1. Using the math formula chart for conversions and measurement
Measuring (part 1)
SHS 2008

2. Using the Math Formula Page
You have been handed a formula page on which to take notes.
As we go over a formula, and what the parts represent, write down what the letters represent.
Being able to use, and using the chart will improve your score.

3. Let’s look at the Chart first . . .
This part of the chart gives you metric and customary length measurement units.
When an = sign is used, it means they can be interchanged so that all the units are the same.
These same units are useful to know for Science!

4. The next part of the chart deals with volume, these are liquid volume measurements.
Solid volume measurements are on the formula page side, and require cubic measurement units such as cm3 or ft3.

5. Mass and weight are considered the same in Math, but not in Science. . .

6. These are to help you with time conversions . . .
Remember, in a problem, units must be the same.
You can not calculate correctly if one unit is in days and another is in hours.
To change, use the factors given.
Don’t guess – LOOK!

7. Example: Four friends took turns using the stationary
bike at a health club. Huan used it three
times as long as Melanie. Susie used it half as
long as David, and David used it 15 minutes
longer than Huan. The four friends used the
stationary bike for a total of 2.5 hours. How
long did Susie use the stationary bike?
F 60 min
G 45 min
H 30 min
J 15 min
There are 60 minutes in every hour. 2.5 hours multiplied by 60 minutes per hour gives us a total time of 150 minutes.
Huan used it three times as long as Melanie so
Huan 3x minutes
Melanie x minutes
Susie
David
Who is the person that the problem names and yet doesn’t give you any hint about time? That is the person who has the “x” minutes for time.
Huan
Melanie x minutes
Susie
David
David used it 15 minutes longer than Huan so
Huan 3x minutes
Melanie x minutes
Susie
David 3x minutes
Now, to attack the problem. There are four people named here. Write down all of their names in a list.
Huan
Melanie
Susie
David
Read the rest of the problem again to fill in the other friends’ times based on Melanie’s time.
And finally, Susie used it half as long as David so:
Huan 3x minutes
Melanie x minutes
Susie (3x + 15)/2 minutes
David (3x + 15) minutes
This problem talks about minutes when speaking about individual times. However, total time is in hours. We need to convert hours to minutes so that we are working with the same unit of time.

8. Example: Four friends took turns using the stationary
bike at a health club. Huan used it three
times as long as Melanie. Susie used it half as
long as David, and David used it 15 minutes
longer than Huan. The four friends used the
stationary bike for a total of 2.5 hours. How
long did Susie use the stationary bike?
F 60 min
G 45 min
H 30 min
J 15 min
Do NOT jump the gun!!!!
Did you say that J is the answer?
Just because 15 minutes is option J does NOT mean that J is the answer.
Now, use the table feature to find the value of x when y = 150 minutes.
As you scroll down the table, you find that x = 15 minutes when y = 150 minutes.
Do NOT mess around with this complicated equation!!!
Type the left side of this equation into y= on your graphing calculator.
y = 3x + x + (3x + 15)/2 + (3x + 15)
Recall, just who used the bike for x minutes? Melanie.
Who does the problem ask about? Susie
If you immediately picked J without going back to see what you were looking for, you would have picked the wrong answer!!!!
Susie’s time is 30 minutes so the correct answer is option H.
Option F is David’s time and option G is Huan’s time.
Quit the y= on your calculator to go back to the home screen.
Now type in Susie’s time expression, using 15 in place of x.
(3x15+15)/2 and then enter
Since we know a total time for the four friends, we need to add all of their times together.
Huan + Melanie + Susie + David = 150 minutes
3x + x + (3x + 15)/2 + (3x + 15) = 150

9. Let’s move onto the rulers that are on the formula chart.
Just about every TAKS test has required students to measure!

10. There are two rulers on the Mathematics formula chart.
One is a centimeter ruler.
The other is an inch ruler.

11. At various times, the TAKS test has asked you to measure with one or the other.
The first year of TAKS, students were asked to measure with both rulers -- on the same test!

12. Very rarely does a TAKS question stop just at measuring.
Most questions ask you, after you find the necessary measurements, to:
Find the surface area
Find the composite area
Find the volume

13. The figures that you are asked to measure vary.
Usually you are given a net of a 3-dimensional figure.
You need to figure out which part(s) are necessary for finding the value they want.
Then, you are expected to correctly measure those parts and use the measurements to answer the question. The question almost always involves using some formula on the formula chart.

14. Today, we will deal with the inch ruler.
Please come back tomorrow when we will deal with the centimeter ruler.
More of the TAKS questions that have been released involve centimeters (but not all, which is why we need to work with inches, too)

15. Let’s study the inch ruler.
The longest line refers to the inch. 1 2 3
The next longest line, half way between the “inches” is the half-inch.
Half-way between the “halves” are the “fourths”.
And, half-way between the “fourths” are the “eighths”.

16. This problem was on the April 2006 Exit-level test.
20 Jackie made a rectangular prism to hold her earrings. The net of the rectangular prism is shown below.
Use the ruler on the Mathematics Chart to measure the dimensions of the rectangular prism to the nearest ¼ inch.
What is the volume of this rectangular prism to
the nearest cubic inch?
First, circle the phrase “volume of this rectangular prism”. You need to look at the chart and find appropriate formula.
Since, you are given a net, you need to imagine what this figure looks like in 3-D. The “B” is area of the rectangular base. What is the formula for that area? For the entire prism? Write it on your paper/test booklet.

17. This problem was on the April 2006 Exit-level test.
20 Jackie made a rectangular prism to hold her earrings. The net of the rectangular prism is shown below.
Use the ruler on the Mathematics Chart to measure
the dimensions of the rectangular prism to the
nearest ¼ inch.
What is the volume of this rectangular prism to
the nearest cubic inch?
Now, locate the inch ruler. Next, locate the slash that notes “fourths”.
Now, determine the lengths that you need. Volume requires a length, a width, and a height.

18. Now, use your inch ruler on your Mathematics chart to measure the length, width, and height of the prism.
Write down your measurements as you go.
Consult your paper again. We were asked to find the volume. What is the formula for finding the volume of a rectangular prism? Enter the measurements that you found and use the calculator to find the volume.

19. Here are the answer choices.
Which is closest to the volume of this rectangular prism?
F 4 in.3
G 1.3 in.3
H 8.5 in.3
J in.3
Hope you chose G.

20. Okay---Now you do some problems on the back page for practice

21. Checking:
One time unit is seconds; the other is minutes. We need the same unit.
Since 1 minute = 60 seconds, 8 minutes = 8(60) = 480 seconds
42 The energy of a certain particle is 3.86 joules. If this particle loses joule of energy every 30 seconds, what will its energy be after 8 minutes?
F joules
G joules
H joules
J joules
480 seconds/ 30 seconds = 16 times that the particle loses joule.
3.86 joules – 16(0.105 joule) = 2.18 joules

22. 36 mi/h( ¼ h) = 9 miles Checking:
One time unit is hours; the other is minutes. We need the same unit.
One hour is 60 minutes so 15 minutes is one-fourth ¼ of an hour.
6 The world’s fastest flying insect is the dragonfly. It can fly 36 miles per hour. If a dragonfly flew in a straight path at this rate, what distance would it fly in 15 minutes?
F 2 mi
G 9 mi
H 25 mi
J mi
36 mi/h( ¼ h) = 9 miles

23. Checking Formula is S = 6s2. 1¼ inch (1.25)
Measuring the length of a side, we got
1¼ inch (1.25)
S = 6(1.25 in.)2 = in2

24. We’ll have more measurement problems to work on tomorrow.
Not only should you come again, we want you to bring a friend or two!