#70Days Projects in Math Class

Today I wrapped up my plans and handouts for the presentations I am doing on Monday.  I am a bit nervous since it has been a while since I presented to teachers ... and because I am relatively new to this district.

One of my goals is to share #MTBoS and all the fun found in blogs and Twitter.  The focus of the morning presentation is on projects.  The focus of the afternoon session is on warm-up routines.

The presentation on projects has been the most difficult to pull together.  I don't have a great list of projects to share!  Last year I did two projects that I thought worth telling about.  One was on "exploring math" ... based on Fawn Nguyen and Sam Shah's posts.  I describe the project we did here.  The second was graphing art with Desmos.  Asking students to graph a picture and label the functions is pretty standard in Algebra classes.  Using Desmos just made the project amazing and reinforced very well the concept of domain and range.

So to help the participants think through projects in math class next week, I decided to do two things.  First participants will complete four short mini-projects that could be adapted for any middle or high school math class. Then I curated projects from the Internet for us to discuss - how we might adapt one or more of them to meet our goals for students.

The four mini-projects that we will do are ...

1. Your life in numbers ... to introduce ourselves, workshop participants will make a mini-poster about themselves emphasizing the numbers that shape their lives. The purpose of this project is obvious - we get to introduce ourselves and of course, we could use this in our classes as well.
2. Round Robin Suspense Story Writing ... in groups of 3 or 4, workshop participants will write a story using this sentence starter, “Last Monday was an average day, it wasn’t odd or weird - till numbers all around our town completely disappeared!” Each person will write for 1 minute, then pass the paper. After about 5 to 8 minutes we'll stop and share our stories. I'll read Missing Math, a Number Mystery by Leedy. We'll talk about how you could use a story like this one or The Math Curse by Scieszka and Smith as a "first week activity."
3. Participants will respond to this prompt ... If the world were a village made up of only 100 people, how many of those people do you think… speak English, are 9 years of age of younger, have enough food, go to school, have electricity, have safe water. I'll share the book, If the World were a Village by Smith and Armstrong. Obviously our discussion could be about percentages in middle school math, but I'm wondering if there might be other statistical projects that could arise.
4. The last mini-project we will do is a circuit (a loop or a scavenger hunt) in which participants work math problems to find the missing words in quotations by Descartes.  Here are the links to the puzzle and the circuit.  This mini-project illustrates how one might mesh routine skills with a project.  Students could research something in math and create a puzzle to challenge their classmates.

Obviously these are all "lightweight" projects.  So in between those activities we will be building a case for doing projects and how doing projects help us to get at the math process standards (similar to CCSS mathematical practices).

Then, I'll share a dozen or so projects I found online.  The projects will be on 3 different pieces of paper - one, two, three!  So I'm going to ask table groups to read through just one page, discuss, determine possibilities, and share out.

The last minutes will be open for discussion.

I look forward to meeting folks in our district!

What projects do you use in your classroom?  Would you share with us?

"Just Flakes Cereal" needs your help! CCSS.Math.Content.7.G.B.6

Looking back through my files, I found a project-based learning task that I'd like to replicate and improve.  I used it last with a group of 8th graders but that was several years ago.  With the advent of the Common Core State Standards, this set of labs would fit better in grades 6 or 7.  The CCSS.Math.Content.7.G.B.6 says, solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

The set of activities consists of two labs that lay the foundation for the project.  The topic is exploring volume and surface area of rectangular prisms.

I asked students to work in small groups (2 - 4 students) to complete the activities.  For the lab activities, students were expected to create lab reports.  Basic information for all lab reports include students' names, a title for each activity, hypotheses, labeled drawings, and math computation.

Lab Activity #1

How many different shapes of rectangular prisms can be formed with 36 cubes, each of which is one cubic inch?  Sketch your responses and label the dimensions.

(a) Of these, which has the greatest surface area?

(b) Given a specific volume, can you predict which shape will have the greatest surface area?  the least surface area?  Explain using complete sentences and correct mathematical terminology.

(c) Test your prediction using a different number of cubes, each of which is one cubic inch.  Again, sketch your responses.  Label the dimensions and the surface area of each.

Lab Activity #2

You will need 7 pieces of 9” x 12” construction paper.  Using one piece of paper, cut a 1” square from each corner, fold up the sides, and tape them.  This creates an open box.  Now, repeat this procedure, each time cutting a larger square (1.5”, 2”, 2.5”, 3”, 3.5”, and 4”) from each corner, creating a series of boxes. 

a)    Without measuring, put your set of boxes in order from the least volume to the greatest volume.  Sketch your response.

b)    Now measure each box, find the volume of each.  Were your choices in (a) correct?  Explain in complete sentences. 

c)    Assuming each box has a “lid”, find the surface area of each box.  A complete response will include a sketch of each box, with the dimensions.  Include the volume and surface area of each.

Project:  As food costs increase, many manufacturers are looking for ways to cut costs.  The Just Flakes Cereal Company is interested in packaging their cereal with less cardboard.  They have come to you for help.

Use a standard cereal box for this project.

a)    Measure the cereal box carefully.

b)    Draw a net of the box on graph paper.

c)    Find the volume and the surface area of the box.

d)    Create a box with approximately the same volume using less cardboard. 

e)  Create a presentation for the Just Flakes Cereal Company demonstrating how they could use less cardboard for their cereals.

f)  Your opinion please:  why do you think manufacturers of cereal use the size boxes that they do instead of ones that use less cardboard?

I like to use cereal boxes in math because of their easy availability.  If you Google cereal box math pages of ideas pop up!