OBJECTIVE: Problem Solving Plans and Strategies

CONFIDENTIAL 1

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 2

3 + n is an "ALGEBRAIC EXPRESSION"

Numbers

Operations

Variables

Algebraic Expressions consist of Numbers, Operations, and Variables.

CONFIDENTIAL 3

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 4

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 5

When solving math problems, it is often helpfulto have an organized problem-solving plan.

U

PS

nderstand

lan

olve

CONFIDENTIAL 6

UTo

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 theimportant facts in the problem.)

CONFIDENTIAL 7

Next, we must

Plan

-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

plussumtotalin all

Subtract Multiply Divide

minusdifferenceless

timesproductof

quotient

CONFIDENTIAL 8

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

CONFIDENTIAL 9

On a beautiful spring day, 525 boyssigned up to play baseball. If the leagueassigns 15 players to each team, how many teams will there be?

U

P

S

nderstand

lan

olve

readidentify facts

estimatestrategy

use operation(s)find answer

Each team has 15 playersTotal 525 boys

No of teams = 525/15 = 35

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

CONFIDENTIAL 10

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

Guess-And-Check Strategy

This strategy is an efficient way to narrow down thefield of possible answers. Examine the problem carefully,choose a possible answer, and then check to see if it iscorrect!

CONFIDENTIAL 11

For example,

The sum of four coins is thirty-two cents.What are the coins?

To solve1. 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 12

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 makethe equation true?

a.) 2

b.) 3

c.) 4

CONFIDENTIAL 13

Let's try a few practice problems:

1.) An adult male walrus weighs about 2,670 pounds. An adultfemale walrus weighs about 1,830 pounds. Their tusks

measureabout 3 feet in length and weigh about 10 pounds. How

much less does an adult female walrus weigh than an adult male

walrus?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?

3.) Identify the solution for 9 + x = 17a.) 7b.) 10c.) 8

2670-1830 = 840 pounds

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

= 12 + 13= 25

CONFIDENTIAL 14

LET US TAKE A SHORT BREAK!!!

CONFIDENTIAL 15

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 16

Explain whether each statement is True or False.

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

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

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

True

False

CONFIDENTIAL 17

If Jupiter orbits the sun at a rate of 8 milesper second. How far does Jupiter travel inone hour?

U

P

S

nderstand

lan

olve

Speed of Jupiter = 8 miles per second

In one second Jupiter travels 8 milesIn one hour = 60 x 60 seconds

Therefore, in one hour Jupiter will travel = 60 x 60 x 8 = 28,800 miles

CONFIDENTIAL 18

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?

2.) The Smith family wants to purchase a television set andpay for it in four equal payments of $180. What is thecost of the television set?

3.) Complete the pattern:

6, 11, 16, 21, ___, __, ___26 31 36

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

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

CONFIDENTIAL 19

4.) Brandon is thinking of four different numbers from 1 through 9 whose sum is 23. Find thenumbers.

1,5,8,9

5.) Identify the solution of the equation:66 = z - 23

a.) 88b.) 89c.) 90

Answer to #4:

1, 5, 8 and 9

CONFIDENTIAL 20

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

An organized problem solving strategy is UPSUnderstandPlanSolve

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

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

Know the "question" that is being asked.

Many times there is more information in the problem than you needto answer the "question"!