Solving proportions and cross products

Does this truly provide a conceptual understanding of cross products?

McDougal

Most of my sixth grade advanced math kids see it as a rule to memorize. So I set out to give a better conceptual understanding.

I tried the algebra approach but the concept was too abstract.

crossproductsa
From Math Forum

Then I related it to checking if the fractions are equivalent by finding common denominators using the existing denominators.

crossproducts

We’re beginning to get somewhere.

crossproducts1 crossproducts2 crossproducts4

Then, again, we’re not.

crossproducts3

I would love to learn how others approach this topic.

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2 thoughts on “Solving proportions and cross products

  1. I am completely cranky when it comes to this topic. I try so hard to be careful and consistent with my vocabulary, so I just won’t say the phrase cross products in most cases. I simply emphasize the common denominator portion of your conversation above. I find that it is way too automatic for kids to employ this cross product strategy anytime that they see fractions on each side of an equation, even if one side has one fraction and the other side has a sum or difference of fractions. I hope that by emphasizing the common denominator and talking about inverse operations clearly that I can help kids avoid that pitfall.

    1. I COMPLETELY agree with you. When I introduced it I wanted to make certain they knew why it worked. Not everyone fully understood, but we’re still working on it. As I write this, I’m thinking in the future I could put a disclaimer on the assessment that states something like, “If you choose to solve using cross products you must provide a complete explanation of the process. If you are unable to provide an explanation, choose one of the other methods.”

      Thanks for your input. It got me thinking about the future.

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