Make Math Moments Academy › Forums › MiniCourse Reflections › The Concept Holding Your Students Back › Lesson 83: Name That Constant – Discussion

Lesson 83: Name That Constant – Discussion
Posted by Kyle Pearce on January 23, 2020 at 9:08 pmShare a scenario involving a proportional relationship and articulate the constant holding the relationship together.
Share your reflection and anything you are still wondering about.
Nicole Jackson replied 6 months, 1 week ago 12 Members · 15 Replies 
15 Replies

A human walks at about 5 km/h. What is this speed in metres per second?
5 km = 5000 m 1 hour = 3600 sec
The ratio is 5000:3600 Divide each by 100
50:36 Divide each by half
25:18
Constant of proportionality is:
The speed is 25/18ths metres per second
Wow. I think I am beginning to “get it”!
It feels weird to think in terms of fractions instead of decimals. We are so used to using calculators. I think it is going to be a challenge to get kids used to NOT using them ALL THE TIME!

Yes it will be tough for US to first get in the habit and then to find ways to help our students along that same journey as well. The calculator robbed them of their thinking early on in the journey which makes it hard to get “off” that train. You can do it though!


Walmart is advertising a special for Irish Spring Original Deodorant Soap 3 bars (2 pack) Total of six for $10.00.
The constant of proportionality is 3:5
I can scale in tandem up and down. In order to find the rate I scaled up to get two packs with 12 bars for $20. To find the bar of soap per dollar you partitively divide 12/20ths reduced to 3/5ths of a bar of soap per dollar. If you want to know the dollar rate per bar of soap you partitively divide 20/12 or 5/3 and get $1. 666 or round to 1.67 per bar.T
 This reply was modified 2 years, 2 months ago by Jeanette Cox.
 This reply was modified 2 years, 2 months ago by Jeanette Cox.
 This reply was modified 2 years, 2 months ago by Jeanette Cox.

Proportional Reasoning is a common concept we cover and I enjoy all the ways the relationships can be revealed. In order to catch students attention we talk about about hours worked and money earned such as in 5 hours Mike earned $75 and in 8 hours he earned $90, what is his rate.
The other part I enjoy is having students make a table with proportional relationships and have them discuss all the patterns they can recognize. Then I provide a nonproportional table and have them do the same thing. Then it leads to the discussion of what is different and then figuring why that difference is happening. This can then lead to comparing the two relationships on a graph as well.

The rate is what unlocks the proportional relationship. I like that. Scaling in tandem allows the students to scale up and down but it is the rate that is the glue that holds the relationship together. It allows students to start talking about what is important about the problem and once we find the relationship we can find that rate, which will lead to the constant of proportionality which will eventually leads to the equation.

YES! I’m seeing things so much more clearly after having done this learning and it seems that you’re having epiphanies as well. Awesome!


An adult conditioned llama can carry 25% of their body weight so the constant of proportionality would be 25 pounds per 100 pounds of body weight. So scaling up by a factor of 3, a 300 pound llama could carry 75 pounds and a 400 pound llama could carry 100 pounds.

Christmas time light decorating math
600 count mini lights on 125 feet wire
I scaled down to 24 lights per 5 feet but the constant is 4.8 lights per foot

I am struck by how much of the content I teach deals with proportional thinking: similar figures, dilations, slope, linear relationships and line of best fit.
Anyway, our textbook always has “shadow” problems: “A 12 foot giraffe casts an 8 foot shadow. If Tom’s shadow is 4 feet long, how tall is he?” The constant of proportionality is 3/2. We can scale up to find the height of bigger building or scale down and convert to inches for an extension.

There are 120 lights on my Christmas tree and I used 4 strings of lights. 120/4 will give me 30 lights per one string. Otherwise stated, I could say that 1/30 of a string equals one light.

Ha! Reading through the other comments I see someone else is thinking about Christmas!


If the length of side of a square is 4 units and the perimeter is 14 units, then the constant of proportionality is 4. The perimeter is 4 times bigger than the side and inversely the side is 1/4 the of the perimeter.

We spend a lot of time in class talking about what students know. Subway sandwiches, burgers, packs of gum, sodas. My favorite is pizzas. We can find the constant of proportionality (price per pizza) and then the find the constant of proportionality per slice!

Pasta is on sale for $4.23 for 3 boxes.
So that means, 3 boxes per every $4.23
6 boxes for $8.46
12 boxes for $16.92
If we fair share the $4.23 across the 3 boxes we reveal a rate of ( 4.23/3) $1.41.
Each 1 box receives $1.41.
Finding the constant of proportionality allows us to uncover proportional relationships that would be hidden if we were simply scaling up and down.
Now that I am aware of the rate, I can determine the price of 5 and 11 boxes as well.