One of my favorite recent technology tools has been the ability to incorporate Mathigon Polypad screens into a Desmos classroom activity. Last week I had the opportunity to work with a high school class learning to change from standard form to vertex form of a quadratic using completing the square. I thought this would be a great opportunity use virtual algebra tiles in a Desmos activity. Students at this school have had lots of experience using physical algebra tiles in previous grades so these students were already familiar with the manipulative. The activity starts out with a review of perfect square numbers and then shows how these relate to perfect square polynomials. Then we moved to using virtual algebra tiles in Polypad to model perfect square polynomials. From there we progressed slowly towards completing the square. Once we built up to generalizing the process of completing the square, students had an opportunity to practice this skill. Instead of giving them feedback on the correctness of their answers, I was able to give them pictures of the algebra tile representation to compare their answers to. I think this helped students reflect on their answers instead of just looking for a green checkmark. I used the pacing tool to make sure most students had finished the question before moving to check their work on the feedback slide. Desmos had an amazing guide to help teachers reflect on the activities they've created. It is called "The Desmos Guide to Building Great (Digital) Math Activities v2.0". I encourage everyone to check it out. Students seemed to enjoy this Desmos activity and the dashboard allowed me to provide targeted support to the few students that appeared to be struggling. After this we did some additional practice and consolidation using a completing the square fill in the blanks sheet from Dr. Austin Maths (a great site for a variety of practice resources). Nova Scotia Mathematics Curriculum Outcomes Precalculus 11 RF04 - Students will be expected to analyze quadratic functions of the form y = ax² + bx + c to identify characteristics of the corresponding graph, including vertex, domain and range, direction of opening, axis of symmetry, x-intercept and y-intercept, and to solve problems.
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