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The Problem With Problem Solving

By Jessica Smith
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"How do mathematicians communicate their ideas to each other and to the public? If math is just numbers and symbols, how can we talk about math?"

 Understandings & Objectives


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Show video, Mathematical Eye: Logic and Problem Solving. Discuss key points of the film. Make connections between the film and math assignments.


 Preview the project using the Webquest page.


Strategy: Make a table

It’s a busy day at Rappo’s Batting Cage, where some of the Little League players come to practice their hitting.  Craig and Matt, two good friends, run into each other.  “How come I haven’t seen you here before?”  Craig asks Matt.  “Well, our coach brings us every 7 days,” Matt said.  “How about you?”  Craig told him that their coach brings his team every 4 days.  How many days will it be until the two friends see each other again at the batting cage?

Nathan is excited because today he gets to help his older brother, Tom, at the local fast food stop.  Tom is assembling hamburgers, and he tells Nathan to put an onion on every eighth hamburger on the grill, special sauce on every third hamburger, and a slice of cheese on every second hamburger.  Out of 100 hamburgers that Tom and Nathan assembled, how many will have all three items on them?

Strategy: Organized list

Lin-Chuan presses his face up against the glass tank at the tropical fish store.  There are three types of fish for sale: a bright pink Gourami ($1.20), the nearly invisible Glass fish ($1.80), and the Neon Tetra ($.60) that has an electric blue band.  Lin-Chuan steps back and counts his money; he has $6.00.  How many different combinations of colorful tropical fish can Lin-Chaun buy with his $6.00?

One evening the small, furry, people-like Weebles, Wobbles, and Widgets hurried about in their secret underground caverns.  One particular Widget named Wally wandered off too far, and fell in a ravine.  Weebles, Wobbles, and Widgets ran over and tried to think of a way to save poor Wally, but no one had a long enough rope.  Then Wendell Wobble had an idea:  If they formed a furry chain, holding on to each other, maybe they could reach down the 40 inches to Wally.  The Weebles were 12 inches high, the Wobbles were 8 inches high, and the Widgets were 4 inches high.  How many different combinations of the small creatures would reach 40 inches high?

Lena is helping her father empty the coins from the commercial washing machines he services.  Lena’s father lets her count the coins in the machine with the smallest amount of money.  The washing machines take only 50-cent pieces, quarters, and dimes.  If Lena counts $2.00 in coins, how many different combinations of coins could Lena have counted?

Strategy: Pictures/Object

Adriana and her mother are buying snacks for the family hike in the Green Mountains.  They are standing in front of two rows of three bins with clear plastic lids at the store.  The banana chips are above the malt balls and to the left of the trail mix.  The nuts and raisins are to the right of the carob chips and below the sunflower seeds.  How are the snacks arranged in the bins.

Frank lies awake in his bunk at the campground listening to the frogs croak.  Frank, his brother, and his two sisters are sleeping in the bunkbeds in the tent cabin.  The sisters and brothers from oldest to youngest are:  Mille, Frank, Stevie, and Irene.  Frank’s younger sister is in the bunk below Stevie’s older sister.  Frank and Stevie flipped a coin to see who would get the top bunk, and Frank Lost.  Where are the brothers and sisters sleeping in the cabin?

Strategy: Patterns

Each winter the elephant seals return to Ano Nuevo State Park on the California coast.  On the first day of their return, rangers count 5 elephant seals lying on the beach.  On the second day, 6 more seals arrive.  On the third day, 7 more seals arrive.  Each day the number of seals that arrive increases by one more than the number of seals that arrive the day before.  At this rate, how many seals will be on the beach at the end of the eighth day?

Robia’s favorite part of the new indoor mall is the beautiful brass and glass sculpture between the two escalators in the center of the mall.  Robia likes to ride up one escalator and down the other and look at the sculpture, as it rotates in the light.  The top part of the sculpture is one brass and glass cube.  The second part of the sculpture has eight cubes.  The third part has 27 cubes.  The fourth part has 64 cubes.  If the parts keep increasing in the same way, how many cubes are in the sixth and bottom part of the sculpture?

Strategy: Guess and Check

Sue, Peggy, Maggie, and Arlene all collect comic books.  Sue collects Superfrog, Peggy collects The Incredible Hulk, and Maggie and Arlene both collect Totally Awesome Wonder Woman.  Sue has collected twice as many comic books as Peggy; Maggie has collected three times as many comic books as Peggy, and Arlene has collected two less than three times as many comic books as Peggy.  The four friends together have collected 97 comic books.  How many comic books does each friend have?

Jarrod and Malcom are at the mini-market once again.  “Good Mornin,” said the manager, “this is the sixth day in a row you’ve been here!”  Jarrod and Malcom have been earning money by collecting cans and bottles, and turning them in at the store.  There is a 5-cent refund on cans and a 10-cent refund on bottles.  In two months they collected 450 cans and bottles altogether and received $32.50.  How many cans and how many bottles did they collect?

Technology Skills

After students have demonstrated mastery on the problem solving strategies, there are a series of technology lessons geared toward the final iMovie product.  The three software programs utilized are  MS Word, iPhoto, and iMovie.

In Word, students create one-page documents that are saved as pdfs into the iPhoto library.  For this task they must transfer their paper and pencil work into a word-processed format.  This requires instruction in changing page margins, font size, highlighting, and the use of tables.  Specific skills are modeled via the computer projector and students working on the same problem collaborate and help each other.

In iPhoto, students create an album entitled problem solving.  All of the pdfs are stored in that album for later use in the iMovie media drawer.

An iMovie sample is shown several times in order to emphasize the purpose and audience of the final product.  A brief overview of iMovie is given and then students use the subscription based Atomiclearning.com tutorial series to learn about the different features of iMovie.

Students work together to edit their movies, revise their scripts, and polish the final product.  In addition to the software skills, students draw upon past experience using laptop computers, and the school server.  A solid understanding of keyboard shortcuts, and desktop navigation is helpful for this project.

Atomic Learning

Website of student work