Megabytes of Memory

In this activity, students explore the relationship between the price and the size of various memory cards for digital cameras. For the investigation in question 4, the students will need to have access to a digital camera, its manual, digital camera brochures, or the Internet.
Introduce an independent group to this activity by discussing how digital photos are stored on a memory card (some cameras use memory sticks or disks), the difference between high and low resolution (the higher the resolution setting, the more memory is taken up by each photo), and how you can buy different amounts of memory. Memory is measured in megabytes (MB).
You may need to define these terms:
• Low resolution: the dots (pixels) that make up the picture are not as close together as they are in a high-resolution picture. A low-resolution picture takes up less memory than a high-resolution picture, but it isn’t as sharp or clear.
• Megabyte (MB): a unit that measures how much information can be stored on a computer.
With a guided teaching group, you could motivate the students’ interest in this activity by letting them take some photos on a digital camera, experiment with the resolution setting, and compare the results. Discuss storage, resolution, and memory as above.
For question 1, encourage the students to identify patterns in the different sizes and prices of the memory cards by suggesting that they organise the information in the picture into a table, with a column for the sizes and another for the prices. Ask: What patterns can you see in the memory card sizes? (They double in size each time.)
Does this same pattern happen with the prices? (No. They increase by $30 or $40 each time.)

For question 2, encourage the students to work out mentally, in groups of 3–4, how many photos will fit on each card and then to share their answers and strategies with the whole group. This will encourage higher levels of participation and give you opportunities to listen, to support thinking, and to make formative assessments of individuals.
Some students may work out that 5 x 32 MB is 160 photos and then double this number successively for each of the other cards, for example, 160 x 2 = 320 photos will fit on the 64 MB card. Others may work out, for each card, “5 lots of  MB” or “5 x , where  is the number of MB on a card”. Strategies for multiplying by 5 include:
 place value partitioning: 5 x 32 = (5 x 30) + (5 x 2)
 doubling and halving: 5 x 32 = 10 x 16
For question 3, again ask the students to investigate this in small groups before sharing their ideas with the whole group.
Encourage the students to work systematically by asking questions such as:
How could you make sure that you have recorded all the different options?
Could you show your information in a table? (See the table given in the Answers.)
Are there any options where Beth can buy 3 cards without having to spend the whole $250? Are there any card sizes that Beth can’t afford? (Remember, she needs to buy cards for 3 digital cameras.)

Extension

If Beth had $300 to buy the 3 memory cards instead of just $250, how might this change her spending decisions?
This activity could also lead into an exploration of the power of 2:
4 = 2 x 2 = 2²
8 = 2 x 2 x 2 = 2³
16 = 2 x 2 x 2 x 2 = 2⁴
Ask:
Can you use this pattern to work out the power of 2 that equals 32, 64, and the capacity of the other memory cards?
Can you use the pattern to work out what 21 and 20 equal? (21 = 2, 20 = 1. For an explanation of 100 (and therefore 20), see the answers and notes for the Power of Powers activity in this book.)

Answers to Activity

1. The cards’ memory size doubles (for example, 2 x 32 = 64; 2 x 256 = 512), but the prices do not double as the memory size doubles. The cards go up by $30 or $40 with every increase in memory size.
2. i. 160 photographs (5 x 32)
ii. 320 photographs (5 x 64)
iii. 640 photographs (5 x 128)
iv. 1 280 photographs (5 x 256)
v. 2 560 photographs (5 x 512)
3. a. Answers will vary. Beth can’t buy any 256 MB or 512 MB cards because then she wouldn’t have enough money left for 2 more cards of any size. A possible table to show the options (including the number of photographs for question b) is:
b. Beth’s best option is 1 x 32 MB, 1 x 64 MB, and 1 x 128 MB cards, which would give her 1 120 stored photographs.
4. Answers will vary depending on the information found. (High resolution photos take between 1 and 5 MB [1 000–5 000 kB], depending on the resolution.)