Dan-
I am a big fan of your work. I teach history and my belief is that relevance and engagement are 2 cornerstones to quality instruction and quality learning. I read your “WCYDWT” and it is fascinating to the point where it makes me want to be a math teacher!

At any rate, as an avid reader, my thoughts always come back to, why aren’t more sports integrated math instruction? See: ESPN commercial…

http://www.youtube.com/watch?v=0TBusqMaCEM

As a 30 yr old male in more fantasy sports leagues than I would like to admit, I see a world of potential math instruction that could be both relevant and highly engaging.

D

What I find most ridiculous about this problem is the grade level. 10th grade?!? This should be a 3rd or 4th grade problem. I guess I have been spoiled by teaching Singapore Math?

What bothers me about this, is this is how textbooks publishers, teachers… seem to think is an authentic way to address the struggles of First Nations students (and other ethnic groups) with mathematics. It is important that students be able to “see” themselves in the resources and in the classroom, but the assumption is that this picture, with the highly culturally-stripped question, is somehow worth a check mark in that column. There is great significance in the dance, the dress, and even what the jingles might be made of, yet none of that is mentioned. Instead, all that’s done with it is to make an excuse for doing some Western mathematics.

If we really want to be respectful of other cultures and their mathematics, it’s about time that we started letting the people who are from those cultures have a real say in our mathematics classrooms. Mathematics is an incredibly culturally biased subject, and it’s about time that we started addressing it in that way. This is not to say that students don’t learn Western mathematics, as it is such a dominant player in our Western society; however, it’s time to learn that it’s not the only way to think and do mathematics.

This is actually one of the reasons that often like the things I find on this blog — because they’ve been stripped to the bones — here’s an idea, a picture, a video, a general question — now you go out and investigate it in your terms, through your understandings, through your ways of knowing (cultural and other), and then lets bring those ideas together.

@Gale #6: can you elaborate on what you mean by “Mathematics is an incredibly culturally biased subject”? Are you refering to the (pseudo)examples we use to teach math? Or are you talking about the actual content of math courses?

While no doubt there is great cultural significance in the dance, the dress, and what the jingles might be made of, none of that is relevant to the math problem. Math does not depend on cultural context; that is what makes it so powerful. “Western” (modern) mathematics may not the only way to think and do mathematics, but it is the only one that is of any importance to contemporary technological society.

I’m going to agree with Diane and Tyler, the fact that this 3rd grade level problem is in a 10th grade Pre-Calculus speaks volumes to the expectations of students.

There are a total of 545 lids. The larger dress has 185 more, so imagine setting those aside:
545 – 185 = 360 lids left.
Those 360 lids are evenly split between the dresses:
360 ÷ 2 = 180.
So there are 180 lids on the smaller dress and 180 + 185 = 365 on the larger.

This type of reasoning is very common in Singapore Math word problems. See examples in my Word Problems from Literature series. The problems are often modeled with bars (a sort of visual algebra), to make the number relationships easy to see.

[—–?—–][–180–]
[—–?—–]
total = 545

Here’s a problem from the Grade 3 Primary Mathematics materials:

Adam and Carly have 135 baseball cards altogether. If Adam has 41 more baseball cards than Carly, how many baseball cards does Adam have?

The fastest way to solve it is by understanding the relationships, which the model method helps students see.

FYI, the math books used in Singapore include National Education in the Teacher’s Resource Pack. In the 3B Teacher’s book for Shaping Maths, the unit on Time is introduced using pictures of festivals and celebrations: Diwali, New Year, Christmas and Hanukkah. Here’s the note in the teacher materials from that page:

“Though we have many different races and religious groups in Singapore, we all still pursue the same dream – The Singapore Dream. NE message: We must preserve racial and religious harmony”

You don’t see that in the U.S. version of the curriculum.

I think there’s a mistake in Denise’s bar diagram. The top right bar should be labelled 185, not 180.

But as Denise’s comment suggests, the only math skills you need to solve this problem are counting and pairing. You can do it on a tabletop with a jar of pennies: Take out 545 pennies. Separate them into two groups to represent the lids on the two dresses. Take 185 pennies out of the larger group. Equalize the two groups by pairing to correct for any error in your original separation. Then put the pennies you took out earlier back into the group representing the larger dress.

You now have two groups of pennies which contain the same number of pennies as the number of lids on the smaller and larger dresses, respectively. If you count the two groups of pennies, you’ll find that the smaller one has 180 pennies and the larger one has 365 pennies. That tells you how many lids are on each of the two dresses.

So you’ve solved the problem. And you didn’t need to subtract or divide. You didn’t need know how to use numerals, much less equations. Counting and pairing sufficed. (Of course, in the real world, with the two dresses at hand, one could solve the problem even more simply just by counting the lids themselves.)

So if the purpose of the problem is to get the answer, or to learn how to solve problems like it using manipulables, or to develop general number sense and mental math skills, then it might be considered a third grade problem. But does the fact that it can be solved in this way mean that the problem can’t (or shouldn’t) be used in higher grades to teach more advanced math skills, such as how to manipulate equations?

@Zeno
Thanks for the correction! I was trying to do too many things at one time yesterday and didn’t edit as well as I should. As for the question of whether such a problem could be used to teach systems of equations — yes, in algebra 1 it might. But did you notice that this book *claims* to be pre-calculus?

@John
I suppose you could use bars for that system, but I don’t know why you would want to. Algebra is much easier when the coefficients are not related at all.

The bar model can easily be used for systems of two variables where one of them drops out. This, for example, might be a 4th or 5th grade problem:

2x + 5y = 20
2x + 2y = 19

Systems with three variables are also used, but these are very simple. For instance, here is one from my Hobbit Math article:

x + y + z = 123
x = y + 15
z = y + 3

And in 5th-6th grade, just before switching to algebra, there are problems where the student needs a multiple of one of the equations, such as:

2x + 5y = 20
x + 3y = 11

Of course, these aren’t given as variables, but as word problems. Usually they have to do with purchasing an assortment of items, or fixing a variety of foods for a party, or collecting and trading stickers, etc. — so that the students have something concrete to imagine.