Helping my 1st grader with place value

[silver]

At first my daughter breezed through math. She finished her kindergarten math program so early that I had her do MEP 1A to finish out her Kindergarten year. Then she did all of MM 1 in first grade and has been doing bits of MM 2A and BA 2A+2B for the remainder of the year. But my child has a really hard time with certain problems, and I think it may be a gap in her understanding of place value.

She knows her 10-facts cold from playing many games of "go to the dump". She can do problems like 188+12 or 198+2 easily in her head. She can do 200-198. She can tell me that 4+3=7 means that 3+4=7, 7-4=3, and 7-3=4. She can do 87-55 easily. She can even handle 74-6 by regrouping. But when faced with something like 200-2, she freezes. I think that if I told her to regroup twice, she could--but she really shouldn't need to regroup at all for a problem like that, especially since she knows 198+2 and 200-198.

Where do you think the gap in her understanding is? How can I help her with this? 

[Sarah0000]

Maybe she is focusing too much on the place value of digits and not enough on the big picture. Having her draw story pictures of the problem or tell a story for the problem might help her think of the big picture. Something like "A cookie factory can make a batch of 200 cookies at one time. But a very hungry rhinoceros snuck two cookies. So how many did the workers ship out?" Could she do it like that?

[Rosie_0801]

My daughter learned place value from CSMP, particularly the mini-computers. 

[HomeAgain]

It doesn't sound like a problem with place value exactly...it sounds like more a problem with visualizing subtraction.  I'd work on having her create number lines and physically moving back.

[8filltheheart]

It sounds like she is doing great for 1st grade. Instead of any of those options, what woumsn she do if you asked her to count backward 2? Maybe just simplifying it would make her not freeze and just think big picture instead.

[PeterPan]

You might teach rounding. What is the nearest 10s, nearest hundreds. You can do it with the thermometer, finding pages in a book, what dollar bills you would give to buy something, etc. She probably just needs to make more connections in her brain, especially connections to real life.

[letsplaymath]

Your daughter's struggle may also mean that she's moved a bit too far ahead in the math books, and her mind needs some time to catch up, to consolidate her understanding. Learning often happens in spurts and plateaus, so perhaps she's ready for a plateau.

When her mind goes blank on a specific problem, you can try the Socratic approach of asking questions.

• What do those marks on the paper mean to her? How does she think about them?
• Can she imagine any situation that might use those numbers in real life?
• Does she know that the answer in a subtraction problem is called the "difference"? What does that make her think about? How different are these two numbers? (Incidentally, "difference" is a more fruitful, less limited way to understand subtraction than "take away." Come back to the idea of "difference" over and over throughout her elementary years, and she'll have a much easier time when she gets to algebra.)
• Can she think of an answer that would be way too low (5?) or too high (3 million?) --- and how does she know those silly answers can't be true?
• Could she make up a problem of her own that is similar to the troublesome one, for you to solve? (My kids always liked trying to stump Mom.)

Math is not the marks on the paper. Math is what happens in our heads as we reason about ideas. You don't want to teach her how to manipulate the symbols, but how to think about the ideas.

And also, while she's in the plateau, you can keep playing games. Math games are a great way to consolidate learning. For example, Snugglenumber is a great (and free!) game for thinking about place value. Or check out the other math games on my blog.

[silver]

I played around with math with her today. She can find a number minus one as long as the first number is 100 or less. When I gave her 190-1, she told me she doesn't know what number comes before because she hasn't counted that high. I gave her 90-1 as a "helper problem", and then she could figure it out. She still couldn't tell me 200-1 though until I had her count up from 195.

When asked to round something like 137 to the nearest 10, she had a roundabout way of doing it. She subtracted 7 units to get 130. Then she added 3 to 137 to get 140. Then she compared how far 137 was from the two closest tens by comparing 7 and 3. Finally she got the answer of 140.

There seems to be some kind of disconnect where she doesn't immediately know the next and previous whole ten once we get into three digit numbers. Both the one less problems and the rounding problems seem to point that way.

[silver]

3 hours ago, square_25 said:

You might do some skip counting to help out with the "whole 10s" thing. It might not be obvious to her that 100 is ten 10s, so she might be getting lost there. 

(Or, personally, I define multiplication with a*b is a copies of b added together and have them calculate things times 10 without algorithms. Same thing, more symbol familiarity.) 

 

She will tell me that 100 is ten tens and that 200 is two hundreds. We've used base ten blocks (both physical and drawn) and an abacus. She can regroup during addition and subtraction. It's part of why I'm having a hard time figuring out where the issue is.

[8filltheheart]

I would go back and spend some time with a number chart and a number line. Let her have a physical visual of what numbers are doing. Reach 9 add a 10. Which numbers are closer on the number line. I don't think you have a serious issue. Just back up to the logical basic and let it seep in for a while.

[letsplaymath]

13 minutes ago, 8FillTheHeart said:

I would go back and spend some time with a number chart and a number line. Let her have a physical visual of what numbers are doing. Reach 9 add a 10. Which numbers are closer on the number line. I don't think you have a serious issue. Just back up to the logical basic and let it seep in for a while.

Ooooh, the idea of a number chart reminds me of this game. Use a blank chart, and choose a large starting number, like maybe 180, so the numbers that go in the blanks flow past 200. Or play several times, with different starting numbers, gradually increasing to build up to 200 and beyond.

[Sarah0000]

Oh ok, this is the stage my MDS is too. I first do work with place value on a whiteboard and c rods or base ten blocks. Take away or add tens to the pile and have child write the new number. Do a series such as 178, 188, 198, etc. Child can practice orally by asking questions like "how many is 1 hundred, 8 tens minus 1 ten?" Do also for ones place and gradually move into saying the regular names for the numbers.

If she still doesn't get the patterns for numbers she hasn't counted, draw the place value chart on a whiteboard but draw an apple, cake, or whatever would amuse her in the tens and hundreds spots. Put a regular digit in the ones spot. Ask "what is cake apple 3 minus 2?" Ask what is 3-2 then guide her answer to cake apple 1. Do this a few times changing the icons, so she can see they don't change then add regular digits back in. 

[rose]

If I were in your situation I would probably take a couple of weeks break and focus on geometry or something else. It always amazes me how letting a concept simmer can bring out the end result with less effort.

Another approach that I like to take is to give a easy word problem like, "if you had 200 dollars and dropped two one dollar bills on the path to the store how many would you have left." Sometimes their young mind just need you to step back into the concrete realm.

I've also found an abacus to be an invaluable aid in teaching place value. I let them answer any problem that they want with the abacus. They seems to absorb the concept of place value on their own just by seeing it over and over again.

I'm currently using MEP1 and I've used MEP all the way through with my oldest two. I must say that some of the y1 problems are very hard. They jump into so much symbolic language so quickly. MEP1 is my least favourite MEP year just because I don't think that they are gradual enough in introducing symbols or problem types. I think that it's worth remembering with MEP that the workbook is mostly done in class as walked through assignments. When an exercise is difficult for one of my little ones I just go back to the teacher book and follow the walk through instructions. I don't stress any more about them finding everything easy. I know that they'll come upon it again later.

[EKS]

I'd work on mental techniques for doing addition and subtraction problems for a while.