TEAS MATH Workbook Hints - Video 1 - Units vs. Square Units vs. Cubic Units

Summary

This 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

00:00

📏 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.

05:00

📐 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.

Keywords

💡Units

Units refer to the standard measurements used to quantify length, area, and volume. In the video, the presenter discusses units in terms of inches and feet, explaining how they are the basic building blocks for measuring distances and dimensions.

💡Square Units

Square units are used to measure area. They are derived by squaring the linear units. For example, a square foot is a square with sides of one foot each. The video explains that one square foot is equal to 144 square inches, emphasizing the need to multiply length by width to get the area.

💡Cubic Units

Cubic units measure volume and are derived by cubing the linear units. The video provides the example of a cubic foot, which is a cube with sides of one foot each. It further explains that one cubic foot is equivalent to 1,728 cubic inches, highlighting the need to multiply length, width, and height.

💡Conversion

Conversion involves changing one unit of measurement to another. In the video, the presenter demonstrates how to convert between linear, square, and cubic measurements, such as converting square feet to square inches and cubic feet to cubic inches.

💡Inches

Inches are a unit of linear measurement. The video frequently references inches when explaining how to break down measurements, such as converting one foot into 12 inches and using these inches to calculate area and volume.

💡Feet

Feet are another unit of linear measurement, equal to 12 inches. The video uses feet to explain basic measurements and conversions, particularly in the context of calculating square and cubic measurements.

💡Area

Area is the measure of a two-dimensional surface. The video explains how to calculate the area of a square by multiplying its sides, for instance, one foot by one foot to get one square foot, or 12 inches by 12 inches to get 144 square inches.

💡Volume

Volume is the measure of the space a three-dimensional object occupies. In the video, volume is calculated by multiplying the length, width, and height of a cube, demonstrated with the example of converting cubic feet to cubic inches.

💡TEAS Math Workbook

The TEAS Math Workbook is a study guide referenced in the video. It provides practice problems and explanations for standard and metric measurements, among other math topics. The video aims to help viewers understand concepts from this workbook.

💡Standard and Metric Measurements

These are systems of measurement. The video focuses on standard measurements, like inches and feet, but it also mentions the importance of understanding both systems as they are covered in the TEAS Math Workbook.

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