Using the math formula chart for conversions and measurement

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Using the math formula chart for conversions and
measurement

• Conversions
• Measuring (part 1)
• SFHS 2008

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Using the MathFormula 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.

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Lets 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!

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• 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.

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Mass and weight are considered the same in Math,
but not in Science. . .
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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.
• Dont guess LOOK!

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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

Who is the person that the problem names and yet
doesnt give you any hint about time? That is the
person who has the x minutes for
time. Huan Melanie x minutes Susie David
Huan used it three times as long as Melanie
so Huan 3x minutes Melanie x
minutes Susie David
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 Melanies time.
David used it 15 minutes longer than Huan so Huan
3x minutes Melanie x minutes Susie David 3x
15 minutes
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.
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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 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)
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 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.
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
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!!!!
Quit the y on your calculator to go back to the
home screen. Now type in Susies time expression,
using 15 in place of x. (3x1515)/2 and then
enter
Susies time is 30 minutes so the correct answer
is option H. Option F is Davids time and option
G is Huans time.
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Lets move onto the rulers that are on the
formula chart.

• Just about every TAKS test has required students
  to measure!

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There are two rulers on the Mathematics formula
chart.

• One is a centimeter ruler.
• The other is an inch ruler.

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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!

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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

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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.

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Now, we will deal with the inch ruler.

• In Part Two 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)

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Lets study the inch ruler.

• The longest line refers to the inch.

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.
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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.
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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.
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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.
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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 13.5 in.3

Hope you chose G.
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Okay---Now you do some problems on the back page
for practice
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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 0.105 joule of
energy every 30 seconds, what will its energy be
after 8 minutes? F 2.18 joules G 1.68
joules H 3.02 joules J 2.29 joules
480 seconds/ 30 seconds 16 times that the
particle loses 0.105 joule.
3.86 joules 16(0.105 joule) 2.18 joules
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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 worlds 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 540 mi
36 mi/h( ¼ h) 9 miles
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Checking

• Formula is
• S 6s2.
• Measuring the length of a side, we got
• 1¼ inch (1.25)
• S 6(1.25 in.)2 9.375 in2

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Well have more measurement problems to work on
in part two .

• Dont forget
• about
• Study Island

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Using the math formula chart for measurement

• Part 2 Applications

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In Part One , we spoke about conversions on the
formula chart.

• We also spoke about the inch-ruler that was on
  the chart and did a problem requiring us to
  measure with that ruler.
• Now, we are going to concentrate on the
  centimeter ruler. More questions on the released
  TAKS tests have use metrics. In addition, only
  the metric ruler is on your science formula chart.

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Lets first talk about the centimeter ruler.

• The longest line refers to the centimeter.

Since there are 10 millimeters in a centimeter,
each centimeter is divided into ten equal-sized
spaces.
Each of those slash marks represents a tenth of a
centimeter.
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Lets use the centimeter ruler to do an actual
TAKS problem.

• You have on your paper the same problem as shown
  here.

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This question was 60 on the Feb 2006 Exit
Level TAKS test.

• Use the ruler on the Mathematics Chart to measure
  the dimensions of the net of the rectangular
  prism shown below to the nearest tenth of a
  centimeter.

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Which of the following best represents the
dimensions of the rectangular prism?

• F. 7.5 cm by 1.5 cm by 3.0 cm
• G. 10.5 cm by 1.5 cm by 9.0 cm
• H. 10.5 cm by 3.0 cm by 9.0 cm
• J. 7.5 cm by 3.0 cm by 3.0 cm

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You should find the centimeter ruler on the
formula chart.

• Before you just start measuring everything, you
  need to figure out what this figure actually
  looks like when it is together.

We would need to measure length.
We would need to measure width.
And we would need to measure height
The figure is a rectangular prism. Its dimensions
would have length, width, and height.
Right now, measure the dimensions and record them
on your paper.
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Here are your options, again. Which answer choice
is best?

• Which of the following best represents
• the dimensions of the rectangular prism?
• F. 7.5 cm by 1.5 cm by 3.0 cm
• G. 10.5 cm by 1.5 cm by 9.0 cm
• H. 10.5 cm by 3.0 cm by 9.0 cm
• J. 7.5 cm by 3.0 cm by 3.0 cm

Hopefully, you selected F as the best choice.
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Many of the questions requiring measurement have
asked for volume or surface area.

• You will need to look at the formula chart for
  the necessary formula as well as for the ruler.

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Apr 04 38 The net of a cylinder is shown below.
Use the ruler on the Mathematics Chart to measure
the dimensions of the cylinder to the nearest
tenth of a centimeter
What is the total surface area of this cylinder
to the nearest square centimeter?
Give this one a try on your own, first.
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Apr 04 38 The net of a cylinder is shown below.
Use the ruler on the Mathematics Chart to measure
the dimensions of the cylinder to the nearest
tenth of a centimeter
What is the total surface area of this cylinder
to the nearest square centimeter?
S 2pr(h r)
First, circle the phrase that tells us what we
are looking for---total surface area.
Next, look on the chart for the corresponding
formula for a cylinder. Copy that formula on your
paper.
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Apr 04 38 The net of a cylinder is shown below.
Use the ruler on the Mathematics Chart to measure
the dimensions of the cylinder to the nearest
tenth of a centimeter
What is the total surface area of this cylinder
to the nearest square centimeter?
Height
S 2pr(h r)
Now, find the radius (r) and the height of the
cylinder (h) on the net. Mark them.
The height of a cylinder will NEVER have the
circles attached.
The radius is easy on this oneit is already
marked.
Be careful on that height!!!!!
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Apr 04 38 The net of a cylinder is shown below.
Use the ruler on the Mathematics Chart to measure
the dimensions of the cylinder to the nearest
tenth of a centimeter
What is the total surface area of this cylinder
to the nearest square centimeter?
So, do you have an answer?
?
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Added problem.

• V Bh
• The base is a circle so
• V pr2h
• V p(1.7 cm)2(7 cm)
• 63.55 cm3

Which of the following best represents the volume
of this cylinder? A 110 cm3 B 94 cm3 C 75
cm3 D 64 cm3
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Try the next two problems on your own. Well go
over them in a few minutesjust to check that you
worked them out correctly.

• Perfect practice makes perfect.

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25 The net of a right triangular prism is shown
below. Use the ruler on the Mathematics Chart to
measure the dimensions of the right triangular
prism to the nearest centimeter.
Find the total surface area of this right
triangular prism to the nearest square
centimeter?
TSA Ph 2B P is perimeter of Base, B
is rt triangleneed measures of a 3 sides
h is height of prismtriangles are NOT attached
to height B is area of BaseBase is
triangleheight of triangle times base of
triangle (they form the right angle) divided by 2
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For the triangular base h 4 cm, b 3 cm,
hypotenuse 5 cm (Pythagorean triple!), P 12
cm, B (4 cm)(3 cm)/2 6 cm2 For the prism h
3 cm
TSA Ph 2B (12 cm)(3 cm) 2(6cm2)
48 cm2
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For the triangular base h 4 cm, b 3 cm,
hypotenuse 5 cm (Pythagorean triple!), P 12
cm, B (4 cm)(3 cm)/2 6 cm2 For the prism h
3 cm
TSA Ph 2B (12 cm)(3 cm) 2(6cm2)
48 cm2
?
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Added problem
V Bh Base is a triangle so V (bhT /2)hP
((3 cm)(4 cm)/2)(3cm) 18 cm3
Use the same net above. Which of the following
best represents the volume of this right
triangular prism? F 18 cm3 G 60 cm3 H 48
cm3 J 36 cm3
?
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Last one!

• This problem is a bit different.
• Did you see the word regular?

That word indicates that all of the sides of the
pyramid have the same length.
We can now find the area of ONE triangle,
multiply it by 4, and have the total area.
A (bh)/2 ((3 cm)(2.7 cm))/2 4.05 cm2
?
TA 4(4.05 cm2) 16.2 cm2
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Remember to come on Tuesdays, Wednesdays,
Thursdays, and Saturdays for the next 2 weeks.We
will have something new each time!

• Thursday, from 230 - 430 April 16 Objective 9
  
• Saturday, April 18 from 900am noon - EXIT
  Level Students ONLY
• Objectives 1, 2, 3, and 4,
• Tuesday, from 230 - 430 April 21 Objective 2
  
• Wednesday, April 22 from 230 400 - All
  Students
• Calculator Review
• Thursday, from 230 - 430 April 23 Objective
  10
• Saturday, April 25 from 900- noon - EXIT Level
  Students ONLY
• Objectives 6, 7, and 8
• Saturday, April 25 from 900-noon- All Students
• 5, 9, and 10
• TESTING The week of April 27 May 1

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Thank you for coming today.AIM For TAKS
SUCCESS!!!