1. Agenda – Week 3 Turn in homework for credit Attendance 4 min
Week 2 information updates 1 min
$15 class fee, room parent
Week 2 homework review min
Organized List min
Make a Table
In-Class Practice min

2. 2. Problem Solving Strategies (Plan)
Today’s Topics
Tree Diagram
Organized list
Make a table
Drawing a picture or diagram
Making an organized list
Making a table
Solving a simpler related problem
Finding a pattern
Guessing and checking
Experimenting
Acting out the problem
Working backwards
Writing an equation

3. Making an Organized List
When a problem requires you to generate a large amount of data, a list may help you account for all possibilities and avoid repetitions.
Bull’s Eye! Three darts are thrown at the target shown below. Assume that each of the darts lands within one of the rings or within the bull’s eye. How many different point totals are possible?
3 Darts Hit Bull’s Eye
2 Darts Hit Bull’s Eye
1 Darts Hit Bull’s Eye
0 Darts Hit Bull’s Eye
9+9+9=27
9+9+4=22
9+4+4=17
4+4+4=12
9+9+3=21
9+4+3=16
4+4+3=11
9+3+3=15
4+3+3=10
3+3+3=9 3 4 9
Answer: 10

4. Tree Diagram Review
Words, Words, Words! How many different three-letter “code words” can you make using the letters P, Q, and R if repetition of a letter is not permitted?
Use Tree Diagram
PQR PRQ QPR QRP RPQ RQP
Answer: 6

5. In-Class Practice
Problem: Suppose that four darts are thrown at the target with point values of 3, 5, and 7. How many different point totals are possible if each lands on this target? 3 5 7
Answer: 9
4 Darts Hit Bull’s Eye
3 Darts Hit Bull’s Eye
2 Darts Hit Bull’s Eye
1 Darts Hit Bull’s Eye
0 Darts Hit Bull’s Eye
=28
=26
=24
=24
= =20
=22
= =18
=16
=20
= =16
=14
=12

6. In-Class Practice
Problem: A domino has two square spaces on its face. Each of the two square spaces is marked with 1, 2, 3, 4, 5, or 6 dots, or it is left blank. A complete set of dominoes consists of one domino for each of the possible combinations of these markings. How many dominoes are in a complete set?
0,0
0,1 1,1
0,2 1,2 2,2
0,3 1,3 2,3 3,3
0,4 1,4 2,4 3,4 4,4
0,5 1,5 2,5 3,5, 4,5 5,5
0,6 1,6 2,6 3,6 4,6 5,6 6,6
Answer: 28

7. Making a Table
When a problem involves data that has more than one characteristic, an effective strategy is to organize the data into a table.
Displays data so it is easily located and understood, and missing data becomes obvious.
An invaluable aid in detecting significant patterns.

8. Making a Table
Take a Chance! Suppose that you roll two number cubes, each of which has faces numbered from 1 through 6. What is the probability of rolling a sum of 8 in the uppermost faces?
First Cube
Second Cube + 1 2 3 4 5 6 7 8 9 10 11 12
Answer: 5 out of 36

9. Making a Table
Barnyard Brainstorming: I know that there are 18 animals in the barnyard. Some are chickens and the rest are cows. I counted 50 legs in all. How many of the animals are chicken and how many are cows?
Observe the pattern: each time we exchange one cow for one chicken, there are 2 few legs. So, to reduce 72 to 50, we would exchange =22/2=11 cows for chickens. Thus, there will be 18-11=7 cows and 11 chickens.
Number of chickens 1 2 3 4 5 … ?
Number of cows 18 17 16 15 14 13
Number of legs 72 70 68 66 64 62 50
Answer: 7 cows and 11 chickens are in the barnyard