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.
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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
3 + n is an "ALGEBRAIC EXPRESSION"
Algebraic Expressions consist of Numbers, Operations, and Variables.
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
3a ÷ b for a = 4 and b = 2 ?
(3 x 4) ÷ 2 = 12 ÷ 2 = 6
Very Good! Let's move on!
to have an organized problem-solving plan.
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.)
-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.
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.
signed up to play baseball. If the league
assigns 15 players to each team, how many
teams will there be?
Each team has 15 players
Total 525 boys
Total no of players = No of teams x No of players per team
No of teams = 525/15 = 35
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
The sum of four coins is thirty-two cents.
What are the coins?
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
A quarter, a nickel, and 2 pennies
strategy to find solutions for equations.
In the equation x + 8 = 12, which value for x would make
the equation true?
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
3.) Identify the solution for 9 + x = 17
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!
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.)
per second. How far does Jupiter travel in
Speed of Jupiter = 8 miles per second
In one second Jupiter travels 8 miles
In one hour = 60 x 60 seconds
Therefore, in one hour Jupiter will travel
= 60 x 60 x 8
= 28,800 miles
1.) In 1990, the population of Sacramento, CA was 370,000.
In 2000, the population was 407,000. How much did the
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:
6, 11, 16, 21, ___, __, ___
from 1 through 9 whose sum is 23. Find the
1, 5, 8 and 9
5.) Identify the solution of the equation:
66 = z - 23
Answer to #4:
An organized problem solving strategy is UPS
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.