IMP Cookies unit problem with a "New" twist

The unit problem in IMP Cookies has to do with finding the maximum profit for a bakery when they meet constraints pertaining to oven space, preparation time, amount of dough and amount of icing. Throughout the unit the students do activities that give them all the information and tools they need in order to answer the unit problem. My often-mentioned teaching buddy Mrs. New has done a couple of really cool things with this unit problem. She is having the students to present their findings to a panel of administrators, our instructional partner and another math teacher. They are going to have to tell them what amount of iced and plain cookies will give them the highest profit and prove to them why.

The BEST part is the idea that Sonya had of telling the students that they could change ONE and ONLY ONE constraint. She has told the students to make a proposal to the panel of which item they should increase. Should they buy another stove, hire another person, or buy more dough or icing? There are some constraints that even if their limits are increased they will not increase the profit. I LOVED this idea. I am doing the "lazy version" of Sonya's activity and just having the groups present to the class. I have tried to encourage the groups to be creative as to why they chose the constraint to increase. I told them they could make up a story to go along with it in order to convince us that it is the best thing to do. However, they are also supposed to have a new graph that reflects the changes in the constraint. I had students to realize today as they were preparing that they chose to increase an item that did not improve their profit. Their feasible region was still the same.

I love teaching with creative people! Sonya is ALWAYS coming up with really cool ideas and activities. I will update this post after her groups have done their presentations...I'm sure she will have some awesome things to share.

UPDATE after presentations:
Things we like:

• We love the problem...especially having the students change one constraint and then explain if it improves the profit!
• Mrs. New loved having the students present in front of a panel
• Mrs. New's students loved that they went in a separate room to present...no other students were present during their presentations
• Mrs. New required them to have a digital presentation - most used Prezi or Powerpoint

Improvements:

• The students didn't seem to fully understand what we wanted from them. We need to somehow do a better job of explaining the purpose.
• To address the above bullet...Ms. Whitt mentioned she wished we could model a presentation for the students...maybe use the Picturing Pictures activity to model a presentation, then let them practice presentations in the classroom using Rock 'n' Rap
• Remind the students to explain the problem like nobody has a clue what they are talking about...give some background info...

The students presented in this small "conference" room

IMP Cookies - Rock 'n' Rap, formative assessment and collaboration

Rock 'n' Rap is an activity that talks about producing rock and rap albums. The students will once again be led to find profit lines which should help them on solving the Cookies unit problem. There are 3 constraints this time. Also some of them shade below but one shades above so there is a little variety.

When graphing the inequalities Sonya New, my IMP teaching buddy, has stressed with the students that one way to graph the lines is to find values for x and y that make the equation true (they really do this by trial and error using number sense). I love that she has done that (even though I have talked mostly about using intercepts or slope-intercept form). She has taught SI form and graphing using intercepts also, but she says alot of her students still graph by finding ordered pairs that work.

When I did the problems with my class we said that there had to be more rock albums than rap albums. However, smarty pants Sonya corrected me (I hate when I'm wrong) and told me that it should have been rock is greater than or EQUAL TO rap. When you read the paragraph about this constraint it says that the company promises that it would not release more rap than rock. Then it goes on to say that the company is more closely related to rock music in the public mind. Even though I know she is right I could really make an argument about why I chose to publish more rock than rap! (But the mathematician in me knows she is right...dang it!)

Lastly, I had my students put this activity on chart paper. I have been in such a rush lately I haven't done this as much. It made me realize that having them put it on chart paper "makes it real" for the students and they invest more in the problem. Also, I get the opportunity to formatively assess at a glance by reviewing their work. The picture below is of a group of students explaining their findings from the Rock 'n' Rap activity.

IMP Cookies - Finding Linear Graphs

We kind of did a "fly-by" on this activity. It has the students create a table in order to graph a linear equation. Then they are asked to graph 5 more equations while looking for shortcuts. Lastly they are asked to discuss in details the steps they use to graph a linear equation and what special methods can be used. They are also prompted to tell how they decided on the numbers to use in the table.

I had to be out one day before this activity and we had already been discussing how to graph from slope-intercept form and how to graph using intercepts. I think that somewhere in this area of the curriculum it is time to explicitly teach these concepts. We have been working on them for a long while now in Overland Trail and in Cookies. Therefore, I gave them a "traditional" worksheet on graphing using the 2 methods. Therefore when my students did #2 in this activity we focused our discussions on which method would be easier to use in order to graph the line.

Graphing lines is such a fundamental part of algebra and it is so frustrating how the concepts seems to escape the majority of the students. If they go a day or 2 without graphing it is like they totally forget. One thing I like about IMP is that they graph over and over and over again. In Cookies we are using constraints to find the feasible region and answer questions about different situations (systems of inequalities). Sonya and I decided that while we are working through Cookies we are going to SIT on graphing until they get it...we hope.

IMP Cookies - Profitable Pictures...very important

This activity builds off of Picturing Pictures. Mrs. New and I decided to draw a graph for Picturing Pictures and make copies of it so the students would for sure have an accurate graph on which to do their "profit lines." It is so wonderful to "share a brain" with Sonya (Mrs. New) because she has already taught Cookies twice. We are needing to trim as much as possible because we started the curriculum late. Therefore she knows when there is an activity that you should not skip and I need to remember NOT TO SKIP PROFITABLE PICTURES.

This activity gives students the tools they need to answer the Cookies unit problem. The students should discover that the profit lines are parallel and that the higher the y-intercept the higher the profit. Therefore they need to extend their parallel lines until they find the highest line that clips a point in the feasible region. After trying to get my students to explore this activity over 2 different days I finally EXPLICITLY told them that the maximum profit is going to come from one of the corners (if you will) of the feasible region. Sonya and I  also EXPLICITLY told them that the methods we used to discover the feasible region for Profitable Pictures are the same as what they need to use to solve the Cookies problem.

Profit Lines...

When I first started the curriculum I was so diligent to read through the teacher's guide for almost every lesson. So far this semester I have not been able to do that! It is a long story... Anyway, I really value having someone (who just happens to share a planning period with me) to collaborate and discuss lessons with! It makes such a difference. Sonya is totally committed to our "new curriculum" and we have so many aha moments that we get to share with each other.