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$15 class fee, room parent Week 2 homework review 15

min Organized List 20 min Make a Table In-Class Practice 10

min

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

Today’s Topics

•Tree Diagram•Organized list•Make a table

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

4

9

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

Answer: 10

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 DiagramQ

P R

R P

P

Q R

R Q

R

P Q

Q P

PQR PRQ QPR QRP RPQ RQP

Answer: 6

In-Class PracticeProblem: 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

57

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

7+7+7+7=28

7+7+7+5=267+7+7+3=24

7+7+5+5=247+7+5+3=22 7+7+3+3=20

7+5+5+5=227+5+5+3=20 7+5+3+3=187+3+3+3=16

5+5+5+5=205+5+5+3=18 5+5+3+3=165+3+3+3=143+3+3+3=12

Answer: 9

In-Class PracticeProblem: 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?

Answer: 28

0,00,1 1,10,2 1,2 2,20,3 1,3 2,3 3,30,4 1,4 2,4 3,4 4,40,5 1,5 2,5 3,5, 4,5 5,50,6 1,6 2,6 3,6 4,6 5,6 6,6

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.

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?

Answer: 5 out of 36

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 72-50=22/2=11 cows for chickens. Thus, there will be 18-11=7 cows and 11 chickens.

Answer: 7 cows and 11 chickens are in the barnyard

Number of chickens

0 1 2 3 4 5 … ?

Number of cows 18

17

16

15

14

13

… ?

Number of legs 72

70

68

66

64

62

… 50