## Activities

**Exploring Decimals**

Give students a list of numbers, some of which are rational, and some of which are irrational. They should be written in various forms. In groups of two have students work through the list determining if each number is rational or irrational. Students should also write all fractions in decimal form. They will see that some decimals may take a while before they repeat, but they do repeat, showing that just because a decimal is long, does not mean it is irrational. Students will also learn to recognize rational and irrational numbers more easily.

*(This activity can be completed in approximately ten minutes. Students are given the opportunity to interact with other students. The list of numbers should be long enough to allow for exploration and similarities to be revealed, but not so extensive as to exhaust students and loose attention.)*

**Display Boards**

Divide students into groups of three to four and have them create an informational poster board about a real number. Split the groups up evenly, so that half the class is doing rational and the other half irrational numbers. Be sure to include at least 2 visuals (the number or symbol, pictures of creators, association of number, or location on number line etc.) Students should also include what the number is associated with and one random fact. Use your imagination to create an eye catching billboard. Provide the following materials in the classroom: computers, printer access, markers, crayons, glue, paint, scissors, construction paper, magazines, newspapers, sales papers, and poster board.

**Class Blog**

Create a class blog which each student can access and post to. Have each student create a post in which they reflect on the media, lesson, or another activity concerning rational and irrational numbers. Students should explain what they understand each to be and the properties of both. They should also use the opportunity to ask questions and state what they do not understand or would like to investigate further. Students can also reflect on an application of rational or irrational numbers such as pi, circumference of circles, root 2, etc. (

*This activity can be assigned for homework. Students have been given information in class and have explored the concepts through activities. They have already mathematically interacted with the material. It will be beneficial to assign students a non-traditional homework assignment. Students will think about and reflect on the information outside of the classroom at a different time. This will also provide the instructor with the opportunity to cover any misunderstood information, etc., in the following class.)*

**Investigating Circumference**

Provide students with a variety of circular objects to measure their diameter and circumference. Students will need a ruler and string or yarn. Have students prepare a paper on which to record their findings. Students will wrap the string once around each circular object and measure the length of the string that was needed to completely wrap the object. Students will then measure the diameter of each. Once all objects have been measured, students should calculate the ratio of the circumference to the diameter for each object and record. Ratios should be around 3.1 and 3.2. Students will then create a scatter plot of the data, with the horizontal axis for diameters and the vertical for circumferences. The slope of the line should be around 3.1. The ratio is pi. Present students with the precise ratio and explain that this is the same for all circles.

*(This is a great activity for students to work in small groups and to allow them to put math to practice and find information for themselves. This activity should be done after introducing concepts, but before covering the specific example of pi.)*

**Pi Worksheet: A Special Pattern**This activity can be found at http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CCgQFjAB&url=http%3A%2F%2Fi-a-e.org%2Fdownloads%2Fdoc_download%2F38-pi-worksheet-approximating-pi.html&ei=OSaGUOGkNIaI8QTg5YHQBA&usg=AFQjCNFYNNOdOx50-keUi203uOqYTOG58A

**Together on the Number Line**

Using index cards create a stack of numbers, half of which are rational, half of which are irrational. Be sure to have enough cards for each student to have one. Have the students decipher which category their number falls into. Students with irrational numbers should move to the left side of the room and students with irrational numbers should move to the right side of the room. Have each set get in order from least to greatest. Then, using a number line drawn on the white board and have each side (irrational and rational) place themselves in front of the approximate location of their number.

*(This activity should not take a large amount of time and can be done in approximately ten minutes. Students will be engaged through interaction with the class. However, be sure not to allow too much time as this will lead to a loss of attention, and students may need to be redirected.)*