Buying Calculators Problem #MFM1P/#MPM1D #PrBL

As an introduction to linear direct variation, I put together a quick problem-based learning task that was proportional for my combined academic & applied class:summary-2017-02-15-m9-1

Scenario:

Buying calculators.jpg

What do you notice?

Capture.JPGI had to use the Pear Deck dashboard to hide some responses that involved calculating the price per calculator as this was part of solving the later problem. I suppose I could have left them up, but I wanted to leave the calculating part until later when students were in their groups.

What do you wonder?Capture.JPG

How much would it cost to buy a class set of 25 calculators?
Best estimate: ________$
capture

Solve:

You can find the Pear Deck slideshow in this folder. Also in the folder is a follow up slideshow exploring the concept of Direct Variation.

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

Yard Space #MPM1D/#MFM1P #PrBL

I took the typical “find the largest area given a specific perimeter” problem and created a hands-on, problem-based learning task for my combined grade 9 Math class (academic & applied combined):summary-2017-02-13-m9

Scenario:
capture
Ms. Wheeler wants to build a fenced in yard for Sally to run around in.
She buys 16 1-metre long sections of fence.

What do you wonder?

Physical & Visual Representations:

The yard must be fully enclosed. Use toothpicks to create show different ways of placing the 16 pieces of fencing (I forgot to take photos of this part but they made stuff like this):IMG_20170220_112029-01.jpeg

Draw your shape & label its dimensions:

Capture.JPG

How should the pieces be set up to create the largest enclosed area possible?

What shape offers the largest area?

square.JPG

We discussed that while a square was the largest rectangle possible, there were other shapes possible with greater areas.

How should the pieces be set up to create the largest enclosed area possible if Ms. Wheeler uses a wall of the house as one side of the enclosure?

We have some more exploration to do here. I left this pretty open and they explored various shapes. But I’m not sure they’ve drawn any solid conclusions just yet for the case where we have 1 side of the shape already accounted for.

Get the Pear Deck slideshow here.

– 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)

Chicken & Goat Legs #MFM2P #PBL

Summary (scroll down for more details):2017.01.11 summary.png

Scenario:Capture.JPG

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

captureWe 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:

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: Capture.JPG
They struggled with this so I did some direct teaching about how to build the equation for this and the next slide:
capture

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

Students were asked to develop an algebraic solution using the elimination method:Capture.JPG
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)

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)

#EdInnovation2016 Recap

I attended the EdInnovation summit this past weekend in Ottawa to present on behalf of Pear Deck. This was the first year that this conference was run by a new organization team (in the past it was an EdTech Team event). There were over 1200 teachers from all of the major (& not so major) school boards in the Ottawa area. The conference is bilingual; in fact 3 of the 5 workshops that I attended were in French! Here are my sketchnote summaries of the keynotes & workshops I attended:

Chris Hadfield keynote

edinnovation2016-chris-hadfield-1

The A-Z of Generation Z by Jean Marc Dupont

EdInnovation2016 Jean Marc Dupont Gen Z.PNG

Pedagogical Documentation by Chantal Picard & Johanne Ste-Croix

EdInnovation2016 Pedagogical Documentation.PNG

Leading & Learning & the Modern Administrator by Jim Jamieson

EdInnovation Digital Leader Administrator (1).PNG

Google Cardboard & Google Street View keynote by John Bailey

EdInnovation2016 Google Cardboard.PNG

GAFE tools to support research & make thinking visible by Jim Jamieson

edinnovation2016-gafe-tools-research-visible-thinking

and last but not least, my own session on Pear Deck:

Pear Deck Sketchnote.png

Keep an eye on this conference if you work in the Ottawa area; it’s a good one!

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

Pear Deck; interactive slideshows+ #edtech

This year I have been working with Pear Deck as part of their certified coach program (similar to the Google Certified Educator). Pear Deck has invited a group of teachers that are heavy users of their product to be trained as coaches. Once trained, the coaches present at various conferences and PD days on behalf of Pear Deck to spread the Pear love. Last weekend while I was at the Montréal GAFEsummit event and took some time to create a sketchnote that summarizes what Pear Deck is, the great features it offers, and the benefits to your classroom. Enjoy!

Pear Deck Sketchnote.png

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

T-Shirt Fundraiser problem #MPM2D

Another quick post to catch up on a problem-based lesson from the other week. This one was co-planned & co-taught with my student teacher, Nicole Darling.Summary (8)

 

We made up a problem to do with selling t-shirts, comparing costs & number of shirts in order to teach the elimination method of solving linear systems.

We posed the problem:

Your class is trying to raise money through selling t-shirts. There is a $150.00 set-up charge and each t-shirt costs $4.00 to make. You will be able to sell your t-shirts for $10.00.

What questions can we ask? Sample responses:

Capture

Estimate how many shirts you would need to sell in order to break even:Capture

Solve: A few (but not all) of their boards:

Most groups solved using a table or just by calculating the 150$ debt divided by the 6$ profit on each shirt to find 25 t-shirts. One group actually did substitution all on their own. Ms. Darling then did some direct teaching on the substitution method w/ the class as a whole & sent them back to their boards to check their answer using this method.

Interactive Pear Deck slide deck available here.

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

Piggy Bank problem #MPM2D

Summary (7)I’m trying to blog more about my lessons/activities/problems this year. Today’s is more of a problem-based learning approach I guess. My goal was to review solving systems graphically with my grade 10 academic students.

I made up a problem about Lisa & Bart saving money in their piggy banks:

Lisa puts $3 in her piggy bank each week. She has a total of $19 in it as of today.
Bart puts $1 in his piggy bank each week. He has a total of $9 in it as of today.

What questions could we ask & solve? Some sample responses:

Capture.JPG

When do they have the same amount of money in their piggy banks?

Estimate:
Capture

Solve:

Everybody used a table. I forgot to take photos of each board, but most groups answered that they will never have the same amount of money. Two groups worked their tables backwards to include negative numbers of weeks (before today). I then asked them to write an equation for Bart & Lisa each which we then graphed using a Pear Deck drawing slide.
Here’s a summary of our work:Summary (7)

Pear Deck interactive slide deck available here.

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

26 Squares – Area #MPM2D #MFM2P

CaptureFor my MFM2P group this followed the Perimeter activity I did with the 26 Squares manipulatives (partially pictured at right). For my MPM2D group, this was their first introduction to working with the 26 squares manipulatives. For both groups this was their first introduction to Quadratic relations and parabolas.

 

 

 

 

Predict: What is the relationship between side length and area of a square?

Capture.JPG

Create a table of values:

This was done in their groups at their boards.
ToV
I had to encourage groups to count the grid on their squares. Many were calculating the side length times 4, while others were trying to square the side length but doubling instead. For each of those groups, I redirected them to our physical squares cut out w/ grids [pictured at top of post] & asked them to count the area of a 2×2 square, then a 3×3 square, and so on.

Graph: Back in their seats students were given this handout & asked to graph by hand the data from their table.

Linear VS Quadratic: Students were asked to choose which type of relation they thought this was.
Capture
And why:Capture.JPGWe then discussed the shape of the graph being a curved line & the first differences being not equal (which only some students had pointed out).

First & second differences: Groups were sent back to their boards & their table of values with this prompt:
Capture
IMG_1123
We discussed that second differences being equal means this is a Quadratic relation; a new key term for us. The black writing on the whiteboard above is my own addition during the class discussion.

Desmos & Quadratic regression: Back at their seats, individually students used Desmos to perform a quadratic regression on their table of values. They had this prompt on their handout from earlier:Capture.JPGThe 2P students had practiced performing a linear regression with Desmos the day before during the Perimeter investigation. The 2D students had mostly never seen Desmos before. I walked around helping students that got stuck or couldn’t find where they’d mistyped something & gotten an error. The result was:Capture.JPGat which point I did some direct teaching about how to use the a, b, and c value determined by Desmos to write out an equation for the relationship between side length and area. I also introduced the word parabola to them while we looked at the graph from Desmos, zooming in & out.

In their groups at their desks they had 4 application questions to work on:Captureand this became the homework for the MFM2P class as we ran out of time in class.

Key features of a quadratic graph:

With the 2D students I had time left to do some direct teaching about y-intercept, x-intercept / zeros, vertex, max/min, & axis of symmetry. Their homework was on Khan Academy to identify these key features given an equation that they could graph using Desmos.
For my 2P students this lesson came a few days later with class time to work on the Khan Academy exercise set.

My reflection: I wish I had asked at the end of the activity for students to restate in words the relationship between side length & area.

Folder w/ handout & Pear Deck interactive slideshow here.

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