Light Bulbs Go On (and Off)

Here is the latest problem that Mustard Seed School students in Grades 6 - 8 are working on.  We hope you enjoy it.  Please feel free to send solutions, questions and comments to Mr. Lawrence at glawrence@mustardseedschool.org.

Be sure to look at the next post to see who our visiting mathematicians will be on I Love Math Day.

Enjoy!

This problem comes from More Thought Provokers by Doug Rohrer and Joe Spooner, 1994, Key Curriculum Press.

Distinguished Mathematicians Coming to MSS

As February 14 approaches, we are preparing for the visit of two exciting mathematicians:

Amy Ackerberg-Hastings is an Associate Adjunct Professor of History at the University of Maryland University College.  She specializes in the history of mathematics and mathematics education, as well as women in science.  She was co-author of Tools of American Mathematics Teaching, 1800-2000.  She works for the Smithsonian, cataloguing mathematical instruments for their website.  You can see an example of her work at this link Smithsonian Math Instruments   She will also share from the Smithsonian collection of paintings by Crockett Johnson, who you may know as the author of Harold and the Purple Crayon.  In addition to writing children's books, he was a mathematician and a painter of mathematically-inspired artwork.  See the link at Crockett Johnson Math Paintings   Dr. Ackerberg-Hastings earned her PhD at Iowa State University in 2000.

Gordon Gault has been a math educator for his entire adult career.  He has taught at the college, high school and middle school levels.  He is traveling all the way from Chicago to celebrate I Love Math Day with us.  Mr. Gault's passion is geometry, specializing in visual and spacial relationships.   Paper folding, mirror applications, kaleidoscopes, and Platonic and Archimedean solids hold particular interest for him, and he will share his thinking and his insights with us.  Mr. Gault spent two summers in Utah at a National Science Foundation summer geometry institute.  Like Dr. Ackerberg-Hastings, Mr. Gault loves mathematically-related art.  He will be wearing a tie bearing an Escher tessellation, and he will bring examples of primitive kaleidoscopes.  Mr. Gault is the grandfather of Titus (Grade 4) and Naomi (Grade 1 Moon) Cooke.

Both of these distinguished guests will spend the day visiting classes, sharing their expertise and their passions, answering questions from the students, and celebrating the excellent work students at all grade levels are doing in mathematics at Mustard Seed School.  We all love math!

Fourth and Fifth Grades Join The Fun

Today, the Fourth and Fifth Grades were given their first I Love Math problem for 2013.  Our hope is that these students will enjoy working on a couple of challenging problems that require some persistence and creativity.

Below, you can see the problem they were given today.  We hope it will inspire them to do many of the things mathematicians do when working through a puzzle.  We hope students will:

             ask lots of questions
             clarify the problem
             restate the problem in their own words
             talk to friends
             talk to parents
             talk to teachers
             draw pictures
             organize information
             look for patterns
             make guesses
             test guesses
             make better guesses
             make mistakes
             think
             count

These are all things mathematicians do.  Mathematicians especially do these things when they are stuck.  Being stuck from time to time is very common in math.  We hope that students will be creative and persistent when they are stuck.  Look at all the things they can do to get unstuck!  When students do these things, they are mathematicians too.

Here is the problem that Fourth and Fifth Graders were given today.  If you have a child in these grades, talk to them and enjoy pondering it together.  You can email Mr. Lawrence at glawrence@mustardseedschool.org if you want to share a solution, ask a question, or make a comment.

A Rabbit’s Sad Story

(but with a happy ending)

A rabbit falls into a dry well 30 meters deep*.  Since being at the bottom of a well was not her original plan, she decides to climb out. 

When she attempts to do so she finds that after going up 3 meters, (and this is the sad part) she slips back 2. 

Frustrated, she stops where she is for the first day and resumes her efforts the following morning – with the same result.   She repeats the pattern each day.

How many days does it take her to get out of the well?

* The well is actually 29.6 meters deep, but we are rounding.  You remember how to round to the nearest whole number, right?  You look at the tenths place, and if that digit is 5 or over……………..  and so on.  You know the rule.

Welcome Back! The Bridges Problem

Welcome back!  Today we are posting the second problem that Middle School students are working on to prepare for I Love Math Day.  This problem is a classic. It involves the map of a lovely old European city. Mathematicians reading this may notice that the name of the city has been disguised.

This problem would appear to be oddly specific.  It seems to lack broad applicability to other problems.  It is, after all, a problem for a specific city with a specific configuration of bridges in the 1700's.

Surprise!  This problem and its solution gave birth to the whole field of topology.  Solving this problem will help students learn to deal with many problems that seem quite different, but which share some essential characteristics.

As always, please feel free to email Mr. Lawrence with questions or comments.   We are always happy to hear your thinking on these problems.  You can email Mr. Lawrence at glawrence@mustardseedschool.org.

  

Welcome to I Love Math 2013

Welcome to I Love Math 2013

Welcome!  I Love Math Day is coming up on February 14.   In the weeks between now and then, Middle School students will work in small teams to solve challenging problems.  They will be given one week to solve each problem and prepare a solution to submit to the judges.

By way of this blog we encourage all school families to read the problems and join in the fun.  We hope parents and students at all grades will find ways to talk about these problems, puzzle over them, and enjoy the pursuit together.  The first problem for this year asks students to recognize and ponder patterns that emerge when specific strings of numbers are added together.  You can read the problem below.

Feel free to peruse older posts to see what went on last year as part of Mustard Seed School's I Love Math tradition.  You will see some of the creative solutions to problems students worked on last year.

The problems will be made available to the school community with a small lag.  Middle School students have already begun their work and will be turning in their submissions shortly.  Parents and school families are invited to work on these problem too, and turn in a solution if they like.  Please email Mr. Lawrence with any solutions.  Also please email Mr. Lawrence with any questions or comments (glawrence@mustardseedschool.org).

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The Sums of

Sequential Numbers

When you add up sequential numbers, something interesting seems to happen:

1 = 1   

1 + 2 + 1 = 4 

1 + 2 + 3 + 2 + 1 = 9

1 + 2 + 3 + 4 + 3 + 2 + 1 =  ________    (you do the math)

1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = ________    (well?)

Check 3 or 4 more.   Can you predict each sum in advance?

Go ahead and do the sums.

What do you notice?  Make as many observations as you can.

For a sequence like this, what will the sum always be?  Will it always be a square number?  Find a way to show that it will always work (in other words, find a way to convince a skeptic.)

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I look forward to hearing from you!  Enjoy.  Mr. Lawrence