We’ve all done it…teaching rules without meaning. For me it was rounding rules. I had found the perfect song. The teacher next door used a baseball metaphor. Our colleague down the hall used the Rounding Mountain. We were all trying help our students remember the rounding rule: “If the digit to the right is 0-4, round down. If the digit to the right is 5-9, round up.” And in each case, of course, we failed to develop any understanding whatsoever.
That’s because rounding is really about “closer to” thinking. The dictionary states that to round is to “alter a number to one less exact and more convenient for calculations.” In other words, rounding is about finding the closer benchmark number for estimation purposes. The benchmark number doesn’t even have to be a multiple of 10!
Here are three ways to develop “closest to” thinking:
1. Use a concrete manipulative such as KP Ten-Frame Tiles. If your students are rounding 68 to the nearest ten, for example, ask them to place 6 tens and 8 extra ones on a large ten-frame. Ask them if the small ten-frame is closer to full or closer to empty? Since only two tiles are missing, they can easily see that the ten-frame is closer to full, and, therefore, closer to 70 than to 60.
2. Use a visual representation such as a number line. If your students are rounding 368 to the nearest hundred, for example, ask them to plot 400 on one side of the number line and 300 on the other side of the number line. Then ask them to mark the halfway point, 350. Finally, ask them to mark 368. Is 368 closer to 300 or closer to 400, using 350 as the halfway point? NOTE: If you’re familiar with “Clothesline Math,” this same visual can be achieved by having students place folded paper strips on a long piece of clothesline rope or string.
3. Write the “closer to” numbers above and below. Simply ask the students to write the possible rounded numbers on above and below the number at hand. If your students are rounding 2.34 to the nearest hundredth, for example, ask them to write 2.3 above and 2.4 below. Then ask them if 2.34 is closer to3 or to 2.4 (note: they may go back to using a number line for help).
Lesson learned – these are now my go-to strategies rather than teaching my favorite rounding song. Know that kids might find these a bit tricky at first, but honestly, they’ll catch on by the second day if you really get them thinking about “closer to” numbers and halfway points.
How about you? What are your thoughts about teaching thinking strategies rather than memorized rules? Please share your stories and comments below.