What is the best way to teach something like: _____ +1 = 12 (or any other number) Obviously this is an "easy" equation, but I'm having a hard time feeling like I'm teaching it clearly enough to my dd. She is a young 1st grader and this is very intro. math. We have a number line, add beans, coins, mental math and a math page that we use with each new number we learn. First, she writes the numeral, then we use our beans (used in groups of ten to teach place value) to do an expanded form equation: 10 + 2 = 12. Next, we have two equations: ____ + 1 = 12 12 - 1 = ____ The subtraction one is easy for her to do (and me to coach/teach). She just uses the beans, coins, or number line to "take away" one. But, for some reason I seem to be at a loss for the best way to do the addition one. In my mind, I just automatically do it backward and subtract. But that doesn't seem practical for a beginner (or is it?). How would you "talk through" a problem like this? Thanks!
We had trouble with that until I put it on stair-steps. I'd have him physically walk up and down stairs to visualize what a problem looked like (starting with 0-9's). Later when we got into 10's, I'd use elevators to skip floors, because we assumed there were 10 steps per floor (my dh works in a large high-rise downtown, so that was easy to visualize).
I would say go ahead and use your beans. Have her put one down. Next, have her continue counting from 1 in a pile right next to the 1 until she gets to 12. Then, have her go back and see how many she has in the second pile. That is her answer.
I am working on this very thing with my 1st grader and she is not grasping the concept. I have tried counting beans, using math blocks, number lines and various other things. I think for us we are going to put it aside for now and revisit it in 2 weeks or so.
Teach it like this: Start with a small numbers, like five or less. Then play a game. Take a small paper bathroom cup. Show your child five counters. Then, have her close her eyes. Put three down on the table, with the cup up-side down covering them. Place the other two on top of the cup. How many are there altogether? Five. We can see two. How many do you think are inside the cup? Make this into a game. Play it with different numbers up to ten, until they get a good handle on it. DO NOT DO ANY WRITING AT THIS POINT! You're not "doing math", you're just playing fun games with counters. After she gets good at that, you can introduce the writing. You can even give her a worksheet with a bunch of upside-down cups drawn on it. Put the main number on top of the page, and have her "play" with that many counters. She puts some under the cup, some on top of the cup and records on her paper how many of each. Eventually, you will phase out the counters. (BTW, to give credit where credit is due, this idea is from MATH THEIR WAY, a curriculum that is very old and is similar to Math U See). Another thought is to draw a number line on the sidewalk. Start at 4. How many jumps will take you to six? So four plus ? jumps will give you six. (That's assuming you don't have all that now right now, lol!)
Some great ideas! And nice to know we're not the only ones having issues with this topic! 2littleboys - I'm assuming I could do the same idea using our number line (not too many steps available here) and a "jumper" - like a cute character that she physically jumps up or down the line... azhomeschooler - I can see that that would certainly concrete the concept...hopefully before we get to _____ +1 = 100! haha Jackie - I love it...that totally works like my brain does! We'll give all of these a try! Thanks again!
First, love Jackie's ideas! Ok, though, for us (because I'm probably boring ), I didn't start with that problem in isolation. My dd worked a lot of problems that were the reverse of each other: 12-1=_ 11+1=_ Then we talked about how the problems all used the same numbers (commutative property). Once she understood that very well, she was ready to move on to 1+_=12 _ - 11=1 My dd is extremely concrete with all of her learning, though. She has to understand the rule first so she can apply it. (In ps, the K teacher complained that when given a group of beans, counting them, then having the teacher cover them up, then shown them again, dd HAD to count them again. The teacher thought dd didn't get number permanence. The truth: no one told my dd that the teacher wasn't removing any beans. So dd thought there *might* be less the next time.) I understand some kids have more abstract thinking than this, so you might or might not need to follow the steps we did.
I'd start with identifying the parts and the whole. The 12 would be the total and 1 would be one of the parts. You could demonstrate it with manipulatives. Then your child could add in the parts until she had the parts equaling the whole. This site has charts for number bonds that might be helpful http://hampsteadstars.wikispaces.com/Number+Bonds Seeing groups of equations like this helped my kids too: 11+1=__ __+1=12 11+__=12 1+__=12 __+11=12 1+11=__ But mostly we have drawn a number bond chart and filled it in.
Or you have two piles. Five in one and two in the other. Cover one up with your hand. How many are all together? How many can you see? How many are hiding? Five (we can see) plus two (hidden) equal seven (altogether). You can do that with the grouping Embassy suggested.
Yes, that's exactly it! She wouldn't have even had to be that exact ("ok, R, now I'm covering them up, but I'm not adding or taking any away. Here they are again, how many?"). It was a miscommunication, I think. And a bit of my dd complicating the game (maybe THIS time there will be a different number!) rather than dd not understanding 5 is 5 is 5 is 5. At ps, She couldn't add or subtract. I said, "+ means you add both numbers together. - means you take-away." 5 second explanation, and she had it. And on... and on. She's my kid who proves discovery-type education is NOT for every child in every subject. LOL on Philip, I bet that's interesting!!
Why would you feel that way? Many people have commented on their child's difficulty in this area, and what they might do. My comments come from classroom experience with special needs children. I speak from what I've seen work, and am passing that knowledge on to others. I've no doubt that you are quite capable to homeschool your child in math. Science is my big trouble area! I sure wish I could have someone else do all the science for me!!!
The more I homeschool the more I realize I don't know. Homeschooling math will give you a second chance to learn math in a way that makes sense to you.
It isn't necessarily a bad thing to have experienced difficulty with a subject. Because I could not learn chemistry the way my hs sci teacher taught it, but yet learned it out of a book (with a 2 paragraph explanation of isotopes), I am much more patient and more creative with the learning difficulties my kids face. It isn't about whether it's hard or easy.. much of the time it's in the presentation of the subject. If you are willing to help your child learn, then you'll do great
I tried the cup idea with my DD (age 4) yesterday and was happy to see that she understood it and knows what numbers make 5 (we only did it with the number 5 as I wanted to see her reaction) Thanks for all the ideas - my DD likes playing with numbers and its always great to get ideas that are hands on and that she can have fun with.
