Fourth and Fifth Graders Get Their First Problem

Now that Middle School students are well underway, Fourth and Fifth Graders will join in the I Love Math activities.  We will use puzzles and problems like this one to give them things to ponder.  We hope they will be drawn into the charm of mathematics so they persist over an extended period of time, and learn to be creative in their pursuit of a solution.

Along the way, we will ask them to consider what mathematicians do.  They will develop a list of things mathematicians do.  They will begin to see that they do these very things all the time.  That list will become a portfolio of strategies for them to try when they get stuck.  They really are already mathematicians.

Here is the problem they will receive in the next 48 hours:

Count the Squares

Look at this checkerboard.  How many squares do you see?

 

In one class, a student saw one square.

Another student saw 36 squares.

Another student said 37.

Another student saw more.

Explain what each student was seeing.

How many squares do you see?  Explain your answer completely.

Count the Squares for Sixth Grade

Here is the problem Sixth Graders will be working on for their third week of I Love Math problems.  Though seemingly simple, this confronts students with the need to "see" in creative ways.  Once they begin to see, they need to organize their thinking, and find efficient ways to count.  Along the way, they will have to look for patterns and test their predictions.

Join the fun.  How many squares do you see?  Please send your solutions to glawrence@mustardseedschool.org

Count the Squares

Look at this checkerboard.  How many squares do you see?

 

In one class, a student saw one square.

Another student saw 64 squares.

Another student said 65.

Another student saw more.

Explain what each student was seeing.

Problem Number 3 -- The Ant and the Crumb

Students in 7th and 8th grade are beginning their third problem.  It is about a hungry ant who is after a cookie crumb.  It is totally within the realm of Middle School mathematicians, yet seems very, very complicated.  Collaboration, creativity and persistence are essential.  Mustard Seed Students are learning these attributes in spades as they tackle problems like this one.  Try it at home.  Share it with your child and spend some time trying to see what "paths" seem profitable.

The Ant

and the Crumb

There was once a very large, rectangular room.  It contained only two things:  an ant and a cookie crumb.  The room had these dimensions:

It was 20 feet tall.

It was 38 feet long.

It was 10 feet wide.

The ant sat 1 foot above the floor in the middle of one of the small end walls.  The cookie crumb is stuck on the middle of the opposite wall, one foot below the ceiling.  The picture below will help you imagine how this looked.

The ant crawls to the crumb along the shortest possible path.  How far did the ant crawl?

 

Big hint:  The shortest path includes both the floor and the ceiling.  Hmmmm…….

Problem Number Two

Students have had a week to work on the Magic Trick problem, and they are doing amazing thinking.  Most students have made significant progress.  To do so, they have had to consider important mathematical issues like place value, the nature of multiplication, prime factorization and the idea that division "un-does" multiplication.

Here is the next problem that students in Grades 6 through 8 will be pondering.  I love this problem because it could not be stated more briefly or with fewer symbols.  Yet it is very sophisticated.  What is it asking?  How do I think about it?

As complicated as this problem appears, it can be solved by Middle School students.  It will require a healthy dose of common sense, creativity and persistence.

It will also require some thought about important math concepts:
What is a square root?
What does it mean to square something?
What does an equal sign mean? (Believe it or not, this is a very big idea for Middle School students to master.  It is an important step in their mathematical development.)
How do I deal with the infinite series?

Enough philosophy!  Here is the problem:

Solve This!

Solve For x:

Welcome to I Love Math 2014

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 try out a magic trick beginning with a three digit number.  If you know a middle school student at Mustard Seed, you should ask her to show you the trick.  It is very impressive!  You can read it below.

Please come back to this blog often over the next month or so.  We will post a new problem or two every week.  We will also share news about I Love Math Day.  Along the way, you will learn more about mathematics at Mustard Seed, and how we encourage students to find the beauty and joy of math.  You will also find helpful hints about how to help your child when he is stuck.  Mathematicians get stuck all the time, so we can learn from them.

Feel free to peruse older posts to see what went on last year as part of the school's I Love Math tradition.  You will see some of the creative solutions to problems students worked on in the past.  You will see other related topics that the school community was focused on last year.

Parents and school families are invited to work on all the I Love Math problems, and turn in a solution if they like.  Please email Mr. Lawrence with any solutions.  We give prizes for really extraordinary work!  Also please email Mr. Lawrence with any questions or comments (glawrence@mustardseedschool.org).

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A Magic Trick

Amaze Your Friends

Pick any three-digit number.

Then turn it into a six-digit number by writing it twice.  (For example, if your three-digit number is 289, your six-digit number is 289,289).

I don’t know what number you have created, but I think it is divisible by 13.  Am I right?  Check and see.

After you divide by 13, I bet the quotient is divisible by 11.  Check this out.

And I bet that quotient is not a prime number.  In fact, I bet it is divisible by 7.  Correct?

What do you notice about the result?  I found your original number, right?

Pick another three-digit number and repeat.  Does it work now?

What is going on here?  Will this always work?  Convince your friends that it will always work – or find an example where it doesn’t