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Finding the surface area of 3 dimensional shapes

Demonstrate an understanding of the meaning and uses of accuracy and precision

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Upper and lower bound

Upper and Lower Bound

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Use a measuring tape to measure tactile items in both imperial and SI units

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Identify the difference between length, area, and volume

Surface area of 3-dimensional shapes

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

Difference quotient: applications of functions

Demonstrate an understanding of the meaning and uses of significant figures

Place value

Comparing and ordering numbers

Comparing Integers

Comparing Numbers

Comparing Fractions

Rounding numbers

Rounding Decimals

Rounding Integers — Up to 9999

Identify, use, and convert among and between SI units and imperial units

Find the exact value of trigonometric ratios

Demonstrate an understanding of and be able to solve problems using the Pythagorean theorem

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Demonstrate mathematical knowledge required for various career choices

Finance: Compound interest

Finance: Compound Interest

Continuous growth and decay

Finance: Future value and present value

Demonstrate entry-level competence in mathematics for specific career choice

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Center of a data set: mean, median, mode

Probability distribution - histogram, mean, variance & standard deviation

Sketch and construct a model to show mathematics involved in a career interest

Applications of polynomial functions

Ferris wheel trig problems

Calculate dimensions of actual objects using blueprints with various scales

Combining transformations of functions

Enlargements and reductions with scale factors

Scale diagrams

Sketch and build representations of three-dimensional objects

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Illustrate and express ratios, fractions, decimals, and percentages in alternative forms

Direct variation

Identifying direct variations

Inverse variation

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Representing percents

Representing Percents

Representing Percents — Word Problem

Representing Percents Two Graphs – Word Problem

Percents, fractions, and decimals

Conversion — Decimal to Fraction

Conversion — Decimal to Percent

Conversion — Fraction to Decimal

Conversion — Fraction to Percent

Conversion — Percent to Decimal

Conversion — Percent to Fraction

Percents – Word Problem

Convert a Decimal to a Fraction

Convert a Decimal to a Percent

Convert a Fraction to a Decimal

Convert a Fraction to a Percent

Convert a Percent  to a Decimal

Convert a Percent to a Fraction

Percents Fractions And Decimals – Word Problem

Percent of a number

Percent of a Number

percent of a number – Word Problem

Percent of a Number  Fraction Percent

Percent of a Number Integer Percent 

Percent of a number number With Decimal Percent 

Percent of a Number  Three Digits Number Percent

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Find and calculate rates in practical applications such as pulse rate

Rate of change

Arc length

Estimate and calculate deductions from a pay stub as percentages of gross earnings

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Adding and multiplying percents

Add and Multiply Percents — Word Problem

Add and Multiply Percents – Word Problem

Sketch enlargements and reductions of objects using various scales

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Use the slope formula to solve trigonometric problems commonly found in industry

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Mathematics Essentials 12

Measurement

Mathematics in the Workplace Investigation

Ratio, Rate, and Proportion

Major Project: Math Preparation for the Workplace

math

- Hi, welcome to this question right here. So what happen is we're trying to determine the dimension of this cut out piece. So we&apos;ve got a little rectangle right here, right? So we&apos;ve got all sort of information down here, so we're going to use each pieces right here to determine the dimension of this part that you're going to cut out which is this part right here. Okay? 
So let's start from the top first. So if you're looking from the top, it says now right over here on the back over here is 20. So I'm going to put a little 20 right there to remind our self, and this part right here. This part here is 15, so that's 15. Okay? So that's going to add it in. So far there isn't too much information that we have to determine the dimension of that little cut out piece. Let's go to the next one, just looking it from the left. So this is your left and side, this piece right here. That's your left hand side. So it says, if you're looking from the left. This part right here is six centimeters, so that six. So we just discovered our first dimension to the cut out piece. This bottom part right here is six. Okay? 
Then, we have nothing else. Okay, that's unfortunate but we do know that 20, that's 20, that's six. So then makes this part here 14. Okay? I don't know if we need that but, let's just put it in just in case we needed that for a later questions. Let's focus on the front. If you're looking from the front, you're looking from this way, okay? So we have the 20-- 
This side is also 20, okay. So I'm going to put a little line right there to represent that as side 20. We know that the bottom part is 27. That's your 27. We do know the next dimension now, because it looks like-- actually we do, because that's 10 right there. See this part right here, the 10? That means this part here is also 10. Okay? I kind of ran out of space, but if you just do a quick math right there. This whole thing is 20, right? That part is 10. So that makes this part here as 10 as well. Okay? That part represents this part here. So we just found out that our next dimension which is this part, that's 10. This is also 10. Okay? 
So the only thing that we're missing is actually-- 
Oh, it's not missing, it's actually-- We know this side, the whole thing is 27, right? Now, if you take that 27 and subtract the 15 on the top, you get yourself just the 12. Okay? That 12 will go right there. So we just figure out our last dimension right here which is 12, okay? So six times 12, times 10 for this cut out piece and if you want to figure out the area right now. Six time 12 times the 10, we&apos;ve got our area turns out to be-- 
Just let me fill the work here, which is length times the width times the height, right? So we&apos;ve got ourselves six times the 12, times the 10. We have 720, okay? 
So that 720 is the area and the dimension for this question, it's six time 10, times the 12. Then let's quickly go to the next question and see what they're asking for. They're looking for-- Just let me see, so I'll remember it. We still have the dimension of 720, right? But as you can see, the next question says, "How does the surface area of the original rectangle object change after cutting out that corner piece?" 
Well, this question here doesn't really need the calculation because if you think about it, the surface area did not change at all. Okay? So the answer to that question right now, I want to say there's no change. Now, you'll probably thinking like, "Okay, how is that possible?" 
Because you cut out a one piece from the original rectangle, right? This piece has been cut out, but surface area is different from the volume. Surface area is we look at an object from all the surfaces, right? So if you just imagine, if you look at this cut out pieces right now, then other cut out piece, this diagram right here with all these dimensions. If you're looking from the top, you still see a perfect rectangle. If you look at it from the left that it's still a perfect rectangle. If you see it from the right which is still a rectangle, right? When you're seeing right here, it's the same as before. Okay, because when you look at it from-- 
Let's say if you're looking from the top, you still see the surface-- Let me just erase all these right here. You still see all the surface area, including that little piece down here. So the surface area actually didn't change from before and after. So that's why the surface area of the original rectangle object did not change even after you cut it out, okay? 
Only the volume changes, okay? Hoping that it make sense. Thanks for watching.

In this section, we will learn how to calculate the surface area of 3D objects. We will also look further into the subject ? What would happen to the surface area if the shapes are 
cut into pieces? How about a piece is cut out of the shape? 

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms