Kids, I’ll tell you why you need math…

So I was at Kroger and I was thirsty.

I went to the cooler to pick out a 20 oz. Coke. $1.69. Reasonable. About what you’ll pay most places, at least around these parts.

2014-09-28 16.47.29
But I had some more shopping to do. So, I kept walking. Gathering the items on my list.

Then I saw some 2-liter Cokes. (Remind me. Which is a bigger amount of Coke? 2 Liters? or 20 ounces?)

The 2-Liter Coke was priced at “2/$3.00”. (Which, I’m pretty sure is less than $1.69.)

(Oh! And you don’t have to buy 2 to get that price. Kroger is awesome like that.)
2014-09-28 16.49.24

 

I get pricing a little bit. I worked concessions at a college football stadium for a while (true story, by the way). I know the shtick. It’s upselling.

“For an extra quarter, you get almost double the pop!”

But this isn’t like that.

You have to buy 4 twenty-ouncers to fill a 2-liter. 4! You include the 10-cent bottle deposit here in the great state of Michigan, and that’s over $7.00!

2-Liter? $1.50

This isn’t even close.

Kids, THAT’S why you learn math.

NPR wants to advise your pizza order…

Quoctrung Bui from NPR says that there are at least 74476 reasons that you should always get the bigger pizza. (The article has an awesome interactive graph, too!)

If we could mix the article with a math exploration, we could provide an awesome opportunity for a math-literacy activity that can combine reasoning, reading, writing, and some number-crunching all in the same experience. That’s a nice combination. Also I suspect the content hits close to home for most students. (The leadership in our district is often looking for opportunities to increase authentic reading and writing in math classes. This seems to fit the bill quite well.)

Here’s an activity:

Although without fail, the menus from a variety of local pizza joints will probably be a bit more engaging. (Look for an update coming soon…)

Shauverino Pizziano

But the big question is why?

According to Bui: “The math of why bigger pizzas are such a good deal is simple: A pizza is a circle, and the area of a circle increases with the square of the radius.” 

Yup… that’s pretty much it.

Coke vs. Sprite – One Class’ Response to Dan Meyer’s #wcydwt Video

2014-04-03 11.08.14

Almost three years ago, I highlighted the Coke vs. Sprite video that @ddmeyer made. It is a very intriguing question (which glass contains a greater amount of its original pop) without a clear answer.

Today, I let a class give it a go and here’s what they came up with.

First, they chose to model it with integers. Said one student: “I pretended it was a jar with 10,000 marbles.” 2014-04-03 11.07.36

Then they assigned “a dropper-full” to be 100 marbles. So, the first dropper took 100 red marbles and placed them into the jar with the 10,000 green marbles.

Now we assumed the stirring made the mixture homogeneous which meant that there was a consistent 100:1 green-to-red marble ratio in the right jar. So, when we pull another 100 marbles to put back, (with a little bit of rounding) we pull 99 green marbles and a single red marble back into the left jar.

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A little number crunching reveals (at least in this model) that there would be 9901 original-colored marbles and 99 other-colored marbles in each jar.

My original assumption matches their investigation. It seems (at least by this model) that at the end of the video, each glass is containing equal amounts of their original soda.

Another teacher Chris Hunter (@ChrisHunter36) also battled with this video and created an excellent read about his experiences. Check them out.

 

The Power of Network: The Wedding Cake Problem

I have another wonderful story about the power of the wider math community to support its own. Earlier in March I presented at MACUL 2014 in Grand Rapids, MI. During that presentation, I led the group through an experience with the Wedding Cake Problem, which ended up being a wonderfully energetic interaction.

Sitting in that meeting was a gentleman named Jeff who teaches at a school in Michigan. He wrote me an email some time later that included a message and the following photos:

“I’m planning on using the cake problem this week as review in my Trigonometry class, as well as later in the year with my Geometry students. Well, here are a few improvements, well, really just pictures. See attached.
Pans are 5″, 7″ and 9″. I think I’m just going to give my class the actual pans without the pictures.”

Cake-Pans

Cake-Pan-Side-View

Cake-Pans-Stacked

Cake-Pan-Top

Cake-Pan-Top-Ruler

 

 

Now, these photos change the dynamic a bit, don’t they? Let’s do pros and cons… What do you like better about giving the problem with these pictures? What do you prefer about the original problem?

I would love some feedback (especially if you have tried either one with your class).

The Hershey Bar Problem (#3Act Revised and Updated)

About a month ago, I posted The Hershey Bar Problem in which I discussed, among other things, the ways in which I rip off other teachers work. This is an example of that. This is a Dan Meyer rip-off pure and simple. I just want to cover myself in that regard.

As usual, all constructive feedback is welcome.

Here’s the rest:

Act II – Dimensions of the Hershey Bar or Dimensions of the segments after the cuts.

Act III

Sequel #1

Sequel #2

Making over another typical geometry problem

It’s time to look at another typical geometry problem to make over. This time Dan Meyer (@ddmeyer) presented this problem for revision.

Dan decided to go in this direction for the revision, which, for the record I really like. I would encourage you to check it out.

I took a try at it, too. I’ll let you decide which you like better.

I like this problem’s basic core idea. Looking at the volume of a sphere (the meatball) and the volume of the cylinder (the cooking pot), in general, this is a pretty tasty set-up (pun intended). Especially considering that I am always a fan of problems that make use of food.

But…

For this problem, food and cooking were actually more of a problem that a support.

First, the cooking pot is sitting on a hot burner and I’ll be the first to tell you, a cooking pot doesn’t have to be full to spill over. So, the question of whether or not sauce will spill over is a bit more complicated that it might seem at first.

Second, meatballs aren’t spheres. They are irregular and rarely are two of them congruent.

So, my first thought was to choose spherical objects that are all congruent: for example, baseballs. Coaches regularly carry baseballs around in 5-gallon buckets, so there is our cylindrical container.

And I figured I’d deliver the task in a video simply because videos tend to improve engagement on their own.

Now, once I made the video (and some meaningful conversation was had among those who are better at this than I am) I found that my task had one glaring drawback. When you put baseballs in a bucket, they don’t pack tightly. There is air between them. A lot of it, in fact.

So, now it seems like if we are to use this video for instruction, we would need to change the question in to multiple parts.

1. How many baseballs can we fit into the bucket? (This would likely end up being a demo or a lab where we collect data. Tricky to calculate this.)

But then we supplement the question above by…

2. How much volume is wasted by packing that many baseballs in the 5-gallon bucket.

This would get back to the original content. Likely the cylindrical volume would need to a unit conversion, and then some analysis of the collective volume of the collection of baseballs.

Now, if we could ind a way to check it. The first thought I had was to fill the bucket with water. Put the baseballs in to displace the water out of the bucket. Take the soggy baseballs back out of the bucket. Find the volume of the water that’s left.

Problems with this idea: 1. Baseballs float which is going to effect the manner in which the water is displaced. 2. Baseballs absorb water. This means that some of the none displaced water would get removed with the baseballs and not counted.

Hmm… I thought of filling the bucket with baseballs and then topping the bucket off with sand. Which would solve both of the above problems, it would also give me an opportunity to make a beach trip.

Any other ideas out there?

The Grill Fries Problem

That's two medium russets.

That’s two medium russets.

So, let’s suppose that I cut up two medium russet potatoes like so and put them on that grill you see up there.

How many medium russets will the grill hold and (perhaps more importantly) how many people can I feed using those fries as a side dish?