Student+Math+Lesson

Materials:
 * iPod Touches with Math Tricks Lite app installed
 * website: Wolfram Alpha (http://www.wolframalpha.com)
 * paper/pencil
 * calculators (either on the iPod Touches or handheld)
 * document camera/LCD projector to share student work
 * place for student reflection on process and conclusion (a math journal, which could be online or off)

Objectives: See http://www.corestandards.org/ for the current draft of the Common Core Standards
 * 1) Students will: reason quantitatively; construct viable arguments and critique the reasoning of others; use appropriate tools strategically; look for and make use of structure; and, look for and express regularity in repeated reasoning.
 * 2) Students will: analyze patterns and relationships and perform operations with multi-digit whole numbers.
 * 3) From the student perspective: "I can explain a trick for squaring numbers in the 50's and test to see if the trick works with other decades."

Learning Activity:
 * 1) Students will learn a trick for squaring numbers in the 50's through the iPod Touch app, Math Tricks Lite.
 * 2) // Guiding question: // // Does it always work? // Let's try some more, since it's called "Squaring Numbers in the 50's." Students will practice it on several 50's numbers and make sure it always works.
 * 3) // Guiding question: // // Why does it work? // Students will build on their observations of __how__ it works to answer the question __why__ it works. (Students who have deep understanding of number (who understand the composition and decomposition of numbers), and who have multiple strategies for showing their work in multiplying 2 digit by 2 digit numbers, will have an advantage here, as they can explore multiple representations of these arithmetical tasks.)
 * 4) // Guiding question: Can we use an online math computational search engine to help us figure out why it works? // Students will go to Wolfram Alpha to see the steps of the problems they have tried to help them understand why it works. (They put in the problem 54x54, for example, and then click on the link "show steps.")
 * 5) // Guiding question: Will it work for other decades? // Students will then choose another decade (40's or 60's, for example) to try some more and see if they work with the trick, If it doesn't work, they will attempt to figure out the trick for that decade.

Assessment: The students should demonstrate understanding of the terminology and "steps" being presented and be able to apply the same steps to different numbers. After a "view lesson" session or two, students will likely be able to apply the steps without the assistance of the app. Students who continue to rely on "view lesson" may need additional assistance or review.

In learning the trick, students will likely see or at least question the patterns and relationships - Why 25? Why add the ones? Why square the ones? Look for the student to attempt to solve the problem in multiple ways, following correct logic and procedure through different approaches. Prompt students to re-write sample problems as many ways as they know how.

It may be necessary to prompt some students to try the same trick with numbers in the 40's or 60's in order for you to bring them back to the 50's. Students may benefit from a discussion about what makes 50's so special. How does 50 connect to our base-10 system?

Listen for sound mathematical reasoning and watch for strategic use of the tools provided. Observe student recording sheets to check for the use of multiple representations of the same operations.