Students know to find the derivative of the position function to get the velocity function, which is used for instantaneous velocity. Here’s an example: we are given a position function and asked to compare an average velocity over an interval to an instantaneous velocity at a particular time. tangent lines, distance – velocity – acceleration scenarios, or a specific example of a function. Compare the algebraic formulas, graphical views of secant lines vs. There’s a lot for students to unpack about the concept of “instantaneous rate of change,” which is one version of the derivative. DifferentiableĮxample 2: Average Rate of Change Instantaneous Rate of Change Here are some groupings to choose from, or mix and match, or create your own images. Or, turn it around and use some graphs as the prompt. Here, students can explain using graphs or verbal descriptions. You can present the prompt with the terms only, or use some of the images as the prompt. Students encounter lots of unfamiliar terminology in Calculus! Same and Different prompts can help deepen understanding of the underlying concepts. With so much detail in the AP Calculus material, using this routine is particularly powerful to help students distinguish between similar looking problems and review as the AP exams approach in a few months. Technology can be used to illuminate some of the numerical and graphical features, although it is not required. The routine is launched by presenting two or more math situations, then have students examine and note how they are the same and how they are different. They may require different solution strategies, be similar except for one feature, or have mathematically meaningful nuances to notice. To recap, “Same and Different” asks students to compare and analyze features of two mathematical situations. I have been using this thinking strategy recently with my Calculus students, and I wanted to share another set of prompts. In a previous post, I shared over 25 images to be used with the “Same and Different” inquiry routine in secondary math classes. SOLUTIONS!! The Answers to the April 1993 Calendar of Problems are HERE. If the image isn’t readable, the pdf of the April 1993 calendar is HERE. I’ll post the solutions pages at the end of the month, and pick a new month from my attic to share for April. Tell us about your worked-out methods either here in the comments, or on whatever platform you use 2. Share with your students if desired, or solve them yourself. If you want to get an email notification when I post the next month’s problems, enter your email address here:Īs we launch into April, I hope you are excited for another month of problem solving! Check out the April 1993 Calendar of Problems from my cache of old Mathematics Teacher 1 issues still hanging around my attic. If you are looking for helpful educators, shared resources, and thoughtful discussions, find us wherever you are online. There are bountiful resources available to members at, along with some free resources.ĢThe hashtag MTBoS is an acronym for “Math Teacher Blog-o-Sphere” and is an online community of math educators using a variety of platforms (Twitter, Facebook, Mastodon, etc.). Contact me & I’ll send some to you (US addresses only).ġThe Mathematics Teacher journal is a legacy journal from NCTM - the National Council of Teachers of Mathematics - the professional organization supporting math educators in the US and Canada. If you’d like to take some old issues of Mathematics Teacher out of my attic storage, I’m always looking for new homes for them. SOLUTIONS!! The Answers to the May 1994 Calendar of Problems are HERE. If the image isn’t readable, the pdf of the May 1994 calendar is HERE. I will be taking a summer hiatus from Calendar Problems for June, July, and August, since the old Mathematics Teacher issues in my attic were only published September through May. I’ll post the solutions pages at the end of the month. Spring is underway here in Connecticut, and we’ve got another month of problem solving! Check out the May 1994 Calendar of Problems from my cache of old Mathematics Teacher 1 issues still hanging around my attic.
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