#MakeOverMonday Week 3 Bedroom Carpet ... Let's Save Money!

Dan Meyer has published his third #MakeOverMonday textbook revision challenge - Bedroom Carpet.  Check it out here!  (Hmmmm ... the problem says her sunroom, OK?)

There are two things I notice about the problem.

• First, the dimensions in the scenario are all in customary measurements and the picture is in meters.  My first revision would be to change the measurements on the diagram to customary measurements.  If I see that the prices are described in customary measurements, I am going to measure my room with feet/yards ... not meters!
• The second thing that catches my eye is this sentence, "Lesa wants to lay out the carpet so the nap is running in the same direction, with the minimum number of seams."  I am guessing that "nap" will need explanation.  And this creates the possibility of two solutions ... the nap could run from left to right in the diagram or it could run from top to bottom.  Thus my revision, is which way costs less?  Let's save money! 

Use the information given in the problem to determine the cost of the carpet if installed from left to right.  Also determine the cost of the carpet if installed from top to bottom (as in the drawing below).  Which installation will save Lesa money?  Would one way be more wasteful than the other?

A second revision might be to question Lesa's choice of indoor/outdoor carpet (ugh!) and suggest that students find an appropriate alternative and determine the cost.  The teacher could provide links to websites for flooring choices like this one. This revision could be combined that with their English class' assignment to create a persuasive argument for a specific flooring.   (If time is limited, and research not desirable, the teacher could provide costs for alternative flooring).

Additional revisions could include students measuring rooms in their own homes, bringing in the layout drawn to scale, and determining the cost of flooring.  Students could research flooring costs in their area, choose their own style, and determine the total cost.

Even though I don't expect to use a problem like this next year, I like the challenge of thinking about revision.  I even went on an Internet scavenger hunt this morning for a project in which students plan their first apartment.  I know such a project exists ... I had created one many years back but today I didn't find any links to share.

How are you revising this problem?  And if not this one, what problem are you revising?

Blogosphere ... Good Ideas Round 3

As I have been reading around the blogosphere, I am in awe of the many excellent ideas shared among educators!

Here are 3 ideas that caught my eye!

Our school is fortunate to have a 1:1 initiative for 9th and 10th grades.  (Last year only freshmen were issued laptops).  I am always on the lookout for meaningful ways to embed technology in my algebra classes.  I ran across Education Rethink: Fifteen Paperless Math Strategies.  I notice that several of the strategies involve a blog and/or a shared document.  I've already committed to learning how to use Google products more effectively - thinking the shared document will work.  One more note at this blog ... this team of two offer their visuals for free ... which may be helpful as I create materials for class!

Mary Dooms writes a poignant post about students and curiosity in response to Dan Meyer's post on The Unengageables. She says, "Students are curious. We just have to give ourselves permission to allow them to pose questions and wonder."  Mary goes on to talk about how we use the summer to recalibrate; this resonated with me!  Mary mentions the Annenberg series and Fostering Algebraic Thinking.  My stack of books is growing and the time I'm spending reading them is shrinking!  Her post inspires me to keep at the work of developing good problems - worthy of students' curiosity!  Check out her 7th grade textbook revision problem!

To follow up on developing good problems, a third site I found interesting is Inquiry maths! As we discuss textbook revisions at #MakeOverMonday and read professional books, developing rich worthwhile mathematical discourse is essential! I'm looking at the inquiries suggested for algebra and considering how I might use these to stimulate creative and analytical thinking. The author at Inquiry Maths says "Inquiry is built on inquisitiveness and curiosity. And for those to be articulated, students need to learn how to ask questions. When students inquire into their own questions, levels of motivation, engagement and confidence rise. Students become self-starters who take responsibility for their own learning. Importantly, they lose the fear of giving the wrong answer because they control the question under consideration."

So much to think about ... so little time ... even in the summertime!   The math blogosphere is an amazing source for professional development!

#MakeOverMonday Week 2 Checkerboard Borders

Dan Meyer published his second #MakeOverMonday textbook revision challenge tonight - Checkerboard Borders.  Check it out here!

The problem states:  In preparation for back to school, the school administration has planned to replace the tile in the cafeteria. They would like to have a checkerboard pattern of tiles two rows wide as a surround for the tables and serving carts.

I wonder ... when a contractor gets a tiling job, does he use math to determine the number of tiles needed?  What planning does he do before laying out a pattern?

I would give students just the context in italics above ... with some thinking time ... and then proceed:

1.  What questions come to mind?

2.  In teams, go to our 9th grade cafeteria and collect information that will be helpful to you.

3.  In teams, use the graph paper and colored pencils provided to create a diagram that fits the problem description.

4.  Determine how many colored tiles will be needed to create the pattern your team drew.

5.  Suppose the school administration changes its mind and now wants to tile the cafeteria in the 1100 building instead of the 9th grade cafeteria.  Create a generalization or rule that will work on any size cafeteria.  Does it matter if the cafeteria floor is square or rectangular?  Explain your thinking.

6.  The cafeteria manager looks at your diagram and comments that his serving equipment will need more than 2 rows of checkerboard pattern.  He requests 4 rows.  How does that change the rule you created for the contractor?

7.  Create a mini poster with your floor design, calculations, and generalizations.

I made two changes.  First, I asked students what they need to know from the problem situation to encourage their own thinking, curiosity, and problem solving ideas.  Second, I took away the square diagram, choosing instead to use real data.

How would you modify the problem?

Textbook Revision Idea #2

I am enjoying the challenge of rewriting textbook problems in order to create deeper thinking, and relevance.

I just learned that I may be teaching Algebra 2 instead of Algebra 1 next year.  So I found an old Algebra 2 book on my shelf and thumbed through the first chapter.  I know that our first unit will be "foundations of functions" reviewing linear functions.

The problem that caught my eye is this one from Holt Algebra 2, 2004:

I understand why the textbook provides the scaffolding in the first question (a) but I'd like to remove that.  I would also reword the question to make it more personal.  Mine might look like this:

Your English teacher knows you are taking Pre-AP Algebra 2 so she quietly asks you to help her with some math.  She gave a test and the scores were lower than she expected; they ranged from 40 to 80.  (In fact, YOU scored an 80!)  She wants to adjust those grades and make them range from 60 to 90 but she isn't sure how to change the scores accurately.  Explain to your teacher how to set up a function and create a table of adjusted scores.

I would expect an equation, a table of adjusted scores (in a spreadsheet, preferably), and a graph.  In a written explanation, I would expect students to interpret the meaning of the intercepts and the slope.

In completing this problem students would explain the variables in the given context, identify the domain and range, and predict the value of the independent variable when given the dependent and the other way around.

Pre-AP students will be grateful that the 80 they scored on their English test is being scaled to a 90.  They may also feel some pride in being chosen to help the teacher with her math!

Would you use the original problem?  If you would revise it, what would you do?

PS ... I look forward to seeing what textbook revision is in Dan Meyer's tweet today!  Are you participating in rewriting problems?

Textbook Revision Idea

I read with interest Dan Meyer's plan for Makeover Mondays this summer.

My workplace, curriculum, team ... they were all new this past year. I was surprised to learn that the Algebra teachers didn't use the textbook at all. I am not a fan of textbooks, but to not use them at all seemed drastic. After all, all resources have some value.  As it was we created almost all of our own materials.  Some were OK, maybe a tad better than the book and some were not.

So, I am taking Meyer's challenge to heart in an effort to create more worthwhile learning activities for my students. I am looking through the textbook that we don't use to find problems that could be revised and made useful in our curriculum.

Today I chose #24, from page 240, of Holt Algebra 1 published in 2007.

I chose this problem because we start the year studying functions and relations.  We do quite a bit of graphing, analyzing graphs, discussing domain, range, continuous, and discrete.

I also chose this problem because this last year while my family was reading "real food" blogs and working on maximizing nutrition, I noticed that my ninth graders ate a lot of junk food.  Now I don't propose to preach "real food" to them, but I thought it might be fun in the first week of school for everyone to bring their favorite snack food.  (I've heard that the way to man's heart is through his stomach and I'm wondering if this maxim will help me win the hearts of my 14-15 year olds!)  The only "rule" is that students must bring the snack in the original packaging so that we can use that packaging for math!  (I'll bring a few snacks myself so that we have plenty to work with).

I'll ask teams of students to chose 5 snacks to compare.  I'll ask students to create two graphs each illustrating the relationship between 2 elements of nutrition on the packaging.  First I'll ask students to examine the relationship between fat grams and fat calories as pictured in the textbook problem.  For the second graph students can choose any of the nutrition facts to compare.  I'll ask students to create a mini poster with their snack packaging and the graphs.  Then we will discuss if the elements of nutrition they compared represented functions or relations and why.

My specific goal in reworking this problem is to provide real data for students to analyze.  Additional side goals include enlisting their interest in math class and bringing attention to the nutritional value of the food they snack on.

PS ... during the summer I hope to find a really good article ... something short and on target for teens that discusses nutritional values as a bonus to this math activity.