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:

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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!

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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)

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Filing Cabinet Post-Its #3ActMath #MFM2P

From 3 weeks ago, here is the filing cabinet post-it activity. It was originally created by Andrew Stadel and available on the 101 Qs website here. I’ve made my own photo prompt for act 1 so that students can do the measuring on our classroom filing cabinet in act 2.Summary 2016.09.29 (2).png

Act 1

2016-09-29-notice-wonder

2016-09-29-estimate

Act 2

Each group was given 1 sheet of paper. Students got busy measuring the filing cabinet and their sheets of paper. They worked at their boards:

There was some confusion to start about how to “read” and thus use the formulas for surface area on their formula sheet. A few groups worked through the areas of each face instead of the formula. I did a little direct teaching about nets and they can be more intuitive to use than the formulas.

Most groups got answers around 60 sheets.

Act 3

After all my years of using this activity, I have yet to get a group interested enough to take the time to cover my filing cabinet with paper to get the actual real life answer to see how close their work is. They always seem content that their Math has found the answer. Perhaps I just need to do it myself one of these days.

The individual practice was 2 sets of exercises on Khan Academy:
Part 1 – Nets of polyhedra (quick)
Part 2 – Surface area using nets

All of my materials are available 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)

Toy House problem #3ActMath #MFM2P

This week’s activity is based on an old exam question that I now often put on one of our tests. And generally the kids are fine until they have to design a box that uses less cardboard than the original. Most of them leave this totally blank (I usually tell them I will not accept their test until they at least draw a box and label each side with a measurement).

So after the test, I decided we should physically build this problem. Physically manipulate the contents of the box. Here’s how it went down:

Problem 1: Volume of the toy house

Volume summary (1).pngThe part here that trips them up on the test is the fact that you need to use Pythagorean Theorem to find the height of the triangular base for the prism that makes the roof. Most make the (false) assumption that it is also 5cm.

Part 2: Surface area of a box holding 20 houses

Surface Area summary (1).pngNo problems here, really, since a rectangular prism is one of the easier solids for working with surface area.

Part 3: Draw a paper net & build a model of the house

IMG_0693.JPGI remembered that last year it took my students a really long time to draw & fold these. I thought it would be better this year. Wrong. It took a full 75 minutes for them to draw 1 net, copy it onto a 2nd sheet (each student needed to build 2) & fold them both into place w/ tape.

Also, I think next time, it would be beneficial to do this part 3 first. Build a model & then ask them to estimate the volume. So that they can see its size in real life. I’ll do that semester 2.

Part 4: Design a box that uses less cardboard

Better box (1).pngThis is the part of the test that they have so much trouble with. But given the model houses as manipulatives, they can really envision the dimensions of the box. Also they’re working in groups of 2-3 which always helps the problem solving process.

As always, here is the link to all of my materials for this lesson.

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

Pepsi VS Canada Dry box activity #3ActMath #MFM2P

Today’s activity was designed to target the surface area & volume expectation in my MFM2P course. I’ve done this one a few times in the past.

This time around I started by asking them to guess whether or not these two boxes had the same volume (I told them they both hold 12 cans – which is also written on the box):CanadaDry VS PepsiOver half of my students said NO – they were not the same volume. I sent them to their boards to check whether or not they were right. The volumes turned out not to be exactly the same, but we discussed that if we measured in cans, they both had the same volume; 12 cans. But if we measure in square centimetres, one had slightly more volume.

Also overheard:

“But why isn’t our answer for the Pepsi box the same as that other group? . . . Oh, we must have measured differently.”

So this spurred a quick discussion of being accurate in our measurements.

Next up I asked them which box uses less cardboard? I said they could assume each side was made of 1 piece of cardboard, and not multiple overlapping flaps. We guessed & then solved:Pepsi VS CanadaDry box Summary

The group working on the whiteboard pictured above used the formula from their formula sheet to calculate the surface area of the box. This group and others had initially misinterpreted the formula, adding instead of multiplying dimensions, etc. I called groups back to their boards, discussed how to “read” the formulas & asked them to revise their work.

One of our 5 groups tried to solve by calculating the area of each face of the box:IMG_0133You can see their volume work from earlier at the top of their board. their surface area work is messy but towards the middle you can see them calculating the length x width of each rectangle. On the left they are multiplying those answers by 2. It doesn’t look like they got to the point of adding them together.

I called attention to the 2 different methods used by the class; surface area formulas VS summing the areas of the faces (working with nets).

The rest of class time was spent working on the homework:
Surface area using nets on KhanAcademy
or Surface area (for the 4 students that have already mastered the previous exercise).
I circulated helping students get started on their homework.

Next time:

In Dan Meyer‘s 3 act math, the 3rd act is checking if we are correct somehow. Lately, the 3rd act in my class has been more about the metacognitive task of discussing their various strategies in solving the problem. Does that make the activity less powerful if we don’t physically check if we modelled correctly after? Perhaps I need to create the act 3 as a photo or video where I lay each box out flat as a net & show the surface area of each. Or should I cut them up to rearrange them into similar shapes to get the visual impact of which one has a larger surface area?

I missed the boat today on having my students generate questions we could solve for this scenario. I should have had a slide in my Pear Deck slideshow at the start asking what Mathematical questions we could ask about these two boxes:CanadaDry VS Pepsi

Next time I’ll add that in.

All the materials for this activity are here.

Update (2015.11.10): Last night I bought another 2 drink boxes so that I could cut them up, measure carefully & calculate the surface areas. So at the start of class today (the day after the original activity) we looked at all of our solutions from the previous day to see which group best modelled the correct surface area:IMG_0143

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