a pencil and paper handy.