Math Analysis
Function Scavenger Hunt
I used this activity, which was developed by a colleague of mine during our section covering function transformations. Students are tasked with finding an image of some kind and using functions to trace some of the lines. Although I used this as an end of unit project, this could certainly be tried as a way to introduce the topic. Either way it gives the students the opportunity to use the 12-basic functions they are already familiar with, and experiment with how to transform them to meet their needs. It can really help them explore and solidify their knowledge of functions and how to reflect, translate, and dilate them. It can also help them to make connections seeing how math can be used to design and define the shapes of buildings, corporate logos, and other objects as well as mimic the natural world. Here is an example of what a student could come up with using an online graphing calculator called Desmos.Repeated Roots Lab
This is another activity developed by a colleague of mine that we used to help introduce what repeated roots are and how they appear on graphs of polynomial functions. Here is the worksheet we use. Essentially, this gives the students the opportunity, in a small group, to look for and identify patterns. The students may have seen this material before, but to many it is new. Through intuition and deduction, students are tasked with finding patterns and developing a hypothesis. They then discuss what they found and compare notes with the rest of the class. This is a great opportunity for students to discover and hopefully own a concept through investigation and pattern recognition, as well as an chance for them to share and discuss ideas with their classmates.Algebra II
Deriving the Quadratic Formula
In this activity, students have already learned how to complete the square, and many of them remember the Quadratic Formula from taking Algebra I. Unfortunately many students take for granted where the quadratic formula comes from and why it works to solve quadratic equations. This activity gives them a chance to investigate and discover how and why it works. Students are given links to videos and articles showing how to derive the quadratic formula by completing the square. They are then given the task, in a small group, of creating their own video or webpage explaining the process.Trying to teach others how something works can be a great way for students to better understand a topic. This gives them that opportunity while also having the chance to make something that others can use to learn how the formula works.
Mortgage Loan Activity
This is a project I've used to help students see how formulas and exponential models are used in real life. Students get to research careers and learn about loans. They see how to use online calculators while also learning what formulas the calculators actually use. Students really get excited about exploring the future and seeing what houses cost and what different careers pay. This also helps to take the mystery out of loan payment calculators and how compound interest works. Students create PowerPoint presentations to share what they hope to be doing in 10 years and where they might be living. They also learn how tax rates work as they work through income calculations and percents.Class T-shirt Activity
This is an open ended activity that can be used before students study systems of equations. With this activity, students are given some information about 3 t-shirt companies and their pricing models. They are also given a budget. They then have to decide how many shirts they want, what style, and how much they need to charge to cover costs. They create a graph of the companies prices and make a decision. This is a great activity because other than the prices of the suppliers, the students get to make their own decisions about the situation. Depending on what their group decides, they could all end up using different suppliers because of the quantities they choose. It also gives them a chance to budget and think about what their friends would be willing to pay for the shirts. Each group has the chance to share their decision and their graphs.It is a great lead in to systems of equations because it shows how we not only care about the solution (where the functions are equivalent), but also where they are different and what that means. It can be set up so that there is not one easy point where all three companies cost the same. This creates a very open-ended approach where depending upon how many shirts the groups order and of what type, each company could be chosen.
Geometry
SSS Straws Activity
This is a great way for students to explore and be introduced to triangle congruence. The set up is fairly simple: students in groups receive a few straws, some scissors and some string or twine. They need to measure and cut straw lengths into triangles, place the string through the straw pieces and tie off the string. If each group does this, then there should be a classroom full of congruent triangles. They can then do this with quadrilaterals. But they will see that given four lengths of straw, they may not place them in the same order and their quadrilaterals will not be stable.As a teacher, the takeaway is clear, when two triangles have all the same side lengths, then they are congruent. For students, this is another great opportunity to hypothesize about what this means. They can also, if there is time, make triangles and quadrilaterals with other side lengths. They can try to see if they can create cases that disprove their hypotheses. It can be a fun opportunity for discovery and generative thinking. This site has a decent description of the activity with the ability to prove a couple other triangle congruence theorems.
Solve Right Triangles Lab
When being introduced to trigonometry, one of the benefits is that students will be able to "solve a right triangle." This means that given a triangle with one right angle and either two sides or a side and another angle labeled already, students have the tools necessary to find all the other sides lengths and angles measures of the triangle. They can now use some combination of the triangle sum theorem, the Pythagorean Theorem, and the trigonometric ratios to find the missing information. Where this can get interesting is when students start solving using different methods and come up with slightly different answers.Often students will be most comfortable using particular methods over others. When they rely too heavily on particular methods, they often end up substituting rounded answers into the formulas. This can then change the measurements slightly. This can lead to a good discussion about why this is happening. Students can learn the importance of being precise and using exact information.
Computer Science
Explain the Program
I have enjoyed doing this from time to time when teaching programming. I will have a completed program on my computer and project it on a screen. The students then are tasked with figuring out how the program works. This can be done using concepts they have already learned in a different way, or to introduce a new concept. One of the benefits is that it gives some of the students the chance to play the role of teacher. Often a handful of students will be able to figure out the program first, or may already know how the program works. They then have to help the other students get it as well. The students can run the program and document the code to help the rest of the group better understand. This can also be done in groups where each group gets to see the program and test it out.Create a Class
When students start to learn more about object oriented programming, they will start creating their own classes. Often we can stick to examples in the book or do whatever is assigned. Another option is to simply let the students create their own class. It can be fairly basic: two or three fields, and some simple accessor and mutator methods; or it can be more complex: more fields, and some more complex methods. It can be a fun, open ended lab or assignment where students can solidify their understanding of classes or create something exciting and useful in their lives and future programming endeavors.Scratch Storytelling
Scratch is a fantastic and free online tool for introducing students to programming principles. The drag and drop interface is easy to learn, and the online community is a great way for students to connect and learn from each other. One of the basics of programming is learning how to order instructions. Student are asked to tell a simple story using Scratch. It can be as simple as one scene with a couple of sprites interacting or talking, or it can be a complicated program with lots of sprites and lots of activity. Either way, it is a great open ended opportunity for students to create a simple animation program on their own.Great discussions can follow as students share what they learned from the experience and share their programs with their classmates.
