Category: Juggling

Grade 6 Science of Circus (Physics) Lesson Plans

11/19/2015

I've had an incredible experience this semester with my Science class. I've developed a full physics unit on Newton's Laws of Motion, using Circus activities to hook, demonstrate and integrate the concepts. I can't wait to teach them!! I now have an integrated 10 lesson unit plan that is fun, engaging, active, and adaptable to younger or older grades. Most importantly, I LOVE what I'm learning!!

The Science of Circus

I now have the following Physics lesson plans in my teaching arsenal:

Juggling Gravity
Keeping it in Balance: Centre of Gravity
Walking the Line: Balance
What goes around comes around: Angular Momentum
Jump Around: Potential, Kinetic, and Elastic Energy
Slinky Physics: Energy Transfer
Having a Ball with Newton’s First Law
Swinging To and Fro: Pendulum Motion
Falling with Style- Gravity, Friction, Air Resistance
What’s that Sound? Sound Waves/ Doppler Effect/ Sound Barrier

I've posted the first lesson plan, Juggling Gravity, on my educational Blog. The rest are available to teachers and education students by request. Contact me for more details!

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Juggling Gravity

11/19/2015

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Juggling Gravity

Lesson Plan (adaptable)
Teacher: Mz.K
Date: 07/Nov/2015
Overview & Purpose
Juggling has always fascinated me.
After the challenge of learning to keep three balls in the air I wanted to do whatever I could to be a better juggler. In doing so I discovered how mathematics and physics applied to the juggling techniques I was learning. The goal of this lesson is to use juggling to illustrate some basic principles of Gravity to students, then provide a context for discussion afterwards.
BC Education Standards (Grade 6)
Core Competencies:

Communication
Thinking
Personal/Social

Big Ideas:

Newton’s three laws of motion describe the relationship between force and motion.
Balanced and Unbalanced Forces
Force of Gravity

Curricular Competencies

Questioning and Predicting
Planning and Conducting
Processing and Analyzing data and information
Evaluating
Applying and Innovating
Communicating

LEARNING INTENTION/HOOK

I have a basic understanding of the force of Gravity
I know what a parabola is and can draw one.
I can practice my juggling skills.

Materials Needed

Juggling balls
Handouts

Classroom Lecture (5 mins)

“What goes up must come down…”

Gravity is the force that pulls everything back down to earth. Gravity also keeps the moon going around the earth and the earth going around the sun. Luckily for jugglers (and rocket scientists), the force is always the same and predictable.
In simple terms, this means that if you drop an object, it will continue to speed up as it falls. Not only that, it will speed up at the same rate, no matter how big or heavy the object is.
Also, if you throw an object up, it will slow down at the same rate. That means it takes just as much time going up, as does to come back down to where it started.
Of course you hardly ever throw something exactly straight up. Most objects travel through the air going across as well as up and down. The curved path is a shape called a parabola. A common place to see a parabola is the path water takes flowing from a water fountain. The shape of a juggling throw is a parabola.
Draw parabola on the board.
Key terms:

Gravity: the force that attracts a body toward the center of the earth, or toward any other physical body having mass.
Parabola: a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

Activity (15 mins)Break out the juggling balls or scarves. Progress and scaffold with the children at their level towards a 3 ball cascade. Remind them to think about the Gravity and other forces that are being exerted on the balls.
Questions to be answered:
What is the difference between a heavier ball and a lighter ball? Do you think they fall at the same or a different rate?
With your partner, define Gravity, and draw a parabola. Design an experiment to test your hypothesis to the above questions. Record your results and share your finding with the class.
Summation (5 mins): Review concepts presented. Facilitate a discussion about their findings.
Verification
Steps to check for student understanding

I understand Gravity and can write the definition down.
I can draw a parabola on my paper.
I can practice my juggling skills.

Sources:
http://www.scienceofjuggling.com/studyguide.html

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Mathematical Patterns in Juggling

11/11/2015

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Math is Beautiful part 3

Mathematics of Juggling

MATH IS BEAUTIFUL: Mathematical Patterns in Juggling
A basic primer for learning Siteswap

Juggling has been defined as manipulation of more objects than there are hands. I've also heard it described as just learning to drop things in more and more complicated ways. The classic definition involves balls moving through the air, with the standard 3 ball cascade involving one ball in the air, and a ball in each hand.

Balls are thrown one at a time alternating which hand does the throwing: first
one hand and then the other. Right, Left, Right, Left, Right, Left...

The basic 3 ball pattern doesn’t take long to figure out – every time a ball is close to landing in a hand you throw another one up to replace it. Timing is also important; a given ball spends about half of its time in the air and the other half in one of the hands. This movement pattern (the 3 ball cascade) can be adapted to produce more interesting patterns by varying each ball's height and timing.

3 ball cascade - the basic juggling pattern

As with all patterns, these movements can be expressed mathematically.However, it was not until 1985 that a model for juggling heights was developed by Bruce Teimann. Prior to this jugglers described the height of the throws either by the estimation of distance (2 feet) or by even looser terms such as "a bit higher".

The mathematical model, called Siteswap, uses numbers to represent the time between a ball being caught, thrown, and caught again. Siteswap denotes time in between throws, and this time can be broken down into beats. The numbers in siteswap represent the number of rhythmic beats until a ball is thrown again. The larger the number the higher the throw as it will take longer for a ball to complete it's parabola (more beats).

Some common three ball patterns are represented by the siteswaps 3, 441, 531, 6316131, 52512. Some common four ball patterns are 4, 741, 534, 6451, 7441, 7531.

Because the patterns repeat, we just write all the numbers once. Instead of 3333333333333, we can simply say "3" and know to repeat it. Instead of 423334233342333, we just write 42333 as the pattern's name.

441

534

Fun Math Fact of siteswap is that the average throw must be equal to the number of balls being juggled. This allows for us to figure out how many balls are being thrown in any given pattern. For example:

441 is 4+4+1= 9 /3 (3 numbers) = 3 ball pattern.
6316131 is 6+3+1+6+1+3+1= 21/7=3 ball pattern
534 is 5+3+4= 12/3= 4 ball pattern

This simple math can be used to engage children as a mathematical 'trick' that can be demonstrated in practice by a juggling teacher of moderate skill or by a siteswap pattern generator online. Children may have fun with a pattern generator online trying different combinations of numbers to make different juggling patterns. Juggle clown juggle!

http://jugglinglab.sourceforge.net/

Siteswap gets more complicated the further down the rabbit hole you go. Juggling mathematicians have been calculating siteswaps and mapping patterns in ever-increasing complexity since it's creation in the 80's. However the scope of this blog is to demonstrate not only my own rudimentary learning on the subject but to explore some ways I could integrate Math into my circus teaching practice. Children who are learning juggling may be more motivated to explore the mathematical representation of the patterns they are creating beyond 3 ball cascade. The availability of online pattern generators allows for them to play with patterns in theory that may be beyond their ability to juggle in practice. Many incredible patterns come only from the direct study of the math behind juggling. The ability to think about patterns in mathematical terms allows us to link numbers with our own artistic expression and to realize that math is, in fact, beautiful.

Kat of Vesta Entertainment Juggling on Lantzville beach at Sunset

Many thanks to Katlan Irvine of Vesta Entertainment for the hours of conversation, demonstration, and laughter in the creation of this 3 blog series, Math is Beautiful.

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Grade 6 Science of Circus (Physics) Lesson Plans

The Science of Circus

Juggling Gravity

Juggling Gravity

Mathematical Patterns in Juggling

Math is Beautiful part 3

Karina Strong

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