Arithmetic

Aircraft Registrations

September 30, 2020September 30, 2020Leave a comment

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GCSE Text:
All aircraft in the UK have a unique registration code painted on the side. The code has 5 letters of the alphabet, each A-Z. For the UK, the first letter must be a ‘G’ followed by a dash and then four more A-Z letters that can repeat.

example: A helicopter has the registration of G – HPDG

a) How many unique codes exist for UK aircraft?

For ‘lighter than air’ aircraft (hot air balloons and airships), there are extra rules. In addition to starting with a ‘G’ and dash, the second letter must be an ‘F’ and this time the letters must not repeat.

example: A hot air balloon has the registration of G – FBES

b) How many unique codes exist for ‘lighter than air’ aircraft in the UK?

Suggestions:
This is a good consolidation question for students who have learned listing strategies and probability outcomes and they will need to consider the repeating or non-repeating nature of the codes. Some students like to sketch a probability tree diagram whilst other just remember the rule of multiplication. students as the method is not specified in the question. Students need to select the appropriate trigonometric approach to take as well as consider different units. The extension task works well for higher paper GCSE students too.

Teachers could extend the learning by considering:

Because aircraft codes are never reused, even for retired or scrapped aircraft, available UK codes are running out as new aircraft are being made. A suggestion is to add an extra letter on the end in future. How many more codes would a 6 letter pattern create compared to the existing 5 letter pattern?

Patio Tile Cuts

September 28, 2020Leave a comment

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As part of a patio laying project, a square tile needs to be cut according to the design shown in this diagram.

Patio cuts

An angle grinder is used to cut the tile, and the cut speed is 1mm per second. How long will it take to make the cut on this tile? Give your answer in minutes and seconds.

Suggestions:
This is a good starter question for GCSE students as the method is not specified in the question. Students need to select the appropriate trigonometric approach to take as well as consider different units. The extension task works well for higher paper GCSE students too.

Teachers could extend the learning by considering:

It is the triangle that is needed as part of the patio, the trapezium will be discarded. What percentage of the full time will be discarded? Give your answer rounded to 1 d.p.

Porcelain Primer

September 3, 2020September 3, 2020Leave a comment

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A patio consists of 92 porcelain tiles, each one measuring 600mm x 600mm. Each tile needs to have a primer painted to the underside before getting placed onto the cement bed.

The primer is supplied in tubs, each tub containing 2 packets of dry power and each packet covering 8m² when mixed with water.

How many tubs of primer are needed to complete the patio?

Suggestions:
This is a good question to test students’ understanding of area, particularly with mixed units. Students normally take 3-4 minutes to answer. The extension task works well for higher paper GCSE students too.

Teachers could extend the learning by considering:

The tiles are 18mm thick and are supplied in packs of 2. Each pack weighs 25kg. What is the density of the porcelain? Give your answer in g/cm³.

Time Lapse Videos

May 11, 2020May 12, 2020Leave a comment

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Charlie’s video camera normally records smooth video at a rate of 25 frames per second.

Today though, Charlie is using it in time lapse mode, where one frame is captured every 15 seconds instead. He records in time lapse mode for 2 hours continually.

a) When the time lapse recording is played back at 25 frames per second, how long will the clip last (in seconds)?

b) The camera has the option to play back at a faster 30 frames per second rate. How much shorter will the clip last if it is played back at this faster rate?

Suggestions:
This is a good question to test students’ understanding of worded questions. Normally words like ‘per’ need to be highlighted, and this is easily a non-calculator arithmetic question. Students take 1-2 minutes to answer this question in full.

Teachers could extend the learning by considering:

The normal frame resolution is 1280 x 720 pixels, but has a full HD option of 1920 x 1080. How many more pixels are there in a full HD frame than the normal frame?