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Playing and Learning to Use Integer Bars |
Tips to Remember
- For any problem you will be working on, think about it and make sure you understand it before working on it.
- Always check your answers and make sure that they make sense.
- Every problem has more than one way to be solved. Different people might solve the same problem in different ways and still come up with the same answer.
- Try to remember the colors for each of the different size bars. Do enough exercises until you memorize the color for each bar size.
- Whenever you see this image below or in other pages, clicking on it will start the integers bar program if it is not already running:
Who invented them?
Emile Georges Cuisenaire, who was born in 1891, came up with the idea of using integer bars, also called Cuisenaire Rods. He was a elementary school teacher in the city of Thuin in the country Belgium in Europe. In 1952 he published the book named "Numbers in Color" which describes the integer bars.
Caleb Gattegno, who was born in Egypt, was a professor at the University of London. He met Cuisenaire in 1953 and realized how good the bars were to teach mathematics. He helped a lot by talking with many teachers in many countries about these bars and made them very famous.
Getting Familiar with the Bars
Purpose - The purpose of this first activity is for you to get familiar with the bars, how to use the program, and learn the colors and sizes of the bars.
<- Click on this image to start the applet
Activity 1 - Building stairs. First build stairs using only white bars. Here is an example for you to see but you should build your stairs to at least 10 steps.
Activity 2 - Building colorful stairs. Now build a 10 step stairs using a different color bar for each step. You should build 2 sets of colorful stairs: one with vertical bars and one with horizontal bars. Make sure that the stairs go up and down. Here are examples of these.
Activity 3 - Draw a large house and make sure that it contains windows and a door. Once you have drawn the house, calculate (or figure out) the size of the house, the width and the height. Again, here is an example of a very small house. Make your house bigger.
Activity 4 - Draw a person. Here's an example.
Trains
To build a train you connect 2 or more blocks together without leaving a space between them and without overlapping. We are going to be using the word trains in the rest of these activities. Here is an example of a train where we also show the sizes of each of the bars and the total size:
The combination of numbers with the "+" and "=" signs, such as "5 + 4 + 3 = 12" is normally called an equation. The "+" symbol means adding the different numbers and the "=" sign is used to indicate that what you find on the left of it is the same as what you find on the right. In all further activities you should write the equation for each train that you build.
Purpose - You are going to practice building trains of specific sizes with lots of different bars.
Activity 1 - Make as many trains as you can using only two bars. The length of the train needs to be 7. Each train needs to be different. Be sure to write the equation for each train. Here is an example showing a bar of size 7 and one train:
5 + 2 = 7
Activity 2 - On this next activity you will make trains of size 8 using 3 bars. Again, each train needs to use different bars or different colors. Remember to write the equation for each train. Once you are done you can check examples of the answers by clicking here: answers.
Activity 3 - Now make trains of size 12. This time you can use any number of bars as long as they add up to 12. Be sure to write the equation for each train
Activity 4- For this last activity make trains of size 15. You can use any number of bars as long as they add up to 15. Be sure to write the equation for each train..
At this point you should be very familiar building trains of any size.
Symmetry
First we need to explain what symmetry means. A picture where you can draw a line in the middle and each side looks exactly like the mirror image of the other side is what is called symmetry. The line in the middle can be horizontal, vertical, or in any direction as long as both sides are the mirror image of each other. The following are examples of symmetrical pictures:
As you can see the symmetry line is vertical and what you see on the left side of the line is the mirror image of what you see on the right. You could fold it on the vertical line and the blocks on the right will fall exactly on the blocks on the left.
This drawing has a horizontal symmetry line. The part of the drawing above the line is the mirror image of the part below the line.
Purpose - To practice drawing symmetric pictures using the Integer Bars.
Activity 1 - Make drawings that are symmetrical where the symmetry line is either vertical, horizontal, or any direction. Examples of what you can draw are letters, houses, donuts, a tree, etc.
Odd and Even Numbers
Purpose - To understand what odd and even numbers are. This will be done by seeing some examples.
If you take any train (or number) and you can break it into two trains which are exactly the same length, then the size of the original train (or number) is even. If you can not do it, then the size of the original train (or number) is odd. Lets do two examples to show this. We'll use 14 and 15 to see which one is odd and even.
14 size bar (left) and
the 15 size bar (right)The 14 size bar works with two 7 size bars.
The 15 size bar doesn't work with either the 7 or the 8 size bars.
Exercise - Use the bars to find out which numbers are even and odd for all numbers from 0 to 30.
To check the results click here: answers.
Instructions on how to use Integer Bars' Applet
Table of Contents
Learning to Add and Subtract
Last Updated: Friday, 28-Feb-2003 00:21:26 GMT
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