Would You Rather…?

WouldYouRatherMath.com is a site with great comparison problems that require students to justify their choices mathematically. They even have a worksheet students can use to show their work for Would You Rather…? tasks. Like the Comparing Quantities tasks shared earlier this year, this is another great way to get students to justify their thinking using mathematics.

More Desmos!

Screen Shot 2016-04-19 at 3.14.21 PMDuring my spring break last week, I has the privilege of spending a day with some incredible educators, Dan Meyer, and the Desmos crew at the Desmos headquarters in San Francisco. We even got to enjoy a chat from Phil Daro during lunch. I learned so much from everyone I spoke and worked with! And Desmos knows how to give a good swag bag. 🙂

If you’d like the details, please view the notes from the day at bit.ly/descon16.


Here is the fruit of my labor for the day: The Tortoise & The Hare, Desmos style. 🙂

Screen Shot 2016-04-19 at 3.02.57 PM

If you haven’t used the Desmos Activity Builder yet to create your own classroom activities, I encourage you to give it a try. I just started using the Activity Builder earlier this year, and it really is intuitive and easy to use. A good read before you start is Dan Meyer’s blog post, Desmosify Your Worksheet.

If you create an activity, please share in the comments!

I’m lovin’ Desmos Classroom Activities!

desmosconicsI began using the Desmos graphing calculator with my students at Maryknoll in 2012 and have LOVED it, but I didn’t really explore the Desmos Classroom Activities in-depth until this year. It all began at our Northshore School District Summer Institute this past August with Dan Meyer when he had us do the Central Park activity. I was hooked.

At a district PD session last week, teachers started off with a quick Desmos graphing calculator overview and learned how to create sliders. Next we explored the iPhone 6s Opening Weekend Sales activity to see an example of a task that was adapted using the Desmos Activity Builder, and we read Dan Meyer’s post, Desmosify Your Worksheet. Then teachers choose a lesson of their own and turned it into a Desmos Classroom Activity. Here are a few examples:

Teachers used these activities with students this week and were very happy with the results. One of the reported advantages was that graph windows are preset for students so they could focus on the mathematical concepts being studied rather than getting sidetracked by technical issues.

The sliders also made exploration MUCH easier. In the past, using these lessons with a standard handheld graphing calculator meant that students had to enter several equations to explore the effect a coefficient has on the graph. Now the sliders allow a student to view numerous graphs instantly.

If you haven’t yet explored the Desmos Classroom Activities or tried out the Activity Builder for yourself, I highly encourage you to do so!

Productive Strategy: Comparing Quantities

Comparing Quantities (qualitative comparisons) is a classroom routine that make student thinking visible and supports the Standards for Mathematical Practice. It can be used at any grade level and with a wide range of content.

The basic idea is to give students two quantities, Quantity A and Quantity B, and ask students to decide if:

  • Quantity A is great than Quantity B (>)
  • Quantity A is less than Quantity B (<)
  • Quantity A is equal to Quantity B (=)
  • There is not enough information to determine (?)

Students make their conjecture and provide two reasons to support their conjecture.

Here’s a 6th grade example for ratios:

Comparing Quantities activities are most effective when they get at a big mathematical idea rather than just computation. In this 6th grade example, the big mathematical idea is understanding the difference between part:part vs. part:whole ratios.

If you are interested in using Comparing Quantities in your classroom, resources are available in this Google Drive folder. The folder contains activities for each grade level grade 5 through Algebra 2 as well as a blank template and lesson guide. If you have questions about these resources, just let me know!

See you at AMLE 2015!

AMLE 2015Middle School Educators, I’m looking forward to AMLE 2015 next week in Columbus, OH! I’m planning to attend some great sessions and will be presenting with my ELA colleague, Jeanne Flahiff, on how we are using DOK and proficiency scaling in Northshore School District to operationalize the Common Core State Standards in ELA and mathematics. Click here to learn more about our session. Hope to see you there!

Following Their Questions: The Dead Horse Lab

The activity that became “The Dead Horse Lab” didn’t start out that way. It actually wasn’t intentional. It started out as a “dead body” problem in our calculus text, similar to this one.

My students asked questions: “Is this accurate in real life? Does this really work?” Instead of answering these questions like I usually would, I said: “That’s an interesting question, how could we find out?”

This led to some VERY INTERESTING discussion which then led me to establish one parameter: We weren’t going to kill any creature just to test this theory, even if Emily didn’t really like her cat. One of my students said his uncle works with a vet and it might be possible to get access to a euthanized animal. We decided this might be a possibility.

It turned out that the vet was scheduled to euthanize a horse. We got permission from the vet and horse owner and made arrangements for the euthanized horse to be brought to school for students to collect data. Then my students had to decide what information they would need to collect to answer their question because I had no lesson plan for this, we were in uncharted territory for me as a calculus teacher. Students decided what data we would need to collect:

  • time of death
  • body temperature of the horse at various time intervals
  • air temperature.

Students also conducted research at home and brought back some interesting facts:

  • Horses have a normal body temperature of 100-101.5 degrees.
  • The most accurate way to take the temperature of a dead body is internally in the liver.
  • When laying on its side, a horse’s liver is about 3 inches beneath the rib cage.

Students gathered a scalpel from the FFA teacher and large thermometers from the science lab, assigned data collection tasks, and had their parents sign permission slips to avoid weird explanations after the fact. When the day arrived, students collected their data. Students recorded body temperatures at multiple times from multiple locations (internally in the liver and rectally) and air temperatures. Then we began our analysis.

What did my students learn from this?

  • First, IT DIDN’T WORK. The data they collected didn’t accurately predict the time of death, and our book was WRONG. My students learned that real life mathematical modeling can be MESSY and not as simple as a textbook story problem. It also lead to more research, where students learned about founder and the possible effects of inflammation on body temperature.
  • Second, they learned how to use mathematics to test their OWN question, not just mine or one presented by the text. I hope that’s a skill they carry through life.

What did I learn from this?

  • Real modeling is MESSY. Don’t be afraid, do it anyway.
  • You can learn more from the “failure” than the perfect lesson.
  • Follow THEIR questions! Kids ask questions because they are interested. If you want them to be interested in mathematics, make time to investigate the questions they find interesting.

The Dead Horse Lab may not be an activity that you want to recreate for your students. 🙂 But I do encourage you to listen to the questions your students ask and to follow them when possible.