How Many Triangles Can You Count

PUZZLES / ACTIVITIES

Teachers – please display new puzzles / activities regularly in the classroom or corridor displays.

Students – have a browse through this site to find some puzzles / activities to share with your class or your friends or to work out for yourself.

Parents – please browse; pick out a puzzle or activity to create mathematical discussion amongst all members of the family.

ANSWERS posted below!  Some examples are given below within WORD borders.

 Further below other ideas are given – teachers can copy, landscape, enlarge and present them very quickly. [Please telephone or e-mail if you have problems.]

 If you have some puzzles or activities to share please contact us. What is worse than seeing a maggot in an apple? Which would you choose…

a clock which loses one minute a day OR a clock which does not go at all?

From: Lewis Carroll What can you find out about him? Multiply together any three consecutive numbers.

Is the product always divisible by 6?

Can you prove this? 6 × 7 = 42 66 × 67 = 4422 666 × 667 = 444222 6666 × 6667 = 44442222

What is 666666 × 666667 ? Can you write out 10 rows of this pattern? Magicians often make a person disappear from a cabinet on one side of a stage and reappear on the other.

Multiply this huge number by 3: 1 034 482 758 620 689 655 172 413 793

What do you notice? Can you think of a sentence which includes five consecutive “and”s ? There are between 50 and 60 eggs in a basket. If I count them out three at a time, I have two left over. If I count them out five at a time, I have four left over.

How many eggs do I have? At home or at school find 6 circular objects.

Draw round them to make

a pattern. How many triangles can you count? What are the next two numbers in this pattern?

31, 28, 31, 30, ___, ___ Which is the odd one out?

2 6 8 5 4 If 3 cats killed 3 rats in 3 minutes, how long will it take 100 cats to kill 100 rats? How many months have 30 days?

Hint: it is not 4. Quadrilaterals are four sided shapes. a + a = 2a a × 2 = 2a 2 × a = 2a Answers

There are 16 triangles:  6 small triangles  3 each containing two small triangles  6 each containing three small triangles  1 large triangle.

The next two numbers are 31 and 30. [Number of days in the months: Jan, Feb….]

The odd one out? There are numerous answers. Ask your teacher to check your thinking.

Here are our answers: 5 because all the others are even numbers 8 is the only cube number OR it is the only number between 7 and 9! 4 has no curved lines OR it is the only square number in the list 6 has more prime factors than any of the others OR it is the only number in the list divisible by 3 2 is the only even prime number. It would take the cats 3 minutes (as long as they didn't bump into each other all the time!)

11 months have 30 days (a sort of joke question!)

There are numerous answers to this one. Your answer might look something like ours below, but check the thinking through with your teacher. Perhaps you could a survey to find out what your class thinks…

Prediction: Oasis because:  they have a new single coming out  based on past performance, they have done well  people have said they will buy it  it has had lots of radio play  they have an established fan base

"What order?" I thought about taking your clothes off and getting into the shower! Find out what BODMAS means. How old are they? Faye is 10 years old and James is 5 years old.

Walking backwards: There are no real answers to this. I would be hopeless walking backwards! If you have written up your answer, you could send it to me – I might be able to put it on the World Wide Web!

[J J Whiteman, The Education Centre, Butterfield Road, Wheathampstead, Herts. AL4 8PY]