Turning Textbook Questions into Problem-Based Learning Activities

Over the last few years I’ve done my best to create a student-centred Math class using a mix of Dan Meyer’s 3 Act Math strategy, Peter Liljedahl’s Thinking Classroom framework and some other routines like Notice & Wonder mixed in, all in a Pear Deck interactive slideshow.

This week I wanted a problem-based activity on volume so I turned to my version of a textbook; Khan Academy practice sets. I picked a problem that my students will see during their independent practice problems on the Khan Academy website and fleshed it out to create a student-centred activity out of it. Thought I’d share the process with you to show that you can take (sometimes boring) problems right out of a textbook & create a student-centred thinking task for your class.

Here’s the original problem from Khan Academy:Screenshot 2017-10-24 at 8.28.49 AM

So my first task was to find an actual image of a tent and use Google Drawings to add the dimensions as well as the volume to the image:Tent

So this is what I show students to start. I do not tell them yet that I want them to find the height. I have a series of questions we run through every time that I build in a Pear Deck slideshow (where students will be able to answer on their phone & I can display their answers on the board). But you can just ask the questions orally if you like.

Here are the questions/steps:

  1. What do you know / notice?
    They should tell me facts that they know.
    Eg. The tent is the shape of a triangular prism. It has a volume of 70 ft^3.
  2. What do you wonder?
    What questions come to mind?
    Eg. What is the height of the tent? How much canvas is need to make the tent?
  3. Now I tell them the question I want them to explore … for this tent the question was “Can you stand up straight in this tent without hitting your head?”
  4. Estimate:
    – too high
    – too low
    – best estimate
  5. What do you need to
    – measure
    – google
    – calculate
    in order to solve this problem? (plan)
    Whenever possible I bring a hands-on object in that they can physically measure. This time I gave them the measurements of the tent.
  6. Then I send each visibly random group of 3 to their chalkboard or whiteboard section to solve the problem. During this time I’m walking around managing what Peter Liljedahl calls FLOW by giving hints (usually in the form of a question) to those that are stuck and extensions to those that are done the original question (for this tent, how much canvas is needed?). Sometimes this involves calling all groups over to one spot & I do some direct teaching if they need to learn something new or review something to move on.
  7. When all the groups have solved the problem, students return to their seats and I debrief / consolidate the activity by “narrating a story” as Liljedahl says of the student work. I found the “5 practices” article really helpful in learning how to do this.
  8. At this point I reveal the correct answer (needed more if they are taking their own measurements to see how close their answer is to the real answer; for example how tall the lamppost outside actually is after we solve for its height using shadows & similar triangles).
  9. We go back & see who’s best estimate was closest to the actual answer. We celebrate the closest estimate.
  10. Which of the overall expectations from our course did we use today? (reflection)
    This is where the learning goal of the task comes out – at the END. If I say this up front, then it takes away all the student thinking about what math they can use as a tool to solve the problem.
  11. I encourage them to take a photo of any group’s board they wish to save in their notes.
  12. Finally, usually the following day, they do some individual practice using some of the problem sets on Khan Academy.

Hopefully that all makes sense and shows a bit about how you can take a typical textbook or worksheet type word problem & turn it into a more student-centred learning task. If you want to see examples of this type of lesson with student work, have a look at my collection of lessons I have blogged about.

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

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Pumpkin Challenge #3ActMath #MFM2P

It all started with a trip to the grocery store where I noticed a giant pumpkin on display & a prize of $50 in gift certificates if you could guess the weight of the pumpkin:20171012_160744-01

I went back a couple of days later to take some measurements of the giant pumpkin, bought 4 smaller pumpkins of varying sizes & we were on our way!

Day 1

Act 1

What do you know / notice?Screenshot 2017-10-26 at 5.49.51 PM

What do you wonder?Screenshot 2017-10-26 at 5.51.09 PM

Estimate the weight of the pumpkin in pounds:
I passed around a 1lb bag of barley that all the student We start with a guess that’s too high (but not silly like 5000 lbs), then too low (but not silly like 1 lb). Then they make their best estimate:Screenshot 2017-10-26 at 5.53.37 PM.png

Then I have them do a turn & talk with their group (visibly random groups of 3) to discuss what they need to a) measure, b) Google c) calculate in order to solve this problem.

Students made a prediction about which characteristic of the pumpkin the weight would depend on most:Screenshot 2017-10-26 at 6.52.09 PM.png

Act 2: 

I revealed some measurements I’d taken of the giant pumpkin:Dimensions

We had 4 pumpkins of various sizes at stations around the room with a scale to measure weight and rulers & measuring tapes. Groups were sent to their vertical non-permanent surfaces to begin collecting & recording data about any measurements they thought they might need for the pumpkins to help predict the giant’s weight:

Groups recorded measurements and started calculations for volume, etc. in order predict the giant pumpkin’s weight:20171018_143719

At this point we hit the end of the class period. Some groups had some volume calculations but none of them had got to (or really thought of) creating a table or a graph of weight depending on another variable to make a prediction.

Day 2

I was away this day & so students had the period to do some independent practice on Volume & Surface area word problems on Khan Academy.

Day 3

I wanted students to graph weight VS diameter, weight VS surface area, & weight VS volume. So I created a Desmos Activity to walk them through that process:Screenshot 2017-10-27 at 10.57.39 AM.png

I provided students with the raw data they would need (as they had already worked on these types of SA & Volume calculations the previous period – today’s learning goal was all about the linear & quadratic relations between different variables):Screenshot 2017-10-27 at 11.00.16 AM

They found the line of best fit and quadratic curve of best fit. We had a class discussion about which one fit the data better … quadratic!Screenshot 2017-10-27 at 11.03.29 AM

They they used that curve to predict the weight of the giant pumpkin based on diameter:Screenshot 2017-10-27 at 11.05.01 AM

I walked them through that first set of tasks step by step as a whole class making sure everyone understood. Then I turned the Desmos Activity to student-paced mode & let them continue the same graphing tasks for weight VS surface area & then volume (although many of my students gave up working on it once I was no longer leading the class through the activity slide by slide).

Each student had filled out an entry slip for the pumpkin contest at the end of day 1, and I allowed them to adjust their entry if they wanted based on today’s work. I then dropped off all of their entries after school:
Screenshot 2017-10-27 at 11.25.46 AM

Day 4

Started class by revealing the weight of the giant pumpkin.
DRUM ROLL PLEASE . . . 166 pounds!!!

I then presented them with a the 3 models we created, each showing the giant pumpkin’s actual weight as an orange dot & asked which model was the best predictor for the giant pumpkin:Choose a modelScreenshot 2017-10-27 at 11.42.02 AM

I finished by having the students drag dots to any Math from our course that we used over the last few days with this activity:Screenshot 2017-10-27 at 11.44.23 AM

Students had the rest of the period to do some individual practice on “Graphing linear functions word problems” on Khan Academy.

My folder with everything for this activity can be found here. The unassociated files are the Pear Deck interactive slide decks.

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

Push-Back to Student-Centred Learning. #sketchnote

I’ve often said that I would hate to be a learner in my own classroom. I was a very strong student in high school. I didn’t need to be in class; if I missed class I would read the section in the book & do the homework problems & learn it myself. I made beautiful pages of copied notes from the teacher’s board and was able to understand the content as I copied. I did not enjoy group work; hated relying on partners to do their bit. I am still the first person to roll my eyes at ice breakers in a staff meeting or workshop.

And yet, my classroom is the opposite of this. I ask my students to work in groups, beginning with a getting to know you question every day since we change groups daily. I don’t give many notes, rather I give students time to summarize their new learning in their course packs. We do problem-based learning with hands-on components whenever possible. This is a far cry from the teacher notes followed by homework problems routine from my day.

But many to most of my students are not able to learn that way (although a small number of them are & would prefer a more traditional teaching style). Most can’t understand the notes they’re copying down because they’re too busy copying. (Have you ever asked your students if they’re able to listen to the teacher while they copy notes? My students tell me straight up that they are not able).

So over the years I have searched for strategies & pedagogical methods that would transform my classroom to be a better learning environment for my students. But my students haven’t always been eager about my methods; group work, problem solving, critical thinking, feedback separated from marks, etc. The workings of our Math classroom are so different from their experience so far that they sometimes push back. And for many teachers, this push back stops them from continuing to pursue different teaching methods. For example, I’ve had students say “you don’t teach us!”. But upon drilling down further as to what they mean, it becomes clear what they really mean, is you don’t write long, detailed notes on the board to copy down. They think that is teaching and don’t view the careful orchestration of a student-centred classroom as teaching also.

My advice to teachers: keep trying! Don’t let that student (or parent) push-back stop you from pursuing new & innovative teaching methods. It’s normal – it happens to all of us! But eventually students (most anyway) get past it. Alice Keeler shared this great article entitled “NAVIGATING THE BUMPY ROAD TO STUDENT-CENTERED INSTRUCTION” by Felder & Brent that likens the student push-back during student-centred teaching to the 8 stages of grief. I love sharing the article with teachers that are frustrated by students that are reacting negatively when they try to transform their classroom to a student-centred learning environment. So to make the ideas even more shareable, I put together a sketchnote version:

Student centred instruction.jpeg

But I really do encourage you to read the whole article as the authors go on to explain some suggestions as to how to mitigate the push-back, such as sharing with students the reasoning behind the methods, and modelling & establishing criteria for the successful use of the critical thinking skills expected of students.

I’ll finish by including a few of the tweets from other teachers on the topic:

What push-back have you experienced in your classroom and how have you dealt with it?

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

Running VS Walking Headstart #MPM1D #MFM2P #3ActMath

A month ago or so I read a post by Mr. Hogg about his Fast Walker activity. I thought it would be a great way to introduce linear systems graphically to my combined grade 9 math class before the end of the semester. I also did this activity with my Grade 10 applied students – next semester I’ll use it as an introduction to systems graphically with them earlier in the course.

What turned out to be super awesome is that a student in my grade 9 class just won gold at OFSAA last week! So I tweaked Mr. Hogg’s activity to use Joe’s winning data in our problem. I also structured the activity to be a 3 act math task. Here’s what we did:

Act 1: Notice – Wonder – Estimate

Runner Speed (1)

What do you know / notice?Capture

What do you wonder?Capture

If you want to cross the finish line at the same time as Joe, what distance head start will you need?Capture.JPG

Act 2: Measure & Solve

Capture.JPG

Students were told they had to stay in class when taking measurements; my idea being to force them to time themselves walking over shorter distances (the length of our classroom) and then use that to model their speed for this problem given. Each student had to calculate their own head start:

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Act 3: Check & Reflect

We went out to our 400m track and students measured out their starting position. They staggered themselves according to their calculation (photo below – tried to take video but my phone battery died). Most students were around 100m before the finish line (~300m head start). We counted down & Joe started running & the class started walking. I so wish I’d gotten the video because it was awesome how close they all finished to each other!DB6mp2rXgAE8O55

I had my grade 9s graph their walk & Joe’s run on the same grid. Here are their graphs overlaid on top of each other:
Capture
Most students had the right idea, and I talked to a few with incorrect graphs individually but when I look at this overlay now I can see that I missed helping a few students correct their work 😦

We discussed which line was partial variation & which one was direct. I then introduced the language of “linear system” and “point of intersection”. My 2P class time to create an equation for each line also.

The next time I try this, I’d like to add an individual follow up question such as if you only had a 50m head start, at what distance would you & Joe meet? At what time would that be?

Here are my files for this activity (the unassociated one is the Pear Deck slideshow).

Tech Tip: Did you know you can add the same Google Doc/file to multiple folders without copying it? I didn’t until recently. It was useful for this lesson because I wanted to have it in the folder for each of the 2 classes I did the lesson with! Once you’ve clicked on the file just press Shift+Z :Capture.JPG

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

Tree Height #3ActMath #MPM2D #MFM2P

Here is a tree height 3 act math activity I do for right angled trigonometry with both my 2D & 2P classes. The screenshots below were taken from my 2P class this semester.

Act 1: Setup

IMG_1636

Some noticings:IMG_2298

Some wonderings:IMG_2299

We do some turn & talk guesses for “too low” & “too high” then we go back to Pear Deck for our best estimate:IMG_2300

Act 2: Measure & Solve

Students downloaded a clinometer app onto one of the phones in their group.

Here are photos of last year’s group out measuring:

Up to the “vertical non-permanent surfaces” to solve in their “visibly random groups”:

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Act 3: Consolidation

This is one activity I don’t have a true act 3 for – I don’t know the actual height of this tree 😦 I led a class discussion going over the solutions from various groups. We discussed the fact that trig would not find the whole tree height & that groups needed to add the height of the person up to eye level to their value found using trig. I sent groups back to their boards to adjust their solution for this (final photos above).

The whole activity, including the Pear Deck file, can be found here.

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

#3ActMath – What is it?

I learned about a great tool this past weekend at the Ontario Summit; Adobe Spark video. A huge shoutout to Rushton Hurley for the introduction to this tool. It’s a super fast & easy way to combine photos, videos & text and narrate over top of it to create a seamless professional looking video.

I tried my hand and created one about 3ActMath lesson style. Give it a watch & let me know what you think:

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

Height VS Foot length #MFM1P/#MPM1D #3ActMath

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:Summary 2017.02.08 (1).jpg

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

Capture.JPG

What do you notice?Capture.JPG

What do you wonder?Capture.JPG

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: _____ cmCapture.JPG

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:Capture.JPG

Her real foot length was 35.5cm!

The following day students were assigned some individual practice with scatterplots on Khan Academy.

Activity materials (include a slide deck for Pear Deck) available here.

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

Flight Costs #MFM2P

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:copy-of-lr-flight-distance-vs-cost

Students were asked:

2016.12.21 notice.JPG

2016-12-21-wonder

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

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:2016.12.22 summary.png

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

Activity available here.

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

Video clip of students at work

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)

Here is a quick (1 minute) video clip of my students working on a visual patterns 3 act math task on vertical non-permanent surfaces in their visibly random groups:

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

Student-Paced mode in @PearDeck for #3ActMath tasks

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:file-DY4DfcYV8V.png

How do I use student-paced mode?

Most of the activities I do in my math class are in the style of 3 Act Math (a concept put forth by Dan Meyer).

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 3 consists 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:IMG_1923.PNG
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)