Solving proportions and cross products

Does this truly provide a conceptual understanding of cross products?


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.

From Math Forum

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


We’re beginning to get somewhere.

crossproducts1 crossproducts2 crossproducts4

Then, again, we’re not.


I would love to learn how others approach this topic.


Preparing for assessments

Side bar: My spring break was fabulous and I hope yours was too. I spent the week skiing with my daughter in Whitefish, Montana. The weather and mountains were majestic, but the warmth made the snow soft and sticky. Towards the end of the week I was skiing in a smoothie but falling down didn’t taste very good. However I had an absolutely wonderful time and would drop everything to go back again.

Now back to business and the business of teaching students how to prepare for an assessment.evidence of study

I wish kids were born with an innate ability for how to study for a test, but they aren’t. I wish kids knew instinctively what study tools to implement, but they dont. I wish, I wish, I wish. If I got everything I wished for I’d be out of a job.

I’ve found that as the end of a unit approaches and the assessment nears, I have to make time to review how to prepare for an assessment. What’s worked for me and my students is this Evidence of Study worksheet. Basically I let the students know one week in advance when the assessment will be and they are to study five days out of seven.

The first colum gives suggestions for how to study because most middle schoolers don’t know how to prepare for an assessment. They can do such things as create a practice test, complete online activities, or review/redo homework problems they got wrong.  We take time in class to write down what they are going to do each of the five days, plus they note the specific concept they are practicing. I’m not telling you anything new when I say students can be vague with their descriptions.  For example they’ll want to write ratios as the concept, but the concept is really rates and unit rates, or solving ratio problems with tape diagrams. I want them to identify the specific learning objective.

The Evidence of Study sheet and physical evidence are due the day of the assessment. I use the old Ronald Reagan, “Trust, but verify” approach by having the students obtain a parent signature for each of the five days. Physical evidence helps too! 😉

I’m always looking for ways to improve so please share your thoughts and ideas.