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OBJECTIVE: Problem Solving Plans and Strategies

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OBJECTIVE: Problem Solving Plans and Strategies

WARM-UP:

1.) 6 ÷ (8 - 5) + 4 x 5 = 6 ÷ 3 + 4 x 5 = 2 + 4 x 5 = 2 + 20 = 22

2.) Evaluate 9 - 3x for x = 4; 9 – 3 x 4 = 9 – 12 = -3

3.) 42 + 33 = 16 + 27 = 43

4.) Is 5,310 divisible by 3? Yes

CONFIDENTIAL

3 + n is an "ALGEBRAIC EXPRESSION"

Numbers

Variables

Operations

Algebraic Expressions consist of Numbers, Operations, and Variables.

CONFIDENTIAL

The VARIABLES in an expression

can be replaced with any number.

3 + x

If I substitute a 5 for the x ...........

I have 3 + 5 or 8

This is how we Evaluate (or find the value of) the Expression

CONFIDENTIAL

Can you evaluate

3a ÷ b for a = 4 and b = 2 ?

(3 x 4) ÷ 2 = 12 ÷ 2 = 6

Very Good! Let's move on!

CONFIDENTIAL

When solving math problems, it is often helpful

to have an organized problem-solving plan.

U

nderstand

P

lan

S

olve

CONFIDENTIAL

To

U

nderstand the problem, we need to

-read the problem carefully

-identify the facts that we know

-identify what we need to know (WHAT IS THE QUESTION?)

-determine if we have enough or too much information

(Many students find it helpful to highlight or underline the

important facts in the problem.)

CONFIDENTIAL

Next, we must

P

lan

-determine how the facts relate to each other

-plan a strategy for solving the problem

-estimate your answer

Key words play an important role in determining which operations to use.

Add

Subtract

Divide

Multiply

minus

difference

less

quotient

plus

sum

total

in all

times

product

of

CONFIDENTIAL

And finally, we

S

olve the problem

-use your plan to solve the problem

-if your plan does not work, revise it or make a new plan

-find the solution

-make sure the answer makes sense and is close to your estimate

Keep in mind that numbers do NOT always appear in a problem in

the order in which they should be used to solve the problem.

CONFIDENTIAL

On a beautiful spring day, 525 boys

signed up to play baseball. If the league

assigns 15 players to each team, how many

teams will there be?

U

Each team has 15 players

Total 525 boys

read

identify facts

nderstand

Total no of players = No of teams x No of players per team

P

estimate

strategy

lan

S

No of teams = 525/15 = 35

use operation(s)

find answer

olve

CONFIDENTIAL

Another method to use when problem solving is the ...

Guess-And-Check Strategy

This strategy is an efficient way to narrow down the

field of possible answers. Examine the problem carefully,

choose a possible answer, and then check to see if it is

correct!

CONFIDENTIAL

For example,

The sum of four coins is thirty-two cents.

What are the coins?

To solve

1.Pick any four coins and find their sum.

2.If their sum is NOT 32 cents, choose four more coins.

3.Repeat this process until you have your answer

ANSWER:

A quarter, a nickel, and 2 pennies

CONFIDENTIAL

I can also use the Guess-And-Check

strategy to find solutions for equations.

In the equation x + 8 = 12, which value for x would make

the equation true?

a.)2

b.)3

c.)4

CONFIDENTIAL

Let's try a few practice problems:

1.) An adult male walrus weighs about 2,670 pounds. An adult

female walrus weighs about 1,830 pounds. Their tusks measure

about 3 feet in length and weigh about 10 pounds. How much less

does an adult female walrus weigh than an adult male walrus?

2670-1830 = 840 pounds

2.)On average, a dog lives 12 years. This is 13 years less

than a horse lives. What is the average life span of a horse?

Life span of a horse – 13 = Life span of Dog

Life span of horse = Life span of Dog + 13

= 12 + 13

= 25

3.)Identify the solution for 9 + x = 17

a.)7

b.)10

c.)8

CONFIDENTIAL

LET US TAKE A SHORT BREAK!!!

CONFIDENTIAL

TRY SOME BRAIN TEASERS!!!

What happened in 1961 and will not happen again until 6009?

The year reads the same upside down!

What letter is next in this sequence?M, A, M, J, J, A, S, O,__

N for November!

CONFIDENTIAL

Explain whether each statement is True or False.

1.) In the expression m + 8 , the variable m can have any value.

True

2.) In the equation m + 8 = 13 , the variable m can have any value.

False

(Notice the difference between an EQUATION and an EXPRESSION.)

CONFIDENTIAL

If Jupiter orbits the sun at a rate of 8 miles

per second. How far does Jupiter travel in

one hour?

U

Speed of Jupiter = 8 miles per second

nderstand

P

In one second Jupiter travels 8 miles

In one hour = 60 x 60 seconds

lan

Therefore, in one hour Jupiter will travel

= 60 x 60 x 8

= 28,800 miles

S

olve

CONFIDENTIAL

Let's see how well you can solve problem!

1.) In 1990, the population of Sacramento, CA was 370,000.

In 2000, the population was 407,000. How much did the

population increase?

Increase in population = 407,000 – 370,000 = 37,000

2.)The Smith family wants to purchase a television set and

pay for it in four equal payments of $180. What is the

cost of the television set?

Cost of TV = 4 times $180 = 4 x 180 = $720

3.)Complete the pattern:

26

31

36

6, 11, 16, 21, ___, __, ___

CONFIDENTIAL

4.)Brandon is thinking of four different numbers

from 1 through 9 whose sum is 23. Find the

numbers.

1, 5, 8 and 9

5.)Identify the solution of the equation:

66 = z - 23

a.)88

b.)89

c.)90

Answer to #4:

1,5,8,9

CONFIDENTIAL

Well Done! Let's review what we learned today!

An organized problem solving strategy is UPS

Understand

Plan

Solve

Know the "question" that is being asked.

Many times there is more information in the problem than you need

to answer the "question"!

Another strategy we can use is Guess-And-Check.

It is important to check our answer and see if it makes sense.

CONFIDENTIAL