“I couldn’t help but admire your large triangular prism,” I wrote. Sadly, this is not the strangest way I have begun an email to a colleague.
“Are you talking about the giant Toblerone-shaped thing? You math guys are weird,” she replied.
Anyway… my three-act math task:
act one
- About how many regular size Toblerone chocolate bars fit inside the giant Toblerone-shaped thing?
- Give an answer that’s too big.
- Give an answer that’s too small.
act two
- What information would be useful to know?
act three
63. Relax. The video is coming soon.
sequel
- If 72 regular size Toblerone chocolate bars fit inside a mega Toblerone-shaped thing, how large would it be?
- If 112 regular size Toblerone chocolate bars fit inside a mega Toblerone-shaped thing, how large would it be?
better still…
- A mega Toblerone-shaped thing is a little bigger than a giant Toblerone-shaped thing. What could its dimensions be?
- How many regular size Toblerone chocolate bars would fit inside?
I like the phrase “a little bigger.” Probably “borrowed” from Marian Small. The ambiguity here allows for multiple solutions. Students could increase the length of the prism or the size of the triangle base. Which has the greater effect?
Also, there’s something interesting happening here with the sum of consecutive odd numbers.
Oh yeah… a shout-out goes to Andrew Stadel for his Couch Coins task.
Chris Hunter 
I really like the video you present for this task. I have another question as well – how long would it take at the rate you’ve got the smaller boxes going into the larger box to fill up the larger box? It requires figuring out the question you’ve answered above, plus doing some calculations around rates.
That video is a gem. I love also how there are different ways we could interpret the prompt. A straight volume / volume calculation would be a good start, but it wouldn’t account for the fact that you might have some air space surrounding the smaller Toblerones. I’m thinking students would have to answer the sub-question, “How many smaller equilateral triangles could I fit into this larger equilateral triangle?”
This is slick man. I’ll relax and can wait for Act 3. Ok, I’m lying, I can’t wait. I’m really looking forward to it! Thanks for the shout-out.
@David Another task that is bouncing around in my head right now would probably benefit from this rate/time approach. I may have to learn how to add a timer and speed up the video to make that part work.
@Dan Yes, I’d expect many students would not take into account that dividing the two volumes only works if it’s a perfect fit. All that empty space that ends up surrounding the chocolate bars will add up to more of them if students just focus on the volume calculations. But then there’s the problem of actually fitting them in the box. Is the sub-question asked of all students or kept in the teacher’s back pocket as scaffolding for some? What about asking them to draw their solution instead? Let’s say a group of students arrived at an answer of 88 by dividing volumes. They might notice 3 * 3.6 cm < 12.5 cm. Or, they might notice that there is an incomplete stack (in which case, why not just add more to make a complete stack?) or that the length of these stacks placed end to end exceeds 153 cm. Fingers crossed, the kids realize themselves they have to answer the sub-question. BTW, the task is now up on 101questions: http://www.101qs.com/1991-toblerone-task
@Andrew Thanks. Your couch coins task as well as Chris Robinson’s function machine on visualpatterns.org have motivated me to see what I can create using stop motion/Keynote.
3rd act, 3rd act?? this is brilliant and I’d love to use it but it’s a bit anticlimactic without the big reveal… any danger? many thanks
I know, I know. I ran into a couple of problems with the reveal. That regular sized Toblerone cost me $2. I imagined showing seven triangular prisms made up of nine marching into the large box. I think students would feel cheated if I just looped as above. $126 is a little too rich for me. I’ve got to think about a workaround.
Hi Chris Am I missing something? Don’t I need the height of the triangular base?
It’s an equilateral triangle, so no? Nine regular-sized Toblerone bars can be arranged in a stack, like here: https://i2.wp.com/reflectionsinthewhy.files.wordpress.com/2018/04/toblerone-stack-001.jpeg?ssl=1&w=450 The side lengths of these add to 10.8 cm, a little less than the side lengths of 12.5 cm of the large box.