# Barbie Bungee Implementation

I think that there are a million and one ways you can do almost anything.  Dan Meyer tweeted this out the other day…

I was quick to comment.

I think it’s important to note that I work most closely with 8th grade (on grade level) students.

After seeing the subsequent comments…I wanted to add that IMPLEMENTATION can be more than just here’s your worksheet, “get on with it.”

I like to lead up with this…

Can you guess what their answer is???

Then I show them this…

Of course this changes their answer.

Then I move onto this…

And I have students come up to put a point…usually around a y-value of about 10 or so.

Then, I click to reveal additional points.

The point is…I make the point that collecting multiple pieces of data helps to make better predictions.  I also ask the question about what mathematical models can we create to help make predictions in math.

• Graphs
• Tables
• Equations

Just what I want.

Then I show one of the many videos that you can find on YouTube.

The last thing I do is pass out a worksheet.

# Equal and Opposite

I don’t know if this is the right title for this post…it feels like it is.  I get to its point at the bottom…

I was supporting an 8th grade teacher that was implementing the Classifying Solutions to Systems of Equations formative assessment lesson from Mathematics Assessment Project.

The students had not yet worked with linear equations in any form other than slope-intercept form.  The students already understood the different types of solution a system might have.

The students started out by completing the assessment task.  I wanted to focus on this part below:

I’ve encouraged this teacher to build a strong foundation for students being able to create and complete a table of values.  Creating a table should be a go-to strategy for students if all else fails.

I stood in the back of the room and I looked at the second equation…

I wondered if I could make a connection for kids…if it would be too much, or would they follow…Here is the gist of what I did:

I interrupted the class to pose a question.

Me: What do we know about an equation that is solved for y?

Students: We know the y-intercept and we know the change in y over the change in x.

Students: It’s solved for x.

Me: What do you think that might tell you?

Students: The x-intercept???? (Imagine a questioning tone here…) Is that a thing?

Me: Yes it is a thing. What about the coefficient of the y? What do you think that might tell you?

Students: The change in x over the change in y??? (Imagine a questioning tone again)

Me: Yep. Let’s pull up Desmos and check it out.

I remember being a math student that naturally made these sorts of connections~that if something happened mathematically one way, I could predict what would happen in an opposite direction.

I want the students to know and wonder about these things for themselves.  But, I think we need to make it obvious to them sometimes that they can do this thinking on their own.

# My Favorite Formative Assessment Tasks

I’m a little late…but, here’s my week 2 “My Favorite” post for the Explore MTBoS blogging initiative.

The Charles A. Dana Center out of The University of Texas at Austin has put together a great set of tasks for eliciting student thinking.

One of my favorite tasks that I have used with 8th graders (for years) is called Mosaics.

Because we spend time making sense of the patterns from the Visual Patterns site, this task works well as an independent assessment task.

I particularly like question one in that it asks students to represent the problem in at least three ways–they are not told how to represent the problem.  I like to see if they will use a table, graph, etc.

Also, it’s interesting to see how different students “see” the pattern growing and how they choose to show that thinking.

And my FAVORITE piece of student work for this task incorporated the independent use of “noticing…”

Here is a link to additional student work from this task.  We’ve used this task, along with the student work, as part of our back-to-school professional development on using a examining student work protocol.

Dana Center tasks are not a free resource…but you can find some sample items for free. Doing a Google search for Dana Center Algebra 1 Tasks will yield these results. You can purchase a book of these tasks here, or on CD here.

# Visual Patterns and Missing Figures

The past few years I’ve used Fawn Nguyen’s Visual Patterns site as the structure for building an 8th graders understanding of linear relationships. Students GET patterns–even the most struggling learners can identify what’s happening in a linear pattern and complete a table of data points. What I’ve done recently is used the patterns to build an understanding of finding the constant rate of change between two points. Here is an example of what the students are presented with… Instead of giving the students something like this:   I give them this:   The students work on their dry erase board to create an input-output table of data points beginning with x is 0.  We’ve spent A LOT of time creating our own tables that it has really started to become second nature.  I didn’t tell them how to figure out the missing figure numbers…they just figured it out on their own. Without prompting…the students even wrote the rule for these situations (I had only asked for the rate of change). We worked through several problems like this on dry erase boards (pulling from Visual Patterns each time) and then went to problems like this: and this… With these problems I asked them to determine the (x, y) values that would fill the purple oval.  Again, without prompting, they wrote the rule for this relationship. The follow up to this activity was via @Mathalicious …I used their Domino Effect task which was a great follow up to the missing figure number dry erase activity.  Students felt very confident in their ability working through that task completely independently. Here is a set of 5 Missing Figure Images…thanks to @fawnpnguyen for her great resource!!!