1. Mathematical challenges for able pupils Year 6 C Counting, partitioning and calculating

2. Cola in the bath A can of cola holds 33 centilitres.
If you had a bath in cola – don’t try it! –
approximately how many cans of cola would you need?
Hint: 1 cubic centimetre is the same as 1 millilitre.
Learning Objective:
Solve mathematical problems or puzzles.
Estimate lengths and convert units of capacity.
Develop calculator skills and use a calculator effectively.

3. Solution for Cola in the bath
A bath 1.5 metres long by 60 cm wide would
have a floor area of approximately 9000 cm². If there was 10 cm of cola in the bath, the volume of liquid would be about cm3 or ml.
This would require roughly 270 cans of cola.
Learning Objective:
Solve mathematical problems or puzzles.
Estimate lengths and convert units of capacity.
Develop calculator skills and use a calculator effectively.

4. after the start of the year 2000?
Millennium
At what time of what day of what year will it be:
2000 minutes
2000 seconds
2000 weeks
2000 days
2000 hours
after the start of the year 2000?
Learning Objective:
Solve mathematical problems or puzzles.
Estimate lengths and convert units of capacity.
Develop calculator skills and use a calculator effectively.

5. Solution for Millennium
2000 Seconds after :33:20 1 January 2000
2000 Minutes after :20:00 2 January 2000
2000 Hours after :00 23 March 2000
2000 Days after :00 23 June 2005
2000 Weeks after :00 1 May 2038
Learning Objective:
Solve mathematical problems or puzzles.
Estimate lengths and convert units of capacity.
Develop calculator skills and use a calculator effectively.

6. Bus routes Six towns are connected by bus routes.
The bus goes from A back to A.
It visits each of the other towns once.
How many different bus routes are there?
Learning Objective:
Solve a problem by extracting and interpreting data.
Add several numbers mentally.

7. Which round trip from A to A is the cheapest?
Bus routes
This table shows the bus fare for each direct route. B to A costs the same as A to B, and so on.
A to B
B to C
C to D
D to E
E to F
F to A
B to D
B to F
C to E
C to F £4 £3 £5 £2
Which round trip from A to A is the cheapest?
Learning Objective:
Solve a problem by extracting and interpreting data.
Add several numbers mentally.

8. Solution for Bus routes
There are six different routes from A back to A:
A B C D E F A
A B D C E F A
A B D E C F A
and the three reversals of these.
The cheapest routes are A B D E C F A
and its reversal, which each cost £21.
Learning Objective:
Solve a problem by extracting and interpreting data.
Add several numbers mentally.

9. Estimate how many people there are in the crowd.
People in the crowd
Estimate how many people there are in the crowd.
Learning Objective:
Solve mathematical problems or puzzles.
Count larger collections by grouping.
Give a sensible estimate.

10. Estimate how many people there are in the crowd.
People in the crowd
Estimate how many people there are in the crowd.
Learning Objective:
Solve mathematical problems or puzzles.
Count larger collections by grouping.
Give a sensible estimate.

11. Estimate how many people there are in the crowd.
People in the crowd
Estimate how many people there are in the crowd.
Learning Objective:
Solve mathematical problems or puzzles.
Count larger collections by grouping.
Give a sensible estimate.

12. Solution to People in the crowd
a. 15 penguins
b and c.
There is no precise answer, but pupils can
compare their estimates and discuss how
they arrived at them.
Learning Objective:
Solve mathematical problems or puzzles.
Count larger collections by grouping.
Give a sensible estimate.

13. How many people live in each house?
Albert Square
36 people live in the eight houses in Albert Square.
Each house has a different number of people living in it.
Each line of three houses has 15 people living in it.
How many people live in each house?
Learning Objective:
Solve mathematical problems or puzzles.
Add several small numbers mentally.
Explain methods and reasoning.

14. Albert Square Learning Objective:
Solve mathematical problems or puzzles.
Add several small numbers mentally.
Explain methods and reasoning.

15. How long is the shortest route Santa can take?
Sleigh ride
In Snow Town, 3 rows of 4 igloos are linked by 17 sleigh paths.
Each path is 10 metres long.
When Santa visits, he likes
to go along each path at least once. His route can start and end at any igloo.
How long is the shortest route Santa can take?
Learning Objective:
Solve a problem by organising information.
Visualise 2-D shapes.

16. Sleigh ride What if there are 4 rows of 5 igloos?
Each path is 10 metres long.
When Santa visits, he likes
to go along each path at least once. His route can start and end at any igloo.
How long is the shortest route Santa can take?
Learning Objective:
Solve a problem by organising information.
Visualise 2-D shapes.

17. Solution to Sleigh ride
With 3 rows of 4 igloos, the shortest route is 190 metres. For example:
With 4 rows of 5 igloos, the shortest route
is 350 metres. For example:
Learning Objective:
Solve a problem by organising information.
Visualise 2-D shapes.

18. The end,thank you!

19. References and additional resources.
The questions from this PowerPoint came from:
Mathematical challenges for able pupils in Key Stages 1 and 2
Corporate writer was Department for Education and Employment and it is produced under a © Crown copyright 2000
Thank You
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These Mental Maths challenges can be found as a PDF file at :
Contains public sector information licensed under the Open Government Licence v3.0. (
All images used in this PowerPoint was found at the free Public Domain Clip Art site. (
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