## Saturday, March 17, 2012

### Math Alive!

The Smithsonian Institute is currently hosting the Math Alive! exhibit.  From the website:

• MathAlive! is designed to inspire, to spark the imagination, to reveal not only math at work, but the endless possibilities of math. Designed for families and students the exhibition brings to life the real math behind what kids love most - video games, sports, fashion, music, robotics, and more - and creates interactive and immersive experiences that bring to life the math at work in each, whether in design, application or use.
If you're planning a trip to the Washington, DC area, be sure to include this exhibit in your itinerary.

Visit the Math Alive! website for more information on the exhibit and to sample some of the online games and activities.

## Friday, March 16, 2012

### Making Predictions

Making predictions is an important step in all data collection activities.  After a brief explanation of the problem or experiment, students are asked to think about what they expect the results to be and make a prediction.  The teacher leads a discussion of the predictions and the reasoning behind them, often posting these on chart paper for future reference during the data analysis phase.

I recently read a study on this very subject.  It found that having students make predictions about new math situations or problems did indeed foster deeper mathematical thinking and understanding in students.  Additionally, this practice also increased student engagement in the task, as they were invested in the results.

One data collection activity I have used with students from kindergarten through middle school, is the Cheerios Investigation.  Students are told about an advertising campaign in which Cheerios randomly includes one of six toys in each box of Cheerios.  They hope that this will prompt families to buy more boxes of Cheerios trying to get all six toys.  Students are asked to think about this and predict how many boxes of Cheerios the average family would need to buy to get all six toys.

The teacher then leads a discussion about the predictions, including the reasoning behind them.   In my experience, there's always the eternal optimist (or naive person) who says six.  Then there's the off-the-cuff response of 100 or some other large number.  The most popular response is 36, although I've yet to hear an adequate mathematical reason for that number.  Nonetheless, the teacher accepts all predictions and reasoning, posting them on a chart for later reference.

Students then conduct the simulation, using a die and tallying the results until they have indeed gotten each of the six toys (each toy represented by a number 1-6 on the die).  They post their results on the class line plot, then repeat the experiment as time allows.

The class line plot is the basis for the data analysis.  Students may compare their small sample to the larger class sample.  Discussion may include mean, median, mode, range, outliers, etc., as appropriate for the class level.  Finally, students are asked to write an analysis of the data, this time in a letter to Mr. (or Mrs.) Oats, explaining why the plan to include toys will increase the number of boxes of Cheerios families will buy.

It's a simple activity but it leads to rich mathematical discussion and students are actively involved and engaged in the results from beginning to end.  Additionally, if several classes in the school conduct this experiment, classes can share results to generate an even larger sample.

See  Mathwire's Cereal Toy Investigation to view a lesson plan and download handouts.

Mathwire also offers the Cereal Toy Investigation applet, designed to allow students to quickly generate larger samples, extending the die-toss experience.  Students simply click the Next Box button to buy another cereal box.  The applet is designed to stop when the student has accumulated all six toys so that students may record this number before running another trial.   [Note:  This app requires Java.]

## Thursday, March 15, 2012

### Dynamic Paper

Be sure to check out the Dynamic Paper app from NCTM's Illuminations site.  This app allows teachers to customize and print out graph paper, grids, number lines, tessellations, spinners, pattern blocks and more.  Users control the number of sections in the spinner and colors.  Likewise, users set the size of the sides of pattern blocks or the range of the number line.

Dynamic Paper is a great resource for teachers designing activities to support math learning.  It's also an invaluable tool for teachers needing to differentiate classroom learning activities to meet the varied needs of learners in their classrooms.

Check out Dynamic Paper.

## Friday, March 9, 2012

### St. Patrick's Day Activities

•  Shamrock Paths challenges students to use Pascal's Triangle to figure out how many different ways there are to spell Shamrock. Included in the PDF file are an explanation of how this problem relates to Pascal's Triangle and the numerical solution to the challenge.
•  Shamrock Patterns requires students to rotate shamrocks to complete the pattern. Download some copies of Extra Shamrocks for students to cut apart and glue on to complete the patterns.
•  Top of the Morning challenges students to identify the 100th and 1000th letter that will be printed on the electronic signboard.

## Wednesday, March 7, 2012

### Writing Original Problems

Students use higher-order thinking skills when they write original problems similar to those they have done in class. Have students proof and solve each other's problems before publishing them on the computer, along with the author's name and the date.

These problems may be used as do-nows, homework assignments, or placed in the math center. Teachers who regularly include student writing find that students are highly motivated to solve problems created by their peers AND teachers develop a larger bank of appropriate word problems over time.

An easy way to start is to give students an open-ended problem to solve.  Then challenge students to write their own version of the  problem to share with their classmates.

## Tuesday, March 6, 2012

### Writing Responses to Open Ended Questions

Use these simple steps to help students master this all-important skill.  Consistent use of these strategies will definitely improve both student confidence and student proficiency.

## Review the Rubric with Students

Most teachers use rubrics to score student responses to open-ended questions. Make sure students understand the rubric so that they know exactly what they must provide to get the best score. Teachers use a variety of strategies to provide this training:  [Read more...]

## Use the Writing Process Approach

Students are accustomed to editing their first drafts in language arts, reworking their writing to craft a better response. Regularly include these practices in math class. After writing, students should use the rubric to examine their response and annotate, clarify or reorganize, as needed, to craft a tight response. Students should be encouraged to use words, pictures and/or numbers to capture their thinking process in these open-ended questions. They must also understand that there are many different ways to achieve a perfect score as long as they accurately show their thinking toward a correct answer.  [Read more...]

## Provide Independent Practice

 Students will complete open-ended problems in both classroom and state testing situations, most likely under timed conditions. Teachers should continue to use a combination of the writing process approach (to grow better math writers) and the independent response situation, in which students must apply good practices to producing their best responses under test conditions. A combination of these approaches, used throughout the school year, is the best instruction and preparation for state testing. Check out the Mathwire Problem Solving collection.

## Monday, March 5, 2012

### Problem Solving: Stoplight

The Stoplights problem challenges students to figure out how many different stoplights they can create with 3 different color linking cubes if each stoplight must have one cube of each color.

Use linking cubes so that students can assemble all possible stoplights. You may choose to have students use any three different colors so that each student pair has enough linking cubes to assemble all possible combinations using one of each color to create the stoplight.

In these kinds of organized counting problems, it is important to question students about how they know they have found all of the possible combinations.  A first grader once responded that he knew he had them all because each color gets to be on top two times.  What a great insight!