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Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

Bike Ride

Age 7 to 11 Challenge Level:

Well done to everyone who sent in solutions for this one. The following people managed to have the correct leaving times for both of the riders as well as explaining how they worked it out:
Chris (Ranelagh,Bracknell)
Thomas and Ben (Yarm Primary School, Stockton on Tees)
Jason (Priory Middle School, Dunstable)
Rowena
Jesse and Sally from Tattingstone School, UK
Jonathon (Crofton Junior School, Kent) Excellent presentation!

The answer was explained well by Emily (Tattingstone School)
"To work out this problem all I did was find out how long it would take them to get there and subtracted it away from the 12:00 deadline.
For example, if it took Nirmala 1 hour to go 6 km, it would take her 11/2 hours to get there because I had to add on the extra 3 km. (I worked out that it would be 1/2 hour extra because 6 is one hour so half of 6 is 3 and 3 would therefore be 1/2 an hour).

PHEW!

If she wanted to get there for noon she would have to leave at 10:30.

I did the same to work out how long it would take for Riki to get there. If it took him 1 hour to go 4 km it would take 2 hours to go 8 km. He had 1 km to go and I found that it would take him an extra 15 minutes to get there because if it takes 1/2 an hour (30 mins) to go another 1 km. So altogether it would take him 2 hours and 15 mins to get there and he would therefore have to leave at 9:45.

PHEW AGAIN!"

Most people did it the way described by Emily, but Daniel (Anglo-Chinese School, Singapore) did it differently. He took the distance to Market and divided it by the distance travelled in one hour. The answer gave the number hours it would take. So....

9 000 m divided by6 000 m = 1.5 hours
9 000m divided by 4 000 m = 2.25 hours