Banquet Hall problem #MFM2P #PBL

This is my 2nd or 3rd time doing this activity, but hadn’t yet blogged about it. So here goes … I made lots of changes, even from one period to the next.

Prompt:Spartan Banquet Hall.png

Notice-Wonder-Estimate:

Screenshot 2017-10-13 at 3.38.20 PM.png

Screenshot 2017-10-13 at 3.39.27 PM

Screenshot 2017-10-13 at 3.40.35 PM

Solve:
At your boards (whiteboard / chalkboard) in groups of 2-3 randomly assigned (VNPS & VRG).

Most groups started calculating the cost per person for each teacher. I stressed to them multiple times that all 3 teachers were paying along the same formula or “price plan”. They really struggled with how that could be. In first period there was 1 group whose board had a table on it & they had started using 1st differences to calculate the rate of change. I called all the groups over & led a discussion about the strategy and asked about what sort of deposit (a cost for 0 people) might have to be made by the teachers & sent all the groups back to continue, strongly urging them to explore the table idea. In 3rd period, none of the groups started the table, so I called all the groups over to some spare board & said “here’s something I saw in 1st period” & proceeded to have the same conversation with them.

Here are their boards:

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We got to the point on day 1 where everyone solved for the cost for 150 guests. Time ran out, & bell rung.

Between periods 1 & 3 today I added some extra slides & questions to my slide deck to make it better.

Day 2:

Yesterday I added a slide asking students to graph the 3 points from the original data set in the original prompt. Today we started on that slide in Pear Deck :Screenshot 2017-10-13 at 3.54.27 PM.png
I asked them if this was linear or nonlinear. Why? In 1st period this also resulted in a conversation about 1st differences when the x values don’t have a constant increase.
I asked if the line of best fit would pass through the origin?

I then sent groups to their boards with the task of using Desmos to find the equation for the line of best fit . Their boards:

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Once they had done a linear regression to find the equation, I asked them to use their equation to solve for the number of guests I invited if my party cost $3545 at the banquet hall. I coached a few groups through the proper format in which to show their work when solving an equation.

The rest of the period was dedicated to individual practice on a Khan Academy problem set called “Slope intercept equation from graph“.

Find the whole lesson here (the unassociated file is Pear Deck).

As a final note, this whole problem-based teaching can be hard for the student to grasp sometimes. Today this happened:

How do you handle it when students question your teaching skills or pedagogy? Let me know in the comments below!

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

 

 

 

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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)

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)

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)

Pyramid SA #MFM2P #3ActMath

Not the most exciting problem, but my students were still engaged even if it wasn’t a contextualised scenario.2016.10.31 summary (1).png

Act 1:

img_20161031_091019

What do you notice (facts)? What do you wonder (Qs)?
– The shape is a pyramid that has a square base.
– The area of the triangle is 1 cm square.
– What is the area of the base?
– What is the volume of the shape?
– What is the surface area of the shape?
– What is the height of the shape?
It is a triangle What is the lenght and height of the triangle
It’s a square based pyramid how many sticky notes do we need to cover the square based pyramid
It’s a Square pyramid
It’s a triangle and it has 1cm squared What are the lengths and widths of the pyramid
Its a shape. what is 10m2?
pyramid
Square based pyramid, with a sticky note that reads “I cm squared) Why is there a sticky note on one of the sides?
That it is a square base pyramid What are the other lengths
There is a square based pyramid What does the 1cm^2 represent?
There is a triangle What is the value of this pyramid
what’s the area of the square based pyramid

Estimate:2016.10.31 estimate (1).JPG

Act 2:

Each group of students was given a plastic pyramid like the one in the picture. They began measuring dimensions of the pyramid and using the formula from their formula sheets in their binder. They solved the problem on their boards:

I asked the group why they thought we got different answers in different groups and they commented that some of our plastic pyramids were slightly smaller than others. I did a little direct teaching about the net of a square based pyramid and how that translates into the formula on their formula sheet:

img_1912

Act 3:

I then handed out grid paper and asked the students to draw a 1 cm by 1 cm square at the top left of the page. They told me that the area was 1 cm^2 and determined that every 4 squares of our grid paper made a 1 cm^2 area.

I asked them to trace all of the faces of their pyramid onto the grid paper to create a net. Then to colour in alternative 4-square blocks to allow us to count the area in cm^2.img_1915img_1913

We counted up the area and found the answer to be 114 cm^2; right on with our calculations!

img_0176

Students were assigned a “surface area” practice set of questions on Khan Academy; different ones depending on whether or not they had completed the previous set I assigned earlier in the semester.

The materials for this activity are available here.

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

Quadratic Block Pattern #MFM2P

This past week I did an activity inspired by Fawn Nguyen’s Visual Patterns work. The last time I did this activity, I blogged about it here.2016.10.25 summary.png

Pattern:
img_0074-2

Notice & Wonder:

What do you notice (facts)? What do you wonder (Qs)?
each step the cubes increase how come the reds arent increasing?
How many blue blocks will they add on the 4th step
Each step, more cubes are added Why is there always 3 red but the blue always increases?
Why Do we only have 3 reds
There are 3 steps in the picture
there are red and blue cubes how much the sides go up each time
The number of blue blocks increase as the number of steps increase. why isnt red increasing?
Cubes, there is steps How many cubes added every step?
I notice there a step 1 , step 2, step 3 Why does the blues always increase and the red stays the same
Always 3 red in the middle the outside length increases by 1 each time Why is the red not increasing
– The number of blue cubes increase each step. (2, 8, 18, etc)
– The number of red cubes stay the same each time.
– How many blue cubes will there be at step 10?
– What is the formula?
3 red squares on each step ,
There’s always 3 red in the middle How much blue cubes will it be in step 4
the red blocks stay they same but the blue blocks increase every time how much the blue blocks are going up by

Estimate:2016.10.25 estimate.JPG

Solve:

Groups used tables to start. Then, most could see the pattern of the two squares on each end with a side length equal to the step number and they used this pattern to calculate the number of blocks for step 57.

A follow up question in the Pear Deck slides asked them if the pattern was linear, quadratic or neither. We discussed how we can determine this, and I sent students back to their boards to find the first & second differences.

The next question in the slides asked them to use Desmos to find the curve of best fit and its equation. I reviewed how to do both linear & quadratic regression on Desmos on the board for them. After students found the equation with Desmos, they were asked to go to their boards one last time and use their equation to verify how many cubes would be needed in step 57.

We then had a whole class discussion on how the terms in the equation represented the visual pattern.

Individual practice on quadratic relations was assigned from Khan Academy; different exercises depending on whether or not they had finished their homework from the last time we worked on quadratics.

Activity available here.

– 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)