A Little More On Addition

OBVIOUSLY UNDER CONSTRUCTION

5 minute lesson. Addition. Drawing, symbols, circling tens...

Drawing basic addition with alge story

Need pics, vids and quote.

AFTER you have spent time playing with blocks, building numbers out of other numbers, making towers, skyscrapers, building walls and houses and playing other games

THEN

get out pencil and paper and start making problems on paper. And/or use a white board and dry erase markers (kids love it) AND paper and pencil.

Start in the concrete, then move to drawing, then go to symbols in a natural progression. This is optimal but I know full well this is not always possible.

What you are about to do is show students how to draw the blocks, and move from concrete to the semi-abstract. Then to the fully abstract: symbols. In fact in classroom situations given time students will move to the symbols on their own because it takes too long to draw the problems. This is the ideal.

The reverse of this is epitomized in this story. One day after having done some demo teaching for a friend who had been one of my teachers in junior high, a kid who I did not recognize ran up to me in at the mall.

“Hey!” he exclaimed. “You're that guy with the blocks!”

I nodded. Suddenly he was a little shy.

“I got an “A” cuza you.”

“Really?”

“Yeah!” He started gushing. “ I was taking this test on factoring equations. And I was failing it, cuz I couldn't remember how to do it and make the numbers add up and stuff. Then I got to the bottom and I was just about to turn it in anyway when I remembered: I could draw 'em! So I went back and I drew the last one, which was the hardest one and I got it...then I went back and drew all of them, you know, counted the sides...and I got a perfect score. First time in my life.”

By now all I could do is nod, because for some reason I was so choked up I couldn't speak. (I still get a little lump in my throat when I tell this story or write it down as it turns out.) I smiled at him.

“Thank you,” he said, and before I could say anything more, he skipped away...and I was hooked.

The point being that sometimes you have to go backwards to go forwards. I had to start with the symbols and then show the blocks and then draw the pictures in that situation. You can't screw up. Just understand that the student needs to be able to relate one to the other and the blocks in the concrete are the basis for this. I know people that think you can skip the blocks and just have cool 3-D images on a computer screen instead. False.

Nothing replaces having your hands on the blocks and being able to manipulate the “problems” for yourself. Further there is a large portion of the population for which the kinesthetic is their primary learning style. The blocks are perfect for them. All learning styles benefit from hands on learning, visual, auditory and of course kinesthetic.

That being said, the majority of the population are not primary kinesthetic learners, and are more comfortable with the visual. This is why classrooms are set up the way they are, and why there are so many more lecture halls than labs on campuses across the nation.

Simple lesson using boxes lines and dots. Start with dots, move up to lines, then add boxes.

If the students are older you can start with dots and lines or all three, as appropriate; however always start easy and breeze through it until it starts becoming more of a challenge. It should never get “hard” but it may become more "challenging." HUGE DISTINCTION. Kids love a challenge they can conquer; they hate it when it gets too hard...usually evidenced by tears.

Start with simple addition problems less than ten. As noted elsewhere there are only so many combinations. Help your students MASTER all of them.

Then go onto single digit addition problems adding up to more than ten. Draw a circle around the ten dots. Some kids will not be able to resist the urge to make an airplane or bus out of the circled dots. Let them have fun. Show them them that ten dots with a circle around it is the same as a line. Show them that a line and some more is the same as the symbol...this helps with place value. We count the big ones first. Ten and three more = 13. Ten and five more = 15.

Then move on to two digit numbers added to a single digit number with regrouping less than 100.

Then move on to even tens added together to make one hundred and some more. For example: 80 + 70. Show them 8+7. Bigger is funner. Do a stretch where you show 700 + 800. (WOW! Thousands!)

Then 90's added to single digits to make more than one hundred.

Then two digit numbers added to two digit numbers equaling more than one hundred (but less than 200 (that's a little math joke.)).

Then move on to three digits under one thousand.

Emphasis should be on the pattern and how it stays the same. Never count past nine in any one place, we make stuff same. We count the big ones first.

Each of these should be “chunked” into short little five minute lessons. When first introducing it to younger students it may take more than five minutes, and the exercises may take up the whole math period but in short order this should be a five minute lesson where you only do a couple of problems at a time and then move on to something else like factoring, or singing songs or multiplication, or sining songs about multiplication. In an hour you have spent time doing at leaste six different things...and the hour is done before you know it, and the kids want to come back for more.

You wouldn't say we can't start teaching a child about adverbs because he hasn't mastered adjectives yet...or only use little words around young children because you wouldn't want to confuse them with words that had five or six letters in them. That would be ridiculous. But it's exactly the way we teach math normally...and wonder why we are getting such poor results.


The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great teacher inspires. ~William Arthur Ward