Let’s just imagine for a moment that you are in the middle of the store to buy a rug. You read the dimensions but struggle to imagine how long the rug really is…what do you do? You connect this problem with something you know…maybe your own height, maybe you picture a ruler or a measuring tape. The key is, as an adult you have life experiences to connect them to. Sadly, our elementary students might not have these real world connections to make quite yet, so we need to give it to them.

I gave my group this problem, which like usual resulted in many blank stares and questioning faces. I certainly do not blame them, the first time I saw a problem like that I had NO idea what to do. None of us did…we just don’t remember the feeling.

At first they wanted to guess what to do with the problem. They suggested just adding 18, them suggested multiplying 75 by 18 to find the total. Many of them wanted to try the algorithm, but to see if they conceptually understood what they were doing I wanted them to show me how 15×5 could be used to solve that new fact.

So of course after a few confusing minutes we broke out the tools and built 15 rows of 5.

We also broke out the language of multiplication…rows of 5, groups of 5. I asked them what the tools could stand for, and this darling little girl said “Dogs on leashes! There are 15 people with 5 dogs on leashes! Each cube is a dog!”

Enter the connection and the ability for them to build just another 3 people who were all walking 5 dogs each on their leashes.

It was quite the dog party, but hey it worked!

Now the goal in this case for these students is to pull tools at some point to see if they can represent these problems with drawings, and better yet area models so that we can link this to measurement and more. Once they do this, they will become unstoppable mathematicians!

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The visuals are the real world that math is trying to organize, and so if we skip the real world part we are not “doing math”, we are just playing with otherwise meaningless symbols. Any student who doesn’t have a picture in their head whenever faced with a biy of symbolized math has been pushed too fast into the current fashion for writing everything down in symbolic form. Fractions is the most glaring example of this approach. Of course, eventually some kids will be able to deal with the symbols, knowing that their methods work, without the pictures. Further into math the pictures in the head are more likely to be examples of the current topic expressed in earlier well understood math terms.

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