A geometric transformation is a way of manipulating the size, position, or orientation of a geometric object. For example, a triangle can be transformed by a 180^o rotation: 

Learning about geometric transformations is a great way for students, teachers and anyone interested in math to get comfortable using x-y coordinates in the cartesian plane, and mapping functions from R² to R². Understanding geometric transformations is also an essential step to understanding higher-level concepts like the Transformations of Functions and Transformation Matrices.
Check out the Geometric Transformations collection on Maple Learn to learn about this topic. Start out by playing with the Geometric Transformations Exploration document to build intuition about how objects are affected by each of the four transformation types: Dilation, Reflection, Rotation, and Translation. Once you are confident in your skills, try using the Single Geometric Transformation Quiz to test your knowledge.
For those looking to expand their understanding of geometric transformations, the Combined Transformations Exploration document will let you explore how multiple transformations and the order of said transformations affect the final form of an object. For example, the blue polygon can be transformed into 2 different pink polygons depending on whether the reflection or rotation is performed first:

Once you have the hang of combined transformations, try answering questions on the Combined Geometric Transformations Quiz. 

How Can Maple Learn Help Address Math Anxiety in Classrooms?

Math anxiety is referred to as negative behaviours such as uneasiness and general avoidance when asked to solve math problems. For teachers and teacher candidates, this can be due to various reasons such as previous negative experiences in math classes, learning styles that conflict with their math teacher, lack of self-confidence, low self-esteem, and stereotype issues related to the belief that math is for men only. Although it is commonly believed that math anxiety only exists in students, research has shown that math anxiety is present among elementary teacher candidates and elementary teachers, particularly women. Furthermore, research has shown that female teachers who suffer from math anxiety have a tendency to pass down their math anxious behaviours to students, particularly affecting more girls than boys. Since the majority of the elementary teaching staff are women, it is possible that a cyclic pattern will arise where teachers will pass down math anxiety to students, and these students will grow up dealing with math anxiety.

As a current PhD candidate, I have taught elementary teacher candidates basic math knowledge. It was clear to me from the first day, math anxiety was very present within the students I had. Many of these teacher candidates had candidly revealed that they have not taken any math classes since Grade 11, which is the final grade in Ontario where math is mandatory. With Maple Learn, because manyof the documents are created by educators, these documents can function as learning materials which a teacher can use for extra practice and guidance. 

One strategy to combat math anxiety in general is developing greater self-efficacy and confidence in their math skills. For example, using the Converting and Decimals to Fractions document, teachers and teacher candidates can use this as a tool to support their understanding and can help double-check their work. Unlike students, when learning about math concepts and skills in class, in addition to using online resources they also can ask teachers for help. Whereas for adult learning, it is possible that some may feel shy or embarrassed to seek help from others. On Maple Learn, there are multiple quizzes where a teacher can use as practice to further their understanding. In addition to the solution, these features also provide hints and a “check your work” button so that it can guide the teacher in solving such problems if stuck on a question. One of the cool features of these solutions is that they don’t just reveal the answer, but also include steps to solve the question whenever a teacher gets stuck.

Furthermore, additional visualizations could be a useful tool for visual learners and serve as another method to understand and solve such math problems rather than solely relying on algebra. 

The documents provided in the example gallery provide multiple different methods on understanding and solving math problems. For example, when multiplying fractions, one can either simplify before multiplying the fractions together or they can first multiply the fractions, then simplify.

The more practice one does, the better they become at solving math problems, and if interested, Maple Learn has many quizzes that one can use to improve their math skills. For more fractions documents, check out this page here!

Happy Springtime to all in the MaplePrimes Community! Though some in our community may not live in the northern hemisphere where flowers are beginning to bloom, many will be celebrating April holidays like Ramadan, Passover, and Easter.

One of my favorite springtime activities is decorating eggs. Today, the practice is typically associated with the Christian holiday of Easter. However, painted eggs have roots in many cultures.

For over 3,000 years, painting eggs has been a custom associated with the holiday of Nowruz, or Persian New Year, during the spring equinox. Furthermore, in the Bronze Age, decorated ostrich eggs were traded as luxury items across the Mediterranean and Northern Africa. Dipped eggs have also played an important role in the Jewish holiday of Passover since the 16th century.

To celebrate this tradition, I would like to invite all of the Maplesoft community to create a decorated egg of their own with the Easter Egg Art Maple Learn document. In this document, an ovoid egg equation is used to define the shape of an egg. 

The ovoid egg equation mimics the shape of a typical hen’s egg. Each bird species lays differently shaped eggs. For example, an ostrich’s egg is more oblong than an owl’s, and an owl’s egg is rounder than a goose’s. Surprisingly, every egg can be described by a single equation with four parameters:

Learn more about this equation and others like it with John May’s Egg Formulas Maple Learn document.

The Easter Egg Art document includes 9 different decorative elements; users can change the color, position, and size of each in order to create their own personal egg! The egg starts out looking like this:



In just a couple of minutes, you can create a unique egg. Have fun exploring this document and share a screenshot of your egg in the comments below!  Here’s one I made:

Several studies, such as “Seeing and feeling volumes: The influence of shape on volume perception”, have shown that people have a tendency to overestimate the volume of common objects, such as glasses and containers, that are tall and thin and underestimate those that are short and wide; this phenomenon is called “elongation bias”. 

Sue Palmberg, an instructor at Edwin O. Smith High School, created and shared with us a lab activity for students to design a glass in Maple and use volumes of revolution to determine the amount of liquid it can hold. This lab was then turned into this Maple Learn document: Piecewise Volumes of Revolution Activity.

Use this document to create your own glass or goblet shape and determine its volume. Simply create a piecewise function that will define the outside shape of your glass between your chosen bounds and another piecewise function to define the hollowed-out part of your creation. The document will graph the volumes of revolution that represent your glass and calculate the relevant volume integral for you.

Here is my own goblet-shaped creation: 

I used this piecewise function to define it:

After creating the outline of my goblet, I constructed a function for the hollow part of the goblet – the part that can actually hold liquid.

Using Context Panel operations and the volume integral provided by the document, I know that the volume of the hollow part of my goblet is approximately 63.5, so my goblet would hold around 63.5 units³ of liquid when full.

Create your own goblets of varying shapes and see if their volumes surprise you; elongation bias can be tricky! For some extra help, check out the Piecewise Functions and Plots and Solids of Revolution - Volume Derivation documents!

The recent Maple 2023 release comes with a multitude of new features, including a new Canvas Scripting Gallery full of templates for creating interactive Maple Learn documents.

The Maple Learn Scripting Gallery can be accessed through Maple, by searching “BuildInteractiveContent Maple2023” in the search bar at the top of the application and clicking on the only result that appears. This will bring you to the help page titled “Build and Share Interactive Content”, which can also be found by searching “scripting gallery” in the search bar of a Maple help page window. The link to the Maple Learn Scripting Gallery is found under the “Canvas Scripting” section on this help page and clicking on it will open a Maple workbook full of examples and templates for you to explore.

The interactive content in the Scripting Gallery is organized into five main categories – Graphing, Visualization, Quiz, Add-ons and Options, and Applications Optimized for Maple Learn – each with its own sub-categories, templates, and examples.

One of the example scripts that I find particularly interesting is the “Normal Distribution” script, under the Visualizations category.

All of the code for each of the examples and templates in the gallery is provided, so we can see exactly how the Normal Distribution script creates a Maple Learn canvas. It displays a list of grades, a plot for the grade distribution to later appear on, math groups for the data’s mean and variance, and finally a “Calculate” button that runs a function called UpdateStats.

The initial grades loaded into the document result in the below plot, created using Maple’s DensityPlot and Histogram functions, from the Statistics package. 

The UpdateStats function takes the data provided in the list of grades and uses a helper function, getDist, to generate the new plot to display the data, the distribution, the mean, and the variance. Then, the function uses a Script object to update the Maple Learn canvas with the new plot and information.

The rest of the code is contained in the getDist function, which uses a variety of functions from Maple’s Statistics package. The Normal Distribution script takes advantage of Maple’s ability to easily calculate mean and variance for data sets, and to use that information to create different types of random variable distributions.

Using the “Interactive Visualization” template, provided in the gallery, many more interactive documents can be created, like this Polyhedra Visualization and this Damped Harmonic Oscillator – both from the Scripted Gallery or like my own Linear Regression: Method of Least Squares document.

Another new feature of Maple 2023 is the Quiz Builder, also featured in the Scripting Gallery. Quizzes created using Quiz Builder can be displayed in Maple or launched as Maple Learn quizzes, and the process for creating such a quiz is short.

The QuizBuilder template also provides access to many structured examples, available from a dropdown list:

As an example, check out this Maple Learn quiz on Expected Value: Continuous Practice. Here is what the quiz looks like when generated in Maple:

This quiz, in particular, is “Fill-in the blank” style, but Maple users can also choose “Multiple Choice”, “True/False”, “Multiple Select”, or “Multi-Line Feedback”. It also makes use of all of the featured code regions from the template, providing functionality for checking inputted answers, generating more questions, showing comprehensive solutions, and providing a hint at the press of a button.

Check out the Maple Learn Scripting Gallery for yourself and see what kinds of interactive content you can make for Maple and Maple Learn!

In an age where our lives are increasingly integrated online, cybersecurity is more important than ever. Cybersecurity is the practice of protecting online information, systems, and networks from malicious parties. Whenever you access your email, check your online banking, or make a post on Facebook, you are relying on cybersecurity systems to keep your personal information safe. 

Requiring that users enter their password is a common security practice, but it is nowhere near hacker-proof. A common password-hacking strategy is the brute-force attack. This is when a hacker uses an automated program to guess random passwords until the right one is found. The dictionary attack is a similar hacking strategy, where guesses come from a list like the 10,000 Most Common Passwords.

The easiest way to prevent this kind of breach is to use strong passwords. First, to protect against dictionary attacks, never use a common password like “1234” or “password”. Second, to protect against brute-force attacks, consider how the length and characters used affect the guessability. Hackers often start by guessing short passwords using limited types of characters, so the longer and more special characters used, the better.

Using the Strong Password Exploration Maple Learn document, you can explore how susceptible your passwords may be to a brute-force attack. For example, a 6-character password using only lowercase letters and numbers could take as little as 2 seconds to hack.

Whereas an 8-character password using uppercase letters, lowercase letters, and 10 possible special characters could take more than 60 hours to crack.

These hacking times are only estimations, but they do provide insight into the relative strength of different passwords. To learn more about password possibilities, check out the Passwords Collection on Maple Learn

The areas of statistics and probability are my favorite in mathematics. This is because I like to be able to draw conclusions from data and predict the future with past trends. Probability is also fascinating to me since it allows us to make more educated decisions about real-life events. Since we are supposed to get a big snow storm in Waterloo, I thought I would write a blog post discussing conditional probability using the Probability Tree Generator, created by Miles Simmons.

If the probability of snowfall on any given day during a Waterloo winter is 0.75, the probability that the schools are closed given that it has snowed is 0.6, and the probability that the schools are closed given that it has hasn’t snowed is 0.1, then we get the following probability tree, created by Miles’s learn document:

From this information we can come to some interesting conclusions:

What is the probability that the schools are closed on a given day?

From the Law of total probability, we get:

Thus, during a very snowy Waterloo winter, we could expect a 0.475 chance of schools being closed on any given day. 

One of the features of this document is that the node probabilities are calculated. You can see this by comparing the second last step to the number at the end of probability trees' nodes.

What is the probability that it has snowed given that the schools are closed?

From Bayes’ Theorem, we get:

Thus, during a very snowy Waterloo winter, we expect there to be a probability of 0.947 that it has snowed if the schools are closed. 

We can also add more events to the tree. For example, if the students are happy or sad given that the schools are open:

Even though we would all love schools to be closed 47.5% of the winter days in Waterloo, these numbers were just for fun. So, the next time you are hoping for a snow day, make sure to wear your pajamas inside out and sleep with a spoon under your pillow that night!

To explore more probability tree fun, be sure to check out Miles’s Probability Tree Generator, where you can create your own probability trees with automatically calculated node probabilities and export your tree to a blank Maple Learn document. Finally, if you are interested in seeing more of our probability collection, you can find it here!

The moment we've all been waiting for has arrived: Maple 2023 is here!

With this release we continue to pursue our mission to provide powerful technology to explore, derive, capture, solve and disseminate mathematical problems and their applications, and to make math easier to learn, understand, and use. Bearing this in mind, our team of mathematicians and developers have dedicated the last year to adding new features and enhancements that not only improve the math engine but make that math engine more easily accessible within a user-friendly interface.

And if you ever wonder where our team gets inspiration, you don't need to look further than Maple Primes. Many of the improvements that went into Maple 2023 came as a direct result of feedback from users. I’ll highlight a few of those user-requested features below, and you can learn more about these, and many, many other improvements, in What’s New in Maple 2023.

• The Plot Builder in Maple 2023 now allows you to build interactive plot explorations where parameters are controlled by sliders or dials, and customize them as easily as you can other plots

• In Maple 2023, 2-D contour and density plots now feature a color bar to show the values of the gradations.

• For those who write a lot of code:  You can now open your .mpl Maple code files directly in Maple’s code editor, where you can  view and edit the file from inside Maple using the editor’s syntax highlighting, command completion, and automatic indenting.

• Integration has been improved in many ways. Here’s one of them:  The definite integration method that works via MeijerG convolutions now does a better job of checking conditions on parameters so that they are only applied under proper assumptions. It also tells you the conditions under which the method could have produced an answer, so if your problem does meet those conditions, you can add the appropriate assumptions to get your result.
• Many people have asked that we make it easier for them to create more complex interactive Math Apps and applications that require programming, such as interactive clickable plots, quizzes that provide feedback, examples that provide solution steps. And I’m pleased to announce that we’ve done that in Maple 2023 with the introduction of the Quiz Builder and the Canvas Scripting Gallery.
• • The new Quiz Builder comes loaded with sample quizzes and makes it easy to create your own custom quiz questions. Launch the quiz builder next time you want to author interactive quizzes with randomized questions, different response types, hints, feedback, and show the solution. It’s probably one of my favorite features in Maple 2023.

• The Scripting Gallery in Maple 2023 provides 44 templates and modifiable examples that make it easier to create more complex Math Apps and interactive applications that require programming. The Maple code used to build each application in the scripting gallery can be easily viewed, copied and modified, so you can customize specific applications or use the code as a starting point for your own work

• Finally, here’s one that is bound to make a lot of people happy: You can finally have more than one help page open at the same time!

For more information about all the new features and enhancements in Maple 2023, check out the What’s New in Maple 2023.

P.S. In case you weren’t aware - in addition to Maple, the Maplesoft Mathematics Suite includes a variety of other complementary software products, including online and mobile solutions, that help you teach and learn math and math-related courses.  Even avid Maple users may find something of interest!

Hello everyone! Alex, Sarah, and I decided to create this collection of financial literacy documents as we noticed a lack of resources for this strand in mathematics. With many curricula around the world implementing financial literacy concepts, we thought it might be useful not just for Ontario, but for many jurisdictions around the world. 

There are 4 documents in the Simple Interest collection; Introduction, Equation Generator, Mental Calculations, and Reflection. The Introduction is designed for intermediate and advanced level students as it introduces students to the concept of interest and how to calculate it. Students get to fill in the table by filling in the calculations on the right. This provides enough scaffolding so students of various grades can participate in this activity. 

The Equation Generator document uses sliders to help students investigate linear equations in the form of y=mx+b. It also relates the simple interest equation (I=Prt) to the linear equation by asking students to compare interest rates. The idea behind this document is to bridge concepts outlined in the 2021 grade 9 destreamed math curriculum; in particular, the financial literacy, and linear relations strands. The document provides some reflection questions for students to think about the relationship between the variables.