Week 12 - Hidden Rods Lesson Plan

Class: Fifth Grade Mathematics

Instructor: Marc Vogel

Unit: Geometry

Lesson: Click here to access the lesson plan and the supporting materials.

Time: 65 minutes

By completing this lesson, students will be able to use a coordinate system of ordered pairs of numbers, recognize the importance of the sequence of the numbers in an ordered pair, and develop strategic thinking skills. Thus, this lesson is excellent for a class that is either starting to learn about graphing ordered pairs or for a class that is already in the process of learning about how to graph ordered pairs.

The most important thing about this lesson is that it is fun. The students will feel as if they are playing the game called Battleship. Thus, a teacher could use this game to get students to learn about plotting ordered pairs on a coordinate plane without the students even realizing that they are learning. Thus, the chances of getting students engaged in the learning experience are very high if this lesson is the one being implemented.

Another aspect of this lesson that I particularly like is the fact that students will need to use different strategies in order to "win". This is why I included questions that probe the students to think about and discuss their strategies.

Also, I practiced playing this game with my girlfriend. The game went smoothly, and all indications were, that this lesson would be an effective lesson to use with students.

Week 12 - Fill and Pour Virtual Manipulative

Click here to access this program.

This program is a lot of fun. It reminds me of the Towers of Hanoi Puzzle and the Peg Puzzle because it requires students to use their problem solving solving skills. In addition, it requires students to use their measurement and arithmetic skills.

A teacher could easily spark interest in this program by showing students a clip from a Die Hard movie where the police officers had to solve a riddle that involved getting a certain amount of water in two jugs. However, the program is interesting even without this hook.

While some of the virtual manipulatives are not such a "big deal" because one might be better off using real manipulatives, this program allows students to do problems that could be very messy if they were solved in "real life". In fact, most math classrooms do not have sinks, so to do these problems in "real life" in a math classroom would be very challenging. One would have to go to a science classroom, an art classroom, or a home economics classroom..

This program can be found under the measurement tab for grades six through eight. However, this could certainly be a fun program that a math teacher could give to lower level high school math classes.

As teachers, it is important to select activities that will get the students to be engaged. Since students are stimulated by "exciting" video games, computer programs, electronic equipment, and television shows, it is important to make class activities and homework assignments as much fun as possible. This program does just this by creating interesting problem-solving scenarios.

Week Eleven - Grab Bag Cuisenaire Rods Lesson Plan

Class: Eighth Grade Mathematics

Unit: Probability and Statistics

Time: 1 Period (68 Minutes)
Lesson: Click here to access the lesson plan and the supporting documents.

After completing this lesson, students will be able to determine the mean, median, and mode for a data. They will also be able to draw conclusions about a data set and recognize patterns in data set. In addition, students will have to make and test hypotheses in this activity, which reinforces what they learn in eighth grade science. As a result, this lesson is interdisciplinary in nature. If other teachers decide to use this lesson then they should consider reaching out to the eighth grade science teachers in their respective schools. It is possible that an interdisciplinary assignment could be developed as an extension to this activity.

The best part about this activity is that it is fun. Students tend to enjoy making predictions and testing them to see if they were right, and this is at the heart of this activity. Thus, when implementing this lesson teachers should find it relatively easy to get students engaged in the learning experience.

Also, this lesson is designed for a sixty-eight minute period. However, it could easily be broken up into two shorter lessons. One lesson could focus on the Grab Bag Activity and the other lesson could focus on the Grab Bag Extension Activity.

Week Eleven - Virtual Manipulative - Right Triangle Solver

Click here to access this program.

A few of the applications of this program could be used in middle school; however, this program is best suited for high school level mathematics. It can be used to help students learn how to solve for a missing angle or a missing side in a right triangle. It also can be used to reinforce the students' understanding of sine, cosine, and tangent. Thus, this program would be great for independent practice in the classroom, and it could also be used as a review activity.

This program is great because it allows students to solve for multiple missing measurements for a right triangle. In step one, students must pick the variable that they would like to determine. In step two, students must determine the method that they need to use in order to solve for the variable that they selected. In step three, students must actually solve for the variable that they selected using the method that they chose in step two.

I particularly like that students must decide what method to use to solve for a particular variable. This prevents students from simply "plugging and chugging". In other words, it prevents students from simply using a given formula and plugging in numbers without thinking deeply about what anything in the problem means.

Another aspect of this program that I like is the fact that if you select an incorrect method to use, the program gives the user some information that is meant to help him or her understand why his or her chosen method would not work. Also, if step three is not done correctly then the program gives the user a helpful hint. Of course, the program also informs students about correct answers. Thus, students can get instant feedback from this program. If this type of assignment were provided to students in a paper and pencil format then it would be much harder to give students immediate feedback. Remember, there is usually only one or two teachers per classroom.

Week Ten - Peanut Brittle Geoboard Lesson Plan

Click here to see the lesson plan and the supporting materials.

This lesson plan requires the use of Geoboards. After completing this lesson, students will be able to find the fractional parts of a whole, represent fractions spatially, add fractions, and find the areas of irregular shapes. There is no doubt that some groups will make this lesson harder than others. When I had my girlfriend complete the lesson she broke the "peanut brittle" into some very complicated shapes. As a result, it was very challenging for her to complete the lesson. However, after an extensive amount of time, she was able to do it. Thus, my advice for those of you who want to use this lesson in the classroom is to allow for some groups to take longer than others.

Week Ten - Box Plot Virtual Manipulative

Click here to access the program.

According to the program:

"Box plots and histograms are both used to summarize data graphically.

A box plot shows the minimum data value, the lower quartile, the median, the upper quartile, and the maximum data value on a number line. A box is drawn from the lower quartile to the upper quartile. The median is marked inside the box.

A histogram divides the range of values in a data set into intervals. Over each interval is placed a block or rectangle whose area represents the percentage of data values in the interval."

This program can be used to introduce box plots. Students can analyze the data that is provided when the program opens. They can also make changes to some of the data or delete all the data and enter their own. The program then graphs then automatically creates a box plot with the data.

This program can also be used to check one's work. Students can create a box plot by hand and then use this program to see if their work is correct.

Week Nine - Pythagoras Delivers the Mail Geoboard Lesson Plan

Click Here for the Lesson Plan and Supporting Materials

This lesson plan is appropriate for eighth grade. Here is the New Jersey Core Curriculum Content Standard that this lesson plan meets:

4.2.8 E. Measuring Geometric Objects
1. Develop and apply strategies for finding perimeter and area.

By completing this lesson, students will be able to devise methods for finding areas, formulate and test generalizations, learn about and apply the Pythagorean Theorem, and use mathematical reasoning to solve a real-world problem.

Lastly, this lesson plan helps make the Pythagorean Theorem more "real" for the students. By completing this lesson, students will see that a squared, b squared, and c squared actually represent the areas of squares. Thus, after completing this lesson, students will be able to picture in their minds what the numbers in the Pythagorean Theorem actually mean.