## Sunday, December 28, 2008

### Multiplying and Dividing Fractions

Last week we talked about adding and subtracting fractions, which most of us know is a very difficult subject for students. This week I want to add to this discussion and give some helpful websites to help students multiply and divide fractions. I think it is vitally important that students be proficient in working with fractions on all levels and with all types of computations. I have found in the past that students will know how to do a problem conceptually, but will struggle with simple computations, mostly involving fractions. Students need to be comfortable with these common computations so that they can start thinking of mathematics on a more difficult and conceptual level in higher classes.

The following is a list of websites that include games, interactives, practice items, and lessons that help students with multiplying and dividing fractions. Please feel free to add to this list as you explore this subject further. Also, please share those findings with the rest of us.

This website has two lessons. Lesson 1 involves multiplying fractions while lesson 2 works through dividing fractions. Both lessons have an extensive list of practice problems with answers that students can use to check for understanding.

Math Workout: Multiplying and Dividing Fractions

These two websites are from the same source. These websites allow students to practice and work on dividing and multiplying fractions.

Multiplying and Dividing Fractions by Using Circles

These sites allow students to see the multiplication and division of fractions visually by using circles.

This site allows students to enter their own fractions and then shows a detailed explanation of how the student’s problem was completed.

This website allows students to practice their skills on computer generated problems.

These are just a few of the activities that are available to students online. I hope that this is helpful in getting you started with your search. Next week we will move into another difficult subject, factoring.

## Sunday, December 21, 2008

Working with fractions is one of the most difficult concepts for students. This week I am going to go through some interactives and web tools that will help students add and subtract fractions with both common denominators and without common denominators. In my experience students have problems with adding and subtracting fractions in all the levels of mathematics, from Math Foundations to AP Calculus. It seems to be a concept that students don’t grasp early on, and then struggle with throughout their math education. The following is a list of interactives and activities that can really help students work through their struggles with adding and subtracting fractions. I believe adding a visual element to this concept will help students tremendously. This list is just a few of the interactives that I have found online. Please feel free to look even further and share your findings with all of us.

This is a tutorial that goes through many concepts dealing with fractions, including adding and subtracting fractions.

This interactive shows a visual representation of a fraction while working through addition/subtraction problems with common and unlike denominators.

This interactive allows students to create their own game depending on what skill they want to practice.

This game asks students to select the correct answer as they are riding in a boat. The answers are held up by bugs flying by the window of the boat.

This is a list of fraction quizzes that students can complete to practice their skills.

I hope that this is helpful for students who are struggling with adding and subtracting fractions. Next week we will work through multiplication and division of fractions.

## Sunday, December 14, 2008

One of the most difficult concepts that students struggle with in mathematics is adding and subtracting integers. This happens for students from math foundations all the way to AP mathematics. Like fractions, this is a subject that students do not always grasp at the beginning of their exploration of mathematics, and therefore struggle with throughout their classes.

I wanted to offer some online resources that I have found to help students work through some of the difficulty of adding and subtracting integers. The first is a great overview of how integers fit into the scheme of all numbers. This tutorial can be found on HippoCampus.org and should be the first place a student starts in their exploration of adding and subtracting integers.

Next, there are some great free videos that can help students. The first two videos talk about adding and subtracting integers using tiles while the next two videos talk about using a number line.

Students can also practice their skills online. The following is a list of interactives that can help students:

## Saturday, December 6, 2008

### History of Mathematics

As we move forward in our discussion of how we can use the internet to help us teach mathematics, this week I wanted to concentrate on how we can link mathematics to history. Our students learn math in a bubble, and they usually have no link to mathematical history or to famous mathematicians. This is a shame because there are a lot of famous problems and historical topics that can be linked to mathematics.

I think the best way for students to appreciate the history behind the study of mathematics is for them to either write a paper or do some research on the topic. In my own investigation of the history of mathematics I came across some good resources that I want to share with you.

1. You may ask students to do research in terms of important history topics. These topics can include the core classes we think of now, such as Algebra, Geometry, or can branch out to analysis, astronomy, and physics. They can also include a broad overview of the history of mathematics.

2. Students can also base their research on famous mathematicians even narrowing down their research to searches such as famous woman mathematicians.

3. Finally, students can do research on famous unsolved problems. Though some of these may be hard for students to understand, the discovery portion of the task and explaining a difficult problem to others is extremely beneficial.

I highly recommend adding this research component to any class. I don’t think we can afford to continue to teach mathematics without giving our students some background information.