Holly's Four Lessons that Started NumberFix

Lesson:
Exploring Patterns & Writing Word Problems

Overview: Students write and illustrate their own book of patterns, similar to how Greg Tang describes different ways to examine common problems in The Grapes Of Math. This lesson can be used with any content, but the focus is having students make formulas understandable for themselves. They will be examining what patterns they notice and snappy ways to remember difficult topics.

Lesson:
How Big
is Hagrid?

Overview: Using knowledge of what makes good persuasive writing, students will critically read a section of Harry Potter and the Sorcerer's Stone, and then use mathematics and the evidence from the reading to decide on the size of the character Hagrid. Students create a life size cut-out of Hagrid, writing their explanation of work according to the state ideas and development portion of the writing rubric.

Lesson:
Useful
Shapes

Overview: After guiding primary-aged students through an exercise on giving reasons for something being useful, students listen to The Greedy Triangle by Marilyn Burns and determine how triangles and quadrilaterals are useful. Students make books that show where the shapes occur in the world.

Lesson:
Summarizing with The Important Book

Overview: By imitating the format of The Important Book, students will write create an illustrated paragraph on a particular math topic. Extension: Students use the important book format to brainstorm previous knowledge on a topic and knowledge after learning a topic. Students create pages similar to those in The Important Book comparing their knowledge before and after learning a topic.

Reading, Writing & Reflecting Mathematics
from Holly Young, NumberFix Coordinator

Teaching students the fine art of problem-solving can be incredibly difficult!  This issue has really come to the forefront lately with the onset of constructed response problems in math and science.  I have found that text-books and "programs" teach problem-solving in a linear fashion, such as, first do this, then do this, etc, until you magically arrive at the answer.  

Unfortunately, step one - highlight important information - usually is the step none of the students can get past.  Instead of following a linear/sequential problem-solving formula, I designed a cyclical process of reading, writing, discussing, and reflecting on problems.  As most brain research reports, humans solve problems in many different ways and enter problems at many different points.  If a teacher uses the reading, writing, and reflecting posters as questions that help students enter problems and provide direction for solving problems, then students have an easier time discussing and writing about their solutions and methods for solving.  Any question provided on the three posters can be an "exit ticket" to check for student understanding  or can be used as a discussion point in a group or as a class.  (Not every question given on the posters can be answered for every problem)  The format for these posters, "ACE," mirrors/extends my instruction used in teaching students how to answer constructed response questions (see the constructed response link).

I also designed a graphic organizer that can be handed out to the students when a new problem is tackled.  As a class, it can be decided which questions need to be answered or discussed on the graphic organizer.

As with all good writing, students need direction.  This strategy can get students to plan their problem writing, write with a purpose, and reflect upon their thinking.

You can find out much more about Holly's ACE Constructed Response materials at her website: Making Mathematicians.

Idea Development

• Rubric
• Post-It Checklist

Organization

• Rubric
• Post-It Checklist

• Ideas for leads and introductions for math writing

Voice

• Rubric
• Post-It Checklist

Conventions

• Rubric
• Post-It Checklist

Build a R.A.F.T.S. Writing Assignment for Math Class
an interactive prompt from the Writing Across the Curriculum Guide

Our Digital Contest's Annual Theme: A picture can raise mathematical questions—or images that would inspire a student to write a word problem to be solved by a classmate!

Great pictures can generate some very interesting ideas for word problems! In 2009, we sponsored our first ever digital photo/math problem contest. We opened up the contest to elementary, middle, and high school students. Students could choose the rigor and topic area for their designed word problems, but the photos had to be original photos taken by the student and the problem was one of his/her own making. Our 2009 submissions had everything from the Pythagorean Theorem to ratios and proportions. This just proves to us that math can be found everywhere!

Our 2009 Contest Winner was Caitlin O., a student from Wooster High School, who won a $50 gift card from Amazon.com for submitting the photo and the word problem you see above. If you click on the image, you can view it larger, or you can print it on an overhead to show your students. Challenge them to write different problems using the same photo. Challenge them to solve each other's problems! .

We are really looking forward to having our contest run again in the Spring of 2010, so get those students working on the assignment early! You can e-mail your students' entries to Holly at HYoung@washoe.k12.nv.us. E-mails must come from teachers, not directly from student photographers.

Below, find some of the honorable mentions from our 2009 Photography Contest.

• Austin M. submitted a word problem and a picture that required fellow students to show their knowledge of geometric shapes.
• Awatef A. submitted a word problem and a picture that required fellow students to link a tossed volleyball and a triangle segment.
• Blake B. submitted a word problem and a picture that required fellow students to determine the missing number on a football jersey.
• Catherine A. submitted a logic problem and a picture that required fellow students to determine which student doing handstands is which.
• Jose V. submitted a word problem and a picture that required fellow students to determine how far a player is away from a thrown football.
• Lily N. submitted a word problem and a picture that required fellow students to solve a problem about the angle of a puppy's legs.
• Lucia S. submitted a word problem and a picture that required fellow students to solve a problem about two months' worth of dog walks.
• Marcus L. submitted a word problem and a picture that required fellow students to determine the area of a baseball field's infield.
• Matt B. submitted a word problem and a picture that required fellow students to solve a problem about a baseball stadium.
• Sam L. submitted a problem about determining the length of a segment within an imaginary circle.
• Tiffany G. submitted a word problem and picture that required fellow students to figure out admission costs to a talent show.

Want to Build a R.A.F.T. Prompt for Math Class?
Click here to access our interactive Math R.A.F.T. Builder.

Not sure what a R.A.F.T. is?
Click here to learn about R.A.F.T. writing assignments for the classroom.

Here's a simple writing across the curriculum project for math class: assign alphabet books on math topics for small groups to complete.

Start by sharing a published alphabet book that bases its content on vocabulary words; most of author Jerry Palotta's alphabet books do this, but our favorite one is The Skull Alphabet Book (pictured at right).

Next have the groups brainstorm words, inspired by a math topic, on this alphabox worksheet. Some great math topics for ABC books are: math vocabulary words; jobs/people that require math skills; great mathematicians; etc.

Give students groups a limited amount of time to create and publish their alphabet books. Each group shares their book, and the teacher gets to keep them!

On our Alphabet Books across the Curriculum Project Page, you can see two really cool examples of math alphabet books made by teachers.

Here's a great way to write weekly in your math class about problem-solving, to celebrate best writing efforts once a month, then to celebrate best work for the entire year by creating a "museum" of creatively published best problems and their solutions.

Click here to access Holly Young's write-up for this project for your secondary math class.

Three Music-inspired Math Lessons Featured at NumberFix

Lesson 1:
Linear & Exponential
Growth Poetry

Overview: Students choose numbers and units of measurements, and then create short poems that compare and contrast exponential (or multiplied) and linear growth. This lesson is inspired by several Schoolhouse rock songs as well as other videos that help students explore numerical growth.

Lesson 2:
Itsy-Bitsy
Math Songs

Overview: Students write instructions for math procedures that can be sung to the tunes of familiar nursery rhymes or songs. Working first in small groups, then as individuals, this activity helps students put ideas from notes into individual words.

Lesson 3:
Dancing with the
Math Stars!

Overview: Using disco music and the inspiration of TV's "Dancing with the Stars," students imagine that--instead of celebrities--different numbers and equations compete on the television show. Students write the biographies of equations and graphs that are dancing on a television show where math-inspired dancers compete against each other.

Lesson:
Follow the Path of Five Dollars

Overview: Pat Brisson’s book Benny’s Pennies provides the impetus for students to discover some reasonable ways to spend a set amount of money following specific criteria. After the students decide how to spend their money, they then must show the path of the spending.

During the 2009-2010 school year, specially invited teachers will be asked to create new NumberFix lessons, which will be posted in these spaces.

Check back with us soon! Watch NumberFix grow!