## U2 L4 Opener.pdf - Section 1: Opener: Percentages of Large Numbers

# Where Does My Stuff Come From? Part 4

Lesson 4 of 10

## Objective: SWBAT gather data and organize it into a two-way table.

Today, students will work Part 4 of the "Where Does My Stuff Come From?" Project. For this activity, they will investigate annual U.S. and world trade data, which is measured in billions - even trillions - of dollars. To prepare for that, I post today's opener and give students a few minutes to come up with their solutions.

When I use this opener, I have to remember to keep the conversation short without letting it bog down the rest of the lesson. Percent is a topic that I'll always wish all students could grasp perfectly, and I always want them to get it *a little better *than they already do. Also, there are some students for whom big numbers present a problem. It's easy to want to really slow down and address all misconceptions here, but I force myself not to: this is * just an opener*. As such, it's used to introduce an idea and to allow me to take the pulse of how kids are doing with this topic.

Today's activity will allow them to practice with big numbers, and eventually, percentages. When I see that kids are struggling with this opener, I'll note it, and I'll address their issues in smaller groups, as they're working on the project. **That's the beauty of teaching with projects** - there are always opportunities to pull students aside and teach a necessary mini-lesson here and there.

I find the last problem in this opener most interesting, and as you'll see, it will play a role on Part 4 of the Stuff Project. As students share their answer to #4, I record them on the board in a place that I'll be able to leave them for reference as the period continues.

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In Part 3 of the "Where Does My Stuff Come From?" Project, students summarized the results of their geographical inventories of their personal belongings. They categorized their "stuff" into **Apparel**, **Electronics**, **Produce**, and **Other** bins, made some maps, and eventually started talking in generalizations, like, "A lot of my stuff comes from China." or "Most produce comes from the Western Hemisphere, but a lot of apparel and electronics come from the Eastern Hemisphere."

I explain to students that today I'm going to show them a tool that will reveal data about all international trade patterns for the last few years. We will start by looking at U.S. import data, but if they want to, they'll be able to look at any country on the planet. I say that we're going to be able to assess the accuracy of the data we've taken so far, and I turn that into a question:

**Do you all think that our data reflects imports into the United States as a whole?**

If I have to, I'll remind students that imports are everything that we purchase or receive in trade from other countries. I'll make sure that they're also familiar with the word **exports**, both as a noun and as a verb. I'll use both words in sentences: "When phones that are made in China are shipped to the United States, we can say that *China is exporting phones to the United States*, or just as accurately, that *The United States is importing phones from China*. Both mean the same thing."

This is all conversational. I'm leaving the floor open to kids to contribute, but I'm leading the way as much as I have to. It's unnecessary for students to take notes. I'm just trying to frame the class and build their curiosity - because the bigger set of all U.S. trade is going to look a bit different, and I want kids to have predictions in mind about what they're about to see.

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**Assessing the Accuracy and the Initial Reveal **

Just to build a little more anticipation, I reiterate what's about to happen: "I'm going to show you a list of the top 12 exporters of stuff to the United States. You're about to see if it matches our list. Do you think it will?" I allow students a little time to share what they think, but I stay quiet for this part of class.

When it seems like everyone is ready, it's time to reveal the real data on www.trademap.org. This video provides an overview of how the web site works, and I share some ideas that I think about with kids as we start to take a look. Just an initial look at the data is enough to get all sorts of new conversations going, and it's up to us as teachers to decide how far to let these conversations go before we move on.

**Part 4 of the Project**

Students will use www.trademap.org to complete Part 4 of the project. Their first step will be to call up the data on their own computers, and in the first column of their table, to write the names of the top 12 exporting countries to the United States.

After recording this list of the top 12 countries, we sort the data by product category (to see how, check out the video) and find that according to the trademap data, the top four categories of stuff imported by the United States are:

- Mineral fuels, oils, distillation products, etc
- Machinery, nuclear reactors, boilers, etc
- Electrical, electronic equipment
- Vehicles other than railway, tramway

These categories become the column headings on Part 4, and now we have a two-way table. It's not *exactly* a "frequency" table, because we're using US dollar amounts to measure the amount of trade, but it's a powerful illustration of how we can take two sets of categorical data, see how they're related, and explore the implications.

Students get computers and use the web site to fill in the two-way table. They dive into the data and look at a list for each category to see get dollar amounts of U.S. imports for each of those top 12 counties. I circulate to troubleshoot, making sure that students understand how to use this powerful tool. It's empowering for kids to explore such a serious resource, because it's a little intimidating at first. When they make sense of it, my students are fired up.

**Thousands and Billions**

As an exercise in number sense, and to allow all these numbers to fit, I explain that students should record these trade values in ** billions of US dollars**. This is a challenge, because trademap publishes its data in

**. Students will have to make this translation. This is an example of how I try to build little skill drills into a deeper context.**

*thousands of USD*The results of our work look like this. As students fill in the table, it's important to continuously ask, "What is the unit of measurement?" I want to make sure that kids are properly interpreting the number they see. When a country doesn't show up near the top of a category list, I show students that they go to successive pages until they find a class. For some countries, we eventually come upon some *relatively* small numbers. We see that Venezuela and Saudi Arabia are pretty one-dimensional in their exports to the US. But then, we note that 0.018 billion dollars is still 18 million dollars, which certainly isn't nothing.

As students finish up, this activity opens up all sorts of new questions -- we're not even touching exports, for example. I look for chances to talk about this stuff - I want students to wonder about all of this! Some students will ask about the "Trade balance" column, and we'll talk about it. The questions that come up go beyond the scope of a high school math class, but they're important questions for kids to ask as they come of age. *Why is there so much red in the US trade balance column?* Or, *What characterizes the exceptions - those categories that are in the black?* Or, *If the US has such a negative trade balance, then what countries have a positive balance?*

And that's where the fun really starts. I hope that you and your students have the chance to geek out on this stuff!

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What we've just done is looked at the small set of data at the top of the US trade heap. Consisting of 12 countries and just four "categories of stuff," these dollar amounts (note that I completed this in 2012, and it's slightly different for 2013) add up to 989 billion dollars. All told, that's over 42% of all US imports. I'm amazed by that number, and I try to get its weight across to students. I ask them to name all the countries they know, and note that these are not on the list. I ask them to name all the stuff that is not fuel, machinery, electronics, or vehicles, and note that none of that is on the list. We're looking at a small subset of all the categories of stuff and all the countries out there, and it accounts for close to half of all US trade. To really consider that is to begin to understand how wealth is concentrated in our country.

It's ok, still if the 42% number still doesn't surprise everyone. This is one of those little mental exercises for the kids who want to engage in it, and I hope that for a few of them it opens up all sorts of new thinking. It always does.

On the back of Part 4 is a series of questions. We return to the Apparel and Produce categories with which we started this project. Students use trademap to gather data about these categories, and when they're done, we can compare this data to see if it's more in line with our original data collection on Parts 1 and 2.

A neat extension is to have students pick a country of their choice, and look at the top imports and exports for that country, as well the top trade partners, and then to consider the roles of geography, history, and power in that country. If you're in a school that values interdisciplinary work, this is a great place to start in a collaboration with a social studies-teaching colleague!

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- LESSON 1: Bivariate Data, Background Knowledge, and the Beginning of the Stuff Project
- LESSON 2: Where Does My Stuff Come From? Part 2
- LESSON 3: Where Does My Stuff Come From? Part 3
- LESSON 4: Where Does My Stuff Come From? Part 4
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