How much is a Right Answer worth?

jazzydoeΛογισμικό & κατασκευή λογ/κού

30 Οκτ 2013 (πριν από 4 χρόνια και 8 μέρες)

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How much is a
Right Answer
worth?


This is a course in Algebraic Skills


It is
not

a course in Right Answers


It is
not

a course in Good Guessing


Skills are proven by showing Work


Word Problems exercise both your language
skills and your math skills.


Work hard in this section


it’s important

1.4

1

Sect. 1.4

Introduction to Problem Solving


The 5
-
Step Strategy

Write an
answer statement

with letters for unknowns

Update

the answer statement

1.4

2

Familiarizing

means

Understanding a Word Problem


Skim over the whole problem statement.


HW: write problem number and brief
summary of the problem


Reread it: Verbalize it, perhaps aloud.


Find the Question asked and think how to
reword it. Pick meaningful variable letters.


HW: Write it as a partial Answer


[gap(s) where information will go]


HW: Put the variables(s) next to the gap(s)


As needed, look up formulas & definitions


HW: Sketch diagrams if needed, make notes


HW: Set up tables that correspond to
formulas, label each column & row


Understanding is a critical step …

You still need to Translate, Solve and Check

23.

Day Care.
A family living in Boston,
Massachusetts pays $1089 per month for
full
-
time day care for their toddler. This is
11/4 of what they paid for comparable day
care when they lived in Billing, Montana.
How much did child care cost in Billings?

23. Day Care
-

$1089 Boston, find cost




(b) $
for Billing care


Billings probably cheaper









25. Photography
-

BOOK

HW

1.4

3



It will take you (t) hrs to go 25 miles upstream.

1.4

4

2.
Translate

to an Algebraic Formula


What kind of formula should be used?



Choose meaningful letters for variables,

and refine the table according to the formula





Write the formula: 25 =
9t and Solve

It will take you (t) hrs to go 25 miles upstream.

1.4

5

Number
-
Value Problems

Some problems deal with
quantities that have a value. In these
problems, we must distinguish between the
number of
and the
value of
the unknown quantity.
For problems such as these, we
will use the relationship

Number value = total value

Examples:

1.
How much did 4 used Xbox games cost if they are $22.50 each?

2.
IBM stock rose $2.40/share. What is my profit for 50 shares?

3.
It cost me $120 for DVDs priced at $6. How many did I buy?

4.
Quon

bought 83 old records for $180. What’s each one worth?

1.4

6



The price of the home theater system is (p)
$ 549



3. Price before tax.

Price + Tax = Total Price

p + 0.06p = 581.94

1.06p = 581.94


p = 581.94/1.06


p = 549

1.4

7

Geometric Problems

These types of problems rely on formulas from geometry.

Examples:

1.
Perimeter: Of a rectangle 2W + 2L = P


Of a triangle P = S
1

+ S
2

+ S
3

Of a circle P =
π
d

2.
Area: Of a rectangle W(L) = A


Of a triangle A = B(H)/2 Of a
circle A
=
π
r
2

3.
Triangles: Sum of 3 angles = 180 degrees

1.4

8

Perimeter of a square= 4 times length of one side

Total glazing length= sum of the two perimeters

200 = 4s + 6s

200 = 10s

20 = s

a = 4s = 4(20) = 80

b = 6s = 6(20) = 120

If s = length of a side of the little skylight,

a = 4s = cut length of the shorter piece of glazing and

b = 4(1.5s) = 6s = length of the longer glazing

The glazing should be cut into two pieces,

one (a)
80

in. long, the other (b)
120

in. long

4. Cutting the skylight glazing.

1.4

9

Number Problems

Some problems deal with
several numbers or quantities, but
only give you the total number. They also give you some
relationship between the numbers. For
problems such as
these, we will
need to express both numbers using different
expressions using a single variable name.

Examples:

1.
Two sequential mile
-
markers add up to 249. What are they?

2.
One number is three times another. Their sum is 76. They are?

3.
Stocks are $3 more than bonds. Ten each cost $230. Each cost?

4.
Ten coins are worth $1.70. How many quarters and
nickles
?

1.4

10



first number = x

second number = y = 3x


6

third number = z = (2/3)x + 2


x + 3x


6 + (2/3)x + 2 = 150

(14/3)x


4 = 150

(14/3)x = 154

(3/14)(14/3)x = (154) (3/14)

x = 33

y = 3(33)


6 = 99


6 = 93

z = (2/3)(33) + 2 = 22 + 2
= 24

The largest of the three numbers is
93

.

5. Three different numbers.

1.4

11

Rate/Time/Distance Problems

These
problems deal with
the formula (rate)(time)=distance.
Sometimes, wind and river current speed are present. For
problems
like these
,
it is often helpful to build an RT=D table
to organize the known numbers and unknown quantities.

Examples:

1.
Bill walks north at 3mph, Sue walks south at 4mph. After 4 hours,
how far apart are they?

2.
It takes Pat 6 hours to row upstream and 4 hours to row back
downstream. The current is 2mph. What is Pat’s rowing speed?

3.
A UFO goes west coast
-
to
-
coast in 22 minutes, against the 100mph
jet stream. Going east only takes 18 minutes. UFO speed?

1.4

12

Rate ∙ Time = Distance

Example


SEARCH AND RESCUE


Two search
-
and
-
rescue teams leave base camp at the same time,
looking for a lost child. The first team, on horseback, heads north
at 3 mph, and the other team, on foot, heads south at 1.5 mph.
How long will it take them to search a distance of 18 miles
between them?



Meaningful variable names:



t


time


State the form of the answer:



It will take the search teams ______ hours to search all 18 miles.


Formula?


distance = (combined rate) times (time)


18 = (3 + 1.5)t


t = 18 / 4.5 = 4

1.4

13

Next time


1.5

Formulas, Models & Geometry


1.6

Properties of Exponents




1.4

14