Using Card Tricks in Algebra

Incorporating short programming projects into high school math can be difficult as upper level math classes include more abstract concepts that do not always transfer well to short programming projects. I did not find any good Hour of Code or CodeHS programs that can be used to apply higher level math concepts and don't require extensive coding background knowledge. Without teaching full programming courses, I believe fun computational thinking exercises can still be emphasized and included in higher level math classes. 

Teaching London Computing created many activities that combine computational thinking and mathematics (https://teachinglondoncomputing.org/interdisciplinary-computational-thinking/computer-science-and-maths/). I evaluated their activity Red Black Mind Meld for the usefulness in an algebra classroom. I think this activity is a winner for high school algebra students. It is an unplugged activity, so no technology is required. It’s engaging, thought-provoking, requires substantial computational thinking, knowledge of algorithms, and also incorporates that dreaded word “proofs!”. It does all this by using a card trick that is sure to initially blow your students’ minds and hook them for the rest of the class period. The step by step instructions for performing the card trick can be found here (*.pdf), but be aware that those instructions also contain the answer. If using this in my classroom, I would provide the instructions for performing the card trick and remove the answers. Encourage students to figure out why the card trick works on their own, providing hints about setting up algebra equations, as necessary. After all, figuring out how it works requires an algebraic proof of the algorithm. It might be helpful to provide some pre-teaching about the words abstraction, algorithm, and computational thinking as these words are referenced multiple times in the Mind Meld instructions. I think this activity is also fabulous for TAG math students as you can easily expand upon it and require students to come up with variations to the algebra that will still provide an algorithm for a new self-working card trick. 

When it's time to reveal the answer, Teaching London Computing has a PowerPoint presentation you can download to explain the card trick. The algebra behind this algorithm is really slick and not too difficult to understand once students create the first basic equation. This activity clearly hits on multiple Iowa HS algebra math standards (2010), including: 

• A-CED-A.2: Create equations in 2 or more variables
• A-CED-A.4: Rearrange formulas to highlight a quantity of interest
• A-REI-A: Understand solving equations as a process of reasoning and explain the reasoning
• A-REI-C: Solving systems of equations
• MP1: Make sense of problems and persevere in solving them 
• MP2: Reason abstractly and quantitatively
• MP4: Model with mathematics

Teaching London Computing, while focused on spreading computer science and computational thinking throughout England, is also a great resource for math teachers in the United States to encourage "thinking outside the math textbook". 

References
Iowa State BOEE (2010) Iowa core mathematics. Retrieved from https://iowacore.gov/sites/default/files/k-12_mathematics_0.pdf

Teaching London Computer. (n.d.) The red black mind meld activity. Retrieved from https://teachinglondoncomputing.org/resources/inspiring-unplugged-classroom-activities/the-red-black-mind-meld-activity/