1. Technique Worked Example – Data Representation

2. Overview -What are the possible subgoals for file size calculation problems? -Exploring an example of a data representation task using worked examples

3. Data Representation -Data representation is a good example of a process that we think pupils should get but we know they can struggle with -More discussion on page about worked examples approach -Why worked examples? Expert knowledge guiding the process Explicit and visible for pupils to follow

4. Data Representation Here are generic steps for file calculations: -Convert to required unit of measurement -Calculate the size in bits -Convert to suitable unit of capacity -Round up to suitable number of decimal places Why generic? Pupils can see the links between similar calculations. See subgoal labelling technique.

5. Data Representation Calculate the backing storage required for a 16 bit colour image 3 inches by 5 inches with a resolution of 40 d.p.i. Express your answer in Kilobytes 3 inches 5 inches

6. Data Representation Calculate the backing storage required for a 16 bit colour image 3 inches by 5 inches with a resolution of 40 d.p.i. Express your answer in Kilobytes 3 inches 5 inches Convert to required unit of measurement Calculate the size in bits Convert to suitable unit of capacity Round up to suitable number of decimal places Units should be in pixels. To do this, you must multiply the inches by the dots per inch. Width in pixels = 40 x 3 = 120 pixels Height in pixels = 40 x 5 = 200 pixels

7. Data Representation Calculate the backing storage required for a 16 bit colour image 3 inches by 5 inches with a resolution of 40 d.p.i. Express your answer in Kilobytes 3 inches 5 inches Convert to required unit of measurement Calculate the size in bits Convert to suitable unit of capacity Round up to suitable number of decimal places The size in bits is the width x height x colour depth. This means we allocate the number of bits needed for a single pixel for every pixel in the image. Size in bits = 120 x 200 x 16 = 384000 bits

8. Data Representation Calculate the backing storage required for a 16 bit colour image 3 inches by 5 inches with a resolution of 40 d.p.i. Express your answer in Kilobytes 3 inches 5 inches Convert to required unit of measurement Calculate the size in bits Convert to suitable unit of capacity Round up to suitable number of decimal places A unit of capacity should be between 1 and 1024, so that it is easy to read. Divide by 8 to convert bits to bytes. Then divide by 1024 to convert to kilobytes, then megabytes, gigabytes etc. 384000 bits = 384000 / 8 bytes = 48000 bytes 48000 bytes = 48000 / 1024 = 46.875 kilobytes

9. Data Representation Calculate the backing storage required for a 16 bit colour image 3 inches by 5 inches with a resolution of 40 d.p.i. Express your answer in Kilobytes 3 inches 5 inches Convert to required unit of measurement Calculate the size in bits Convert to suitable unit of capacity Round up to suitable number of decimal places The final stage is to round the answer up to 2 decimal points, to make the answer readable. Rounding down would mean losing part of the file. 46.875 to 2 d.ps = 46.88 kilobytes

10. Worked example – what is important? Each step can vary in its level of detail. o Simpler steps can be omitted or combined later on. A walkthrough and description of the purpose of each step helps clarify. Pupils should be able to see all steps in the process (e.g. the previous part of the calculation)

11. What to watch out for Being explicit for every step when the process is already understood by pupils can cause problem with progress Free problem solving is more effective for learning once the process has been understood by learners.

12. Possible Next steps Material for worked examples with data representation Exploring the worked examples approach Exploring the subgoal labelling technique