Chapter 1: Number Relationships
Number tricks are everywhere and they are all based on mathematical principles. Tricks that seem mysterious can be explained, if you know the mathematics behind it!
Online there is a magical gopher who can read your mind to find out what number you are thinking. You have to solve the mystery of the mind-reading gopher and figure out how he knows what number you are thinking. To do this, you will analyze the numbers 1 to11 and test their divisibility against the numbers 1 to 100 in order to develop rules for divisibility. When you have gathered all of your data, create a presentation, using either multi-media or posters, to show your divisibility rules and reveal the secret of the mind-reading gopher. Work with a partner to complete this task.
To find out more about the mind-reading gopher, visit this link: The Magic Gopher
Follow the directions and see if the gopher can read your mind too!
It is now time to defeat the gopher. To accomplish the task, you will need: eleven copies of your data collection sheet 100 Chart and a highlighter or yellow broad tipped marker.
Test the divisibility of each number (1–11) on a separate data collection sheet (100 Chart). Highlight each number that divides evenly by your divisor. By doing this you will begin to see a pattern emerge for each divisor that you are testing. This information will be very helpful as you unlock the secret of the mind-reading gopher!
Analyze your patterns and the data that you have collected. Discuss your findings and record notes from your discussion.
Using your notes and data, write a "divisibility rule" for each divisor.
Go back to the gopher link. Which divisibility rule proves that the gopher is not really magic?
Create a presentation that shows how divisibility rules work and proves that the gopher isn’t magical after all. Be sure that you show how the gopher’s number trick works and how you came to your conclusions.
The Magic Gopher
Eleven copies of a 100 Chart
A poster or multi-media materials to create a presentation
|Understanding of Concepts
||Content is minimal or there are several factual erros. Has no understanding of divisibility rules.
||.Includes essential information about the topic, but there are 1 or 2 factual errors. Understands very few divisibility rules.
||Includes essential knowledge about the topic. Subject knowledge appears to be good. Understands most divisibility rules.
||Covers topic in detail and uses examples. Subject knowledge is excellent. Good understanding of divisibility rules.
||Use of font, colour, graphics, effects etc. is lacking, or distracts from the presentation content.
||Makes some use of font, colour, graphics, effects etc. but occasionally these detract from the presentation content.
||Makes good use of font, colour, graphics, effects etc. to enhance the presentation.
||Makes excellent use of font, colour, graphics, effects etc. to enhance the presentation.
||There was no clear or logical organization of the material.
||Content is logically organized for the most part.
||Content is logically organized. Makes use of headings or bulleted lists to organize the material.
||Content is very well organized. Makes use of headings or bulleted lists to organize the material.