Warm Ups: Find the GCF

5a and 35a

6m3n and 8mn2

Warm Ups: Simplest Form

4bc/16b

12/16

6m/15m

x2y/3yz

Section 4.5: Reasoning Strategy

Accounting for All Possibilities

October 15th, 2008 Notes

There will be notes, so take them.

Read, Plan, Solve…

Find EVERY Possibility.

You need to be sure that you have found EVERY possible combination.

Organize lists and diagrams to help you keep track of possibilities as you find them.

Example Problem:

Mandy, Jim, Keisha, Darren, Lin, Chris, and Jen are friends. They want to take pictures of themselves with two people in each picture. How many pictures do they need to take.

Jim

Keisha

Darren

Lin

Chris

Jen

Mandy

Keisha

Darren

Lin

Chris

Jen

Jim

Darren

Lin

Chris

Jen

Keisha

Complete the list of paired friends.

What pattern do we see?

Friends and Pictures

The first person, Mandy, takes a picture with the 6 other friends.

Jim takes a picture with 5 other friends. Keisha takes a picture with 4 other friends. 3…2…1… So: 6 + 5 + 4 + 3 + 2 + 1 = 21 pictures are

taken. This is the same as the Tennis Player

Problem.

Sandwiches…

A sandwich shop serves turkey, ham, tuna, chicken, and egg salad sandwiches. You can have any sandwich using white, wheat, or rye bread. Suppose you eat there every day. For how many days can you order a sandwich that is different from any you have ordered before? Make a chart of all the possibilities.

Sandwiches

White Bread: Turkey, Ham, Tuna, Chicken, Egg Salad. (5 different sandwiches)

Wheat Bread: Turkey, Ham, Tuna, Chicken, Egg Salad. (5 different sandwiches)

Rye Bread: Turkey, Ham, Tuna, Chicken, Egg Salad. (5 different sandwiches)

5 + 5 + 5 = 15 different sandwiches. 15 Possibilities of sandwiches, 15 days of

different sandwiches.

Mystery Party…

Eight people are at a party. Everyone shakes hands once with everyone else. How many handshakes are there all together?

Make a list or chart. Solve…GO!

Mystery Party…

Person 1 shakes hands with 2, 3, 4, 5, 6, 7, and 8. Person 2 shakes hands with 3, 4, 5, 6, 7, and 8. Person 3 shakes hands with 4, 5, 6, 7, and 8. Person 4 shakes hands with 5, 6, 7, and 8. Person 5 shakes hands with 6, 7, and 8. Person 6 shakes hands with 7 and 8. Person 7 shakes hands with 8. Person 8 has already shaken everyone else’s

hands. 7+6+5+4+3+2+1+0 = 28 Handshakes.

Change In Your Pocket.

You have one penny, one nickel, one dime, and one quarter. How many different amounts of money can you make using one or more of these coins?

Make a list of all of the possibilities. 1 Penny, 1 Penny + 1 Nickel +…. How many different combinations

of change can you have?

Change In Your Pocket…

1P, 1N, 1D, 1Q 1P+1N, 1P+1D, 1P+1Q, 1N+1D, 1N+1Q,

1D+1Q 1P+1N+1D, 1N+1D+1Q, 1P+1N+1Q,

1P+1D+1Q 1P+1N+1D+1Q 15 Total Combinations of Coins.

Assignment #24

Page 189: Checkpoint 1: 1-13 All. Pages 192-193: 5, 7, 9 and 12.

Math Game!