Create a Graph

http://nces.ed.gov/nceskids/createagraph/

This applet is a showcase of the many different types of graphs available to display data. Students are choosing and manipulating a graph of their preference- inputting data to display and correctly labeling the different pieces and parts of a graph. What the program aims to show is that there are many types of graphs that can show and represent a set of data accurately. This program serves as a great tool for allowing students to quickly and accurately create graphs.

First in Math
http://www.firstinmath.com

"First in Math" is an online version of the game, '24'. 24 is a popular card game in which students must make a total of 24 using four numbers on a given card. This site promotes the practice and increase in skill of mental computational fluency. The varying levels of difficulty (from whole numbers to fractions to integers to even algebra!) offer students of all abilities to find this site beneficial. Students can earn virtual stickers for completing various activities, and their is even a ranking and leader board of student sticker count, from the school level all the way to a nationwide leader board.

Function Machine
http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_2.html?from=category_g_3_t_2.html

This technology plays to the common metaphor that functions are like “machines”- you put a number in (input), you get a number out (output). This applet allows students to put a given set of numbers into the function “machine” and have the machine generate an output. Students must also try and decipher the function “rule” in order to determine missing outputs for inputs.

Number Balls
http://www.sheppardsoftware.com/mathgames/Numberballs_algebra_I/numberballsAlgebraI.htm

The program allows students to practice their algebra skills by having them solve one-step equations that are written inside "number balls". Once students solve each equation, they must put each answer from least to greatest order. They then will click each ball going from least to greatest in order. Students get points for correctly clicking on a ball, and lose points for incorrectly choosing a ball. All-time high scores are saved and posted, giving this applet replay value and motivation for students to do well.

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.

The Secret World of Cookie Man

http://www.learningwave.com/preview/integers/cm1.html

This program was designed as an engaging activity for secondary students to practice using basic formulas, like distance and area. Students have to help “Cookie Man” in his adventure, solving problems along the way. Students must be able to set up formulaic equations correctly, substitute values for variables, as well as solve for missing amounts. The program offers amusing and laughable problems that make solving them fun and engaging for all students.

Function Machine
http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_2.html?from=category_g_3_t_2.html

Description
This technology plays to the common metaphor that functions are like “machines”- you put a number in (input), you get a number out (output). This applet allows students to put a given set of numbers into the function “machine” and have the machine generate an output. Students must also try and decipher the function “rule” in order to determine missing outputs for inputs.

Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Algebra, 6-8: Students will be able to understand patterns, relations, and functions through analysis of data and input-output tables.

What is the nature of the mathematics?
The main concept being shown is functions. Students are going to recognize functions as “machines” that process inputs and outputs. Students will also become familiar with reading and using an input-output table and analyzing an input-output table for patterns.

How does learning take place?
Learning takes place as students begin to analyze the outputs of the function machine for patterns. Using the input-output table, students have the opportunity to analyze the values the function machine has produced. By doing this, a pattern will begin to emerge (for example, for every input, the output is the input plus three). Using this pattern will help determine the nature of the function and allow the students to figure out the three missing outputs that are omitted from the input-output table. By analyzing the function’s data, examining relationships between the inputs and outputs, and recognizing patterns, student learning of functions can occur.

What role does technology play?
This technology allows students to physically move inputs into the function machine. This plays to the metaphor of functions being a “machine” as it brings the metaphor to life. The technology also generates the outputs for the student, and places both the inputs and outputs into an input-output table that is presented. The applet also allows for students to enter the values for three missing outputs in the table, which the students must determine from the pattern of the function.

This technology affords students the opportunity to represent knowledge and thinking based upon the student’s ability to show the recognition of a function’s pattern by naming the three missing outputs to the applet’s function. The technology also automates and simplifies the task, as students do not have to do any work in figuring out the first four outputs of the input-output table (the function machine does that for them) and do not have to fill out must of the input-output table (the applet fills out the first four input-output pairs for the students).

How does it fit within existing school curriculum?
This technology works well as an introduction to functions. Students in secondary schools will see this technology as beneficial as they are familiar with functions being termed “machines”. This applet would crystallize this image for them, as well as provide an engaging and interactive activity for students to practice recognizing patterns, filling out input-output tables, and learning about functions. This technology is to be used as a supplement to algebra lessons dealing with patterns and functions.

How does the technology fit or interact with the social context of learning?
There are some functions that involve non-numeric outputs. For example, in one particular function an input of ‘one’ will result in an output of ‘F’. This abstract thinking tests students’ abilities to think outside the box as well as think critically about patterns. Because some of the patterns aren’t as easily recognizable as others, for beginning classes first dealing with functions, it is recommended that students pair together and work with this function machine together.

What do teachers and learners need to know?
An understanding of functions is a must for students. This technology is not to be used as an introduction to a unit or the concept of functions, but rather as an assessment or skill builder. It is important for students to understand the terminology associated with functions to give this technology more meaning and purpose.

The Secret World of Cookie Man
http://www.learningwave.com/preview/integers/cm1.html

Description
This program was designed as an engaging activity for secondary students to practice using basic formulas, like distance and area. Students have to help “Cookie Man” in his adventure, solving problems along the way. Students must be able to set up formulaic equations correctly, substitute values for variables, as well as solve for missing amounts. The program offers amusing and laughable problems that make solving them fun and engaging for all students.

Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Algebra, 6-8: Students will be able to represent and analyze situations with equations and will be able to solve equations using given values.
-Numbers and Operations, 6-8: Students will be able to develop and analyze methods for solving problems.
-Measurement, 6-8: Students will be able to understand and convert between different units of measurement.

What is the nature of the mathematics?
The nature of the mathematics is to be able to read and analyze a word problem, extract useful data, and to be able to successfully apply the data using a given formula. The problems are all in word form and students are expected to use problem solving skills to solve them. Students are using the area formula for a rectangle, the distance formula, as well as simple conversion methods to solve the word problems.

How does learning take place?
Learning takes place as the student apply strategies to find the missing values requested in each of the problems. Students are substituting values into equations and correctly and evaluating them for a numeric answer. Students are able to check their answers in the solution box, as an incorrect answer will lead them to the next problem, while an incorrect will keep them on the same problem. This ensures that the students will have to complete each problem and achieve success in order to make it through the entire program.

What role does technology play?
The technology affords students the opportunity to represent their knowledge and thinking by solving complex equations and applying useful formulas. Students’ knowledge is represented as they make their way through the “Cookie Man” program, solving each given problem.

The technology itself provides the students with an engaging backdrop to complete word problems dealing with algebraic concepts. While the story presented by the technology is silly and goofy, the problems themselves are excellent examples for using formulas and equations in mathematics. The technology offers the students these problems to students while keeping them interested with an funny story.

How does it fit within existing school curriculum?
This program fits well into any secondary school curriculum. At the secondary level students are being introduced to many algebraic concepts, like equations, variables, and using formulas. “Cookie Man” promotes all of these in a manner that engages students. “Cookie Man” would be a wonderful supplement to any algebra unit, or even used as an assessment of students learning by teachers.

How does the technology fit or interact with the social context of learning?
The program itself does not offer much in the way of a “hint” to students. The problem solving is done strictly by the students themselves- which is rigorous work. Because of the nature of the problems, “Cookie Man” is a fantastic program to do in partners. Students analyzing the problems in partners would have opportunity to discuss their methods for solving with one another, thus leading to some fruitful mathematic discussion.

How are important differences among learners taken into account?
Differences amongst learners are not addressed with the program, as it is one of its downfalls. The program lacks any levels of difficulty or assistance to lower-level learners. If students have poor reading skills they are almost certain to struggle comprehending the story and problems presented. Another problem with the program is that there is only one set of problems- once students have correctly answered the problems there is nothing else for them to do. Once the program is completed once, there is no use for using it again.

What do teachers and learners need to know?
This program is part of a preview for a website, http://www.learningwave.com/, which is devoted to creating engaging online activities for secondary students. Many of the activities are designed by teachers for classroom use, including “Cookie Man”. “Cookie Man” is one of the preview programs available to teachers for free.

Students need to be prepared to have a pencil and paper (or calculator) handy as they go through the “Cookie Man” program. The program does not offer much assistance in the solving of each problem, so students have to be persistent and patient, especially those of lower levels. Reading skills are also very important for this program, as all of the problems and story is reading based.