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The Duck Story
by Gail Englert

A response to the question:

How do I teach rounding to fourth graders who just don't seem to get it?

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I am trying to teach rounding to a group of students and several of them still don't seem to get the concept yet. The strategy that seems to work the best is to have them round up if the number before is 5 or more, or round off if it is 4 or less. Do you know of any other strategies that other teachers have found successful? Thanks for the help!



Dear Alden,

I tell my fifth graders the duck story before I begin a lesson on rounding. Believe it or not, many of them don't "get it" yet either. I think the reason for that is that they have been given this set of steps to perform that don't make any sense to them.

Here is the story... (I act it out for them, quacking and waddling around like a duck... they enjoy that, and it makes the story stick in their memories... otherwise, I wouldn't dream of acting undignified! And I don't tell them what in the world it has to do with math... of course, I do pause every so often and make them laugh by saying something like, "What in the world does this have to do with math?")

Once there was a duck that needed to cross the street. She waddled to the corner and looked carefully up and down the street for cars or trucks, and when she was sure she was safe, she began to waddle across the street. She got only a waddle or two when suddenly a huge truck appeared. She knew she would need to get out of the street. What were her two choices? (The kids usually tell me to go back to the first corner... and I press them for the other option, which is to go ahead to the far corner. Some will try to play games, dreaming up all sorts of other options, and I have to playfully rein them in by saying "work with me on this" or "whose story is this?")

The truck barrels past, and once again the duck can venture out into the street, after looking both ways, of course. She gets most of the way to the other corner when, wouldn't you know it... another huge truck is bearing down on her. What can she do? (I have the students repeat the two options... and we chose the best one, which is to move on to the far corner, because you are closer to it.)

Now, I go back one more time to the first corner, and give the duck one last waddle across the street. This time she gets exactly halfway across the street, and there comes another truck, and I ask them what she should do. I remind them that she always picked the closer corner to waddle to, and now both corners are the same distance away. They decide that she should go on to the far corner since that is where she wanted to go anyway.

Now, on to the lesson... I draw some number lines on the board, and have student suggest multiples of 100 to use in labeling them. Then I choose a pair of multiples (like 200 and 300) and draw a new number line. I ask students to mark the middle of the line when they draw it on their own papers. We name that middle point 250. I have several numbers that can be found on that line (like 237, 279, 281, 246, etc.) We take each number, one at a time, and graph it on the number line, then decide whether it is closer to the first multiple, the second multiple, or if it is exactly in the middle. At some point right about now, someone in the room usually bursts out excitedly that this is the duck story... only in numbers. If it doesn't get "discovered" just quack a few times as you place the points on the graph, and they will make the connection.

We do the same thing using multiples of 1000 and 10,000. Then we do the opposite, selecting a number, and choosing the multiples to go "around" it, finding the midpoint, and graphing the number to see which end it is closer to.

The end result is that my students understand that we are looking for whether an amount is halfway there, or not. When they explain how they have rounded a number, I never let them say, "I looked at this digit on the right, and it was 4 so I..." Instead, they must explain what "halfway" would be, and where that number fell in relation to "halfway". This understanding transfers to many other situations. It is easy to understand, and to remember.

This understanding transfers to many other situations. It makes working with fractions easier, since they are using some fraction language in a way that is concrete. It forms the basis of some algebra instruction, since students are representing numbers by graphing them. It is easy to understand, and to remember.

I hope this gives you an option to try...

-Gail, for the T2T service

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