Will was having a lot of trouble with rounding down-she kept wanting to round 7.1, say, down to 6-until I asked her to mark each number on the number line. With a number line, there's no WAY that you can mistake 2.4 as 2.04, something that's so easy to do if you have no concept of those numbers in your head.Ī number line like this is also essential for demonstrating the concept of rounding numbers, with decimals or without. I call this essential because it's another way to visualize the extreme difference between a tenth and a hundredth and a thousandth. It really only has to go up to maybe 5 or so, as it's just another method of having the kids model the numbers, and so you can simply only have them model numbers between 0 and 5. I had to Google Image for a while before I found one that I liked, but when I did, I laminated it so that it can be re-used and the kids can write on it with dry-erase markers. I should have given her more room to work, but I thought that she was clever with using the space that she had-for instance, a hundred flat stamp with a "x3" written next to it means "three tenths."Īnother absolutely essential manipulative for dealing with decimals is a number line that is marked with hundredths and thousandths. I then gave Will several decimal numbers and asked her to model them using the Base Ten stamps (I'd rather have had her build them with the blocks, but she'd have flat-out rebelled at that). A hundred? Well, then the ten bar must represent the hundredth.Īfter that, the unit cube was easy to pick out as the thousandth. This one confused Will, probably because she's so familiar with the idea of one hundred unit cubes, so she first picked out the unit, and we talked about that for a while, and I had her lay out ten bars to cover the hundred flat, and asked her how many of those ten bars would equal one thousand cube. The next step is to ask, "If this cube represents one whole, what block represents the hundredth?" To reinforce, we used the hundred flats to count up to one whole. Since Will is familiar with Base Ten blocks, she knows that ten hundred flats make one thousand, and since she's had a couple of lessons on decimals, she knows what a tenth is, so she thought for several seconds, then labeled the hundred flat as the representation of a tenth. Now, if the thousand represents one whole, what block represents tenths?" To begin, then, I handed her a thousand cube and told her, "Imagine that instead of representing one thousand, this thousand cube now represents one whole. The way that I introduced Base Ten blocks as decimals to Will may be different from the way that you'd need to introduce them to your kiddos-Will is perfectly comfortable with Base Ten blocks, and had a few lessons on decimals prior to this, and so understood the concept of tenths, hundredths, and thousandths. I mean, if you're going to mistake a tenth for a hundredth, and a hundredth for a tenth, then you REALLY don't understand what that decimal number represents.įortunately, decimals ARE easy to represent, using the very same Base Ten blocks that Will has been using since she was three years old:Ībove, you see a representation of the decimal system, as well as a sheet of models that I asked Will to make as part of her math one day. Unfortunately, Will loathes manipulatives (she knows that solving a problem with manipulatives takes waaaay longer than using an algorithm, and always wants to just skip to the shortest method possible), and so I let her get a couple of lessons into decimals before I pulled them out for her, specifically when I saw that she was having trouble reading the difference between tenths and hundredths in a decimal number. It's even more important, then, that the kids have access to decimal manipulatives when learning these concepts. I mean, the kids have been dealing with fractions, at least in the kitchen, since they were toddlers, but never have I said to them anything like "this recipe calls for. Once again, my favorite math manipulative, the Base Ten block, comes out to play!ĭecimal numbers, in my opinion, are harder to visualize than fractions.
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