The Need for Speed!

Here was our lesson today on Instantaneous rates of change/slope of a tangent line

Yesterday we completed the awesome Desmos activity Function Carnival!! Some students were extremely competitive when trying to match the motion of the cannon shot to their graph…..some students not so much……here are their graphs

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After showing the kids this picture we talked about the motion of the guy and how it relates to the graph…..Questions we had

  1. When would he be travelling the fastest? How do we know?
  2. When would he stop? How do we know?
  3. What happened after the parachute opened?

My goal here was to get talking about the speed of the guy. I asked:

If the guy was carrying a speedometer or a GPS…..what would his speed read out the moment before his parachute opened?

We stopped and made some estimates based on our intuition.

We talked about how to determine instantaneous speed from our knowledge of average rates of change, average speed, and slopes of secants lines.

We finally came to the conclusion that we could calculate the average rate of change between two points REALLY close together!!!!!! BINGO.

So I said let’s drop this image in Desmos! (we came to a decision that the cannon ball guy’s max height could have been around 9 metres).

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We looked at the graph and decided that it was HARD to estimate two points really close together.

So we added in some transformations to a basic quadratic function and fit the curve to the graph.Screen Shot 2014-09-12 at 8.44.11 AM

I had pre-loaded some “extra” info in the sketch to demonstrate graphically the idea we were coming up with……the idea of looking a the slope of a secant line and as one point gets closer to the next the slope of the secant line approaches the slope of the tangent line.

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After looking at it graphically…..we used the equation we came up with to algebraically calculate the slope of the tangent line (the instantaneous rate of change).

We then practice that calculation using other points the students were interested in knowing about.

That was our lesson on Instantaneous Rates! Thanks Desmos!!

Guess Who!!!

One of my kids’ favourite game is Guess Who…..remember this one?

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You remember it! I wanted my students to practice recognizing characteristics of polynomials without having to just complete questions out of the text book…..so I thought this game could work great! When you play this game you ask characteristic questions about the person you have picked and try to narrow the choices down…..all before the other person has guessed yours!

Perfect for characteristics of functions!!! Could also be great for my grade 9s who will later learn characteristics of linear relations.

I put this “board” together for the possible choices.

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And kids will use dry-erase markers and “paper protector” sheets so they can re-use the Game boards.

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Here are some pictures of my students playing the game

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Math is Like…. [first day]

Teaching mathematics is a journey that presents its own set of challenges and rewards. One activity that I have incorporated into every semester since I began teaching is what I call “Math is Like…”

This exercise aims to tap into students’ creativity and reshape their perception of math from something rigid and uninteresting to a subject that offers endless possibilities and connections.

To begin the activity, I distribute Post-It notes to each student and instruct them to write down the phrase “Math is like…”.

This simple prompt serves as a starting point for their creative expressions. I also share examples from previous years to spark their imagination.

It’s crucial to emphasize that there are no right or wrong answers, as long as the responses remain appropriate for the classroom environment.

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Unleashing Diverse Perspectives:

As students embark on their journey of self-expression, they unleash a myriad of thoughts and emotions through their “Math is Like…” statements. Some choose to inject humor into their descriptions, infusing math with laughter. Others reflect on past negative experiences or frustrations, seeking a fresh start. Additionally, there are those who offer insightful analogies, drawing connections between math and real-life situations. Allowing these diverse perspectives enables students to feel heard, understood, and acknowledged.

I have found that this activity gives students an opportunity to “air out” their past experiences with math. It allows them to express any preconceived notions or biases they may have developed and provides a fresh start for us to embark on a positive mathematical journey together.

As a teacher, I understand that my students come from diverse backgrounds in math, with varying levels of proficiency and different experiences. Some have had great experiences, finding joy and success in their mathematical endeavours, while others have faced challenges and setbacks. So I let them know that one of my goals this year is to help them change any negative beliefs they may hold about math and transform their experiences into positive ones.

Here are some “Math is Like…” statements that my students came up with. Looking at them, I realize I have my work cut out for me, but I’m excited for the challenge because each statement represents an opportunity to make a difference in these students’ mathematical journeys:

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As I read through these statements, I’m both humbled and motivated by the task ahead. I am committed to nurturing a love for math in each student, helping them realize their potential and embracing the wonders of this beautiful subject. Together, we will rewrite their math stories and create a positive, empowering narrative for their future mathematical adventures.

Minnie’s Juice Cup [3actMath]

Here is a 3-Act Math problem I’ve been working on. My first unit in the fall is measurement and I wanted something to do with volume.

Minnie’s Juice Cup!

Act 1:

Question: How many juice boxes will fit in the cup?

Act 2:

Make them guess for each of these measurements.

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I am open to suggestions on how to handle the two different diameters. I tried averaging them and came up with a pretty accurate answer.

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Act 3:

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