turn in homework for credit attendance4 min week 2 information updates1 min $15 class fee, room...
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Turn in homework for credit Attendance 4 min Week 2 information updates 1 min
$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