Hi, I’m Pam, and today I want to introduce you to an activity called Millions and Billions. When we talk about population numbers, we’re talking about very large numbers. And this is an activity to help upper elementary students understand what a million is, what a billion is, and understanding scale, that a billion is a thousand times a million. Then that will help us comprehend these numbers in a real world context.
This is a great activity for upper elementary math, and it also brings in an art component as well. Here are the different objectives for Millions and Billions.
- First, recognizing that one billion equals one thousand times a million, and that a million is a thousand times one thousand.
- Second, evaluating the difference in scale between a million and a billion.
- And finally, solving math problems using standard measurement conversions and base ten operations.
Let’s get started.
Activity Procedure, Part 1
Part one we call Big Riddles. And these are riddles that help students understand that idea of scale between a million and a billion. I’m going to give you one as an example. We call this one the Rich Uncle Riddle.
Have your students imagine that they have a rich uncle who has just left them a billion dollars in his will. But there’s a hitch. In order to keep the billion dollars, the students have to count all billion dollars. And they have to count it one dollar per second, eight hours a day. And they can’t keep the billion dollars until they’re finished counting. Ask them if they’d take that deal.
Well, if they did, it would take them over 95 years to count a billion dollars. So that’s not feasible.
Then change up the riddle and ask them if the deal was for a million dollars, counting it at the same rate. Would they be able to accomplish that task then? Well, with a little math, they’d find that in 35 days they could count that million dollars. And then they’d be a million dollars richer.
So that’s the difference in scale between a million and a billion in that riddle. 35 days or 95 years.
Activity Procedure, Part 2
Part two of this activity is called Seeing One Million Stars. This is great for visual learners. Each student is going to create a quilt square. And each quilt square is going to be made up of 100 triangles. They’re going to create these using pattern blocks that we provide. And they’re going to place that on a provided grid to make their own design. Each of these squares will be put together to make a classroom quilt.
So, for instance, if you have about 20 students in your class, and each one has a quilt square made up of 100 triangles, that’s 2,000 triangles in the quilt. Now you might ask students, how large would a quilt be that had one million triangles? Well, that would be equivalent to 500 of their class quilts. And just to give you an idea, that would be about the size of a tennis court.
So now you’re going to ask them, alright, if that’s the size of a million triangles, how large would a quilt that has a billion triangles be? So that’s going to be 1,000 times the size of that tennis court, or even larger than the Mall of America, which has 500 stores.
Activity Procedure, Part 3
Part 3 of Millions and Billions is called Measuring a Million. And this is where students are going to work in cooperative groups to do some mathematical problem solving, primarily with linear measurement. It uses simple props like measuring sticks that have gradations for both metric measurement and imperial measurement. One group will use a map, others will use stacks of paper, markers, simple things that you have around the classroom.
Each group will have worksheets provided that will have scaffolding for doing the math problems. Now what I like about these worksheets is it gives you an opportunity for differentiation in the classroom. If you have some students who don’t need the scaffolding, well, then you can simply provide the problem and have them come up with the method for solving it. So I want to give you an example. There are five problems altogether, one on each of the worksheets. And the one I want to explain to you today is one that uses linear measurement in the following way.
You’re going to ask students, if you take one million steps from the door of this classroom where will you end up? And then by extension, if you take one billion steps, how far will you travel? So, on the worksheet, the first question that’s asked of the students is determine what direction they want to travel in. I’m here in Washington, D.C., so if I was doing this, I might say that I’d like to travel south. Then you ask the students to estimate where do they think they’ll wind up if they take a million steps. Well, I don’t know, maybe Florida? Then you actually have them come up with a pretty good idea of where they’ll wind up by measuring out student steps.
One way to do this is to have a student take ten steps and measure the distance that they go in ten steps. The students might even want to measure each of their ten steps and average it to come up with an idea of what an average person in their group, how far they would travel. So, just to give you an idea, for an average nine-year-old student, ten steps would take them about 18 feet. So, then they’re asked, well, if 18 feet gets them ten steps, how far is a million steps? Well, that means they’re going to have to multiply this out by 100,000. So, ten steps is 18 feet, they’ll find that a million steps is 1,800,000 feet.
Then the worksheet tells them how many feet are in a mile, 5,280. So, they divide that into 1,800,000 to find out that they would travel 341 miles. So, going from D.C., going southward, you’d wind up around Fayetteville, North Carolina.
So, how about a billion steps? That’s a thousand times as far as going to Fayetteville, North Carolina. In fact, if you tell them that the circumference of the Earth is about 25,000 miles, they’ll find out that a billion steps would take them around the globe 13.6 times. So, that’s just one example of one of the problems. You can see that it’s very hands-on.
Now, after they do their different problems, and they are differentiated, so some groups will have problems that might take a little more time and a little more calculation than other groups. But once they’re all done, you can talk to them about the real-world connections between understanding millions and billions. Where do they hear millions and billions in the news? Maybe they hear it when they’re hearing news about the economy or, in this context, population.
Now, if you want to use this activity with middle school students, we have a version that’s called Measuring a Million, and it’s very much like the activity I described, but the math is a little bit more complex. Instead of just linear measurement, students are using two-dimensional and three-dimensional measurement. So, their problem-solving will take them a little bit longer, and they may or may not need that scaffolding depending on their math proficiency.
So I’ve been happy to share with you Millions and Billions. To find out more activities like this, please visit www.populationeducation.org.