Question

Dear Mitch,

My niece was a student of yours the very first year you taught a classroom, and she still talks about some kind of "raisin box lesson" you did with the class on Valentine's Day. She cannot remember exactly what happened or how you managed it, and now she's too shy to write to you to review it. The reason I'm taking the time to do so on her behalf is that she's secretly dying to recall the lesson because she herself is now in the midst of her first year teaching! (As you might guess, she wants to do the lesson with her class, so when I heard about your website I figured I'd surprise her. Frankly, I have no idea what all this fuss about raisins is, but you must know just what she means. Can you fill me in so I can print it out for her?

Thank you,

Mother of S. Hanson

Answer

Dear Mother of S. Hanson,

Sure!

First, I remember your daughter! She was a delightfully motivated student, always eager to help others, and I always hoped she might consider teaching.

I believe I know the lesson she's thinking of, though I believe her memory may be combining two separate lessons. Thank goodness, because the slight confusion just inspired me to combine the two into a single lesson she might like.

First, for several years I taught a lesson using a collection of different sized packages of Sun-Maid Raisins. It began when I noticed how neatly the company's different sized boxes worked together mathematically. I also liked the visual aspect: bright red packages all adorned with the same design so that they not only held the students' focus but quietly conveyed the idea that only one variable was at issue: the package's size. Specifically, the lesson was part of an investigation into the geometric idea of volume (or 'capacity') because packages of food – other than flat envelopes of tea, etc. have three dimensions – height, depth, width.

O.K. There may be a bunch of sizes from the same company of which I am not aware, but as I write this I am looking at the group I accumulated this afternoon in a single local grocery. It was the first store I entered after reading your note; thus we might conclude that this product should not prove difficult to find in various sizes. So, from smallest to largest:

We have the mini box: a 1/2 ounce package which only seems to come in bags of 14 labeled "mini-snack". The entire bag states its weight as seven ounces, and its contents as 14 boxes. So, our first bit of math is to figure out the approximate weight of* each *little box contained in the bag: So, a 7-ounce bag divided by 14 boxes = 7/14 = 1/2 ounce per box.

This bag itself is important here for its information, because the boxes within do state their weight, as they are not packaged for individual resale.

Next size up is the one-and a half inch box, which comes in shrink-wrapped packages of six.) Math 6 x 1 1/2 ounce of raisins gives you a total of nine ounces of raisins.)

Next size up is the 9-ounce box, which is sold individually.

Next size up : 15-ounce box, also sold individually.

Finally, there is a 24-ounce container. It has a unique shape: not quite a cylinder, not quite rectangular, but a cross of these two shapes with rounded vertical edges.

O. K. Now, there are many ways to turn this into an enlightening and engaging math lesson for the Valentine's Day season; the reason I use the term 'season' is that this investigation could easily span several math periods over the course of 3, 4, or even five days.

Lesson 1:

Prior to the lesson, empty several boxes of each size, so that there is both an unopened and an emptied box for students to examine.

Arrange students into groups and provide each group with various sizes of raison boxes, to examine.

Next, introduce a supply of those famous chalky hearts which are sold for Valentines Day, called "Sweethearts", or other similar product. You may want to stress the importance of the quantity you've supplied so that the necessary number for the mathematics would be available, to discourage any from disappearing until the agreed upon final day.

Have students estimate how many hearts can be placed in the smallest box

Then have them test their estimates. Then based on the number that does fit inside, have the estimate the number they might be able to fit in the next size up...

Point out: 1/2 ounce box and the 1 1/2 ounce box... do the numbers have any noticeable relationship? Might that help in the predicting of volume? Why or why not?

Next, test students' estimates and, based on results, estimate the number that may be squeezed into 9 ounce box, and so on through the 15 ounce pack. Save the 24 ounce pack for the entire class to do together at the front while you turn it into a demonstration. This cuts down on number of large packages required, the number of candy hearts required, and the potential chaos of too many separate sources of action within a single room.

Discuss: Does shape of container matter? Does shape of candies matter? Etc.

Lesson 2:

For a more advanced lesson (in my opinion), note: On each sized box (other than the smallest, 1/2 ounce size), there is one and only one corner that reveals the net weight in ounces. Cover that information with a permanent marker, tape, etc, and conduct a parallel estimation investigation, this one with rulers and package size.

In this lesson the estimations are based on the actual capacity of each box, which I calculated from its height, length, and depth. Supply rulers and plenty of paper for calculating, review formulas, and well, good luck!

As far as the cylinder/rectangular prism, well, you are on your own!! Be creative, and/or have the students come up with their own creative methods of calculating its capacity. Then test it out!

Hope this helps,

Mitch