Ice Cream #MFM2P

From end of September, my “would you rather” styled ice cream problem. It’s not fully would you rather style, but it’s a good question prompt for this. The problem is probably mostly styled after Garfield Gini-Newman‘s “choose the better or best” style problems.Summary 2016.09.27 (1).png

Students were presented with the three ice cream options above & asked to guess which one offers the most ice cream? Looking back I wish I had made the images to scale … I think I will adjust that before I use this one again. (Editable image file here)

Most students guessed the block would have the most ice cream.

Groups were sent to their boards to solve:

I had to answer questions about what the various formulas on their formula sheet meant. For example, many are unsure how to read V = lw + wh + lh and how to then use it, which operations to use, etc.

Many groups did not notice the discrepancy in units between the various shapes. We had a discussion about converting units. I did some direct teaching about how students tend to make less mistakes if they convert the lengths BEFORE calculating volume, rather than trying to convert cubic units (if calculating by hand). I sent students back to their boards to correct their work so that they have comparable units for each shape.

First time I’ve done this one. I like it & will use it again w/ a few tweaks.

All materials here.

– 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)