Used to be to get this info on teaching fractions using manipulatives you had to come to a seminar or training, usually held in Idaho...now I think the next one will be in LA or maybe Las Vegas...if we ever do one again. It's on my list but it could be a while. Nothing like in person training but it's costly and you have to travel and all that goes with it and blah, blah, blah. Much easier to just learn how to use base ten blocks by going the the house of math. Yes I know my fraction page needs serious work.
Now you can learn to use your base ten blocks for much more than addition, subtraction, and place value plus you have all the pages on this blog. First we see fraction multiplication and why nothing is getting smaller, we are just counting parts of a part and if you insist yes a third of a half is smaller but we were counting not doing magic and with 1/2 ÷ 1/4 = 2 really nothing got bigger we were counting quarters. Two of them. Observe:
Here is a quick lesson with the symbols no blocks for why invert and multiply. Division of fractions. Also easy to understand. If you want to see the whole lesson go to Sarah's page. There you will see us use manipulatives to make fractions clear and easy. And you will get the joke about "clear"...
If you actually take some time to study the picture above you can see that the symbols are quite confusing to some students particularly to deaf students who couldn't for the life of them figure out the relationship between those numbers if they didn't understand division, or even if they did. How the heck does it turn into 2/9?!?
Well, it doesn't turn into anything: we are counting. The rectangle we see has the one sixth in lowest terms instead of 6/36 which is what you get if you multiply 3/4 x 2/9...which is equal to 1/6...but getting there with symbols only and no concepts is impossible and modern math teaching doesn't even attempt to clear this up they just give you the rule INVERT AND MULTIPLY.
And it's right about here many students make the fatal decision that math doesn't make any sense...I mean the rules changed for addition and subtraction, you can just add 1/2 and one 1/3 and get 2/5, it works for multiplication though, and then it's some crazy rule for division and they get bigger when you divide: this math is arbitrary crazy stuff.
No. It's not. It is consistent and beautiful and simple. The five basic concepts are alive in well in our fractions games...knowing what one is, same, rectangles, the how many part the what kind part, and economy of symbol...but the problem with that last part is 95% to include the teachers don't understand what the short cut is doing. It's economy of symbol: fewest symbols possible, and it's a short cut and work saver. Now, if you want to see more with manipulatives to make it clear why we invert and multiply a 15 minute video on this (and a lot more vids) is on Sarah's page you need a password. Just get a month and I think you will see an annual pass is worth it because you won't get through everything I have up in a month and as the months go by I add more and more. I will be offering a special where you can apply your monthly to the annual if enough people get a monthly pass.
One example with symbols only may not have been enough, a couple more examples with manipulatives should clear the whole thing up. The idea being if an autistic student can glean the concepts SO CAN YOU. Same when you see me using 5 and 6 year olds as students for algebra...if they can "get it" so can teen-agers.
Passwords used to cost a buck. Now they cost 5 times as much...inflation and the fact that there's 10 times as much stuff on the password protected pages and then someone sending me a $24.99 vid that had basically 30 minutes on it, and not even a good 30 minutes just 4 math concepts poorly explained with lots of special effects and production. Here you get ZERO special effects and very, very low production value but very heavy on the information and concepts, well explained...or so I am told. AND HOURS AND HOURS ARE NOW UP. It's worth the 5 bucks. Here is a free page on addition and subtraction using manipulatives. But I digress.
What we are doing is finding how many times one number is contained in another number. In order to do this we have to make them same or we can avoid all that work with the rule...basically we are just skipping a lot of steps and in the process skipping a lot of students who throw in the towel and change their belief to math is hard and arbitrary. How do teachers teach students who already know they can't learn whatever math it is later on in high school? This will be discussed in depth with another little girl who got a convenient label put on her. She loves playing math but as soon as we bust out the school work, math is no longer fun and she knows it's hard even though we were just doing it with ease a minute before. That's how powerful beliefs and paradigms are. Her page is here. Both of these pages will grow over the coming months, and are especially good for home schoolers and teachers.
Also now lots of Mortensen Math Materials available on my site, if you buy something there, a password used to be free. As of 20014 this is no longer the case. The fractions Page was going to go up in it's new form Monday but it's MLK day so I will have DBoyz and I doubt it will get done...although it is on the agenda for Wednesday...fractions from beginning to end.
People on face book and twitter got the vid FREE for a day...it has since been taken down...joining us there has it's benefits.
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Learn how to use base ten blocks at my website.