# Least Number of Linear Equations

I just created another linear Graphing activity to hopefully make graphing linear equations fun as we practice this over and over.

Today we did Barbie Bungee and it was great. Tomorrow I want to go back and make sure they can write the equation of a line through 2 points. After an activity on writing the equation of a line through two points at the beginning of class we are going to do this fun challenge.

leastnumberoflinearequations

Best part of this activity – Easy to understand the task:

Hit all the points with the least number of lines. (I might go back and write only this statement in the instructions. [I did!])

- I’m looking for any ideas to make it better here: Starting with a blank slate – Least Number of Linear Equations Planning

I’ve added the picture below of what I expect someone will try. Curious to see what else they’ll come up with. I’m going to make a Desmos activity(see below) to go with it so that they can check their own lines after they’ve completed the assignment.

Link to Desmos Activity

I’ve really liked this option for the activities I’ve created recently. First I have them write their equations by hand to go through some points. Then they open desmos and the points are in the same place as the worksheet. Then they enter their equations. It becomes painfully obvious if their equations are incorrect and even in a low Algebra class almost everyone wants to fix them. Win. I don’t want them doing desmos to begin with because they can just keep changing values in the equation without much thinking.

**A couple new thoughts for next time:**

The same activity 3 times in 3 different ways:

- Have each student pick a y-intercept and tell them every line has to go through that intercept.
- Have each student pick a slope and tell them that every line must have the same slope.
- Then give them a free for all with any equation they want.

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I like this activity, and it’s giving me all kinds of ideas for my Algebra 2 and Pre-Calc classes. One suggestion and a few questions:

1. On the second Desmos screen, change the word “less” to “fewer.”

2. What is the difference between the two Desmos screens?

3. How do you keep kids from sharing information and getting in to Desmos early?

4. With all these points, how are you certain that your answer has the fewest lines?

I really like the big potential discovery, where students realize that they can use one line (y=x+2) to hit a whole bunch of points.

Bruce Rhodewalt

Thanks for the wording help. I switched it.

I did not display the desmos on the screen and only gave students the code to join the desmos activity when they showed me their paper with all their lines and equations.

The difference between the desmos screens:

The first one is just for them to put the equations in that they have written on their paper to check them and make sure they wrote the correct equation for each line. I try to impress on them that it’s OK if some of them are not correct. They just need to now use desmos to investigate and see if the can get the equation they want.

I need to maybe write down some instructions for this. I think it would be great for them to have all their original equations in red and then their corrections in blue.

The second screen is for them to mess around and try to get all the points in less lines than they did previously. I think that many students just found lines that went through the points and didn’t try to hard to get the least number of lines. The second slide is essentially identical to the first but gives me a glimpse into them trying to do better than they did the first time. When the activity is done, I can go back and see what each student tried.

It might be cool to have the second slide be a completely different set of points, or add a third slide with a completely different set of points as an extension.

Posted on Twitter but this will be better to get all my thoughts out:

I love the idea of Desmos to check.

You can have a slide at the beginning with the graph and dots and the prompt/task.

You can make it so students are allowed to draw lines on the graph. I think (I am in the process of learning about Desmos for this first time this week) you can add on the same slide (maybe it will have to be the next one) a text or math box where they can type in their equations they made.

There is a lock feature so they can only be working on that slide until you are ready for them to check. I do not know if you can unlock one student at a time though, so they may not work.

You’re right. This is something that Desmos can make themselves, but I can’t add in. They can have one slide where you enter equations and then they show up on the next slide. Teacher created slides are stuck with individual slides.

Here was my idea: https://teacher.desmos.com/activitybuilder/custom/5939c5bcf576406568f1bdd6

Good idea!