QUIZ Count out your chance! Big Maths Day 2011 Grades 5 and 6

Question1 What is your chance to give the wrong answer for all questions in this quiz? 0% chance 50% chance 100% chance No idea You can discuss a is impossible (if you choose that, you will already have one question correct); all the others are possible.

Question 2 Why do so few children end up at the outer endpoints in the grid walking game? Because they are cheating Because there is very little place there Because there is only one route that leads there Because they are further away C only routes with just L-s or R-s lead to the edges. There are more routes to the other points: for example all routes with exactly 2 L-s will get to point d, it doesn’t make a difference whether you take LLRRR or LRLRR. So there are more routes to the other points.

Question 3 Which of the Left-Right rows below will take you to the same endpoint as you would end up in with LLR LRR RRR R R L R L L L L L L L R R L R R R L L R L R L R L R R L L L R R R R R R D. There have to be 3 L-s and 6 R-s, the order doesn’t matter (see the previous question as well). Perhaps this has been discovered during the activity in the carousel where all routes and endpoints were written down.

Question 4 Using two eight-sided dice, which result (sum of the pips) can be thrown in the most different ways? 7 8 9 10 C. You can make a table (see the assignment in the carousel), and you will find that you can throw 9 in 8 different ways.

Question 5 How many different combinations of pips can you throw using two twenty-sided dice? TAKE CARE: 3 and 17 is the same as 17 and 3, but not the same as 15 and 5 About 400 About 200 About 100 About 50 b. Make a table and you will see. About (20 x 20)/4 = 200. Divide by 2, because 3 and 17 is the same as 17 and 3; but that isn’t entirely true, because you will then also have half of all 20 double throws (1-1, 2-2, 3-3, 4-4 etc.) and that is incorrect. So you add back that half again. The exact answer is 210.

Question 6 If this booklet has 5 pages (that is 5 heads, 5 bodies, 5 pairs of legs) you can make more than a 100 different figures. That is correct That is incorrect You cannot know That is correct, make a tree diagram to see it. You can choose 5 bodies with each head, and 5 pairs of legs for each head+body. So you will have 5 x 5 x 5 =125 different figures

Question 7 How many different colours do most of the mandalas that were made in your class have? 1 2 3 4 5 6 Check in your class, probably 3 or 4

Question 8 In the Game of Hog you have the best chance to win if you …… … use 1 dice to throw every time … use 7 dice to throw every time … use all 10 dice to throw every time … just do something. It doesn’t matter. B. This is not very easy to calculate, but pupils may already have noticed while playing. It is a kind of balance between more points (and more dice) and not as large a chance to throw a 1 as well (i.e. fewer dice). All answers can be counted as correct.

Question 9 The new Dutch numberplates have 2 numbers – 3 letters – 1 number. How many different numberplates can be made like that more or less? 100.000 1.000.000 10.000.000 100.000.000 C. is the closest. 10x10x26x26x26x10=17.576.0000 so well over 17 million. Perhaps pupils happen to know that not all combinations are allowed. Vowels are not used to avoid odd words; abbreviations with insulting meanings are not allowed etc. See: http://auto-en-vervoer.infonu.nl/auto/21407-geschiedenis-van-het-kenteken-op-de-auto-in-nederland.html (in Dutch).

Question10 How many letters and numbers can you make with exactly 5 LED lines. Diagonal lines are not allowed. We already give away that the number 2 is possible. About 10 About 15 About 20 About 25 A. It depends on how creatively you can draw. We get about 10, i.e. : 2, 3, 5=s,, E, H, n, U, d, p, q =9(?), b. If you calculate the number of shapes you can make with 5 out of 7 lines, you get 21, but not all of those are letters or numbers. This question can also be done as an open question. Let the pupils make drawings in that case.

Extra question In a book with 5 pages you cut through the figures so that you have 5 instead of 3 parts. How many extra figures can you make now? 2 times as many 5 times as many 10 times as many 25 times as many D (see also question 6): first you could make 5x5x5; now the number of possible combinations is 5x5x5x5x5 , and that is 25 times as many.

And now……..

…. the answers All except A C D B A Counting in class! B C For explanations, see the comments with the questions. And the extra question: D