Another Way to Remember Multiplication Rules for Integers

Back when Mike Cirre was my principal, he told me this way to help kids remember the rules for multiplying integers. (The same rules are used for division--just substitue the sign.)

I start by making a chart on the board with the headings: person, enter/exit, and we feel.
I explain that there are two kinds of people: positive and negative. Then I explain that those people can use the classroom door to come into our class (thus adding to the number of people in the room)or they can leave (which subtracts from the number in the room. And whenever people come or go, we feel either good or bad deending on what kind of person they are and whether they came or went. All of these situations can be represented by + or - signs.

So we start to fill in the chart on the board. When a positive person enters the room, we feel good because they cheer us up. (+ + + ) When a positive person leaves the room, we feel bad because we are sorry to see them go. ( + - - )When a negative person enters the room, we feel bad because they bring their negativity with them. ( - + - ) But when a negative person leaves the room, we feel good because we are glad to get rid of them. ( - - + )

By this time I have filled in the chart so it looks like this:



+ + +
+ - -
- + -
- - +

The chart is then interpreted, a positive times a positve is a positive, a positive times a negative is a negative etc.

This is an amusing way to remember the rules for multiplying and late dividing integers. Invariably, while I am doing this with the class, someone will walk in the classroom door which will send the students into a burst of laughter, but that ultimately contributes to the effectivveness of learning.

Mathematics and Art: Symmetry

Symmetry is a mathematical principle that is used a lot in art as well. Students learn about symmetry and lines of symmetry in geometric shapes during the elementary grades. Their understanding of symmetry helps them in higher level geometry, but can also help them appreciate and analyze a number of works of art as well. Imagine that--mathematics is a basis for aesthetic experiences.

Symmetry is all around us in nature, and many works of art are judged to be more attractive when there are clear lines of symmetry which come from a central point.

Last year for a skills lab series, I did a two-week exploratory titled "Mathematics and Art". Symmetry was the first topic studied. I made a powerpoint using pictures of nature, buildings, and works of art that had clear lines of symmetry. I found the pictures by searching www.images.google.com. I just put in the word "symmetry".

This year, I briefly revived that powerpoint and students once again enjoyed viewing the pictures and identifying the lines of symmetry.

Adding and Subtractting Integers: A Flow Chart

The seventh grade is in an integers unit. Some are still having a hard time keeping the procedures straight. On Friday, we created a flow chart which served to further illustrate the process. This exercise and the resulting visual, served as the catalyst for the AHA! I GET IT! experience for a number of the students.

Computation vs. Calculator

There are those who feel that the use of calculators make students dependent on them so they never learn the basic facts. There are others who maintain that calculators are necessary as a time-saver and for those with disabilities who cannot learn math facts and computation skills. But having a successful middle school math program actually depends on a healthy balance between the two: computation and calculator.

As students start to solve higher level math problems, using a calculator allows them to do it faster. They can effectively perform and learn the steps required in the math problem without getting bogged down in the sometimes laborious task of computation.

On the other hand, students who don't regularly use their computation skills, sometimes lose some or all of them. Most middle school math curriculums don't come with computation exercises. Teachers who choose to include this piece usually do so with a daily drill or problems of the day at the beginning of the class. My favorite resource for this is the A.D.D. (Arithemetic Daily Developed)series by Cuisenaire. These small practice sheets give three mental math questions, a word problem, and several review problems. The drill sheets are based on NCTM standards. I have seens students'abilities and test scores improve as a direct result of using this resource.

I recently posted a poll where I surveyed about the importance of learning basic facts. Even though there were few responders, they both answered that it is very important for students to learn basic facts. I agree wholeheartedly--students who know the basic facts and can perform computation problems acurately will have more options in life and will do better in math overall.

But when you teach math to middle schoolers, the stark reality is that some of them have not learned the basic facts. This could be for a number of reasons: poor memory, gaps due to moving or truancy, immaturity, poor educational practices, lack of support for learning...and the list goes on.

Middle school math teachers and especially title I and special ed remedial math teachers must decide how much time to spend on basic computation and how often to allow calculators. Some students who don't seem to have the capability of remembering math facts are able to reason and problem solve because they understand math concepts. These students should be encouraged to use the "tools" they need. The danger of focusing only on math facts computation is that students view the exercises as drudgery and may not achieve success, whereas they may enjoy some other aspects of the math curriculum.

So like all aspects of life, we must seek a balance. Computation and calculator useage are both necessary to help students to learn and improve.

A Math Dictionary: Terrific Website

My husband told me about a fabulous website. It is www.amathsdictionaryforkids.com (Sorry, I haven't figured out how to post it as a link here yet.) I immediately went to the library and have scheduled a day for my students to use the computers. I made a worksheet that instructs them to go to this site and then use the site to answer the questions. This site is an online interactive math dictionary. My description sounds boring, but please check it out--it's great. My purpose in wanting my students to be familliar with it, is to provide them with a tool for finding math definitions and information.

The questions I am asking them to answer are:

1. In the number sentence 6 / 3 =2, which number is the dividend?
2. If you have two gross of pencils, how many do you have?
3. How many square meters are in a hectare?
4. What is a vinculum?
5. What is an algorithm?
6. Why are 31 and 36 relative primes?