Big  idea (s)

What is/are your big ideas?

1.       The materials  such as spider silks, amyloid fibrils are mainly maintained by the atomic van  der Waals (VDW) interactions based on weak attractions and strong repulsions  between the atoms and atomic hydrogen bonds (HBs). The theory is same for  heavenly bodies in the Milky Way.

2.       Scientists and  engineers are constantly using theory about VDW and HB bonding to develop and  improve these materials/products in laboratories.

3.       Mathematicians  can also use theory about VDW and HB bonding to develop and improve these  materials/products by computations on computers.

4.       Why to choose  this topic is due to Year 2013 is the International Year of Maths of Planet  Earth that we were ordered to teach students mathematics linked with Planets.  

What are your (smaller) content points  for this lesson

1.       (CP1) A  precursor to getting at this is that all atoms attract each other by VDW  attraction forces and HB forces, but the strength of these attractions varies  a lot and that other forces of the VDW repulsions are also important.

2.       (CP2) Building  on Content Point 1, we are clear about the theory but we cannot see the tiny  atoms and the huge planets. However, we can see the balloons by eyes and we  can do experiments in class to show students how to feel these attraction  forces and repulsion forces. Our experiments using colourful balloons just  reflect the theory.

The  resources of colourful balloons are chose to support the learning, because  the balloons can effectively make students feel and then understand the  attraction forces and repulsion force so that know the nonlinear concave and  convex curves, and feel and find out nothing of attraction and repulsion  happens at the linking /minimal point.

3.       In this lesson  we will focus on the convex curve and the concave curve of repulsion force  and attraction force respectively, and the curves link at the minimal point  to form a non-linear function graph. In conclusion, at the end of the class  the students should understand this mathematical focus.

What are you doing with it: intended  learning outcomes/objectives

1.       The students  will be able to find out and feel the attraction forces and repulsion forces  through their own balloon experiences.

2.       The students  will be able to explain and well understand the mathematical graph of the  nonlinear Lennard-Jones function, and find out its minimal point of this  function.

3.       The students  will be able to explain widespread applications of the attraction forces and  repulsion forces in materials and in the Milky Way.

Generating  engagement

Affective engagement:

Can you generate this? How?

I am relying on an intriguing set of  balloon interaction experiments of students. They can easily find out the  repulsion forces by pushing two balloons together. They can easily find out  the attraction forces in the use of their hair or quickly moving balloons on  the carpet and then putting on the wall.

What student background do you expect?  How will you find out and use this?

They will have the concepts of a  ‘straight line’ and a ‘curve’, and can image the graphs of a ‘straight line’  and a ‘curve’, and know the graph of a ‘curve’ is not straight (not  ‘linear’).

I do not intend to tap into these  until after I have developed the concept of ‘non-linear’ of the Lennard-Jones  function. We will use the Lennard-Jones function to make students understand  the attraction forces and repulsion forces among planets in the Milky Way  (because Year 2013 was the International Year of Maths of Planets).

So how will you begin?

State content point CP1 (which I could  never develop from experiment anyway) to provide a focus for thinking and  interpreting observations. Push hard to balloons to each other, and ask what  they feel about the two balloons, students will be sure to feel there are  repulsion forces between the two balloons repulsing them to leave away each  other. Rubbing the two balloons on the hair (especially the long hair of  girls), the students will be sure to feel the attractive forces between the  hair and the balloon, and at this time putting the two balloons onto each  other they can find out the attraction forces between the two balloons. If  putting the balloons on the wall they can find out the attraction forces  between the balloon and the wall. They also can rub a balloon on the carpet and  then immediately put it onto the wall; thus easily find out the attraction  forces.

Cognitive engagement

What will be your tasks and why

Interpret their observations using CP1.

I always asked students questions and  communicated with them when they did balloon experiences by themselves.

What do you intend students will be  doing

See above.

Behavioural engagement: -what will be  your instructions?

Ensure they can all see and feel the  repulsion force and the attraction force.

During  the lesson: Feedback/communication/ongoing  evaluation

What will you be attending to as signs  of success

·          Students  engaged in attempting to interpret using CP1.

·          (Later)  students willing to offer and defend predictions about the behaviour of  balloons.

·          (Later again)  trying to link the idea of repulsion forces and attraction forces to the  forces between planets in the Milky Way, and between atoms in a small  molecule.

·          (At last) I  guide students to watch the graph of the ‘curve’, on left size of the minimal  point it is a convex curve and on the right side it is a concave curve. I  draw a straight line, a convex curve and concave curve on the board, the  students can easily understand the straight, the convex and the concave  concepts.

How will you know/find out if you are  achieving your goals?

·          When I asked  students “this is the case in 1-dimensional space, what are the plane, the  convex and the concave in 2-dimensional space looking like?” Students used  their small belly to illuminate me the plane, convex and concave concepts.  Some naughty students input the balloon into their shirts to show me the  concept of convex and said “I am pregnant” (I unintended to find out this learning  point). I found out I achieved my goals and furthermore I requested students  to image the things in 3-dimensional space, even 4-dimensional space  (time-space space). They were very active.

·          Students  continue to offer ideas. I told them we are living in the 11-dimensional  space and asked the students how to understand and image the nonlinear or  curve function/space in our 11-dimensional space. I used a narrow strip of  paper to make a multi-dimensional space to cause their interests to image.  Students can find out the ‘curve’ (or ‘non-linear’) in daily life.

·          Students can  find applications of the repulsion force and the attraction force in daily  life.

·          Some naughty  students said they found very weak attractive forces when they kicked the  balloon like a football. This should be an unintended learning opportunity.

What teaching moves will you make to  sustain engagement?

·          I will provide  hints if needed on the initial situation. Nonverbal communication strategies  will be used here.

·          Extend the thinking  by asking why there are big holes on the earth: it is the repulsion forces of  stones from other planet crashed onto the earth.

·          Some students  put a balloon into another one and then blew the gas and found out  interesting phenomena (this is an unintended learning from this class).

·          Introduce the  properties of spider silks and explain to students the repulsion forces and  the attraction forces of atoms in a molecule of spider silk: show the graph  of molecular structure of spider silk.

·          Introduce the Alzheimer’s  disease etc neurodegenerative diseases, and say when open the brain of these  diseases we can find the amyloid fibrils: show the molecular structure of  amyloid fibrils and, similarly as that of spider silks, to let students  understand the repulsion forces and the attraction forces in the amyloid  fibril molecular structure. Use CP1 to sum up as needed.

·          If time,  request students to find out more examples of the repulsion forces and the  attraction forces in the world and in daily life.

Debrief

I will ask for something they learnt,  how they understand the repulsion forces and the attraction forces, and their  graph in the sense of Lennard-Jones nonlinear curves to really make sure they  are really understand.

Post  lesson Evaluation

Were there unexpected successes

Some students may not directly  understand the nonlinear curve. I will use the balloons to make them be  interested in and find out the repulsion forces and the attraction forces,  and make them really feel the repulsion forces are very strong but the  attraction forces are weak, thus with ‘nonlinear’ curve. Some students may  not image how small in a molecule or how huge in a Milky Way – just make them  focus on the real balloons to feel and understand our lesson.

What could be improved?

We may also bring a spring with two  small balls linked at the both ends to show the repulsion forces and the  attraction forces.

Draw the non-linear curve the  Lennard-Jones (LJ) function and put more spirits to explain the curve is  non-linear, and consists of convex and concave parts.

Find YouTube movies of the LJ  nonlinear curve, or molecule movies and movies of planets to show students to  make them really watch and feel our theory is true, nothing but truth only.