Two Truths & a Lie: Features of f(x)

I search the internet A LOT to find ideas. I had noticed teachers starting to do Two Truths & a Lie, so I thought I would try it with Calculus.

We have been discussing characteristics of functions and how to sketch the graphs of polynomials and rational functions using Calculus. I love this part of the unit - students finally see how calculus relates to topics that they have learned in the past. My students on the other hand aren't so happy...I hear all the time - We have a graphing calculator, why not use it? Thank you AP for making part of the exam calculator inactive so my students don't complain AS much since they know that it will be on AP exam. :)

The gist - students are given one function, instructions (I didn't use that this year), and a post-it note. They found critical numbers, inflection points, increasing, decreasing, concave up, concave down, extrema, and sketched the curve for their ONE problem. I also made them write a justification for each characteristic. Once finished, the students wrote down two truths and a lie about their problem on the post-it. There were no restrictions on their truths and lies (except it had to come from features of their function.)

On the board, I had the 4 functions posted. Students took their post-it and placed it under the correct function. Once all students were finished, I had students walk around and select a "new" function and a post-it where they decided which was the lie. If I had more time, I would have let the students work on more functions. But you know...I can never find extra time in a semester long AP class. :(

Instead of the gallery walk, you can also place the students in groups and do this:

I only had time for students to do one match and I wanted them out of their seats if only for a brief moment, so I changed it up a little this year and didn't use the instruction sheet.

Here is the activity: TTL Features of f(x)

~RJ

Comments

Polynomial Picture Project

Projects allow the students to show off their creativity and math skills! This one requires students to use Desmos to help create a polynomial function that fits a picture of their choice. As you can see with some of the projects below - the ideas vary immensely. Some of the students are very clever and others just use the McDonald's sign. However, each year, the students amaze us at what they find. Instead of using their calculators - here's how Desmos will find the regression line. In my video, I just did a simple quadratic, but our students have to create a regression equation that requires at least 3 relative extrema. Typically, we show the students how to use the Desmos regression option before sharing the project. Some students have trouble fitting the graphs because they choose too many points, and others are upset that it doesn't fit perfectly! We reassure our students that this is the best fit - not a perfect fit. Once students have the reg...

Limit Project

Well...we just got back into school after being out for almost 3 weeks because of hurricane Florence. Our school is okay, but there are many people out there suffering from losing so much. :( I had planned on a project for Calculus before the storm but will have to put that aside until next year! We have just lost too much time. However, I wanted to still share the project with you guys in case you would like to try it or something similar to it. I like to make projects a unique experience. I hate when all students do the same thing. #1 - students can and WILL copy. #2 - It's boring to grade! The idea of this project is floating somewhere on the web. I honestly can't remember where I got the idea. But I have altered it over the years to meet the needs of my students. It has gone through many alterations, and I will continue to change things. So it is not perfect! The gist - students find a recipe that has at least 5 ingredients. (The recipe ...

Arithmetic & Geometric Recursive Investigation

Investigation and student accountability is extremely important in education today. Students need to be challenged! They will learn so much more by discovering the formulas rather than me just placing the formula on the board! While talking to my intern about not finding anything cool dealing with recursive sequences, I got an idea. I wanted my kids to find a pattern and develop the arithmetic and geometric recursive formulas using the information that they already know. I created a cut and paste activity where students had to match the sequence, the type, the common difference/ratio, the explicit formula, and the recursive formula. From that, I hoped that students would be able to see a pattern! On a note card, I had them answer three questions...describe any patterns that you see, write a general recursive arithmetic formula, and write a general recursive geometric formula. The students did an awesome job until they were asked to produce the general rec...

Girl Math

Search This Blog