Solution: We can use the following Binary number system to solve this puzzle. First, number the bottles from 1 - 1000. Convert the bottle number to binary. Number the rats D1, D1, D2, ...., D9 representing the binary digits. Then, rats will drink wine in the following rule: Binary number of bottle 1 is 0000000001. Rat D1 will drink wine from bottle 1 Binary number of bottle 5 is 0000000101. Rats D1 and D3 will drink wine from bottle 6. Binary number of bottle 12 is 0000001100. Rats D3 and D4 will drink wine from bottle 12. ..... Hence, by seeing which rats have died, we can figure out which bottle is poisoned. For example: If rats D3 and D4 die, then we know the bottle 12 is poisoned. 1000 bottles can be represented with 10 binary digits (binary number of bottle 1000 is 1111101000) , and we have 10 rats (each rat represents 1 digit), so we are able to use 10 rats to test 1000 bottles of wine.
Thanks Danielle, Wanyi and Anwar! Your lesson plan is OK, but I have a few suggestions as well:
ReplyDelete• The 4-minute video is cute, but it doesn't seem to add much that's really helpful from my point of view. It is mostly procedural/ mnemonic (how to and procedures) rather than promoting deeper relational understanding. Is it really worth taking up 1/3 of your lesson?
•Much of your lesson is a recap of procedures. What is new in what you are teaching the group?
•I'm not clear from the slides or the lesson plan exactly what the problems are that you are asking your class to solve. The problems on the slides seem to include the solutions already.
Think it over, and see if you can make some small tweaks to the lesson to make it clear what is new and what you would like the students to engage in. (And if you want to use the video, go for it -- just think about what it might add to the students' knowledge, attitudes, etc.)