Happy New Year! I am working with one 4th grader in particular who is having difficulty grasping the concept of decimals -tenths and hundredths specifically. We have used the base ten blocks where a flat is one, a long= 0.1, and a cube = 0.01. This alone has caused confusion because they used to represent something else! One of the biggest challenges is getting him to realize that the ones place when looking at a decimal is the same ones place when reading whole numbers. We have discussed decimals in terms of food, rainfall, measuring to give them a real life connection. At times, he seems to be getting it but then falls back on subsequent days. we have also related tenths to more common fractions such as fourths and halves. Furthermore, he has difficulty writing the decimal correctly. He often puts the decimal in the wrong place. Any ideas as to what prerequisite skills I may be overlooking or any other suggestions?
Thanks,
Karen
1 comment:
Hi Karen,
First of all, let's talk about all of the things you are doing that are right. Real life context... bang on. Using materials to represent the ideas... again, that's solid. Relating decimals to commonly used fractions is always a really good idea. The fact that you are giving it such careful consideration is indispensable. Although I cannot say for certain what the issue is (since I would have to have more information and possibly work with the student directly), I can suggest typical issues that you could consider.
1. Typically when kids are confused by base ten materials to represent decimals, it's because they have become accustomed to associating them with whole numbers only. Do you remember the work we did in the summer around changing what you are calling 1 (it sounded like "if this is 1, what is this"? I wasn't kidding about the importance of switching those pieces back and forth so that kids can see that a particular piece (let's say a flat) is only 100 because we are calling the little cube 1. Alternatively, we could call the flat 10 if we are calling the rod 1 (1 whole rod). The flat can be called 1 if we are referring to the number of flats (1 whole flat). It can also be called 1 tenth if we are calling the large cube 1 (1 whole large cube) ... since there are 10 flats in the large cube and we are just talking about 1 of those flats. If you are having trouble following this explanation, get your base ten materials out and follow it along using your blocks. It should become abundantly clear that it always comes back to what you are calling 1. Kids need to develop the habit of asking "what is 1?". When that is in place, it literally erases the issue of being locked onto a material, thinking the material is the idea itself. A simple analogy would be if you want to teach the idea of red and you always only show an apple to do that, a child could think red means the apple, not the color... so you show an apple and the child says 'red' even if the apple is green. Make sense? Since you are talking about a grade 4 student here, you undoubtedly have the grade 4 "I Get It!" book... turn to page 6 for an illustrated version of this explanation. The remedy? Back up to include many examples such as I have just explained... include those where you identify what you are calling 1 as well as those where you name the value of the piece and ask what 1 is. Regardless of the concept you want to teach, it is ALWAYS critical to use a wide variety of examples and representations so that kids come to associate the IDEA with whatever those examples have in common.
2. Re: same ones place whether decimals or whole numbers... typically this happens when those 2 ideas (decimals and wholes) are taught separately. To establish the relationship between the two, decimals need to be taught as an extension of whole numbers and vice versa. They should be tuning in to place value patterns.. where 10 of each piece is equivalent to the next biggest piece, and 1 tenth of each piece is equivalent to the next smallest piece (so lots of experiences with trading up and trading down). Be sure to go slowly to guarantee success, but continue to vary what you are calling 1. Each example you do with them needs to include both decimals and wholes in the same example to link those ideas. Do you remember the game we played 'Race to 100'? It's excellent for exactly the issue you are having. As an example, let's call the flat 1... in which case the small cube would have to be 1 hundredth (follow along with your base ten blocks).. each die roll tells you how many hundredths you get. When you get 10 of those, you MUST trade up for a tenth (in this case, the rod). Continue in the same way, trading small cubes for rods whenever you have 10 of them. When you have 10 of those rods (10 tenths) you MUST trade up for 1 whole flat. Get it?
3. Dump the symbols until you have the idea straightened out, then use the symbols as a REPRESENTATION of the idea while still using the materials... unless there is another problem that I am unaware of, the student will transition to using the symbols in a meaningful way without the materials (they will be in his head).
4. Regarding where to place the decimal... if you have access to the grade 3 "I Get It!" book, refer to page 15. In the trading up game described above, a counter representing the decimal separates parts of a whole (decimals) from wholes.
5. ONE MORE THING... Watch your language! What you say makes all the difference! Be sure to use natural language for understanding... here is an example... "I have 3 whole rods and 2 tenths of another", or something similar.
Okay then, before this turns into a dissertation, I'll sign off. If you are still uncertain, be sure to tell me next week when we meet and I'll work through it with you and anyone else who needs to know.
Until then...
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