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)

Coffees & Muffins #MFM2P #PBL

This is 2nd time blogging about this problem. 1st time-around post is here.

2016.10.24 summary (2).png

Scenario:
LR3

What do you notice (facts)? What do you wonder (questions)?
different prices why are they buying these
Adding 3 extra coffees cost more by a little How much with it cost for 4 coffees and 4 muffins ?
why is the kid buying coffee? whys the kid buying coffee?
The totals are different on each side.

One side has less drinks.

How much is each item?
nothing
2 different cost How much the cupcake cost each one
How much the coffee cost each one
there’s money, drinks, cupcakes how much each coffee and cupcake is
For the first indivdual, it costs $8.85 for three cupcakes and three coffee cups.

For the second person, it costs $5.35 for three cupcakes and one cup of coffee.

Im curious about what brand of coffee that they are buying. It seems potentially no name or even something like a corner store kinda coffee. ew.

oh yeah also how much do they each cost?

The total cost are different How much it cost in each item
I notice cupcakes , coffee , a boy and a girl how much is each
The person on the left has more coffee and is going to spend more What is the individual price of the coffee and the muffins
– They both ordered 3 muffins, but one had 3 cups of a drink and the other ordered one.
– The one that ordered 3 cups, have to pay more.
– How much does one drink cost?
– How much does one muffin cost?
– Does the person on the right have a better deal than the person on the left?
Different prices and different subjects How much does it cost for each item
Adding 3 more cups of of coffee is a little bit more than getting one cup of coffee how much is one cup of coffee
Different objects in both pictures Why did the person on the left buy more
diffent how much money does it cost to for one cup of coffee and one muffin

2016-10-24-estimate

Solve for the cost of 1 muffin as well for the cost of 1 coffee (red/orange annotations are mine during whole class discussion):

They all solved it by subtracting what was common to both orders & splitting the remaining cost amongst the remaining coffees. The follow up questions on Pear Deck asked them to create an equation for each order. I then did some direct teaching on the side showing them how to do elimination using 2 different equations. Then I asked them to go to their board and use elimination to solve this problem. They started this on day 1 above but we class ended & we hadn’t finished. So on day 2, with a new group of partners & fresh boards, I sent them up to use elimination to solve fully:

We compared the solutions of the different groups and picked out the one board that had the most correct formatting of an algebraic solution. I drew parallels between their work during elimination and their earlier logic, pointing out how they are both eliminating something (I explained this more in depth & more eloquently).

We then did a quick check with Desmos:
2016.10.24 desmos.PNG

The individual practice to wrap up was a Khan Academy exercise set on elimination not involving any multiplication of equations.

Activity available here.

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

Phone Plans #MFM2P #PBL

I’m already behind on my goal of blogging all of my MFM2P (grade 10 applied) activities for the semester. We did this one about 3 weeks ago.summary-2016-09-23-1

The prompt:lr3-phone-plans-info
2016.09.23notice.JPG

2016.09.23wonder.JPG

Today’s question:2016.09.23estimate.JPG

They went to their boards to solve. Most groups used a set of table of values. After they found their answers, I walked them through creating an equation to represent each phone plan and then using Desmos to find the point of intersection between them. They then sketched their graphs next to their tables. I only took a photo of one group’s board:IMG_20160922_114324.jpg

The next day students individually worked through a problem set on Khan Academy to solve linear systems graphically:
 Linear systems; solve graphically (use Desmos – help video here)

All materials for this activity are here.

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

Problems We Solved in #MFM2P

My plan was to blog about every problem-based learning activity I did this year. I did not succeed; I think I blogged about two from the my MFM2P course? So as a runner up to a full blog post reflection on each, you’re getting one post with a summary image of each activity or problem & a link to my materials for it.
I’ll group them by strand here, but they are not listed in the order that we did the activities. If you’d like to see the progression of activities I used, you can see that here.

Linear Relations

26 Squares: This one I did manage to blog about.Summary (11).jpg

Banquet Hall2016.04.22 2P summary.png

Phone Charging2016.05.19 2p.JPG

Phone Plans2016.04.27 2p.png

Gummy Bears: I did blog about this one here.Summary 2016.02.29 2P.jpg

Measurement & Trigonometry

Lamppost: w/ shadows 2016.04.15 2P Summary.jpg

School Height: w/ mirrors 2016.05.25 (1).JPG

Tree Height: w/ clinometer 2016.05.11 2p summary.jpg

Wheelchair ramp2016.06.08 2p (1).JPG

Filing cabinet post-itsSummary Filing Cabinet 3-Act.jpg

Pyramid Post-its2016.05.13 2p (1).JPG

Quadratic Relations

26 Squares: I did blog about this one2d 2016.02.08 (1).JPG

Visual Pattern2016.04.12 2p summary (1).JPG

Not every lesson we did was problem-based. Sometimes I need to do some direct teaching right from the get go, like with expanding & factoring. Other times we explore & investigate by drawing & cutting out shapes, like with similar triangles & trigonometry. But in any case, maybe someone new to the MFM2P course (or not so new to it) will find these activities useful!

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

Gummy Bears #3ActMath #MFM2P

I’m catching up on blogging about a couple of activities I did before my student teacher took over my classes. Here’s a brief overview & reflection about our Gummy Bear problem for linear systems.2016.02.29 2p

Act 1

The prompt:
Gummy Bear Problem
I asked (via PearDeck):

  • What do you notice?
  • What do you wonder?
  • Estimate the cost of a red gummy bear?
  • Solve for the cost of a red gummy bear
  • Solve for the cost of a blue gummy bear2016.02.29 2p estimate

Act 2

I gave the groups access to some fake coins and some blue & red blocks to represent the candies. I didn’t get shots of everybody’s work, but here is an example from one group:IMG_1281

Act 3

The solution:IMG_1282.JPG

Consolidation:

Using some direct teaching, I asked them to come up with an equation for each purchase if x represents the cost of 1 red candy and y represents the cost of 1 blue candy. Then I asked them to graph the two equations in Desmos & we looked at & talked about the point of intersection.

The next day, we worked on this consolidation handout reviewing the most important new learning from yesterday. The rest of the second day was dedicated to this problem set on Khan Academy (they were encouraged to use Desmos to help them with it).

My reflections

  • A colleague suggested showing students one purchase at a time and asking them what some possible prices for each colour could be.
  • I wondered whether or not this is a good context, because in reality, the blue & red gummy bears would not have different costs. Thoughts? Might this be a problem for students trying to understand the problem & context?

All materials for this activity are here.

– 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)

Cheese Pies & Drinks #MFM2P #3ActMath

Last catch-up post from December; our cheese pies & drinks problem for linear systems in the Grade 10 applied class. Overview:Summary (10).jpgI’ll break it down into the 3 acts.

Act 1: Notice, wonder, & estimate

Cheese Pies & Drinks (3).pngWhat do you notice & wonder?Capture

Capture

Act 2: Data collection & solving

Presented the class with the cost of each order:Cheese Pies & Drinks (1) (1).png

Groups went to their boards to solve:IMG_0556.JPGIMG_0557.JPGIMG_0558.JPGIMG_0559.JPGIMG_0561.JPGAll of the groups subtracted the smaller order from the larger order twice in order to eliminate the cheese pies and leave the cost of 2 drinks, from which they easily determined the cost of 1 drink. Then went back to calculate the cost of a cheese pie.

Act 3: Answer check / resolution / consolidation

We confirmed that every group had the correct answer:Cheese Pies & Drinks (2) (1)

Then I did some direct teaching on how to use the elimination method when you need to multiply one of the equations in order to eliminate a variable:
IMG_1456
We discussed how the multiplying of “her” equation by 2 mimics how my students subtracted the smaller order two times in their solutions.

Day 2

We consolidated our learning about the elimination method by describing each step in the solution. Handout here.

They had time to complete the homework on Khan Academy here.

As always, the full folder of materials for this activity is here.

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

Coffees & Muffins for Linear Systems #MFM2P #3actmath

Today I presented my students with this image:LR3

I asked them what Mathematical questions they could ask related to this. They came up with some really great questions today:questions

Perhaps this isn’t the best “Act 1” I’ve given – it might be a little “too helpful” as Dan Meyer would say. I could strip it down more by taking off the prices & only revealing them in Act 2. Thoughts as to whether or not that would make this a better activity are welcome – comment below.

Next I asked them to estimate the price of 1 coffee & the price of 1 muffin. Then they went to their boards w/ the small groups to solve:Summary

All the groups found it pretty easy to solve. Then I showed them how to write the two equations using c for coffee & m for muffins. I showed them how to solve algebraically using elimination. I really tried to get them to see how the steps they followed were the same as those in the algebraic solution:
IMG_0171

They had the rest of the class to start on the homework: some basic elimination exercises on Khan Academy.

Folder w/ all lesson materials here.

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