# Ways to Represent a Relation Foldable

After creating a frayer model over the word relation, we created a Ways to Represent a Relation Foldable to glue in our Algebra 1 interactive notebooks.

I focused on the four representations of a relation that my students will see on their end-of-year exam: ordered pairs, input/output table, coordinate plane, and mapping diagram.  My students were convinced that an input/output table was the same as a stem and leaf plot.  At least they have heard of a stem and leaf plotâ€¦

In 2014-2015, I did this same foldable, but I simplified the inside A LOT.  I also made all of the examples represent the SAME relation.

In the future, I would definitely pre-print the coordinate plane!

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1. Unknown says:

Helpful ideas . I Appreciate the points ! Does someone know if my assistant would be able to get access to a blank TN LB-0441 copy to work with ?

2. BlaQue says:

Thank you for sharing. Very insightful for someone using interactive notebooks for the first time. Be Bless and Stay Encouraged

3. Unknown says:

Hi Sarah, you tweeted asking for help with ideas for independent/dependent variables, and I reckon here is the best place to respond because there's more space!

First, I feel you. My UNIVERSITY students also have trouble with this sort of thing, though I am talking here about statistics rather than algebra. I long ago ceased to be surprised by how the language impedes this sort of activity! But it's still frustrating!

Anyway, one problem is the very words we're using here. They are two very similar-sounding words and it's easy to mix up which one is called which if the words themselves mean little to you. Like the names of twins, you're always mixing up which name goes with which twin.

Most of them probably do know what "depends" means and this is good. The problem with many of my students is actually the word "independent". In natural English it means "not related to anything", which is not at all the situation we're in here since we're explicitly relating these things together! Alternatively it might mean "happening without intervention", which often doesn't apply to these situations either, or can be interpreted in the opposite way. For example, if you have some number of cucumbers, the number of pickles happens by itself with no input from you.

I like to tell them that the word independent has its own special meaning here, and in this context it simply means NOT dependent. That is, the dependent variable DEPENDS on the other variable, and the independent variable is NOT the dependent variable.

There is a more serious problem in my mind, though, to do with causation and relationship. In some of those stories, the causation could actually be the opposite way than you are suggesting. For example, someone planning a concert might have a fixed duration in mind, which would CAUSE them to choose a certain number of songs. In this context, the number of songs is the dependent variable and the length of the concert is the independent variable. Without knowing the full story, you actually can't decide!

Even worse, in statistics and science, there's no particular reason that there has to be a causal relationship, but you still might be interested in predicting one variable from the other. Even if there is a causal relationship, the thing doing the causing doesn't have to be the output variable! When a car breaks at high speed, it is clear that the speed the car is going will cause the skid marks on the road to be longer. But if you are a crash scene investigator, you want to calculate the speed from the length of the skid marks.

So it seems to me that in order to choose the dependent and independent variable, you actually need the full story including the information the person has and the information they want to find out. Without that, I can't be completely sure.

I'd recommend having a three-way match up: story-dependent variable-independent variable. It will be easy to match the variables to their story, and the story will give more info to help choose the dependent and independent variable.

1. Unknown says:

I had the same thought David! I really like your views on this, I will be using them in my Methods class ðŸ™‚

4. Unknown says:

Thanks. You shared a good thing that i need in my class.

5. dohamag says:

1. Sarah Carter (@mathequalslove) says:

6. Anonymous says:

Hello, I love your blog and come here often for ideas! I am currently teaching this, and wondered if you ever found a way that helped your students? I can't find a way for some of my students to get it! Thanks!!

1. Sarah Carter (@mathequalslove) says:

Still haven't found a fool-proof method. I've found it helps to have students write __________ depends on __________ before deciding dependent vs independent.

7. Anonymous says:

Hey, That's pretty good

8. Unknown says:

Thank you so much for this. I had created some guided notes to use with a PowerPoint but I find that boring and the kids seem to not really grasp the concepts. So this year I am trying your items.

9. Anonymous says:

First of all, thank you for sharing so much on your blog. I agree,the fill in the blank statement of ________ depends on ________ helps students to understand. In addition, the variation in order using the phrase ______ determines _______ helps as well to bring attention to the action rather than order mentioned, which is a symptom of overgeneralization. I do like to introduce the topic to students relating dependent as one who depends on another for food, shelter, transportation etc. Independent is what their parents are as they work to provide the shelter, food, transportation, etc. Independent is what we all hope they become someday. And so when revisiting equations/functions I point out that the independent variable will be the variable doing all the work.
Also, I've once had them create picture statements using magazines.

10. Anonymous says:

I'd also meant to address the issue of the average students' ever increased limited vocabulary. Two words, teachable moment. Perhaps before beginning the activity the students could generate a list of words and definitions. I like to emphasize that like no man, no subject is an island…And again thank you so much for all that you share with the teacher community.

11. Unknown says:

Absolutely love this activity and all of the freebies! Thank you! I recreated your sort into a powerpoint activity to try and save on paper (even though paper sorts are the best). Let me know if you would like a copy. I put mine in Google classroom for them to move the text boxes around.

12. Anonymous says:

I'm teaching Algebra 1 for the first time, and this is excellent. Things are different this year with COVID so if I use this I might have to find a way to modify it and speed it up. Thank you so much!