1. Make up three examples of applicatons of addition of whole numbers.
2. Make up three examples of applicatons of subtraction of whole numbers.
3. Discuss which of the alternate subtraction algorithms are valid, and explain what would need to be done to make the invalid ones valid.
4, Make up three examples of applicatons of multiplication of whole numbers.
5. For each of your examples of applications of multiplication, write out the two associated division problems.
6. a) How would you measure 4 gallons using an 18 gallon bucket and an 8 gallon bucket? You can either fill up buckets or dump them out but you have to use whole buckets. You can assume that you have an unlimited source of water for filling the buckets and that you have a tub of unlimited capacity into which you can dump whatever is in your bucket at the time, or you can dump whatever is in your bucket down the drain. However, if you fill up a bucket you have to fill it up to the top no matter how much water is in the bucket at the time, unless you are dumping the contents of the other bucket into it, and if you dump a bucket out you either have to dump the whole thing either into the tub or down the drain or you have to dump it out until you fill up the other bucket, no matter how much water is in the other bucket at the time.
b) Using the rules from a) above, measure out 5 gallons.
7. Make up three examples of applications of addition of fractions and three examples of multiplication of fractions.
8. a) Use the Euclidean algorithm to find the GCD of 309 and 708.
b) Express the GCD as a difference of multiples of 309 and 708.
c) Given a 309 gallon bucket and a 708 gallon bucket, what is the smallestnumber of gallons you can measure and how would you measure it?
9. For each of your applications of addition of fractions, write out one of the related subtraction problems.
10. For each of your applications of multiplication of fractions, write out both of the related division problems.
11. Do the fraction word problems.
12. Compute the square root of 1263.
13. Given the following scores
14. Do the combination problems.
15. In the Christmas Carol, "The 12 Days of Christmas", how many gifts did her true love give to her?
16. Explain where all of the numbers in the computations of the poker hands come from.
17. Do the one sided and two sided balance beam problems.
18. Find a route in the map of the first city and the second city that crosses each bridge exactly once.
19. Do the Frog Problem.
20. Do the Locker Problem.
21. Do as many of the problems from Musser & Burger as time permits.