As an introduction to Linear Relations with my combined 1D/1P grade 9 Math class we investigated height VS foot length and the guinness record holder for the tallest woman:

I asked students to measure their height and foot length and record it on a Google Spreadsheet we had up on the projector:

What do you notice?

What do you wonder?

I posed this question:

Zeng Jinlian was born in 1964 in Yujiang village in the Bright Moon Commune, Hunan Province, China. She holds the record as the tallest woman. She measured 2.48 m (8 ft 1.75 in) when she died on 13 February 1982. How long were her feet?

Estimate: _____ cm

Students were sent in their VRG groups to their VNPS boards to solve. Here are their boards:

Since it is still early in the semester I scaffolded the activity a bit by instructing them to create a scatter plot of the data on their board to help them solve the problem. I did not however instruct them to use a line of best fit, although many groups used that strategy to help them come up with an answer. Some groups had graphs with a Height axis that went high enough to lookup Zeng’s height and find the corresponding foot length from the line of best fit. Other groups made an educated guess based on the trend the points were showing.

Each student was asked to determine her foot length based on their graph:

I asked some questions on Pear Deck to get students thinking about the parameters of the problem:

We discussed some of the above responses that did not meet the criteria of a total of 70 legs and why.

Students went to their boards in their small groups to solve this problem:

She has 26 animals all together. There are 70 chicken & goat legs all together. How many chickens? Goats?

Most groups were very unsure as to how to proceed in their solving. Most were simply guessing & checking various pairs of numbers. After a few minutes of allowing that productive struggle, when I noticed frustration setting in for some, I asked if anyone had considered drawing animal bodies & assigning legs to them? Here are the student boards:

This group’s work is a combination of the divying up legs strategy & them finding the answer on other groups’ boards.

This group never got to the answer. They were drawing 26 of each with plans to take & give some legs from one group to the other.

Was floored by the amazing explanations by this group!!!

We returned to our seats and our Pear Deck session & I put it into student-paced mode. I asked them to create the equations for the various parameters of the problem:
They struggled with this so I did some direct teaching about how to build the equation for this and the next slide:

Students were asked to use Desmos to graph their 2 equations & then sketch the graph and point of intersection:

Students were asked to develop an algebraic solution using the elimination method:
Not all of my students are comfortable with the algebra still (even though we’re at semester’s end now).

I like that we used 3 different methods of solving this problem; diagramming, graphing & algebraic. I want my 2P students to know they can always fall back on “less sophisticated” methods to solve these problems at evaluation time (as opposed to the algebraic solution).

The resources can be found here (including the Pear Deck interactive slideshow).

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

I’ve done this activity once previously. I changed how I did it for this second go. I will change it again for next semester.

Here’s how it went this time …

Students were presented with this data:

Students were asked:

The task for day 1: Determine the initial value & rate, on average, for flights with Air Canada.

this group started trying to find the average cost per kilometre. they then switched to a linear regression on desmos after seeing others doing that.

This group worked with a quadratic model. And while it wasn’t the target learning goal for the lesson, it turned out to be a better fit than linear! Made for a great class discussion.

this group was working on a average rate per kilometre after seeing another group try the same

love how this group labelled the rate & initial value

Some groups went to Desmos straight away. Others needed some reminding that Desmos can be very helpful with data like this.

On day 2, groups were asked to determine the distance they could fly for $500 using their equations from the previous day. I only took a photo of one group’s board that day:

I think next semester I will change this up. I think I will present the name of a city & ask students to estimate the cost of flying there. Then I’ll give them the set of data for cost & distance for multiple cities, but with the first city blanked out; perhaps allowing them to adjust their estimate if they like. We’ll do notice & wonder, and then proceed to solve for the price. I won’t specify modelling algebraically but will perhaps create a Desmos activity builder they can do to practice that in the case where they don’t use an algebraic model to solve.

Update: Find the Desmos activity builder follow-up here

I started out sharing on Twitter, and it wasn’t until I felt the real need to move beyond 140 characters that I tried blogging. My blog has been a place to go into more detail on activities I’ve done with my classes or strategies I’ve been implementing. But I wanted to look back and archive some of what I shared on Twitter here on my blog. So I’ve compiled a rough list of top-ish tweets (as best as I can tell using analytics.twitter.com):

The Ottawa Slow EdChat was the brainchild of Derek Rhodenizer & Sandra Walker. It fizzled out at the end of 2015, so with their permission I tried to get it back up and running for 2016. It now has its own Twitter profile so everyone can easily find the weekly question. If you live in the Ottawa/Gatineau area I hope you’ll consider giving it a follow!

People seemed to really like my sketchnotes of the OAME conference Ignite sessions. They’re a bit wordy -should be more visual, but it made for a good review of the talks. And got a lot of people asking more about sketchnoting too!

Students need to be doing more Math than you are. You should be watching them solve problems, not vice versa. #bfcedu

This tweet proved popular and I wanted to make sure to include it as it’s one a few top tweets not including a sketchnote. The #BFC530 chat is a great 15 minute chat in the morning for early risers!

This last one is sort of cheating as this exact tweet was posted in January 2017. But as I finished the sketchnote for each section of the book through the fall of 2016 I posted them to Twitter & they each got big views. So I finally used some holiday time to finish the book and posted all 4 sketchnotes in this tweet above. So it’s summarizing the earlier tweets here.

Mostly I notice that all except one of my tweets that did the best contain sketchnotes. People really love the visual summaries of talks, videos, articles & books! Get in touch if you’d like to learn more about sketchnoting. I will hopefully blog about the topic in 2017 as well!

A big thank-you to my Twitter PLN for sharing, listening, advising, and pushing. I can’t being a teacher without all of you to work with!

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

My blog has steadily increased its views over the years which is great:

It’s pretty neat to see where in the world readers are from:

It turns out that none of my top 5 blog posts for this year were written in 2016. Not sure what to make of this fact. Perhaps I’m not blogging about things that interest others as much; I have been blogging more about specific activities than big ideas lately. Thoughts?

Here are the top 5 most viewed posts from my blog in 2016:

Teacher Interviews: April, 2014. All about the topics that teachers in the OCDSB should be ready to speak to in an interview. Viewed 2.5 times more often than the next place finisher. When I meet new teachers in my school or board, this is the post they mention to me most often.

Number Talks in High School: November, 2013. Written at a time when I still opened each class with a bellwork / warm-up. I no longer do, but I still use the basic concept of a number talk to structure discussions in class about a given calculation. Also, with my ELD (pre-ESL) math class, I had my student teacher doing one number talk a day to start each class in December.

Visibly random groups & vertical non-permanent surfaces: November, 2014. Incorporating VRGs & VNPSs into my classroom was a game changer for me and my students. Teachers often find this post when they Google the acronyms VRG & VNPS to find out what they are. I also share this post online often with teachers if I think it’s something they might be interested in.

A day in the life of a Math teacher: November, 2014. This was a blogging challenge put forth by the Explore MTBoS team a year previous. It also happened to be a very strange teaching day due to a scary incident that ground much of our city to a halt for lockdowns.

Assessment & Evaluation in the OCDSB: March, 2014. My school board implemented a big shift in our assessment & evaluation policies & strategies. Many teachers were reluctant, but I found a lot of great things about the new system. I created a 4-part series about the new system to try to share what I knew about & how I was using the new ideas in my classes.

Did I peak in 2014 in terms of blogging?

Thanks to everyone that has read something I’ve written this past year! I appreciate all the great feedback I get on Twitter, in the blog comments and face to face. It’s this online community that helps pushing my thinking and encourages me to keep trying new things, so thanks to all of you!

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

The first time I’ve heard a group of my colleagues excited for an education-related book was for Innovator’s Mindset by George Couros. We all bought a copy of the book and met after each of the 4 parts to discuss the ideas he puts forth. The discussion questions at the end of each chapter made hosting a book club so easy and really made us think as we read through the book. I sketchnoted summaries to help myself remember the information better & want to share them here:

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

Today while Ms. Fahmi, my student teacher, was teaching I went to take a photo of the students at their boards solving in their groups. Then realised that I should try taking some video since there are several of us in the room & I can take the time to do so (I had parents choose at the beginning of the year whether or not they were comfortable with me including photos & videos of their child in class on my professional learning network platforms)

This past weekend I presented at EdTechTeam’s summit in Rosemere, QC. Their summits are designed to immerse teachers in EdTech for the weekend, learning all about the Gsuite tools (formerly GAFE; Google Apps for Education). Here are my sketchnotes from the weekend:

My pen & paper notes from the sessions I attended:

My digital sketchnotes from the 3 keynote speakers:

This summer Pear Deck announced the introduction of student-paced mode; the ability for the teacher to allow students to work through the slide deck at their own pace. This is a feature I enjoyed in the Desmos activities I’d been building for graphing (interesting also that Desmos introduced their teacher-paced mode around the same time that Pear Deck introduced student-paced; both platforms now offering both pacing options).

Not sure what Pear Deck is or does? Watch this quick video before reading further:

How to turn on student-paced mode:

Click the 3-dot menu icon on the bottom right of your screen while presenting your Pear Deck, and the option to turn student-paced mode on (or off later) will be there:

Act 1 consists of present my students with a scenario via photo or video & asking them

What do you notice?

What do you wonder?

Then I show them the problem I’ve chosen for the day (usually it’s one that most kids write down for “what do you wonder?” since I’ve carefully selected the scenario to lend itself to asking the question I want based on our learning goal).

Estimate the answer: too high, too low, best guess?

Act 1 happens via Pear Deck in TEACHER-paced mode. Students are at their seats in their visibly random groups for the day assigned by playing cards. They use their own phone or a loaned chromebook (I have 6 that live in my classroom) to answer these questions on Pear Deck. We often have a quick class discussion here too about reasonable estimates and their strategies for that. I, as the teacher, am choosing when to move the slides forward for the entire group.

Act 2 consists of sending each group to their assigned vertical non-permanent surface (ie. chalkboard or whiteboard) to solve the problem. Often groups also need to do some data collection or measurement here in order to solve the problem.

At this point I have a slide with the original picture & the problem to solve written on it projected on the board while the groups are solving. The moment the first group to finish solving heads back to their seats, this is when I turn on STUDENT-paced mode. The rest of the slides will be follow up questions to reflect on their solution or to apply their thinking to extension problems. Students work on these at their own pace at their own desk.

When all groups are done and back at their seats, I lead a class discussion about the solutions from each group using the 5 practices for orchestrating productive mathematics discussions. During or after this discussion, we might also look at some of the responses to specific follow up questions on Pear Deck. If we do, I turn OFF the student-paced mode to bring everybody’s screen back to whichever one we are discussing.

Act 3consists of checking our answer either in real life (as we did for the cup stacking activity) or by showing a video or image answer (as we did for the phone charge activity).

Normally, in Pear Deck, there is a projected screen being shown on the board to the whole class by the teacher. The students see a “response” screen on their own device that is different than the one being projected. When in student-paced mode, the student can see both the content slide AND The student response slide on their own device. On a tablet or laptop the two screens are shown side by side when in student-paced mode:
When using a smaller device such as a phone or iPod, the student will see a blue bar across the bottom of the screen allowing them to toggle back and forth between the “content” & “response” screens:

Have you used student-paced mode in Pear Deck yet? Share in the comments below how you use it with your own students!

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)