Fractions and Percentages using Little Caesar’s Quattro Pizza

Little Caesar's Quattro Pizza / Courtesy: LCE, Inc.
Little Caesar’s Quattro Pizza / Courtesy: LCE, Inc.

Pizza is a delicious way to talk about fractions and percentages. In the food service industry, catering managers keep track of pizza consumption, which provides important information for future budgeting and planning.

Let us say that a food service manager is catering a pizza party, where the host specifically asks for Little Caesar’s Quattro pizzas.

The Quattro is a specialty pizza that has four sets of toppings: cheese, pepperoni, Italian sausage with bruschetta, and Italian sausage with pepperoni.

Pizza Slice Counts

During food service, the banquet servers kept the pizzas warm and presentable to the partygoers on multiple serving tables.

The number of empty boxes were counted at the end of the pizza party.

There were 62 boxes delivered to the banquet. When food service concluded, 47 boxes were empty. The remaining boxes had leftover pizza slice that were counted and displayed in the table below.

Box # Cheese Pepperoni Sausage/Bruschetta Sausage/Pepperoni
1 0 0 2 1
2 0 0 1 2
3 1 0 1 2
4 1 1 2 1
5 0 1 2 2
6 0 2 1 1
7 1 2 1 0
8 1 1 1 0
9 0 2 1 1
10 0 1 2 1
11 1 1 2 2
12 1 2 2 0
13 1 2 1 2
14 0 0 1 0
15 1 0 2 1

Pizza is traditionally divided into slices for convenience.

Each slice of the pizza may be considered a sector of the pizza. A sector is a portion of a pizza (or a circle) that has boundaries marked by the two edges of pizza slices and the crust of the pizza (the perimeter).

In the case of the Little Caesar’s Quattro pizza, eight slices are part of one of the four sectors. More precisely, there are two slices of pizza in each sector. Each section contains a specific topping group.

The catering manager can use the leftover slice count data set for predicting customer need, which help control costs. After food service, the manager can also control costs by storing the leftover pizza in the kitchen freezer.

Pizza Slice Totals

Now, let us look at the slice counts and the totals for each pizza box and totals for each topping group.

# Cheese Pepperoni Sausage/Bruschetta Sausage/Pepperoni Total
1 0 0 2 1 3
2 0 0 1 2 3
3 1 0 1 2 4
4 1 1 2 1 5
5 0 1 2 2 5
6 0 2 1 1 4
7 1 2 1 0 4
8 1 1 1 0 3
9 0 2 1 1 4
10 0 1 2 1 4
11 1 1 2 2 6
12 1 2 2 0 5
13 1 2 1 2 6
14 0 0 1 0 1
15 1 0 2 1 4
T 8 15 22 16 61

There is a total of 61 slices remaining. Eight (8) slices of cheese, fifteen (15) slices of pepperoni, twenty-two (22) slices of sausage/bruschetta and sixteen (16) slices of sausage/pepperoni.

Fractions and Percentages

We already mentioned the importance of this information for food storage planning. The owner of the catering company wants to know more details about the leftover slices for business analysis.

To deliver that information, we must summarize the leftover slice counts with fractions and percentages.

Toppings Group Counts Fraction Percent
Cheese 8 8 / 61 13%
Pepperoni 15 15 / 61 25%
Sausage/Bruschetta 22 22 / 61 36%
Sausage/Pepperoni 16 16 / 61 26%

Percentages are “fractions of 100” and are best visualized using pie charts.

Pie Chart for Leftover Pizza Slices #yswidt

Let us look at these percentages in the pie chart and see how they relate to the proper fractions that describe each topping group.

First, as soon as we know the total number of leftover slices, we can calculate the unit fraction.

CCSS.MATH.CONTENT.3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

For total parts T, we know that the unit fraction is 1/T. There are 61 total (equal) leftover slices. This means the unit fraction is 1/61. Let us calculate his unit fraction in decimal form.

= 1 / 61 = 0.01639

The Percentage Package

Decimals help us calculate percentages. In fact, we can look at percentages as if they were “packages” used to described values.

For example, we can convert any decimal into a percentage by “multiplying the number by 100”:

= 0.01639 * 100

before adding a percent sign (%) to the end:

= 1.639%

🤔🤔🤔 Pay attention!!

We are not arbitrarily multiplying a number by 100. Instead, we are multiplying a number by exactly 1. Let us recall the identity property of multiplication.

A x 1 = A

It is extremely useful. The property says that we can do anything we want to any number as long as the expression simplifies to that same number. In other words, we can say the same things in a different way.

Another way of saying “one” is by saying “one hundred over one hundred” (100/100).

= 100 / 100 = (100) * (1/100) = 1

The “per one hundred” (1/100) portion of the above expression is called percent (“per cent”) for simplicity. In other words, the above expression can be re-written as “100 percent”, which is equal to 1.

The same goes for any number, including fractions and decimals.

= A x 100 * ( 1 / 100)

Like many things in mathematics, the percent sign (%) is just another symbol used to save time and resources (and reduce error) for communication of specific values.

= (A * 100) %

THINK. THINK. THINK.

How would you describe “percent” in scientific notation?

Percentages with Unit Fractions

We know the unit fraction that describes the total amount of leftover slices, so we can multiply that equivalent percentage by the total amount from each topping group to find each percentage.

Topping Group Counts Multiply by Unit Fraction Percent
Cheese 8 ( 1 / 61 ) * 8 = 13%
Pepperoni 15 ( 1 / 61 ) * 15 = 25%
Sausage/Bruschetta 22 ( 1 / 61 ) * 22 = 36%
Sausage/Pepperoni 16 ( 1 / 61 ) * 16 = 26%

CCSS.MATH.CONTENT.4.NF.B.4.B: Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Pizza Storage Memo

The catering manager must figure out how many storage containers are required for placing the leftovers in the kitchen freezers. The leftover pizza slices must be separated by topping group for more effective logistics. The storage containers can only hold 3 slices each.

The more urgent matter is storing the pizza in the kitchen freezers.

We must divide each topping group total {8, 15, 22, 16} by 3 to get a quotient. However, we are not concerned about the value of each quotient as we are about the amount of storage containers that must be allocated for this task.

Some of these quantities are not whole numbers.

If there are any quantities with decimals (fractional parts), we want to find the best whole number that makes sense in the real world. To do this, we will use the =CEILING(number) function, where the result is the smallest integer greater than an input number.

The =CEILING function is used everywhere.

Here are a few example:

Using Wolfram Alpha, simply divide each of the topping group totals by 3 and use the =CEILING (or the =CEIL) function.

Sample Wolfram Alpha input
=SUM(CEIL(8/3), CEIL(15/3), CEIL(22/3), CEIL(16/3))

When you add all the calculations, the result is:

= 3 + 5 + 8 + 6 = 22

To store the slices of leftover pizza, we need 22 storage containers.

Conclusion

The catering manager now has a point of reference for future budgeting and planning of pizza parties. About 88% of the total delivered pizza was consumed. The remaining slices show more detail about the popularity of the topping groups.

The specialty pizza discussed in this math practice activity reorganized 496 slices across four equal topping groups for 62 pizzas.

We were able to regroup these slices for analysis that used fractions and percentages as tools. Analysis of business operations may be helpful for making better decisions. With more data sets, the catering manager may be able to minimize costs and optimize procedures.

MathForWork delivers distributed learning systems, instruction support, and test preparation for all learners. Learn more at MATHFORWORK.COM. MathForWork is a Bitwise Thermodynamics project.

UPC Barcodes: World’s Largest Homeschool Math Workbook

UPC Barcode / Generated using Wolfram Alpha

Good news! The world’s largest workbook is free and available for anyone who knows where to find it. That workbook is full of real-world math practice problems that use addition, subtraction, multiplication and division.

The workbook is basically all the UPC (Universal Product Code) product identifiers in the known universe.

UPC barcodes are everywhere. We can find UPC barcodes in the house, in the supermarket, and pretty much any place that you may find consumer packaged goods (CPG).

In the CPG industry, UPC barcodes are essential for managing inventory through automated scanning. The beeping sound that you hear at the grocery checkout counter represents millions of dollars that have been invested in supply chain management and customer service.

That same beeping sound confirms the completion of a validation process, where 12 UPC numerical digits (ranging from 0 to 9) are used to make calculations using a specified algorithm.

An algorithm is a series of logical steps that generates a specific and predictable solution. In this case, the algorithm is calculating the UPC check digit, which is an industry standard for validation.

From a broader perspective, algorithms are very important in computer science, business analytics, and supply chain management. We can use algorithms to help manage costs and add opportunities for new revenue streams.

UPC Check Digit Algorithm

There are many types of UPC barcodes.

In this activity, we will focus on the UPC-A barcode and its corresponding check digit algorithm.

A valid UPC-A barcode has exactly 12 digits. You may see barcodes with only 11 digits recorded for product inventory. If you see 11-digit barcode numbers, simply add a zero to the beginning of the UPC-A character sequence.

We find the UPC-A check digit by applying an algorithm that uses the first 11 digits of the UPC barcode. The check digit should equal the final digit.

  • Here is the algorithm for calculating the UPC check digit:
    • Step 1: Add the odd-indexed digits. Multiply that first sum by 3.
    • Step 2: Add the even-indexed digits for a second sum.
    • Step 3: Add both sums from Step 1 and Step 2. Divide that combined sum by 10. Subtract the remainder from 10. The difference is the check digit. If the remainder is zero, the check digit is zero.

Let us use an example to better understand how this algorithm works in the computer whenever the UPC barcode is scanned and validated. Download a blank worksheet, and use it to follow along during the walkthrough below.

Worksheets

UPC Barcode Check Digit Walkthrough

We will use the following UPC in this example:

040000527152

This UPC is probably more familiar when it is printed on CPG products in its iconic barcode visual representation:

Interestingly, you can create UPC barcodes in Wolfram Alpha.

Sample Wolfram Alpha input
UPC 040000527152

To begin, enter all the UPC digits in the order they appear. The digits are indexed by their position in the UPC character sequence. There are odd-indexed digits, and there are even-indexed digits.

1 2 3 4 5 6 7 8 9 10 11 12
0 4 0 0 0 0 5 2 7 1 5 2

Remember, we are only using the first 11 digits for this calculation. The final digit (in the 12th position) should always match the check digit for the UPC-A barcode to be considered valid.

Step 1: Add all the odd-indexed digits. Multiply the sum by 3.

1 2 3 4 5 6 7 8 9 10 11 12
0 0 0 5 7 5

3A = 3 * (0 + 0 + 0 + 5 + 7 + 5)
3A = 3 * 17 = 51

Step 2: Add all the even-indexed digits (except the last digit).

1 2 3 4 5 6 7 8 9 10 11 12
4 0 0 2 1

B = (4 + 0 + 0 + 2 + 1)
B = 7

Step 3: Combine both sums. Find the “modulo 10” of that result. Subtract the “module 10” value (the remainder) from 10 to get the check digit. If the remainder is 0, the check digit is 0. The check digit should equal the final digit of the UPC-A character sequence.

3A + B = ( 51 + 7 ) = 58

check digit
= 10 - (3A + B) modulo 10
= 10 - (58 modulo 10)
= 10 - 8 = 2

CCSS.MATH.CONTENT.4.OA.A.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.

NOTE: Markdown tables were generated with Google Sheets using MarkdownTableMaker, another Bitwise Thermodynamics project.

Discussion

All four operations of arithmetic are used in this math practice activity. Addition, subtraction, multiplication, and division are used to calculate the check digit.

In addition to the four basic arithmetic operations, we had the opportunity to use a specialized operation called the modulo operation. The modulo operation (or function) focuses on the remainder of the division operation instead of the quotient. In other words, modulo is specifically asking the amount leftover after the division operation is completed.

Modulo is very useful for determining properties of numbers. For example, even numbers have a “modulo 2” equal to zero, while odd numbers have a “modulo 2” equal to one.

In computer programming, this modulo operation is often used in algorithms related to the processing and rendering of consecutive data records (e.g., positions of a character sequence, rows in a table, etc.).

In this math activity, we used “modulo 10” to help find the check digit. Computational platforms (such as Wolfram Alpha), search engines and some smart speakers can provide modulo operation results.

Sample Wolfram Alpha input
88 modulo 2 OR 55 mod 2 OR 55 % 10

Conclusion

UPCs are ubiquitous, which provides unlimited opportunity for math practice on shopping trips or activities involving pantry inventory. Every CPG package in the grocery store is now part of the world’s largest math workbook. The math problems are free and the added math practice will pay off with improved recall of multiplication facts.

Every UPC is a math practice problem with the “answer” provided. However, every UPC must be checked because some UPCs fail the validation process, which may cause issues during inventory audits and customer checkout (when the cashier calls for a “price check”).

In addition to the worksheets in this activity, personal math journals are great places to record interesting UPC barcodes found for future reference.

MathForWork delivers distributed learning systems, instruction support, and test preparation for all learners. Learn more at MATHFORWORK.COM. MathForWork is a Bitwise Thermodynamics project.

Kitchen Math: Soup Ladle Sizes

Commercial cloud kitchens are always busy. Food orders are received and delivered around the clock, but some parts of the day are busier than others.

During off-peak hours, chefs often expect kitchen workers to make time-saving preparations for food service with important tasks, such as equipment cleaning and utensil organizing.

Soup ladles (or ladles in general) are kitchen utensils that are used for the safe and sanitary transfer of liquids during food preparation and food service. Ladles are best described as bowls with long handles.

Soup Ladle
Soup Ladle / Courtesy: Amazon

The size of each ladle bowl is usually standardized using the traditional (avoirdupois) fluid volume units, such as fluid ounces, cups or pints.

New Vocabulary:
Learn how to say the word “avoirdupois” by hearing the pronunciation on Google Translate.

Common measuring instruments, such as rulers and tape measures, use inches and centimeters, so measuring fluid ounces directly is not very intuitive.

A math solution must be developed to make length measurements more relatable to volumetric sizing.

Sorting the soup ladles

You have been given a box full of soup ladles to organize for the kitchen chef. This is an important responsibility and an opportunity to impress your boss.

One of the keys to a successful kitchen is the amount of preparation for food service. Preparation time is designed to optimize cooking time.

Timing is crucial in cooking. If the ladles are well-organized during preparation time, then the chefs and cooks will require much less time and effort to choose the correct ladle while cooking.

There are no size labels on the soup ladles given to you, but there is a way to measure and confirm each ladle size. For this math practice activity, our strategy will be to measure the width (i.e., the diameter) of the soup ladle bowls in inches and convert that measurement into standardized units in fluid ounces.

Set of soup ladles / Courtesy: Amazon
Set of soup ladles / Courtesy: Amazon

Finding fluid ounces from diameters

The shape of the soup ladle bowls are best described as hemispheres (half spheres). We are familiar with the formula for a sphere, so this is a good starting place for calculating the formula for half of a sphere.

CCSS.MATH.CONTENT.HSG.GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

The volume of a sphere can be described with the following equation:

Thus, the volume of a hemisphere is half that volume.

We can measure the diameter D of the soup ladle (in inches) with a measuring tape.

Tape measure / Courtesy: Amazon
Tape measure / Courtesy: Amazon

The radius R of the soup ladle is half the measured diameter (D/2). So, we can rewrite the equation of the hemisphere in terms of the diameter:

The volume V (in cubic inches) is now a function of the diameter D, as given by the formula for the volume of a hemisphere.

After the volume is calculated, the units of cubic inches can be can converted into fluid ounces by multiplying the volume by 0.554113.

Below is the Wolfram Alpha input for this developed math solution.

View this solution on Wolfram Alpha

Sample Wolfram Alpha input
D=4.5;R=D/2;
V=((4/3)*pi*R^3)/2;
Z=V*0.554113

Notice how we can build the math solution without needing to explicitly use substitutions. That is one of the many powerful features of Wolfram Alpha.

It is a good practice to do the computations by hand. However, Wolfram Alpha provides an extra tool – one of many math tools – in the workplace for working through your computational thinking.

Additionally, once you have developed a good workplace math solution, you can simply repeat the calculation for a variety of input values.

The following table provides a list of standardized soup ladle sizes. Your calculations do not exactly match the these sizes, but they are close enough to help you finish the sorting task that the chef has assigned to you.

Soup Ladle Diameters and Sizes

Diameter, D (in.) Volume, V (fl. oz.) Size (fl. oz.)
2 1.16 1
2.5 2.27 2
3.25 4.98 4
3.5 6.22 6
4 9.28 8
4.5 13.22 12
5 18.13 16

NOTE: Markdown tables were generated with Google Sheets using MarkdownTableMaker, another Bitwise Thermodynamics project.

Conclusion

With more math practice, you will discover that the unit volume (e.g., cubic inches, cubic centimeters, etc.) provides a convenient way for you to convert between various workplace measurement systems.

Let us say you were tasked with buying new soup ladles for banquet service. The product descriptions may use gallons, quarts, or pints to describe different volumes. Calculating price per cubic inch is a useful method of comparison shopping based on a single variable.

MathForWork delivers distributed learning systems, instruction support, and test preparation for all learners. Learn more at MATHFORWORK.COM. MathForWork is a Bitwise Thermodynamics project.

Finishing the Pyramid in TINKERCAD with Math in Wolfram Alpha

The frustum can be seen as a Rorschach test. Some people see a gold bar, and some people see an unfinished pyramid.

Frustum in TINKERCAD

One way to create a frustum in TINKERCAD is to start with a solid pyramid basic shape. The top part of the pyramid is then removed by a “hole” that adds negative volume to the shape. The result is a frustum. The following video demonstrates this method:

Before removing the top part of the pyramid, we need to know the dimensions of the solid pyramid’s base. We also need to know the height of the pyramid.

We can do this by using our prior knowledge and best practices. One of the most basic uses for algebra is providing a simple way to express how two things add up to one thing.

We know that a frustum is the “bottom section” (in blue) of a pyramid. This means that if we add the missing “top section” (in pink) to the frustum, we will have a complete pyramid.

That relationship can be described by the following equation:

We know the formula for the volume of the complete (big) pyramid,

with the base area B, the height of the frustum h, and the unknown height of the top pyramid H.

We also know the volume of the top section of the complete pyramid (which can also be described as a mini pyramid),

with the base area A (the same area as the top area of the frustum), and the unknown height of the top pyramid H.

The volume of the bottom section of the complete pyramid can be described as a frustum.

With a base area B of 6″ x 6″. let us suppose that the height of the frustum h is 10 inches, and the top area of the frustum A is 2″ x 2″. This means that the total height of the complete pyramid H + h provides us clues to the information that we need finish the pyramid.

To help finish the pyramid, we now have a useful equation that can be re-used and re-purposed in different workplace contexts:

In Wolfram Alpha, type this:
h=10;A=2*2;B=6*6;(1/3)(H+h)*B=(1/3)A*H + (h/3)(A+B+SQRT(A*B))
(view query)

Notice that we never actually calculated the volumes in the equations. Instead, we used the additive relationships between the volumes, areas and heights to complete a specific workplace task.

The 3D models related to the “finish the pyramid” math practice activity are available on GitHub. Also, the 3D models can be directly imported into TINKERCAD. NOTE: Model units are in inches.

MathForWork delivers distributed learning systems, instruction support, and test preparation for all learners. Learn more at MATHFORWORK.COM. MathForWork is a Bitwise Thermodynamics project.

CCSS.MATH.CONTENT.7.EE.B.4: Decorative Cake Box

In this activity, you work in a cloud kitchen, a business that has no dining room — only online orders. Cloud kitchens combine pre-planning with just-in-time preparation to optimize kitchen resources and stay competitive.

As the kitchen shuts down for the business day, you are tasked with the responsibility of storing a slice of special order decorative cake in a 9.6 cup plastic storage container. The cake will not be ready until tomorrow, but you already have the dimensions from the customer order.

The cake is 7″ long and 5″ wide , which is no problem because the plastic storage container has the dimensions of 9.5″ x 6.25″. However, the pastry chef is concerned about the height available when the container is sealed with its lid.

The plastic lid is designed to seal the container and protect the freshness of its contents. However, if the decorative cake is somehow damaged, it will become undeliverable and will be discarded as a loss.

The cross-sectional area of the container is a rounded rectangle with a 1″ radius on each corner. We now have a description of the geometric shapes involved, so building a solution requires us to put the pieces together into a system of equations.

CCSS.MATH.CONTENT.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

We begin with a review of our prior knowledge and best practices. First, we want to use inches to communicate the usable height. To be consistent, the units we will use for the volume of the container are cubic inches.

In Wolfram Alpha, type this:
9.6 cups in cubic inches (view query)

For voice assistants, try this command:
9.6 cups in cubic inches

We find that volume of the container, which is 9.6 cups, can be converted to 138.6 cubic inches.

Second, we recall the formula for the volume of a prism:

with base area A for the rounded rectangle and height h. The actual area of a rounded rectangle is defined by:

The variables a and b describe the length and width between the rounded regions of the container, with radius r. We can subtract the radii of the corners from the overall width and length of the container.

We now have enough information to solve the problem.

In Wolfram Alpha, type this:
V=138.6;r=1;L=9.5;W=6.25;a=L-2r;b=W-2r;V=(ab+2r(a+b)+πr^2)h
(view query)

We find that as long as the decorative cake is less than 2.37 inches, the lid should close without damage.

Even though we used equalities in this math practice activity, the concern for product quality may have changed the nature of our expressions into inequalities. For example, notice how we compared the dimensions of the cake slice to the dimensions of the container before any other calculation were made.

Putting in extra work:
Try experimenting with the above calculation in Wolfram Alpha with inequalities. What happens?

Additionally, we may want a factor of safety to further protect the decorative cake, so we may decide eventually that all cakes measuring no more than 2.25 inches will be stored in that particular container. Of course, final decision is made by the pastry chef.

Comparison Shopping:
Try shopping for this and similar plastic storage containers on Amazon. What did you find?

MathForWork delivers distributed learning systems, instruction support, and test preparation for all learners. Learn more at MATHFORWORK.COM. MathForWork is a Bitwise Thermodynamics project.

CCSS.MATH.CONTENT.8.G.C.9: Work TINKERCAD with Cone, Cylinder, Frustum

In this short video, we explore the relationship between cones, cylinders, and frusta (the plural form of frustum). The three shapes are connected by a general equation, and we explore the impact of changing the top radius for each of these shapes. TINKERCAD is the 3D modeling platform used for this activity.

The general equation for the volume of a frustum (volume V) with any cross-sectional area is defined as follows:

V = π/3 h (A + B + sqrt(A B))

where, height h, and areas A and B are the independent variables.

In Wolfram Alpha, type this:
V = (h / 3) * (A + B + SQRT(A * B) (view)

Let us use a more specific cross-sectional area: the area of circle. Now, we have a conical frustum:

where, height h, base radius R, and top radius r are input variables. Also, the top radius must be a value between 0 and R; that is, 0 < r < R.

In Wolfram Alpha, type this:
V = (pi / 3 ) * h * (r^2 + r*R + R^2) (view)

When r = 0, we have the formula for a cone:

V = 1/3 π h R^2

In Wolfram Alpha, type this:
V = (pi / 3 ) * h * (0 + 0 + R^2) (view)

When r = R, we have the formula for a cylinder:

V = π h R^2

In Wolfram Alpha, type this:
V = (pi / 3 ) * h * (R*R + R*R + R*R) (view)

In this activity, we demonstrated that not every math problem has a numerical answer. There is no answer “at the back of the book” in the real world because design decisions require some careful thought and planning.

Math Work is Work.

One very important concept at MathForWork is the practice of working through ideas.

TINKERCAD provides a great opportunity to work through different ideas related to geometry and trigonometry.

Mindless rote learning for standardized testing is not work. Mindful exploratory learning and computational thinking is meaningful work that leads to meaningful learning.

TINKERCAD has a simple interface that creates a wonderful environment for 3D modeling. This job skill requires a good understanding for how to choose and modify basic shapes for tasks in the workplace. Also, the 3D models can be exported for 3D printing in maker spaces, which allow the model to be inspected more closely for future reference.

TINKERCAD is a great entry-level software applications for learning 3D CAD modeling and design. It may feel like a toy, but TINKERCAD is very useful. The 3D CAD software used in basic design does not need to be too fancy, because the exported 3D models are standardized formats.

CCSS.MATH.CONTENT.8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

MathForWork delivers distributed learning systems, instruction support, and test preparation for all learners. Learn more at MATHFORWORK.COM. MathForWork is a Bitwise Thermodynamics project.

Create Instant QR Codes on any Device with a Bookmarklet: waferQR

Creating QR codes can improve usability for any mobile experience. Many camera apps and web browsers now include features that read can and interpret QR codes, allowing fast mobile-friendly access to web sites, social media, videos, and podcasts.

waferQR is a bookmarklet that converts any web page URL into a QR code by using Wolfram Alpha. The QR code makes the URL scannable by any compatible camera app.

The input command used for Wolfram Alpha is straightforward. Type “qrcode” in the input box followed by the text that will be converted into a QR code image.

waferQR automatically detects the current web page URL in your web browser and runs the query for you.

The following example converts the Northern Arizona University Library home page into a QR code with the following Wolfram Alpha input command:

qrcode https://nau.edu/library/

Wolfram Alpha is a leading technical computing web platform that provides powerful interpretations of command line inputs for mathematics, science, and much more.

In addition to processing complex computations, Wolfram Alpha also provides an input command that generates a QR code image. The resulting QR code can represent any text information, including web addresses.

A bookmarklet is a special kind of bookmark that contains JavaScript, which adds functionality to specific web pages. Bookmarklets are ideal for cloud-based platforms, where bookmarks sync seamlessly across devices. For example, adding the waferQR bookmarklet to Safari on a desktop will allow the quick QR generator to be available on iPhones, iPads, and other compatible devices.

There are many methods of adding bookmarklets to bookmarks folders. Drag-and-drop is a popular method.

More methods are described on the waferQR project page on GitHub.

No sign-up or sign-in is required to use waferQR. However, this means that all updates must be made by manually re-adding the bookmarklet.

You can sync the waferQR bookmarklet in your Chrome, Firefox, and Safari bookmark folders. More cloud-backed browser platforms are being tested and are expected to be supported by the end of October.

The waferQR bookmarklet was developed by Bitwise Thermodynamics to generate QR codes for instructions support for projects like MathForWork.. The QR code is generated by the Wolfram Alpha platform, which belongs to Wolfram Alpha LLC and Wolfram Research.