QR Challenge: DISPROOF BY COUNTER EXAMPLE

Created using the ClassTools QR Treasure Hunt Generator

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Teacher Notes

A. Prior to the lesson:

1. Arrange students into groups. Each group needs at least ONE person who has a mobile device.

2. If their phone camera doesn't automatically detect and decode QR codes, ask students to

Download a QR reader (e.g. I-Nigma | NeoReader | Kaywa ) onto their mobile devices
Bring these devices into the lesson.

3. Print out the QR codes.

4. Cut them out and place them around your class / school.

B. The lesson:

1. Give each group a clipboard and a piece of paper so they can write down the decoded questions and their answers to them.

2. Explain to the students that the codes are hidden around the school. Each team will get ONE point for each question they correctly decode and copy down onto their sheet, and a further TWO points if they can then provide the correct answer and write this down underneath the question.

3. Away they go! The winner is the first team to return with the most correct answers in the time available. This could be within a lesson, or during a lunchbreak, or even over several days!

C. TIPS / OTHER IDEAS

4. A detailed case study in how to set up a successful QR Scavenger Hunt using this tool can be found here.

Questions / Answers (teacher reference)

Question	Answer
1. THE SUM OF TWO PRIME NUMBERS IS NEVER PRIME	NOT TRUE
2.
3. IF A,B,C AND D ARE POSITIVE REAL NUMBERS AND A/B=C/D THEN A/B =(A+C)/(B+D)	TRUE
4.
5. All prime numbers are odd	This statement is false.Counterexample: n = 2. 2 = 2 (1) so n is even. 2 and 1 are the only factors of 2 so it is prime. We have found an even prime number so the original statement is not true.
6.
7. real numbers a and b, if b2 > a2, then b > a. We need to find real numbers a and b such that b2 > a2 and b < a (b is not greater than a)	Counterexample : Let a = 3 and b = -4. Then a2 = 32 = 9 and b2 = (-4)2 = 16, and so b2 > a2 .But b < a since -4<3
8.
9. We need to find real numbers x, y and z such that x > y and xz < yz (xz is not greater than yz)	Counterexample : Let x = 10, y = 8 and z = -3. Then x > y, since 10 > 8. But xz = 10(-3) = -30 and yz = 8(-3) = -24. -30 < -24, and hence xz < yz. real numbers x, y and z, if x > y, then xz > yz.
10.
11. FOR all integers m and n,if 2m+n is odd then m and n are both odd	let m=2 and n=3 therefore 2(2)+3=7. m is even and n is odd.
12.
13. for all prime numbers p,2p+1 is prime	this statement is true for 2,3,5,..11,23. however not for 7 since (15) 5 3.