Baruch Step Bridges 2013

Marshmallows make awesome tools for math instruction!

A catapult is a device used to throw or hurl a projectile a great distance without the aid of explosive devices—particularly various types of ancient and medieval siege engines.  Although the catapult has been used since ancient times, it has proven to be one of the most effective mechanisms during warfare. The word ‘Catapult’ comes from the two Greek words “kata” (downward) and “pultos” (a small circular battle shield).  Katapultos was then taken to mean “shield piercer”.

There are many types of Catapults. In modern times, the word catapult can be used to describe any machine that hurls a projectile. This can include a slingshot used to hurl pebbles, a machine that launches airplanes off aircraft carriers, and of course, the ancient weapons of smash destruction!

Gravity² + (distance) x (time)

Remember from algebra that the equation of a parabola is y = ax² + bx + c.  Also remember that when we handle these trinomials you were able to factor them to find the two binomials that when multiplied were equal to the expression. Lets’ use the value of -5t² to represent the constant pull of gravity on our marshmallow.   Now we need to determine how long the marshmallow was hurling through the air.

One of the advantages of having so many catapults in one place is all the data that becomes available to us.  So the first part of our equation is -5t².  Now we need to determine how long the marshmallow was hurling through the air.   The average time in the air was 3 seconds and the average distance was 35 feet.  If we look at the class data we can throw away the outliers and focus on the mean and median of the data.  Using these numbers the average quadratic we can find is -5t² + 17t.

How do we use this information?  When we used the catapults for target practice we instinctively  knew that we had to move closer or farther from the target.  The starting point and the target became the roots of the quadratic equation!

Day two and three of the first week were spent building catapults!  Catapults are medieval siege machines.  They were developed to penetrate the strongest defenses at the time.  Catapults came in a variety of shapes sizes and designs.  The ones that we worked on in class employ several principles that we will use for constructing our bridges later this Summer.

One of the main concepts in the catapult is that we are actually creating a parabola!  Wait a minute?!  More math?!?

Well just a little to explain what happened.  The parabola that we use is of course based on the quadratic equations that we all used way back in Algebra I.  They describe what happens when gravity is applied to a moving object.  The quadratic -16t(squared) is the secret to all things falling from the sky.  Take into account the force of the arm on the catapult, factor in the time it travels and distance to find the second root or point of impact.  Whew, made it.

OK, now what happens in regular talk is the marshmallow flies through the air and hits a target!  That’s where the individual decision making comes in.  Each of the builders make adjustments in their designs to improve accuracy, distance and overall awesomeness of their catapult.

Let the hurling of marshmallows commence!

Welcome to our first week at Baruch Step for the Summer of 2013!  I am really looking forward to getting to know all of you over the month of July.  I think we are off to a good start so far.  We have a classroom full of some very bright and interesting students.

Today we spent time getting to know each other and taking care of all the small details.  There are bound to be a few small glitches over the next few days so just be patient.  Remember it’s Summer so lets have fun.

We started off by interviewing each other and finding out more about our class mates for the Summer.

Our first task was to construct the tallest building.  Our only supplies were 100 index cards. And the rules, well there were none!  Students were split into five groups and got to work.

The winning team was treated to fresh made ices at Ralph’s!  Mr Tobias helped himself to Black Cherry Vanilla.