Bank Balance problem

A few weeks ago I was ready to do my first Linear Systems of Equations problem with my MFM2P grade 10 applied class. The first step is to get them to solve systems graphically (a review of gr9 essentially) and interpret the solution. The last few times I did that topic, I used a scenario of a race between a runner and a dog-walker w/ a head start; where/when do they meet? It’s always complicated and requires more hints from me than I’d like. So I decided to design a new scenario – something that would allow us to practice our linear relation skills at the same time. I came up with this scenario of 2 different bank account balances as they grow over time:

1. Presented with the above data, we worked through our notice & wonder routine using Pear Deck.
2. Then I showed them the question I had for them:
   “When will they have the same bank balance on the same day?”
   Students estimated how many days before that would happen via Pear Deck.
3. Then we had turn & talk time with our visibly randomly grouped (VRG) partners to discuss what we should measure, look up, and/or calculate in order to solve the problem. We shared our thoughts to the whole group.
4. Then I sent students to their group’s board (VNPS) to solve the problem in any way they saw fit. Periodically when the majority of groups seemed either stuck, or ready for it, I called them all over around some board space to do some direct teaching. The things I called them over to talk about at different moments:
   – first differences & whether or not each table is linear
   – Desmos: plot the tables
   – Desmos: linear regression for line of best fit
   Asked them to sketch their graph from Desmos on their board.
   Here are their boards:
   

   

   

   

   

   

   
5. We had a follow up day where I walked them through interpreting a couple of different graphs of system of equation scenarios.

The whole activity is available in this slidedeck that has added Pear Deck interactivity if you use their add-on.

– 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

What do you know / notice?

What do you wonder?

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

Act 2: Measure & Solve

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!

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:

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 :

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

Chicken & Goat Legs #MFM2P #PBL

Summary (scroll down for more details):

Scenario:

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)

Coffees & Muffins #MFM2P #PBL

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

Scenario:

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

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:

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.

The prompt:

Today’s question:

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:

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.

Banquet Hall: 

Phone Charging: 

Phone Plans: 

Gummy Bears: I did blog about this one here.

Measurement & Trigonometry

Lamppost: w/ shadows 

School Height: w/ mirrors 

Tree Height: w/ clinometer 

Wheelchair ramp: 

Filing cabinet post-its: 

Pyramid Post-its: 

Quadratic Relations

26 Squares: I did blog about this one. 

Visual Pattern: 

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.

Act 1

The prompt:

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 bear

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:

Act 3

The solution:

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.

 

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:

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

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

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:

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

Estimate:

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:

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:I’ll break it down into the 3 acts.

Act 1: Notice, wonder, & estimate

What do you notice & wonder?

Act 2: Data collection & solving

Presented the class with the cost of each order:

Groups went to their boards to solve:All 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:

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:

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)