Math 104 - Cooley Math for Elementary Teachers I OCC

Math 104 - Cooley Math For Elementary Teachers I OCC

Activity #1 – Problem Solving

California State Content Standard – Mathematical Reasoning – Grade Six 1.0 Students make decisions about how to approach problems: 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.

 Exercises:

1) Using the numbers 1 through 8, place them in the following eight squares so that no two consecutive numbers are in touching squares (touching includes entire sides or simply one point; in other words, not touching across, up or down, or diagonally).

2) Place the whole numbers 1 through 9, each only once, in the circles in the triangle so that the sum of the numbers on each side is 17.

3) Place the numbers 1 through 8 in the circles on the vertices of the accompanying cube so that the difference of any two connecting circles is greater than 1.

4) Who am I? If you multiply me by 12 and subtract 17, the result is 91.

5) Solve the following number riddle:

a) The sum of the digits is 14. b) The number is a multiple of 5. c) The number is in the thousands d) The number is not odd. e) The number is less than 2411.

What number is the largest such number? Are there other possibilities?

1 Math 104 - Cooley Math For Elementary Teachers I OCC

Activity #1 – Problem Solving 6) Solve the following number riddle:

a) I am a positive integer. b) All my digits are odd. c) I am equal to the sum of the cubes of my digits. d) I am less than 300.

Who am I?

7) How many squares are there in the figure to the right? Are you absolutely sure?

Here are some more challenging ones for you to think about. Try these at home!

8) What is the next term in the sequence? (Hint : It is not an “ E ”!)

O , T , T , F , F , S , S , E , ___

9) In the movie “Die Hard With a Vengeance” the hero was told that in order to stop an explosion from taking place he would have to place a plastic jug with exactly four gallons of water in it on a scale. The wrong weight would set off the big bang. Unfortunately, the villain had left only two jugs, one that would hold exactly 3 gallons and one that would hold exactly 5 gallons. There was a fountain with enough water in it. Explain how to get exactly 4 gallons into the 5 gallon container? (There are no other measuring devices of any kind nearby!) (Note: If you have a solution, challenge yourself by\ finding another!)

10) Four people named A, B, C, and D, are trying to cross a tunnel-bridge. The problem is that the tunnel is extremely dark. There is only one flashlight and no more than two people can cross the bridge at the same time with the flashlight. The other problem is that person A can cross the bridge in 1 minute, person B can cross the bridge in 2 minutes, person C can cross the bridge in 5 minutes, and person D can cross the bridge in 10 minutes. All 4 people in the group must be on the other side of the bridge in exactly 17 minutes. How can this be done?

Example: C & D take the flashlight and cross. Time going across is 10 min. (You take the max of both times.) Then, C goes back with the flashlight. Time going back is 5 min. Total time is 15 min. Now, C takes A over with the flashlight. Time going across is 5 min. Total time is 20 min. Then, A goes back with the flashlight. Time going back is 1 min. Total time is 21 min. Finally, A takes B over with the flashlight. Time going across is 2 min. Total time is 23 min. So the total time was 23 minutes. we want a time of exactly 17 minutes. Good Luck!