By now you have seen me use algebra for teaching more than just factoring to little kids. Here we see the boys playing with one problem, using their critical thinking skills to make rectangles. They learn many math concepts in addition to addition and multiplication, they also get to practice writing their symbols which is a source of a great sense of accomplishment for youngsters. The 6 year old again much more impressed with his 5 and 2 than his ability to factor x2 + 7x + 10. People don't think of algebra as one of the fun preschool activities but it is...if presented correctly.
I cannot stress enough that you must be patient and let them do it. Don't do it for them and don't give hints...just let them fool around with it. AFTER they have done the work talk about their discoveries and emphasize the fact that they weren't/aren't wrong just getting more information. Also when the older boy starts building his with the blocks on the wrong side he was building for you the viewer, being a silly adult I thought he was building it the "wrong" way. He wanted to make so "the people could understand it"...so he was going to try to build it up side down and backwards for your benefit. Next time I'll let him....
Here are the problems we did in order. At about 5 minutes a problem this is an hours worth of work. They had to get out the blocks, and form them into rectangles and count the sides. I talked about the partial products and made them point to them but that is ancillary to learning the addends and the multiplication of the factors. I also talked about the distributive theory and what that meant but again the main lesson was about counting out x and figuring out how to make the numbers fit in the corner.
x2 + 2x + 1.
x2 + 3x + 2.
x2 + 4x + 3.
x2 + 4x + 4.
x2 + 5x + 4.
x2 + 5x + 6.
x2 + 6x + 5.
x2 + 6x + 8.
x2 + 6x + 9.
x2 + 7x + 6.
x2 + 7x + 10.
x2 + 7x + 12.
The discoveries made here are too numerous to mention but a few I noted were, you can't build a 10 with 3's. 3 times x and x times 3 are the same thing, 5 twos and 2 fives are the same thing but it's easier to get out 2 fives than fooling around with all those twos...adding x's is easy...x2 + 2x + 1, x2 + 4x + 4 and x2 + 6x + 9 are square numbers. Again these are their discoveries I didn't tell them these things...
You may note that there are 45 addends and thus 45 problems you can build and master. Ending with
x2 + 18x + 81. Soon there will be worksheets on the Password Protected Pdfs Page with all of these problems on them. You should get comfortable with these and positive problems with two or more x2 BEFORE you move on to negative expressions.
Here is the Password Protected PDF's Page. You need a password. Buy one, they are cheap.
Speaking of PDFs here is a one that covers the practice polynomials from x2 + 2x + 1 to
x2 + 18x + 81...
You may want to down load this and use it as a guide. DO NOT do each problem in order. The natural inclination will be to start at the beginning and work your way up. START with x2 + 3x + 2. DO a few and and skip around, keep to the lower ones with the younger students who are just starting to skip count. In the first session I usually end around 7 or 8x...then next time do a few more (some of them the same as the first time...and then end with 10 or 11x...and then next time do a few more. This pdf represents several lessons even if the child is "older"...for more you may want to check out my Parent Teacher Training.
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