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.) 4 2 + 3 3 = 16 + 27 = 43 4.) Is 5,310 divisible by 3 ? Yes. - PowerPoint PPT Presentation
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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"!