Introduction to Integers and Integer Arithmetics

Markus Winkler, May 25, 2015

This GeoGebra book contains a few applets to visualize and practise Integer arithmetics.

Table of Contents

  1. Introduction
    1. Thermometer
    2. Two Thermometers
  2. Integer Addition and Subtraction
    1. Number line
    2. About Integers
    3. Addition of integers with arrows
    4. About Integer Addition and Substraction
    5. Integer game - Addition
  3. Integer Multiplication and Division
    1. About Integer Multiplication and Division
    2. Integer Multiplication
    3. Integer Division
    4. Integer game - Multiplication
  4. Conclusion
    1. Integer Arithmetics Exercises
    2. The Integers Song

1.

Introduction

Introduces Integers by using base knowledge about thermometers.

  • 1. Thermometer
  • 2. Two Thermometers

1.1.

Thermometer

Below you see a common Thermometer with a Celsius scale.[br]By pressing the "New temperature" button it will display a random temperature.
Task:[br]Read off the corresponding temperatures and write them down.[br]In which relation are the temperatures below zero to the temeratures above zero?[br]What role does the "-" sign have?
– Markus Winkler

1.2.

–

2.

Integer Addition and Subtraction

  • 1. Number line
  • 2. About Integers
  • 3. Addition of integers with arrows
  • 4. About Integer Addition and Substraction
  • 5. Integer game - Addition

2.1.

Number line

Imagine that you tilt the thermometer and put everything away except its scala.[br]Then you would get something like below, where the two points A and B represent the values of two seperate thermometers.
Tasks:[br]1) Calculate the difference between the two values on the scala of A and B.[br][br]2) Tick the box "Show arrow" and try to find out, what the red arrow exactly means.[br][br]3) Tick the box "Show calculation" to see the background calculation.
– Markus Winkler

2.2.

–

2.3.

–

2.4.

–

2.5.

–

3.

Integer Multiplication and Division

  • 1. About Integer Multiplication and Division
  • 2. Integer Multiplication
  • 3. Integer Division
  • 4. Integer game - Multiplication

3.1.

About Integer Multiplication and Division

Multiplication and Division of integers work similar as you have learned before.[br][br]Just multiply or divide the values of the two integers and then consider, that if the two integers have the same sign the result will be positive, if their signs are different, then the result will have a negative sign.[br][br][center][b](+) * (+) = (+)[br](-) * (-) = (+)[br](+) * (-) = (-)[br](-) * (+) = (-)[br][br](+) : (+) = (+)[br](-) : (-) = (+)[br](+) : (-) = (-)[br](-) : (+) = (-)[/b][/center]
– Markus Winkler

3.2.

–

3.3.

–

3.4.

–

4.

Conclusion

  • 1. Integer Arithmetics Exercises
  • 2. The Integers Song

4.1.

Integer Arithmetics Exercises

With this applet you can practise integer arithmetics. Just figure out the result of the displayed calculation and check it via the "Show result"-checkbox.
– Markus Winkler

4.2.

–

Information