I've been hearing about Daily Desmos on Twitter, but never thought too much about it. Once it was part of the challenge for MTBoS, I figured I had enough time to look into it. Currently, my Algebra 1B classes are studying lines and we are just getting into writing equations with certain given information. I decided to give the students the following challenges and allow them to decide which one they would prefer to work on.

I haven't asked the students to do anything like this so far this year, and you can imagine how frustrated they were. However, a few students persevered. In my one class, a girl who was ready to give up decided to give it one more go. At that point she noticed a patterned and asked me to go away because she wanted to figure it out all on her own. Once she was successful, I asked her to see if she could continue her pattern. You can see her two attempts below:

Ali's:

# Daily Desmos 217b (Basic) – Think outside the box

Can you draw 4 lines that cover all 9 points? Whoa, whoa, whoa. Not so fast.

Rules:

Rules:

- One one vertical line allowed (x = #)
- Only one horizontal line allowed (y = #)
- You can only have your 4 lines intersect on, at most, one of the given points. And the origin can’t be one of these intersection points.

# Daily Desmos 218b (Basic)

## Creator

Justin Lanier (@j_lanier)

## Difficulty

Basic

## On to the Challenge!

Can you create the following graph using desmos.com or some other graphing tool?

**There are ten lines and ten equations in all.**If you’re victorious, leave us a note in the comments when you’re done.I haven't asked the students to do anything like this so far this year, and you can imagine how frustrated they were. However, a few students persevered. In my one class, a girl who was ready to give up decided to give it one more go. At that point she noticed a patterned and asked me to go away because she wanted to figure it out all on her own. Once she was successful, I asked her to see if she could continue her pattern. You can see her two attempts below:

Ali's:

Her equations:

y = -10x + 10

y = -9/2x + 9

y = -8/3x + 8

y = -7/4x + 7

y = -6/5x + 6

y = -5/6x + 5

y = -4/7x + 4

y = -3/8x + 3

y = -2/9x + 2

y = -1/10x + 1

She noticed that the y-intercepts were decreasing by 1, all the slopes were negative, the numerators were decreasing by 1 as the denominators were increasing by 1.

To the original 10 equations she added 10 more simply by taking the opposite of each slope and each y-intercept:

y = 10x - 10

y = 9/2x - 9

y = 8/3x - 8

y = 7/4x - 7

y = 6/5x - 6

y = 5/6x - 5

y = 4/7x - 4

y = 3/8x - 3

y = 2/9x - 2

y = 1/10x - 1

For the other problem, students googled how to draw 4 lines with 9 dots. But writing the equations were difficult for them. I even heard one student ask a group member if their graphs really were correct (she had a lot of doubt in her voice), when he said yes, she didn't question it. Too bad, because I think she was on to something. Here is their submission. Oh, so close.

#### What are my thoughts?

I enjoyed it. I'm realizing that my curriculum doesn't have to be in these finite chucks of instructions. So what if we're not writing equations from graphs yet? The students have all the knowledge they need to do this, so give it a whirl.
I found that many of my students were so afraid of being wrong, that they didn't even want to start. What's wrong with being wrong?

I plan to use this again. I feel that it allows students to think more deeply about what they're doing, and it doesn't require a step-by-step manual from me. What I would do differently next time, is to perhaps make one that's even less challenging. The students were overwhelmed by the number of lines in the one challenge and the other challenge had too many options for lines.

Thanks MTBoS for this opportunity!!!

*Update* 10/23/2013

Today a student held up the paper I gave for the Daily Desmos and asked when we could do it again because he really enjoyed it. Yaaaaay!!

*Update* 10/23/2013

Today a student held up the paper I gave for the Daily Desmos and asked when we could do it again because he really enjoyed it. Yaaaaay!!

How often we math teachers contribute to students' fears by teaching, even without meaning to, that there is one right way to do everything in math. No wonder they are afraid to try new things. Doing these activities is a great way to get them thinking, but we need to help them learn to be confident in their own ideas, to persevere through frustration, and to love challenge rather than safe answers. Many students have never had to do those things in a math class before, unfortunately.

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