1. You Don’t Have to be Afraid….
Word ProBLEMS
You Don’t Have to be Afraid….

2. WORD PROBLEMS Look for KEYWORDS. Draw a PICTURE or VISUALIZE.
Create a PLAN.
ESTIMATE and think about your UNITS.
SOLVE for the answer.

3. Example
As you go through the presentation, work through the strategies to solve the following word problem:
Mrs. London fenced in her yard a year ago but the fence is already falling down. The new (more reliable) handyman is going to charge her $5 per foot of fencing. Last year, Mrs. London spent $1020 altogether to fence the perimeter of her yard. Her yard is 70 feet by 30 feet minus a 4-foot entrance, plus she tipped the person $20 last year. How much did she pay per foot last year? Is she being charged more than last year?

4. Find Operation Keywords
Addition
Subtraction
Multiplication
Division
plus
increased by
more than
altogether combined
total
sum
added to
both
in all
additional
extra
raised by
minus
decreased by
less than*
less
reduced by
lost
difference
subtracted from
left
remaining
dropped
fell
*switch the order
multiplied
increased (+) by a factor decreased by (-) a factor by
of times product
Every
Double (*2)
Triple (*3)
Quadruple (*4)
per
divided
rate of out of
split or shared ratio of
fraction of quotient of
each
percent

5. Find Other Keywords ≤ < ≥ > less than or equal to at most
no more than
minimum
is less than
is smaller than
below
greater than or equal to
at least
no less than
Maximum
is greater than
Is larger than
Above
Word
Math Symbol
Equals
Is/ Are/ Was/ Were / Will be
Same as
Equivalent to
Yields
Sold for
Results in
variable
unknown quantity
the number of
a number
an amount

6. Identify Keywords Keywords Per - indicates multiplication
Mrs. London fenced in her front yard a year ago. This year she is going to fence in her backyard. The new handyman is going to charge her $5 per foot of fencing. Last year, Mrs. London spent $1020 altogether to fence the perimeter of her yard. Her backyard is 70 feet by 30 feet minus a 4-foot entrance, plus she tipped the person $20. How much did she pay per foot last year? Is she being charged more than last year?
Keywords
Per - indicates multiplication
Altogether - indicates addition
Perimeter - indicates we will have to find the total distance around, indicates addition
Minus – indicates subtraction
Plus – indicates addition

7. Draw a Picture Represent the words using pictures. Draw:
a picture for every object
a circle or bar to represent fractions
a number line

8. Draw a Picture
30 feet
70 feet
4 feet

9. Create a Plan Decide: how many steps you need operations
Then, test with numbers to see if it will produce the predicted answer.

10. Create a Plan 1) Find perimeter.
Perimeter = = 196 feet
2) Find the unknown.
The question asks about price per foot. So the unknown will be the price per foot. Let x= price per foot.
3) Write an equation.
See next slide
4) Estimate an answer.
196x + 20 = 1020, you can estimate the answer with 200x = So you should expect the answer to be about 5.
5) Solve and compare to estimate.
NO SPOILERS! Keep reading!

11. Create a Plan 196x + 20 = 1020 so…… 70 feet 30 feet
THINK: If fencing costs $2 per foot then, the cost for this side would be $30*2. In general, the cost is the length * price per foot.
30 feet
4 feet
Price per foot = x
Perimeter = 196 feet
Total cost = 1020
196x = cost of fencing
20 = tip
196x + 20 = total cost
so……
196x + 20 = 1020

12. Think about Units
Does the answer seem reasonable? Ask yourself the following questions:
What type of quantity was mentioned in the question?
What were my original units?
Can my answer be negative?
Can my answer be a decimal or fraction? (People can’t be fractional!)
Which quadrant should my answer be in?
Can my answer be that large/small given what I started with?
Can my answer be that large/small given what I know about the world?

13. Think about Units The question asks you to find price per foot.
The units for your answer will be dollars per foot ($/foot)
Dollars cannot be negative in this case.
The answer should have two decimal place values.
The answer should be close to our estimate of $5/foot.

14. Solve for the Answer 196x + 20 = 1020 -20 -20 196x = 1000 196 196
196x = 1000
x = $5.10
Mrs. London paid $5.10 per foot of fencing last year. She is paying slightly less than last year!
Note that we had to round our answer to $ The answer made sense given our estimate.

15. Another Example
A remote control car moves 1.5 feet every second. If the car starts 2 feet away from me, how long before it is in the next room (10 feet away)? 1 2 3 4 5 6 7 8 9 10
1 sec.
2 sec.
3 sec.
After 3 seconds, = 3(1.5) or s(1.5)
So… s= 10 and solve to get ~5.3 seconds