Lesson Plan : Pythagoras Theorem

 Teacher Name: Janis and Luba Grade: Grade 7-8 Subject: Math

 Topic: Pythagoras Theorem Content: Problem of the snitch and its case. This will lead to the discussion of Pythagoras theorem. Goals: Define the Pythagoras Theorem Objectives: Solve (as much as possible) the snitch problem. Materials: Ball, cube and Sphere. A few sheets of graph paper. Rulers. My white board markers!!!!! Introduction: Begin by formulating the problem. Harry Potter wants to give Hermione the golden snitch (that has a diameter of 6 centimeters) as a present for her birthday. In order to do this he encases this snitch in a box, and then wishes to place this box in a decorative sphere. Question...What should the dimensions of the box around the snitch be? Also what should be the dimensions of the outer sphere? Development: How is the size of a sphere measured? (Diameter) What does this tell us about the cube? (All sides are equal to 6cm.) THE BIG ONE: What measurement is equal to the diameter of the outer sphere? (WE MUST GO SLOW! Get all of their answers until we get to am answer that leads to the "diagonal of the cube"). Can we draw this problem in a simplified two dimensional diagram? (Draw the diagram, explain that his is meant to simplify the problem so that it is easier to visualize, but ask WHAT POTETIAL PROBLEM CAN THIS IMAGE HAVE, IF SOMEBODY WERE TO TRY AND SOLVE THIS QUESTION BASED ON THIS IMAGE? the answer is that it doesn't show the diagonal of the cube). Let’s use the image that we have developed and see if it can help us get to our goal. Does the triangle have any particular distinct features? (Maybe to help them as what kind of a triangle this is, and what are the different sides of the triangle are? i.e. adjacent, opposite, and hypotenuse). What are the measurements of the adjacent and opposite? What is the measure of the hypotenuse? (Here direct their attention to the fact that solving the length of the hypotenuse leads to the solution of the diameter of the circle on the picture). Practice: PROBLEM: If they are familiar with the Pythagoras theorem we will have to skip to the next session, because they will get restless with this. If they are not familiar with the theorem then we can proceed with this practical section. We can ask the students to draw any kind of a right angel triangle, of a piece of paper (one for each group) and then ask them to measure sides a, b, c, a², b², c², and a²+b². Then display the results of each group. P.S. I SAY WE SKIP SECTION 1.3 AND GO STRAIGHT TO THE PROOF. Accommodations: Here each group will be provided with a large square of sides a+b and four smaller triangles of sides a, b, and c. And we will display the C squared formation. Checking For Understanding: How does this Pythagoras theorem help us in solving out initial problem? (Look for all kinds of answers). [If we are close to end of class then stop here, if we have a time left then solve the problem. BUT if we A LOT of time left then we need to after solving the problem, continue with the set up of the spider and fly problem] Closure: Good job! Evaluation: How far have we come along? How much still needs to be covered? Basically how is the pase working for us? Teacher Reflections: Is there anything that we feel that has been not clear in this discussion? Is there anything that we should come back to next class?