Exploring maths through problem solving

Problem of the Week

Queue Tracking

Queue Tracking

The British love to assemble in an orderly line. ‘The Queue Tracker’ (https://www.itv.com/news/2022-09-14/official-queen-lying-in-state-queue-tracker-shows-length-and-end-of-line-live) tracked the queue to view Queen Elizabeth II lying in-state at Westminster Hall. On 15 September, it showed the queue to be 4.9 miles long with an estimated wait time of 9 hours. ABC news stated that in the hall, people file each side of the coffin and stop to pay their respects for 10 seconds.

Based on this assumption, how many people on average, would there be per 10 metres of queue?

Is this number realistic? What would be a better estimate of the average stopping time per person?

The Magician’s Numbers

The Magician’s Numbers

This magician has drawn up a table of numbers to indicate the value of a 2-digit number that was chosen by a man in the audience. Can you see a relationship between the numbers in this table? What do you think was the 2-digit number chosen by the man in the audience?

Potato Planting

Potato Planting

Vince plans to plant his potatoes in a rectangular array.

The potatoes need to be at least 25 cm apart and at least 50 cm from the brick edges of the garden bed.

The garden bed is 2 metres wide and 6 metres long.

What is the greatest number of potatoes he can plant?

Ice-Block Trays

Ice-Block Trays

These ice-block trays mould ice into blocks called “hex cubes”. Are they cubes? What is their geometric name?

There are two sizes of blocks that can be made. Estimate the ratio of the volume of a large ‘hex cube’ to the volume of a small ‘hex cube’.

Burwood Building

Burwood Building

There are two diagonal sets of white parallel lines marked on the side of this building in Burwood, with one set of lines perpendicular to the other set.

How many angles can you find that are the same size as the angle marked in orange?

What is the size of the angle?

Gold Rush!

Gold Rush!

This photograph from https://commonwealthgames.com.au, shows some of our Australian swimmers who competed at the Commonwealth Games in Birmingham.

At these games, there were 280 medalled events with 52 of these events being swimming events.

Australia won 25 swimming events. 

What percentage of the swimming events did Australia win?

Australia won 67 events altogether.

What percentage of the non-swimming events, did Australia win?

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