TEAS MATH Workbook Hints - Video 1 - Units vs. Square Units vs. Cubic Units
Summary
TLDRThis video serves as a guide to understanding standard and metric measurements, particularly focusing on units, squared units, and cubic units. The presenter clarifies the conversion between inches and feet, and how to calculate areas in square feet and square inches, as well as volumes in cubic feet and cubic inches. The video emphasizes the importance of squaring or cubing the conversion factor when moving from linear to area or volume measurements, offering a shortcut for conversions and inviting viewers to seek further hints on other workbook sections.
Takeaways
- 📚 The video is the first in a series of workbook hints for T's Math Workbook.
- 🔊 The presenter apologizes for a voice bug and encourages viewers to stay with the video.
- 📘 The workbook covers standard and metric measurements, with the latest version being 1.1.
- 🔗 Links to the workbook can be found in the video description for easy access.
- 📏 The video explains the difference between units, squared units, and cubic units using inches and feet.
- 👣 Twelve inches make up one foot, a basic conversion that is important to know.
- 📐 For square units, the area of a square foot is calculated as one foot times one foot, or 12 inches times 12 inches, equaling 144 square inches.
- 📏 To convert square inches to square feet, remember that 1 square foot is the same as 144 square inches.
- 🗽 When discussing cubic units, the volume of a cube with one-foot sides is one cubic foot.
- 🔢 The conversion for cubic inches to cubic feet is found by cubing the 12-inch measurement, resulting in 1,728 cubic inches per cubic foot.
- 🛑 The presenter advises not to memorize these conversions but to understand the process of squaring or cubing the conversion factor.
- 💬 Viewers are encouraged to leave comments for additional hints on other sections of the workbook.
Q & A
What is the main topic of this video?
-The main topic of this video is to explain the concepts of standard and metric measurements, focusing on units, squared units, and cubic units, particularly in the context of the T's math workbook.
What is the latest version of the T's math workbook mentioned in the video?
-The latest version of the T's math workbook mentioned in the video is version 1.1.
How many inches are there in one foot according to the video?
-According to the video, there are 12 inches in one foot.
What is the area of a square that measures one foot by one foot in square feet?
-The area of a square that measures one foot by one foot is one square foot, which can also be written as one foot squared.
How many square inches are there in one square foot?
-There are 144 square inches in one square foot, which is calculated by multiplying 12 inches by 12 inches.
What is the volume of a cube that measures one foot by one foot by one foot in cubic feet?
-The volume of a cube that measures one foot by one foot by one foot is one cubic foot.
How many cubic inches are there in one cubic foot?
-There are 1728 cubic inches in one cubic foot, which is calculated by cubing 12 inches (12 x 12 x 12).
What is a shortcut for converting square inches to square feet mentioned in the video?
-The shortcut for converting square inches to square feet is to square the conversion of inches to feet. Since 12 inches is one foot, squaring this gives 144 square inches, which is equivalent to one square foot.
What is the shortcut for converting cubic inches to cubic feet as explained in the video?
-The shortcut for converting cubic inches to cubic feet is to cube the conversion of inches to feet. Since 12 inches is one foot, cubing this gives 1728 cubic inches, which is equivalent to one cubic foot.
Why should one not memorize the conversions mentioned in the video?
-One should not memorize the conversions because the video provides shortcuts and methods to calculate them easily whenever needed, making memorization unnecessary.
What does the video suggest for viewers who need more hints on other sections of the workbook?
-The video suggests that viewers who need more hints on other sections of the workbook should leave a comment below, and the creator will be happy to post those hints.
Outlines
📏 Introduction to Units Conversion in the T's Math Workbook
This paragraph introduces the video as the first in a series of workbook hints, focusing on standard and metric measurements. The speaker acknowledges a voice issue and expresses the intent to release videos to support the newly released T's Math Workbook. The main topic discussed is the conversion between different units of measurement, specifically inches and feet, and their squared and cubic counterparts. The speaker clarifies the difference between linear units (inches and feet) and their squared (square feet) and cubic (cubic feet) forms, using visual examples to demonstrate the conversion from square inches to square feet and from cubic inches to cubic feet.
📐 Understanding Square and Cubic Units Conversion
The second paragraph delves deeper into the concept of square and cubic units, emphasizing the importance of understanding the conversion between these units for solving problems in the T's Math Workbook. The speaker provides a step-by-step explanation of how to convert one square foot to square inches, highlighting the common misconception that a square foot is equivalent to 12 square inches, which is incorrect. The correct conversion is 144 square inches for one square foot. Similarly, for cubic units, the speaker explains that one cubic foot is equivalent to 1,728 cubic inches, which is derived from cubing the 12-inch conversion. The paragraph concludes with a shortcut for conversions, suggesting that squaring or cubing the conversion factor (12 inches) simplifies the process. The speaker invites viewers to leave comments for additional hints on other sections of the workbook and wraps up the video with a hope that the information provided was helpful.
Mindmap
Keywords
💡Units
💡Square Units
💡Cubic Units
💡Conversion
💡Inches
💡Feet
💡Area
💡Volume
💡TEAS Math Workbook
💡Standard and Metric Measurements
Highlights
Introduction to the T's workbook hints video series.
Explanation of units, square units, and cubic units, starting with inches and feet.
Basic conversion: 12 inches equals one foot.
Introduction to square feet and the concept of area measurement.
Visual demonstration of converting square feet to square inches.
Clarification of the common mistake in converting square feet to square inches.
Explanation of the correct conversion: 1 square foot equals 144 square inches.
Introduction to cubic units and volume measurement.
Visual representation of a cube with one-foot dimensions and its volume.
Conversion of cubic feet to cubic inches with a step-by-step guide.
Clarification of the large number of cubic inches in a cubic foot.
Shortcut for converting standard units to square units: squaring the conversion factor.
Shortcut for converting standard units to cubic units: cubing the conversion factor.
Emphasis on not needing to memorize the exact numbers, but understanding the conversion process.
Invitation for viewers to leave comments for hints on other sections of the workbook.
Conclusion of the video with an offer of further assistance.
Transcripts
[Music]
all right in this video this is the
first video to the t's workbook hints
and this is the first video I've done in
quite some time where I am coming over a
bug so sorry about the voice just hang
tight with me I want to get and get some
of these videos out especially since
I've just released the t's math workbook
the stuff we want to be talking about
here is going to help you with the
standard and metric measurements and the
most current version of the workbook is
version 1.1 and you can find a link for
this workbook in the description of any
of my videos so units vs. squared units
versus cubic units let's just start with
plain old units and in this case I'm
gonna be talking about inches and feet
twelve inches equals one foot you
definitely want to know that but if we
start talking about square feet or cubic
feet even for example let's look at this
square down here and let's suppose this
square is one foot by one foot
well the area of that square is going to
be one foot times one foot that is one
square foot and another way that we can
write this is we can write it as one
foot squared now if we want to talk
about this square what's the area of
this square in square inches well what
you're gonna have to think about
visually and I'm going to show this to
you is we've got to break this foot up
into inches so I know this looks like a
hot mess but what you got to think about
is this okay remember one foot is 12
inches so I'm taking this foot and let's
just count 1 2 3 4 5 6 7 8 9 10 11 12
there's 12 inches across there well
there's 12 inches going down as well so
therefore since one foot is 12 inches
and one foot is 12 inches be my guest if
you want to come in here and count how
many square inches you have I know it's
not perfect but I'm trying to get the
point across here if you take 12 inches
times 12 inches then this one square
foot that we have
one square foot one square foot that's
going to be 144 square inches and that's
where some people get confused they
think okay if 12 inches is a foot then a
square foot just gonna be 12 square
inches and that's not right you have to
remember you're taking length times
width 1 foot times 1 foot that's one
square foot that's the same thing as
saying 12 inches times 12 inches that's
144 of those square inches and if you
were to pause the video and count all of
these what are supposed to be squares I
know my drawings not perfect you would
have 144 square inches inside of this
square foot so that's the conversion
there to convert from square inches to
square feet now imagine taking that same
concept if we took one foot we have a
cube now so we're talking about cubic
units that's volume if we have one foot
this way one foot across the side and
the height of the cube is one foot the
volume of a cube the volume is going to
be length so that's one foot times the
width which is one foot times the height
which is one foot and one foot times 1
foot times one foot is one cubic foot
alright so I'm gonna go ahead and write
that over here one cubic foot now if we
wanted to figure out how many cubic
inches there would be inside of this
cube there's gonna be a lot of them I
mean y'all imagine taking one foot by
one foot by one foot you have a box and
you know a basketball would kind of fit
inside of that box pretty good if you
want to wrap it up for a Christmas
present
well imagine taking a cubic inch which
is only a little bit bigger than a dice
that you roll at Vegas imagine filling
up that box with those dice you'd have a
bunch of them because a dice is kind of
close to a cubic inch but now let's use
our conversions one foot twelve inches
times another foot well that's another
twelve inches times another foot oh my
we have another 12 inches and 12 times
12 times 12 is 1728
and this is cubic inches that is going
to be our conversion now you don't want
to memorize these by any means here's
the shortcut if you want to go from
standard units like inches or feet to
square units all you do is square the
conversion twelve inches times 12 inches
is 144 square inches just like one foot
times one foot is one square foot now
let's look at the cubic conversion one
foot times 1 foot times one foot that is
one foot all of that cubed that's a
cubic foot that is this blue key we have
over here so essentially we're taking
this 12 inches and we're cubing it
twelve times twelve times twelve is 1728
and we do have cubic inches
so hopefully with those tips there it
will help you get through some of the
questions in the standard and metric
measurements section of the Tees math
workbook feel free to leave a comment
below for some more hints on other
sections of the workbook and I'll be
happy to post those and that's it for
this video I hope it helped
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