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.

Week Nine - Venn Diagrams Virtual Manipulative

Click Here to Access the Program
Grades: 6 - 8
Category: Number and Operations

This is a very simple virtual manipulative. However, it is very effective for giving students an opportunity to practice depicting the union and intersection of sets on venn diagrams. If a teacher were to give students several problems of this nature, it would be challenging for that teacher to give each student individual feedback. However, this program makes this possible. Students can click on the "check" button to see if their answer is correct. They can also click on the "show solution" button to get the answer to a problem that they cannot solve. These two options make it possible for students to get immediate feedback, which is something that a teacher likely cannot provide without the help of technology.

Another nice feature of this program is that the problems it creates get progressively more difficult. Thus, more advanced students can work quickly and get to the harder questions, and students who are struggling with either the concept of venn diagrams or unions/intersections of sets can take their time and work on the easier problems.

However, there is one thing that could improve this program. This would be the addition of a "hint" button. While I like that students can check their answers and also get solutions to the problems that they cannot solve, I would like there to be an option that helps students without giving them the answer. I suppose this option could be provided by the teacher; however, I think students might jump to click on the "show solution" button too quickly. In essence, the desire for immediate feedback could get in the way of true learning by struggling to solve difficult problems.

Extension of Geoboard Activity from Class

Area of Quadrilaterals

Posts Trees Area
4 0 1
4 1 2
4 2 3
4 3 4

5 0 1.5

6 0 2
6 1 3
6 2 4
6 3 5

7 1 3.5
7 2 4.5
7 3 5.5

The formula A(P,T) = 0.5P + 1T - 1, where A stands for area, P stands for the number of posts, and T stands for the number of trees, still works for all of these examples.

Lesson Plan - Week Eight - Shelf Brackets Geoboard Lesson

Click Here for the Lesson Plan and Supporting Documents

This lesson is great if you are trying to get students to develop a deeper understanding of the properties of right triangles or trying to get students to use more than one method for finding the area of right triangles. It is also very good for getting students to think deeply about proving that they have found all of the solutions. It is not an easy task to develop and present a convincing argument that one has found all possible solutions to a particular task. This lesson requires that students do this.

Once again, I tested this lesson out on my girlfriend. It worked very well. However, in my opinion, her argument that she had found all possible solutions was weak. Thus, I think the discussion on proving that one has found all possible solutions could take a considerable amount of class time. Also, if students have not been trained on how to develop such an argument throughout the course of a school year then this might be challenging. Thus, in the future, I will try to train my students on how to prove that they have all possible solutions starting in September. Lastly, I feel that requiring students to prove that they have found all possible solutions is very important because it forces students to think like mathematicians.

Virtual Manipulative - Week Eight - Point Plotter

Click Here to Access this Virtual Manipulative

This is a great virtual manipulative to use if you are going to teach students to graph on a coordinate plane. Even though this virtual manipulative is very simple, it is an excellent learning aid because it gives students immediate feedback as to whether they are correct or not. In order to get this feedback, all students have to do is plot the points and click on the check answer button. The program will tell a student whether he or she got all the points correct, some of them correct, or none of them correct. It will even indicate which specific points are correct and which ones are not. The ones that are not correct will show up red, and the ones that are correct will show up green.

Another nice thing about this program is that it makes it easy to provide differentiated instruction. For the students who are good at graphing, they can do the program without the grid values. However, the teacher can set the program to show grid values for the students who are not as strong at graphing. Also, the program contains many different problems, so students who are good at graphing can do additional programs while the students who are not as good at graphing can complete fewer problems.