Week 28 – Let’s Talk About (Proportional) Relationships

It seems it was all about proportions in both my 6th grade and 7th grade math classes this week.  I’ve written about this in the past but I find that these classes tend to have a bit of overlap.  Partly because I have some 6th graders that are placed in 7th grade math so while they have a pretty solid foundation, I don’t think it would be wise to just assume they know everything that I teach in 6th grade math.  Let’s see how things differed this week.

PRE-ALGEBRA

This has been one of our quickest units yet.  These are the three objectives:

  • 6.1 RATIOS, RATES, AND UNIT RATES – SWBAT compute the unit rate associated with a given ratio
  • 6.2 PROPORTIONS – SWBAT represent proportional relationships between quantities & solve ratio problems using proportions
  • 6.3 SIMILAR FIGURES – SWBAT to use proportions to find missing lengths in similar figures

In reality, I feel all three of these are talking about the same things.  To talk about ratios and unit rates, you need an application of those ideas, which were equivalent ratios (proportions) for several of our problems.  For example, one of their problems was the following:

The year is 2045. Khabele has 945 students and 35 teachers on their campus…ON THE MOON! If the number of teachers and students both increase by 5, does the unit rate of students to every 1 teacher remain the same? Explain.

Many of them found unit rate and said they weren’t equal to each other, which led us into the second lesson on proportions.  The big push on this was to keep relationships the same when you write the proportions.  I used this visual to help (thanks Randy Brown for sharing this idea with me a while back).

proportionsIdeally, I would have had them all create these little models but didn’t think it was worth the time investment (would’ve added another 20 minutes or so of class).  Just presenting the model seemed to still do the trick.  They put it in their own words:

The connections can be next to each other or on top of each other but not diagonal.

It doesn’t matter if you flip one of them as long as you flip the other.

The colors have to stay together.

I asked them to come up with a proportion that wouldn’t work as well as one that would work that I didn’t have listed up there.  I followed it up with THIS Khan Academy exercise, which they gave a lot of positive feedback on (they usually aren’t super fond of Khan Academy).

We talked about solving proportions using scale factors going across from numerator to numerator and denominator to denominator, scale factor going down from numerator to denominator, or using cross multiplication to create an equation we can solve.  I tried to present different problems that would lend themselves to use different methods.

We also did this 3-Act problem about a Ferrari which was fun.

6TH GRADE MATH

I struggle more with this class, mainly because I feel there is a bigger disparity between those who get the concepts fairly quickly and those who are confused.  We started venturing into ratios & proportions but a lot of is looking fairly similar to what I’m doing in Pre-Algebra.  We’re moving much more quickly than anticipated.  Here are the objectives for this unit:

  • WRITING RATIOS- The swbat to write a ratio given a relationship expressed in a word problem
  • UNIT RATES- The swbat to calculate the unit rate of a given ratio
  • EQUIVALENT RATIOS AND RATES- The swbat calculate equivalent ratios that have a whole number scale factor
  • CONVERTING PERCENTS, FRACTIONS, AND DECIMALS- The swbat to make all conversions between percents, fractions, and decimals
  • PERCENTS- The swbat to find the percent of a quantity

Writing ratios was a breeze for a lot of them as it’s a pretty basic skill.  For unit rates, I presented this problem.  They were supposed to look at the following:

They were asked to figure out which one was the best deal.  I was hoping students would use unit rate but many of them didn’t.  A lot of them used pesky logic!  Some of them found out how much it would cost for 120 tickets at each value. I think I should have had a question like ‘order these from cheapest price per ticket to most expensive price per ticket’ but that question isn’t as meaningful as ‘which is the best deal.’

I like what Dan Meyer says about teaching math:

If [math concept] is the aspirin, how do we create the headache.

In other words, how do we create a need in their mind for the mathematics we’re trying to teach them.

I tried to create the headache but they went for the organic tea instead of the aspirin.

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