The Guitar Class: MAPs Activity- Cutting out what you don’t need

Once again I am using the Shell Center resources for class, this time looking at Modeling Situations with Linear Equations.  Once again, I am looking at the student handout and although it is designed as a pre-assessment, I am wondering why they are supplying students with so much information- time to get the scissors out….

The Guitar Class:

To be totally honest here, I’m scrapping pretty much the whole handout and start from scratch, here is what I will show students.

Guitar Student Handout

Students should come up with ideas about rent, how many students are in the class, and how much each student should pay for the class.  They should also sketch a graph starting at a negative balance (showing the rent for the space) and increasing with each student enrolled.  I will then ask them to write down answers to the following questions on their paper:

Teacher Questions:

What values for each factor did you assign?

How did that determine where to start your graph?

How did that effect your Axes? How did it effect your scale?

What do you notice about your graph?  (hopefully they say 2 things, it’s increasing at a steady rate per student, and that is crosses the X axis)

Students will have a varied set of values for each factor, and that is OK, their graphs will all have the same general look, and they should recognize that where it crosses the X axis is where the music teacher breaks even for cost.  I don’t want to give away anything with this question, it provides a great platform for students to provide ideas and values, as well as creating their own ideas on how to graph the scenario.  Looking at each individual’s work will give me instant information on how much the student comprehends the material and what I need to address.

As students are done with their graphs and our group discussion is when I would put back in the original scenario from their handout:

Guitar Class

I do not think I will ask students to write an equation right away, giving students the proposed values instead. I would then ask these questions for students to answer on their paper:

Teacher Questions:

What is the situation the music teacher faces? (using these values)

What is the teacher’s balance at the beginning of the class?

How does each student effects that balance?

Write an equation representing this situation.

I also would not show them questions 3 or 4, I would instead ask verbally these questions, have students record their thoughts and discuss each one as a whole class at the end of the hour:

Teacher Questions:

How can we determine the teacher’s total cost.  Write that as an equation.

How can we determine the teacher’s total profit?  Write that as an equation.

What factors do we need to consider to determine the cost for each student?  Write that as an equation.

Are there values that are unreasonable to charge students for taking his class?  Explain.

I will be trying this out with my groups tomorrow.  I plan on engaging their creativity and mind- which will produce great ideas to discuss.  I realize that this is a pre-assessment for their unit, but students will provide me with enough information on where their skills lie with my student handout and follow up questions.  I will write a follow-up to see if I “Cut too Much.”

Taxi Fares: MAPs Activity- Cutting out what you don’t need

I really enjoy using MAPs tasks in class, but with my recent “cutting out what you don’t need” outlook, I am finding myself looking twice even at this resource.

Consider the following graph:

Taxi Cab Graph

What do you notice?  What patterns do you see?

Depending on the level of student, you can get a variety of answers.  It has a positive correlation, or that it’s an increasing function that is not continuous.  You can get responses about statistics: the range, min/mas, mode, median, etc.  All of those observations are great for what the original worksheet has students do.  I have even considered cutting out the last sentence in the directions, hiding the axis labels- having students provide them as well.

One question a student asked: “Why would he graph his fares?”  A good question- where would this problem be placed in Dan Meyer’s (Real World,Fake Work) quadrant?
I answered: “That is a good question,  I think he did that so he could look for a pattern.”
Student: “Do I need to use the graph?”
Me: “How do you want to look at it?”
Student: “Didn’t it say he wrote down the times and distances?  I’ll use his list.”  Well, that is a problem since I didn’t create one and part of why I am having students work on this problem is to gather that information from graphs.
Me: “I don’t have it with me, is there a way you can re-create his list?”
Student: “Yes, I can use the graph.”
The student then starts working to make his list.

My point is: students can connect a lot of background experience to the graph, and it does the class a world of good to talk about them.  After you get those ideas floating around in their heads you hit em with the real math:

David needs to make $30 per hour.  Should he charge by hour or mile?  How much should he charge?  Explain your reasoning.

I can walk around and look at student work, asking questions here and there to understand their approach and thinking.  Students would solve this question in whatever manner makes sense to them.

This is what the problem actually looks like from MAPs:

Taxi Problem

I tried this with one class, and they blindly followed the directions for 1 without considering why 4 hours was chosen.  The bad thing about that is that they assumed that the work they did for 1, they were supposed to extend to 2.  They came up with 14min 40 sec for a 4mile trip, which they then approximated to 4 trips per hour, and 16 miles total.  They then got an answer of $1.88, which was close.  They did all of this work without thinking about what or why they used 4 mile trips, so when the second handout came- they were lost because it did not resemble their work.  We then backtracked and re-examined their work (I knew this was coming so I didn’t intervene right away), and they did the process using all of David’s trips.  Many students struggled with this, they did not have the academic stamina to redo a problem that was solved (in their minds).  To make this less painful for my students, I asked students to write why the sheet had them examine a 4 mile trip.  Once they saw a point to re-working the problem, they went back to the graph and measures of central tendency.

I plan on hitting students with this same type of problem next week, cutting out what I don’t need, and see how students progress.

Irrational Numbers on the Number Line- Cutting out what you don’t need

This problem has received a lot of attention on my blog the past couple of weeks…

Consider the roots of the first 9 Natural Numbers (√1 to √9), how many of them produce Irrational Numbers?

List them.  Graph their approximate location on a number line.

number-line-600x271

Explain how you determined where to place them on the graph.

 

Is √10 Rational or Irrational?  Explain how you know.  Where on the number line would you graph it?

 

Although I do like this problem, I’m going to cut out what I don’t need.  I think I am going to go with this:

 

Consider the roots of the first 9 Natural Numbers (√1 to √9), what do you notice?

Graph them as accurately as you can.

Blank Number Line

Explain how you graphed them.

 

Consider √10 and compare it to your other roots.  What do you notice?  Where on the number line would you graph it?

 

I want the conversation to come up about how √1, √4 and √9 become “numbers” (as I anticipate students to express), and the others are not as familiar.  Hopefully we can get to classifications from this conversation.  I took away the labeled number line because I also hope to get students thinking about where those numbers lie and how to label the above graph to most accurately display their position on that line.  I anticipate a few misconceptions about labeling the interval.  Hopefully by the time we get to √10, students will automatically be thinking of Irrational and Rational numbers and where it belongs.  They can do all of that, I need to get out of their way.