# Jelly Beans or No Jelly Beans

What’s not to love about Would You Rather; I use it with my students and always recommend it as one of the great warm-up routines. This one caught my attention last week.

Each entry always includes this statement:

Whichever option you choose, justify your reasoning with mathematics.

This statement is important, especially the word “mathematics,” because you might have a student who says [truthfully] that she doesn’t like jelly beans or is allergic to them and will prefer to give them all away. Then, you might have another student in the same class who [untruthfully] makes the same claim to avoid having to do any maths. There’s also that thoughtful student who wants to give more to his friends and keep fewer for himself. Or a student might consider giving more away to make friends. If I were to pose this question to my students, I’d mention the above possible reasonings, but then I’d add, “This question assumes that you love jelly beans and want to keep more of it for yourself. For now, it’s the mathematics we’re after.”

I didn’t ask my students this question though, I asked them to choose between this question and the one on the right.

As a student, would you rather be given the problem on the LEFT (jelly beans) or the one on the RIGHT?

Using the same image above, I asked on Twitter and of my colleagues.

As a teacher, would you give your students the problem on the LEFT (jelly beans) or the one on the RIGHT?

*****

Out of my 68 sixth graders, 71% of them chose the left problem. The words they used for their reasoning:

colorful, vivid imagination, visual, more pleasant to the eyes

interesting, engaging, not boring, not basic

better reason because you like jelly beans

My fellow educators, meanwhile, overwhelmingly chose the left problem — of the 781 people [at this moment] who took the survey, a whopping 90% chose the left problem.

Well, I prefer the one on the right [that I’d typed up]. How did I get it so wrong? I’m normally not this lame. But, truth be told, I don’t love the jelly beans question. At all. Maybe the one on the right is the wrong “fix” for the left one. If I could retype the problem on the right, I’d remove the equal signs since the question is just asking which one yields a larger difference, not caring exactly what each difference is.

I want to believe that anyone who spends 5 minutes with me learns that I love mathematics. I love numbers, I love math problems and don’t give two shits if they are real-world either. I’m the one who loves the problem about carrying 3,000 bananas across the desert and the one about the emperor pouring oats on every other guest’s head. One of my 247 all-time favorite problems is Noah’s Ark, even if I grew up in a house with a Bible in every corner and found it hard to wrap my head around this story. (However, Eddie Izzard’s take on the Ark — language caution — makes me laugh.) I love problems that are simply stated, yet they beg you to savor your perseverance as you think deeply and creatively. There’s great joy in solving a good problem, especially the ones that at first blush, you weren’t even sure how to begin.

The jelly beans problem above is not one of these problem-solving tasks. It asks for a mathematical justification, so I’m going to assume that the mathematics is finding the difference or another arithmetic operation. I see it as a number talks problem. Students get to share their strategies. Mine might include:

364 minus 188… I’d need 12 more to go from 188 to 200, then 164 more to get to 364, so the difference is 176. Similarly, to do 281 minus 137, I’d need 63 more and 81 more, or 144. Problem A has a bigger difference of 176.

Comparing the two totals, 364 and 281, the difference is 19 plus 64, or 83. While the difference between the give-away quantities 188 and 137 is 51. I start out with 83 more in problem A, but I only have to give away 51 more, so problem A leaves me with more to keep.

That’s why I prefer the one on the right. Numbers are beautiful. I want students to focus on the numbers and play with them, learn to regroup, try massaging them and making them flexible, be comfortable with numbers. Math is badass, so let’s do maths for maths’ sake. I feel protective of numbers and don’t see why they need to be dressed up in colors or dunked in forced contexts. (I suddenly think of little dogs in ridiculous outfits that I doubt if anyone asked for the dogs’ permission.)

Nine out of ten of you disagreed with me. That’s okay because I can make phở better anybody. But guess what though? My own 23 and 25-year-old kids chose the one on the right. This fact was comforting! Sabrina (23):

If you were one of the survey respondents, I thank you thank you thank you.

1. Danny Whittaker
Posted January 14, 2019 at 9:21 pm | Permalink

I guess I like the one on the left because it IS more open ended. I don’t think it necessarily requires a difference comparison. I could mathematically argue the second as better because I’m keeping a larger percentage of jelly beans. Then there are more lame, but also mathematical answers regarding my hatred of odd numbers. A bit deeper is the fact that I love prime numbers, so I’d rather the second option. I also like the ability to answer that I’m generous and want to give as much as possible.

2. Posted January 15, 2019 at 1:48 pm | Permalink

Context is pretty critical here, I think. As a student, I only saw problems like the ones on the right, and as a student who was pretty confident and keen to show people that fact during classtime, I would have no problem jumping in and getting it done. For the problem on the left, I believe that more of my peers may have an opinion on it, whether or not they had done the maths “yet”. My mathematical justification would have, perhaps, emphasised how powerful it is to know for sure, which one leaves you with more jelly beans, an answer of which cannot be reached without completing the maths. The arguments of whether or not I want to be generous are not necessarily relevant to the mathematics, but this hopefully comes after the fact because they know what the answer of both is. I, personally, might use both. First the left, to pull in as many students as possible, and then the right to show what the problem is when it has been undressed. Then, depending on what I want to do with the students, I might have them create their own ones for their peers to solve. Through this, some students might go for a similar approach to the one you posted (one has a higher starting amount that ends up as the lower amount after the subtraction), whereas others might do something different (use addition or another operation, start with a higher amount that ends up as still the higher amount, or have both amounts equal the same). These opportunities may not be as natural to take up by using just one of them.

3. Seth Leavitt
Posted January 27, 2019 at 9:10 am | Permalink

As a warm-up, I think the left problem is much better than the right. Students are likely to read it and start talking about jelly beans. Things that you mention (allergies, preferences, friendship) will probably come up. Students come into the classroom and focus their attention on the problem. They “warm up” for what will follow. They are with you (the teacher) because there’s something to talk about together.

Most will do the calculation. But if we’re talking about middle school, this particular problem doesn’t push thinking. It’s the conversation in the room that matters. Jelly beans stimulate conversation. Subtraction problems, mostly, do not.

4. Gloria
Posted April 29, 2019 at 4:21 am | Permalink

There’s nothing wrong with a number talk that has just numbers. But when you start talking about give-away quantities and more to keep, doesn’t that assume the jellybean context?

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