Lesson Plan : Intro + Pythagoras

Teacher Name:
 Janis and Luba
 Grade 7-8

 Pythagoras Theorem
 Ball v. Sphere. Problem of dimensions (one-, two-, three-, dimensions). Harry Potter Problem. Ball & Shadow??? Simplifying complicated problems.
 Get to know the students. Introduce the Pythagoras Theorem.
 Create a familiar environment by introducing ourselves to the class and getting to know them. Introduction of the program, and basic concepts. For the future: Make students comfortable with the Pythagoras Theorem. Develop the student's ability to visualize geometric relationships, esp. in 3 dimensions. Better understanding of squares and square roots. Expose students to proof mathematics.
 To model Three dimensions, a water bottle (cup of water). Models of a Ball (Snitch), Cube (that hopefully fits the ball) and a Sphere. Mobius Strip (x3) + One that has not been constructed yet.
 1) Names (our names, students names) 2) Program (who we are...Ask if they have taken part in this program last year, and if they have then what did they like about it, and what they did not like about it) 3) How do they feel about math. Do they like it? (what do they like about it?) If not, then what is it that frustrates them about math? 4)Introduce the fact that the focus will be on Geometry. Remind them that regardless of their feelings towards mathematics this class is meant to be fun, there is no pressure or competition. There will be no TESTS. We do require them to be on good behavior but relaxed in the sense that they should learn as we go along just by listening and participating. We need then to cooperate because otherwise we will not be able to work effectively and they might loose the privilege of being in the class.
 Show them the Escher pictures (the final products as well as the patterns). Get them interested. Bring out the Ball/Sphere Ask, what is the difference between a ball and a sphere? (don't expect many answers, but ask for guesses. If somebody does get it right, still follow up with own explanation to make sure everyone got it). Dimensions: What does a person mean when they say one dimensional, or two dimensional? (one-dimension; only have length but no thickness, 'metal hangers'. Two-dimensional; have length and thickness, 'table tops'. Three dimensional; have length, thickness and depth, 'glass of water). Ball=Three-dimensional Sphere=Two-dimensional Practice I; Mobius Strip (two dimensional)
 I) Mobius Strip: Colour one side Cut the strip lengthwise Harry Potter Problem 1)How to measure the size of a sphere or a ball? (Diameter, two books on the opposite ends of the ball and measure the distance between the books). ---Should we discuss the ball/shadow?--- 2)what measurement of the cube is equal to the diameter of the snitch? (This will take a little while I think, and we need to use props. There is a suggestion pg. 8 to take several 'detours'...What kind of things might we want to ask?) 3) What measurement of the cube is equal to the diameter of the outer sphere? (Vertices, diagonal of the cube-diameter of outer sphere). DONE (for the day)
 NOTE: it is common in many mathematical problem solving to try and reduce the problem to something simpler. Finding a similar problem that is simple and straightforward will help you understand the more complicated problem. You will be able to apply the understanding of the simple problem to the complicated one and thus find the answer.
 See you next class. And try and recreate the Mobius Strip for your parents and ask them to colour in one side of it. This will drive them crazy:)
 How did it go? How much did we get done? Where did we have trouble? Did we loose the class at any point? Things to remember for next time? (1. recap last class)

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