Here’s a suite of three ten-minute videos to be shared one at a time, in order.

Each discusses a single problem and how solving it is relevant for 21st-century practice. Each video ends with some extra examples to think about. (Head right to the end slide of each video to see the final questions,  if you are curious.)

Graphing Factored Polynomials

Graphing Rational Expressions I

Graphing Rational Expressions II

After the three videos are some resources on the algebra of polynomials and dividing polynomials. These resources can be shared and discussed with students too.

As usual …

INSTRUCTIONS

In the current universal state of “scrambling” to bring meaningful mathematics learning, exploring, and teaching to our students remotely, I offer here my recent scrambles too.

Here are some videos to share with students and discuss with students about how very standard curriculum topics can be absolutely relevant to 21st-century living, doing, and practice. We have loads of technology available at our fingertips and getting answers to problems is as easy as typing into Google. So let’s do that! Let’s get answers out of the way, type things into Desmos, or WolframAlpha, or hunt on the internet, and then get to the 21st century matters at hand–namely, sharpening our thinking and processing skills and practicing the confidence to take first steps–any steps– to handling problems in life. Math is a perfect vehicle to practicing exactly that.

So even if standardized testing is behind the times (no technology – pencil, paper, and calculator and focus on answers), fret not! The puzzling and noodling is way more important, is relevant, and way more fun, and there is plenty of time to noodle and puzzle and think. We can leave that testing as a side issue to be attended to on the side.

INSTRUCTIONS:

Have students look at and discuss as a whole group each video in turn. Have students try as many of the problems presented as they feel like doing, even if it is zero.  I say don’t worry about “instruction,” per se. Just make it all conversation about sousing your way though scenarios and relying on one’s own fine wits.

Bring in your curriculum materials as you see fit and discuss how thoughts and matters all beautifully tie together. 

WARNING: It might take some gentle work to establish that thinking and puzzling and conversing is the desired norm here. Work to establish that safety. Assessment no longer needs to be the defining factor of “success” in mathematics. Have participation and contribution to conversation be the definition now, of offering ideas that might or might now lead to a partial solution yet spur the conversation on nonetheless. Let question-asking and willingness to play with mathematical ideas  be the key marker of a mathematical thinker (which, by the way, I would fully argue actually is). Let the joy of conversation shine through.  

The Algebra of Polynomials and Rational Expressions

For the algebra of polynomials the place to send students really is Exploding Dots here, but this is leaping into the middle of a story. Have your students just blast through experiences 1 – 5 and then the algebra of polynomials will be a mind-blowing and astounding revelation!

I don’t have any explicit materials on the arithmetic of rational expressions, but you can divide polynomials, even with remainders, and that is often key to graphing rational expressions. Lesson 6.6 in the link above does the remainder theorem.

If your curriculum includes synthetic division, well, Exploding Dots naturally does that (and more!) with ease.

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