Tag Archives: Directions Puzzle

November 2014 News

Another month has flown by and already it’s November. When I was younger, November meant one thing and that was bonfire night. We looked forward so much to the fifth of November and lighting up the sky with the fireworks we had bought from the corner shop. You too can enjoy the November excitement in the classroom by using the Firewords starter, complete with sound effects.

The mathematical puzzle that has captured my interest this month has been a twist on the old classic. You may have heard the one about the explorer who is chased by a bear for one kilometre in a southerly direction, then one kilometre due east then finally one kilometre north. At the end of all this the explorer realises that he is exactly back where he started. What colour was the bear?

The answer to this plus the twist that has captured my interest can be found at the end of this newsletter. I’ll give you a chance to think about it first.

Another thing that I found interesting this past month was the first edition of the BBC’s Newsnight programme with its new presenter Evan Davis. He interviewed British Prime Minister David Cameron and asked him whether we should be teaching metric or imperial units of measure in school. I’ll include his full answer as a sound clip in the November Transum podcast but in a nutshell he opted for imperial units.

Most pupils would learn about many systems of measures in school and as you are probably aware here at Transum we have a topic called Measures containing links to relevant resources.

 Did You Know?

One of the most popular single pages on Transum.org is the Random Student generator. This web app allows you, in a very visual way, to select a pupil from your class at random. By default you can store all of the names of the pupils in one class using the cookie save button. Transum subscribers have the advantage of being able to store the names of pupils in many classes by using this web app from their Class Admin page.

You may decide to use this selector as a ‘select and replace’ simulation or, by deleting the names from the list on the right side of the page, use it in ‘select without replacement’ mode.

Last Month’s Updates

During October both the Quadratic Equations and Simultaneous Equations online exercise have been updated. The interactive Word Search was given a make over and a brand new activity called Polygon Angles was unveiled. The Trick or Treat true/false activity attracted hundreds of users and I changed the way MSDD (Multiply the sum by the difference then divide by 5) checked the answers typed in.

Subscribers

This month we welcome to new subscribers from the UK, US, Australia, New Zealand and the United Arab Emirates. You are all very welcome.

Comments

As usual a number of people have sent in comments and observations.

On the subject of the Broken Calculator starter Mr Simon Perry from Orley Farm, Harrow says “My year 4 Maths set managed to work this out in 34 steps – needless to say I was pretty impressed as I gave them the target of 40!”

After doing the Family Buses starter, Bhavin from Southampton says “Excellent starters. Kids have really enjoyed most of the starters. Thank you.”

After persevering with the Four Make 999 starter Primary 7 from Meethill Primary Peterhead says “We managed to get 6 different combinations. Our STAR pupils were Patrick and Jamie. We showed good perseverance throughout this challenge.”

On the subject of the Hot Estimates starter 4W from Havergal College says “Our Grade 4 class came up with multiple strategies, some of which were very similar to the older students! We are super smart awesome!”

Thinking about the Five Digits starter Mr Parsons from Ashcroft High School says “I love these questions. It makes you think. I will use this as a lesson started with my smart year 8 students tomorrow.”

Cooling down the Hot Estimates starter Mr Winter’s Maths Group from Kuala Lumpur says “First we divided the shape up into 64ths.
Then we counted the number of chillis in one of the squares.
After that we used the grid method to work out the answer and we found that there were 768 chillis.
It was great to see that we were only 5 away from the estimate of the school in Surrey.
Thanks for the challenge.”

On the subject of the Mult Sum Diff Div starter Benjamin from Sydney says “Ok, thanks! Anyway, I finished it and the prize was very funny!”

Puzzle Answer

The answer to the classic puzzle is white. The only place the scenario described could have taken place is at the north pole so the bear must have been a polar bear.

The twist is that it could also have taken place near the south pole. It the explorer started off a certain distance away from the pole, let’s say d kilometres where d is a little more than one, and ran towards the pole (south) for one kilometre. He then ran east for one kilometer but because he was so close to the pole his journey was  a circle around the pole with circumference one kilometre. Finally running north for one kilometre would get him back to where he started.

Your pupils may be able to calculate the radius of that circle and hence find d.

But let’s not stop there. What if d was such that after he had run one kilometre due south, the circumference of an easterly circular journey around the pole was half a kilometre so he has to run twice around the circle twice to make up his one kilometre of easterly travel. What would d be then?

This can be extended to running around the circle three times, four times etc to produce a sequence of values of d.

That’s all for now.

ps What did the zero say to the eight?

Nice belt!