CHAPTER 4: ANALYZING DATAPROBLEM 1There are 15 purple steels balls of similar size. There were almost of the same weight, expect one is slightly heavier than others. Using a double-pan balance, what is the minimum number of weights necessary to find the heavier balls?Step 1: Understand the problemClues / Information (asking question) 15 purple steels balls

Same size, similar weight

One slightly heavier balls - using a double-pan balance

Step 2: Devise a plan

The effective strategy Diagram methodStep 3: Carry out the plan Group of 3, there will be 5 groups (group A,B,C,D,E) Weight 1: Group A, B, C, D, if balance- the heavier balls in group E.

Separate the balls in group E, label x, y, z

Weight 2: if x, y are balance, the heavier ball is z.

A

B

C

D

E

Make comparison at each others.

AB

BA

AC

CA

AD

DA

AE

EA

So, if A=B, C, D and so E maybe the heavier ball.

E

X

Y

Z

If x=y

So, z

Z is the heavier ball.Step 4: Check the answer

Weight every ball compared to z (8 times)

PROBLEM 2Lorna Left foot has started to walk for exercise. She walked 1 mile the first week, 5 miles the second week, 9 miles the third week, 13 miles the fourth week, and 17 miles the fifth week. If she continues to increase her walking distance this way, in which week will Lorna first walk 37 miles?

Step 1: Understand the problemClues / Information (asking question) Lorna has started to walk

1 mile the first week

5 miles the second week

9 miles the third week

13 miles the fourth week

17 miles the fifth week

Step 2: Devise a plan

Look for a pattern

Make a table of the weeks and the number of miles walked each of the first four weeks

Step 3: Do the planWEEKMILES WALKED

1

2

3

41

5

9

13

How many more miles did Lorna walk in Week 2 than in Week 1?(5 1 = 4 more miles)

How many miles did Lorna walk in Week 3 than in Week 2?

(9 5 = 4 more miles)

How many miles did Lorna walk in Week 4 than in Week 3?

(13 9 = 4 more miles)

WEEKMILES WALKED

5

6

7

8

9

1013 + 4 = 17

17 + 4 = 21

21 + 4 = 25

25 + 4 = 29

29 + 4 = 33

33 + 4 = 37

Lorna will first walk 37 miles in the tenth week.

You may realize that you didnt have to extent the table all the way up to the tenth week to solve the problem. Notice that, the number of times that you add 4 miles is one less than the week number.Week 2: 1 x 4 = 4 additional miles

Week 3: 2 x 4 = 8 additional miles

Week 4: 3 x 4 = 12 additional miles

In the week that Lorna first walks 37 miles, she has added 36 miles to the original distance of 1 mile. Because there are 36 4 = 9 groups of 4 in 36, it must be the tenth week, since the week number is one more than the number of groups of 4 miles added.

Step 4: Check your answer

Solving the problem by observing patterns in two different ways, and getting the same answer, provides a check on the solution.PROBLEM 3Hassan was given a jug (unlabelled) and two containers of 4 liters and 7 liters. Using these two glasses, how can Sahara measure exactly 3 liters and 9 liters of water into the jug, and then followed by 11 liters and 13 liters. Think of different possible combinations for measuring of liquid capacity.Step 1: Understand the problem Use two label glasses of 7 liters and 9 liters.

Measure 3 liters, 9 liters, 11 liters, and 13 liters.

Possible combinations?

Jug 7 liters4 litersStep 2: Devise a plan

Experimenting is an effective strategy.

Step 3: Carry out the plan To find how can get 3 liters

Fill up the water into 4 liters of the glasses.

Then pour off the water into 7 liters of the glasses.

The remaining is 3 liters.

7 liters - 4 liters = 3 liters To find how to get 9 liters

7 liters - 4 liters = 3 liters

3 litersAnd then pour into the jug.

3 liters + 3 liters + 3 liters = 9 litersAdd 3 more liters twice into the jug: 3 liters + 6 liters = 9 liters

To find how to get 11 liters

7 liters + 4 liters = 11 liters

To find how to get 13 liters

7 liters + 3 liters + 3 liters = 13 liters

Step 4: Check the answer

3 liters = (7 4) liters

9 liters = (7 4) liters + (7 4) liters + (7 4) liters 11 liters = (7 + 4) liters 13 liters = 7 liters + (7 4) liters + (7 4) litersPROBLEM 4

Last year, Cara Caker invited 10 children to her birthday party. This year, she invited 35 children. What is the percent increase from the number invited to last years party to the number invited to this years party?

Step 1: Understand the problemClues / Information (asking question) Last year, she invited 10 children This year, she invited 35 children What the percent increase?Step 2: Plan a strategyFirst, find the increase in the number of children invited from last year to this year.Then, find the ratio of the increase to the number invited last year.

Change the ratio to a percent.

Step 3: Do the plan

Find the increase in the number of children invited.

35 10 = 25

From the ratio of the increase in number to the number invited last year

Increase = 25

Number last year 10

Change the ratio to a percent by dividing, multiplying by 100, and adding a percent sign. 25 10 = 2.5 = 250%

There was a 250% increase in the number of children invited from last year to this year. (Remember that you may also use a proportion to find the percent.)Step 4: Check your work. Work backwards.

Check your division with multiplication.

2.5 x 10 = 25 more children invited this year than last year.

Check your subtraction with addition. 25 + 10 = 35, the number of children invited this year.

Percent of discount or decrease and percent of increase or inflation are used in business, in shopping, and in population studies, to name just a few applications.