Windows and Mirrors: Fair Shares for Eid al-Adha

A man’s true wealth is the good he does in the world.

Hadith attributed to Prophet Mohammed (ra)

Eid al-Adha

Eid al-Adha was a little over two weeks ago. It is one of two major religious holidays for people that practice Islam — like my family does. It does not garner quite as much press in the US as Eid al-Fitr, which marks the end of Ramadan. I assume that’s because Americans find it easier to understand why we might celebrate the conclusion of a month of fasting.

Eid al-Adha honors the willingness of Ibrahim (Abraham) to sacrifice one of his sons, as well as a commemoration of the time in which the Qu’ran was revealed to Mohammed (ra) and the period of Hajj. On this holiday, Muslims across the world observe the tradition of Qurbani: the ritual slaughter an animal (often a sheep or goat). The family keeps one third of the meat, then gives one third to family, friends, and neighbors, and the final one third is for people in need.

A Laib Family Celebration

Living as we do, in population dense metro Boston, we usually give qurbani in the form of a cash donation to a charity abroad. Then we bake. Before I had two small children to lovingly occupy all of my waking hours, I used to whip up a few things to give away.

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You know, just a few.

I would package everything somewhat equally into boxes and bags to give way at our local masjid (mosque). (In case you’re wondering: yes, I did the graphic design for those bags myself. Look at all that time I used to have!)

As I planned out the baked goods for that Eid, there were several mathematical calculations I had to make. How many bags and boxes should I purchase? How many treats should I put in each bag? Or the essential question: why didn’t I make more salted chocolate covered caramels?

This is relatively simple division when compared with the original task of determining each third of the sheep to keep or give away as qurbani. Presumably most families ‘eyeball it,’ but I like to think that there are some precision-driven people breaking out a scale. (These are my people.) 

Or I could think about budget: spending one-third on Eid gifts for family, one-third on gifts for friends, and 1/3 on charity, although I think those ratios feel a little off. While I do spend roughly equivalent amounts of gifts for family and gifts for friends, charity (zakat) is one of the five pillars of Islam. We give more.

Kinds of Division

These different scenarios represent different ways of thinking about division. In the most classic Eid al-Adha example, cutting up the qurbani, we are partitioning into three equal size pieces.  is called partitive division: dividing into a known number of groups. The mathematical question that naturally arises from this context is “how much meat is in each portion, which is 1/3 of the animal?” which calls for us to determine the amount in each ‘group,’ which is a 1/3 size piece of the entire qurbani.

In the example of the Laib family sweets, I typically wanted to know how many bags or boxes I should buy, after determining a standard amount to put in each container. This is quotative or measurement division: dividing an amount into groups of a set quantity (e.g. 5 treats per bag). 

However, if I had pre-purchased the bags, and then had to figure out how many items to put in each bag, that would again be partitive division. It all depends on the specifics of the scenario, and the question being asked.

Or is it Multiplication? 

Instead of dividing the qurbani into 3 equal pieces, we could think of each portion as 1/3 of the total. The equation to solve how many pounds of meat are in each portion might then be 1/3 multiplied by the total amount of meat. 

Or if we know how many bags of treats we will package, and how many treats go in each bag, we would multiply to determine the total number of sweets made.

This is the beauty of inverse operations. 

So What: Broadening Cultural Representation in the Classroom

Dr. Rudine Sims Bishop’s essay on mirrors and windows (and sliding glass doors) may have been originally applied to books, but it holds true with mathematical contexts, as well. The big idea, which I am ruthlessly paraphrasing here, is that students/all people need opportunities to see themselves both reflected in their work — like a mirror — and also opportunities to observe the beautiful diversity of the world, like through a window.

Last February, Janaki Nagarajan (@janaki_aleena) and I presented a session at NCTM on ‘Making Choices that Broaden Cultural Representation.’ We realized that there is no such thing as a context that is ‘culturally neutral.’ Even something that might feel neutral, like baking in a kitchen, is endowed with all sorts of cultural nuances, particularly if we show an image of the kitchen or describe what it is that we are baking. Is it brownies? Or is it matlouh, the fluffy Algerian bread that I watched my daughter make with my mother-in-law this morning? The more details we add, the more vivid the context. This can be powerful. We can also make decisions about who in the room will experience this context as a mirror or as a window. How can we balance these opportunities?

I would love for my own Muslim children to get to do some Eid al-Adha math in their classrooms someday! The majority of their current classmates are not Muslim, and none of their teachers at their school have been Muslim. So how would any of the teachers or students know about the mathematical possibilities?

I certainly don’t know about all of the rich mathematics in other people’s holidays or celebrations or food, etc. 

How can we help share these contexts?

And then… The Math!

Once the context has been introduced, it’s time to focus on the mathematical strategies.(I chose the qurbani context, even though I might not choose it for a deep dive in a classroom. I am well aware that vegetarians, like my brother, might squirm — the way I do whenever people want to talk about bacon. Oof.)

There are certain types of strategies that might lend themselves to dividing up a 48 lb. qurbani, for example.

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Some students who are less familiar with division strategies might directly model it by 1s. 

A student might draw three portions, and then a dot for each lb. Here, one dot was distributed to each of the three portions, round and round, until all 48 dots (lbs) had been distributed.

Or a student might invent an algorithm, e.g. one that involves partial quotients.

I have seen students distribute quantities in more familiar chunks. For example, a student might represent the three portions with three bars, then put 10 lbs in each bar. 3 x 10 = 30, which is smaller than the total amount, so there is more to distribute. Adding 5 to each portion means that another 15 lbs have been distributed, or 45 lbs. overall. Adding one more lb. to each portion will fully distribute all 48 lbs. of the qurbani.

10 + 5 + 1 = 16 lbs. per portion.

Or any number of other grouping strategies!

I would not expect a student to use a skip count strategy here, like “3, 6, 9, 12, 15…” to see how many 3s go into 48, because that wouldn’t match the situation.

Or maybe the focus is on fractions, and finding 1/3 of the total. I would expect different strategies to emerge if students interpreted the context like this:

Honoring Students and Their World

Focusing on the mathematical strategies to solve the situation pushes student mathematical thinking forward — and isn’t that the goal? — while also honoring that this is a context worth talking about, and that student ideas are worth talking about, too.

The next Eid al-Adha is in July 2022, which is not exactly an opportune time for many Northern Hemisphere schools, but I am hoping that this post broadens our ideas about mathematical contexts to use.

I also wonder about all of the opportunities to engage in math about my students’ world for which I have no background knowledge. I’m completely in the dark. How can I learn more?

1 Comment

  1. Jenna, your questions about how to incorporate more cultural contexts that honor the students in our classes about which we may have no background knowledge is a thought-provoking one. I wonder what would happen if we asked our students to go home and think about where in their lives they, their parents, or their culture uses math and have them share aspects of their culture with us and their classmates? I wonder if we would get even more if we asked students to bring ideas that they think are unique to their families or culture.

    Like

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