Thursday, October 29, 2009

Ultimate Number Line Game: Number Sense on a Massive Scale

When I wrote about games and puzzles recently, Mister Teacher left an interesting comment about his frustration over students' lack of number sense. He teaches 3rd graders, but my high school students always had the same problems. One tool I used, even at that level, was the number line.

Number lines are used for a number of topics at the elementary level, but they pop up when least expected in higher grades. They help with counting and measurement for younger students and later become part of measures of central tendency (box-and-whisker plots) and graphing inequalities. By using it, you're modeling something that appears throughout all levels of mathematics but is still criminally underused.

So I was considering this issue and was struck with the idea of creating a giant number line that student could actually walk along. I envisioned all ages of students rushing up and down the line frantically, as I used to do when we played a version of Ship to Shore in PE in elementary school.

This game is designed for 1st grade and up, and is scalable and adaptable for higher levels of difficulty.

Ultimate Number Line Game

Creating the Number Line

You need space to make a huge number line on the floor or ground. Try to secure as large a space as possible (the bigger the better):
  1. Classroom: Use brightly colored painter's or electrical tape to mark several parallel number lines on the floor. Create enough hash marks as possible (-10 to 10 at an absolute minimum). Move desks, tables and chairs out of the way (out of the room if possible).
  2. Gym: If there's any lines already on the floor, use them as the hash marks of your line, but create the line students will follow as described above.
  3. Outdoors [large sidewalk/playground]: Use sidewalk chalk to mark number lines.
  4. Outdoors [football field]: Perhaps the best option of all, especially if the field is lined but not numbered, in which case you don't need to do anything except get out there.
Parents and homeschoolers: you have a distinct advantage if you try this game--there's no excuse not to use the largest space available.

Game Procedures
  1. Students stand at zero to start. If you're in the classroom, use teams and have students rotate out when they're eliminated (see below).
  2. Teacher calls out problems with ample pauses between numbers and operators ("8... plus... 3... next: 2... minus ...7!"), allowing students to move accordingly. If someone stops on the wrong result or is the last to get there, they're eliminated. Eliminated students stand off to the side, and are welcome to help with answers and identify cheaters or other problems.
  3. Increase the speed and difficulty of problems until the round is done.
  4. Start over and encourage improvement, but accelerate the game more quickly. The ultimate goal is that the class will get to the point that everybody is moving to the right spot almost as one!
Introducing the Game

Discuss the type of problems you're going to do. Some questions you might ask, depending on the level of questions you'll be working on: "How many of you know how to add? ...subtract? What happens when you subtract a bigger number from a smaller number? What is a negative number?"

Introduce or review the number line. We start at the first number given in any addition or subtraction problem. We move right for addition and left for subtraction (and if you're using negative numbers, that sign reverses your direction). Explain the game procedures outlined above.

Options and Considerations
  1. How do you want students to move? Do they make big steps over large intervals, hop (as we draw on paper number lines often), or can they run?
  2. Are you going to announce problems separately (which will require more movement) or just add or subtract to the last answer (which might be quicker)?
  3. How difficult should the problems get? Will you just add and subtract positive numbers, positive and negative integers, fractions, or decimals? Will you change your intervals to 10 or 100?
  4. Who do you need to talk to in order to use one of the spaces outside your classroom? The unique setting and large scale of this game is what will make it more memorable and effective with your students, so you have to do everything to get the most possible space.
Why This Will Work

Notice that I didn't suggest students could do this on a paper at their desk; of course they could. Yet that would miss the entire point: this is an engaging, fun, kinesthetic activity. Students will be paying attention, quite literally on their toes, and that's a big deal in and of itself.

More importantly, the number line is an easy to understand model of addition and subtraction, especially for more difficult problems like subtracting larger numbers from smaller ones, and adding and subtracting positive and negative integers.

This game avoids any written component, by you or them. You're helping them develop number sense by solving the problems quickly and mentally, with only a slight aid from the number line. By not even seeing the written problem, let alone being able to work it out on paper, they're forced to use the natural math ability we all have.

To go back to Mister Teacher's example, imagine starting at zero and giving students the problem "0 minus 8". It sounds like in his class, you'd have half of the students go to 8 and the rest to -8. Who's right? Can one of the students explain the answer? It's a great teachable moment that will stay with your students.

Moving around the line doesn't take too long, so you have the opportunity to do a lot of problems, multiple rounds, and reverse and repeat problems that students struggle with.

By the end, you should be able to call out almost any problem and have everybody moving to the right answer simultaneously! In other words, it should get to the point that they don't need the number line by the time you're done.


If you attempt this in class, please report back with your experience! I'm really excited about the possibility that this simple idea will make a difference for your students.

Have you done anything similar on this topic or others? I'd love to hear about that as well.

Stay tuned for more games for students young and old!


j4luck said...

I love this idea! I am definately going to be writing this one down for use in my future, thanks!

Betty said...

I did something similar to this when I taught sixth grade math, but didn't think outside the box like you did. Your ideas are awesome! I hope it's okay if I share them on my blog.:)

Dana Maize said...

This is great - I needed a lesson to help us learn about negative numbers, and this will work perfectly!

Anonymous said...

I teach Grade 5, so I get the kids to write a number on a piece of scrap paper, and they have to silently (this is very important - they are out if they make a sound) arrange themselves (the whole class at once) into a line from smallest to largest. They love it, and this term, I'm introducing fractions.

Mr. D said...

Here's some pictures of this game in action (thanks Dana!):

Muriel said...

Hi! I did something with a hundred board on my floor. I had a big room with square tiles on the floor. I blocked off a 10 x 10 space and drew in the grid with magic marker. I used 0 to 99 instead of 1 to 100 as the numbers come out better. The number of things you can do with this is astounding. First I used it to develop the concept of the patterns. Kids would take turns standing on a number I called out. Surprisingly a lot of them had no idea how to find 56 or that 83 was far away from 47. I had them make patterns such as having a group of 10 kids stand on any number that had 2 digits alike, or any two digits that add up to 8, or any number with a second digit of 3. And so on. The kids were soon making up their own patterns. I had a guess the number of objects each week in a jar. To count the objects at the end of the week and find the winner, we took the objects and put them one at a time on the squares. This gave them a great concept of size vs. quantity. When we came to the jar of rice where there were more than 99, we put multiples on each square and got some practice multiplying. We used it in lots of other ways all year. If you've got the space and won't get in trouble for writing on the floor, you'll find it a highly valuable experience for your kids.

Mr. D said...

Muriel: Great idea! We use a similar model where I tutor in a variety of ways just like you describe. The simplest things are often the most effective.