This is a fun activity that engages and challenges the students.  I heard of a similar activity during a visit to Nueva School in San Mateo.  By introducing an “approximately” proportional relationship, they have to think carefully about what it means to be proportional.  Depending on the depth and time you can bring to the class discussion, the students can apply most of the Standards for Mathematical Practice during this activity.
 
I began by asking who knew a good tongue twister.  Most of my students did, and we took a few minutes to share some.  Then I explained:
 
“I am going to give each pair of you an unfamiliar tongue twister.  One of you is going to repeat the tongue twister as many times as you can while the other one counts and watches the clock.  You will time your partner for 10 seconds, 20 seconds, 30, 40, and 50 seconds, and record the number of times they say the tongue twister for each time in table.  What I want to know is: do you think that table will show a proportional relationship?”
We had a good conversation about that.  I was surprised that most of my students said no.  They thought saying a tongue twister was just too unpredictable.  You can challenge them to explain how they will know if it is or it isn’t, and see how much of the previous lessons they have understood and can apply on their own. 
 
Then they got to work.  We have just finished collecting the data.  In conversations with pairs we looked at tables that seemed to not be proportional at first, but then seemed more proportional as we noticed other patterns.  At one table we realized the number of times the student said the tongue twister was always 1 off from 1/5 of the seconds.  At another it was always just above or just below.  When we reconvene after our annual trip off-campus, I will be sharing all the tables with students, asking which tables have a constant of proportionality or something close, writing equations for those tables, and talking with them about the roles of approximation and modeling in applying math to science.  I think this will be a great way to lock in some of the key concepts for this unit, and make them memorable.

I love language almost as much as I love numbers, so I tend to get excited about vocabulary.  We talk about Latin roots in my class, and why we use the terms we do in math class.  I have always stressed “constant” and “variable,” but I really got excited when I saw how contrasting the variety of possible scale factors in a table with the constancy of the “constant of proportionality” highlighted the concept of a mathematical constant.  By talking about proportional tables and asking questions like “What’s the same throughout the table and what keeps changing?” my students have already heard me say the word “constant” (with something I could point to) more times than all of last year.  When we start to write equations, it will be the word “variable,” and I expect that the idea of a variable will make perfect sense in the context of the proportional relationships and tables.  And by spending as much time as we are going to on proportional y = ax equations before we move on to y = ax + b, students will have a deeper understanding of the subtler differences between constants, constant terms, and coefficients.

In my prealgebra classes I have used my own curriculum for a number of years, but it seemed that I was always re-writing or re-sequencing.  This year I decided to try out the Illustrative Mathematics curriculum for Grade 7, and let someone else make the decisions for me.  So far I think I put myself in the right hands.  These are good problem-based units, they stretch the students in ways that I realize I have been shying away from, and they develop multiple threads of skills at the same time.  Sometimes that sequencing is obvious, sometimes more subtle.
 
The first decision I made for myself was in fact a mistake: I was concerned about time for some of my own topics and activities that I wanted to keep, and I thought I could do without Unit 1.  Scale drawings and Proportional Relationships seemed like they would be covering similar ground, and scale drawings weren’t as critical a topic as proportions.  But the two units together develop the two kinds of relationships you find in proportional relations:

Scale factors are the relationships between pairs of ratios and the constant of proportionality is the relationship across each equivalent ratio … which stays constant for each row of the table.  Unit 1 develops the idea of scale factors and Unit 2 applies scale factors to tables and adds the constant of proportionality.  So they really build nicely on each other.
 
Fraction skills are also a concern of mine (more on that later) and Unit 1 is an important part of that sequence as well.  In Unit 1, the students multiply by unit fractions and are reminded of the equivalence of dividing by 4 and multiplying by ¼.  They also find 3/5 of a number or 2.5 of a number, and are reminded of reciprocals.  In both Unit 1 and 2 IM ventures into fractions gently, introducing a skill with whole numbers, then using numbers that the students can make sense of mentally or with relatively easy calculations.  I have tried to do that myself in the past, but it is nice to have the details thought through for me, and so far it has worked well for my students. 
 
I have been able to make things work this year with a little extra time and attention to scale factors, but I will be using Unit 1 next year.