Pythgors Theorem S Topic 1 Level: Key Stge 3 Dimension: Mesures, Shpe nd Spce Module: Lerning Geometry through Deductive Approch Unit: Pythgors Theorem Student ility: Averge Content Ojectives: After completing the ctivity, students will gin experience of informlly proving Pythgors Theorem Lnguge Ojectives: After completing the ctivity, students should e le to understnd English terms relted to the topic (e.g., squre, squre root, Pythgors Theorem, right-ngled tringle, hypotenuse, proof (n), prove (v), nd the converse of); use the key terms to stte Pythgors Theorem (e.g., In right-ngled tringle, the sum of the squres of the length of the two legs is equl to the squre of the length of the hypotenuse); use the key terms to stte the Converse of Pythgors Theorem (e.g., If the lengths of the three sides of tringle ABC stisfy c, this tringle is right-ngled tringle.); nd follow English instructions on solving prolems concerning this topic nd work on relted prolems written in English. Mteril required: Grph pper, pper, scissors nd rulers Prerequisite knowledge: Students should hve studied the concept of Pythgors Theorem in Chinese nd prctised the relted clcultions. Time: lessons ( x 40 minutes) S Topic 1: Pythgors Theorem 1
Procedure: Lesson 1: 1. The techer should tech students the mening of the relevnt mthemticl terms (shown t the top of the worksheet), demonstrting the pronuncition of the terms in English.. Assuming tht students hve lernt the concept of Pythgors Theorem in Chinese, students should then e guided to explin the theorem in English. 3. The techer should sk students to form groups of 4-5 nd complete proof 1. Then, the techer cn sk the students to present their findings. Lesson : 1. The techer should sk students to cut 4 identicl right-ngled tringles (using the grph pper) nd use those figures to explin Pythgors Theorem.. Students should e redy to explin their proof to other clssmtes using the terms they lerned in the previous lesson. 3. Students should e given time to prepre the presenttion with their group-mtes eforehnd. Explntory Notes for Techers: 1. The im of this teching mteril is to give students the opportunity to hve hnds-on experience of mthemticl proof nd to prctise their presenttion skills relted to the topic of Pythgors Theorem. It is therefore expected tht the lesson will e conducted fter the study of the topic through the medium of Chinese.. The techer should sk students to work in group (4-5 students) for the hnd-on experience of cutting the ppers, discussing the possile proofs nd prepring for the presenttion (Activity, proof 1). In this cse, students collorte to ssign tsks within their groups nd help ech other to work out the proof. S Topic 1: Pythgors Theorem
3. In proof 1, the sizes of the squres cn e different for different groups. Thus, the techer cn explin to students tht this theorem cn work for ny size of tringle. For the sme reson, the identicl tringles cn lso e of ny size. 4. Students cn prctise delivering the presenttion efore they re ctully clled on to do so in front of the clss. They cn lso prepre, for exmple, y writing notes first. This will help them overcome ny fer they my hve of speking English in front of group. 5. The techer should provide support to groups if they hve ny difficulties. 6. It is importnt tht the techer should e flexile in djusting the teching schedule to suit the needs of students. The techer cn rrnge single lessons or doule lesson for this. Students could finish ll the prts (i.e. thinking, discussion nd presenttion) during the lesson time. On the other hnd, the techer cn sk students to try out proof t home s homework nd then present it during the second lesson. However, for doule lesson, students my not hve time to try out proof nd write down the presenttion eforehnd. In this cse, the techer hs to provide more time for group discussion. Moreover, depending on the ility of the students, the techer cn sk them to hnd in individul ssignments of proof (nd skip the second presenttion). S Topic 1: Pythgors Theorem 3
Secondry Extended Lerning Activities for Mthemtics Pythgors Theorem Nme: Clss: ( ) ACTIVITY 1: Revisiting Pythgors Theorem Voculry: Squre 平方 Squre root 平方根 Pythgors Theorem 畢氏定理 Hypotenuse 斜邊 Proof(n) / prove (v) 証明 Converse 逆 Write down Pythgors Theorem (using symols): B c Complete the following description of Pythgors Theorem: C A In tringle, the sum of the of the two legs is equl to the of the. Write down the converse of Pythgors Theorem (using symols): Complete the following description of the converse of Pythgors Theorem: If the of the three sides of tringle ABC stisfy, this tringle is. S Topic 1: Pythgors Theorem 4
ACTIVITY : Proof Proof 1 1. On the grph pper provided, drw two squres of different sizes next to ech other (Fig. 1).. As shown in Fig., find the point on the se of the lrge squre the distnce of which from the left of the lrge squre is equl to the length of the smll squre. 3. Join the lines s shown in Fig.. 4. Cut the figure into three prts, I, II nd III. (Fig. 3) 5. Try to form squre using the three prts. 6. Stick the squre formed on the pper provided. 7. Lel the sides of the squres nd tringles. Fig. 1 Fig. III I II Fig. 3 S Topic 1: Pythgors Theorem 5
8. Explin how you cn use the res of the squres to prove Pythgors Theorem: Proof 1. Drw 4 identicl right-ngled tringles on the grph pper (they cn e of ny size).. Cut them out nd then lel the sides, nd c s shown. c 3. Try to form one squre using these 4 tringles. 4. Stick the squre formed onto the pper provided. 5. Explin how you cn use the squres to prove Pythgors Theorem: S Topic 1: Pythgors Theorem 6
Suggested nswers for techer: Activity 1 Write down Pythgors Theorem: or In ABC, C =90 c or In ABC, C =90 AB AC BC Complete the following description of Pythgors Theorem: In right-ngled tringle, the sum of the squres of the two legs is equl to the squre of the hypotenuse. B Write down the converse of Pythgors Theorem: c If c, then C =90 Complete the following description of the Converse of Pythgors Theorem: If the lengths of the three sides of tringle ABC stisfy right-ngled t C. C c, the tringle is A Activity Proof 1 Step 1: Construct two squres with sides nd, respectively, plced side y side. The totl re of the two squres is +. S Topic 1: Pythgors Theorem 7
Step : Drw lines with the sme length s follows: Step 3: cut the tringles out nd then rotte them to form squre. - Techer shows tht: the re of the resulting squre would e c Thus, it shows tht + =c Proof : Possile outcome 1: c = ( ) + = + + = + Possile outcome : ( + ) = 4 + c + + = + c + = c Reference: www.cut-the-knot.org/pythgors/index.shtml S Topic 1: Pythgors Theorem 8
Grph pper S Topic 1: Pythgors Theorem 9