Worked example · Music · Year 9
DCF: Interacting and collaborating → Storing and sharing
Also assessed, LNF: Numeracy → Number system → Calculation
A secure Year 9 response, annotated against the success criteria. Steps 1 to 4 are the numeracy evidence (calculation with large numbers, order of operations, powers of 10, percentages): mark the working, not just the answer. Steps 5 and 6 are the DCF evidence. Key answers: the concert lasts 3,150 s (52 min 30 s); whole concert 907.2 MB (recorder WAV), 555.66 MB (CD WAV), 126 MB (320 kbps), 50.4 MB (128 kbps). Savings: 77.3% and 90.9%. Answers within rounding are fine.
| Format | Working | Bits per second | Bytes per second |
|---|---|---|---|
| WAV, CD quality | 44,100 × 16 × 2 | 1,411,200 | 176,400 |
| WAV, recorder setting | 48,000 × 24 × 2 | 2,304,000 | 288,000 |
| WAV, CD quality, mono | 44,100 × 16 × 1 | 705,600 | 88,200 |
| MP3 at 320 kbps | 320 × 1,000 | 320,000 | 40,000 |
| MP3 at 128 kbps | 128 × 1,000 | 128,000 | 16,000 |
(a) 24 ÷ 8 = 3, so 48,000 × 3 × 2 = 288,000 bytes per second. Check: 2,304,000 ÷ 8 = 288,000.
(b) 500 MB = 500,000,000 bytes = 5 × 108 bytes. 4 GB = 4,000,000,000 bytes = 4 × 109 bytes.
Uses the formula correctly, divides by 8 at a sensible point to keep the numbers small, and checks one answer a second way. Writes large numbers using powers of 10. Numeracy evidence. Evidences criteria 1, 2 and 3.
3 min 30 s = 3 × 60 + 30 = 210 s.
| Format | Working | Bytes | MB | Under 20 MB? |
|---|---|---|---|---|
| WAV, CD quality | 176,400 × 210 | 37,044,000 | 37.04 | No |
| MP3 at 320 kbps | 40,000 × 210 | 8,400,000 | 8.40 | Yes |
| MP3 at 128 kbps | 16,000 × 210 | 3,360,000 | 3.36 | Yes |
320 kbps: (37.044 − 8.4) ÷ 37.044 × 100 = 28.644 ÷ 37.044 × 100 = 77.3% smaller.
128 kbps: (37.044 − 3.36) ÷ 37.044 × 100 = 33.684 ÷ 37.044 × 100 = 90.9% smaller.
Brackets are done first, bytes are converted to MB by dividing by 106, and each file is tested against the email limit. Numeracy evidence. Evidences criteria 1, 2, 3 and 4.
(a) Minutes: 1 + 3 + 4 + 3 + 4 + 2 + 2 + 3 + 5 + 4 + 2 + 4 + 5 + 5 = 47. Seconds: 40 + 10 + 5 + 30 + 20 + 45 + 20 + 25 + 15 + 40 + 50 + 0 + 30 + 0 = 330 = 5 min 30 s. Total 52 min 30 s = 52 × 60 + 30 = 3,150 s.
(b)
| Format | Working | MB | Folder | USB | |
|---|---|---|---|---|---|
| WAV, recorder setting | 288,000 × 3,150 = 907,200,000 | 907.2 | ✗ | ✗ | ✓ |
| WAV, CD quality | 176,400 × 3,150 = 555,660,000 | 555.66 | ✗ | ✗ | ✓ |
| MP3 at 320 kbps | 40,000 × 3,150 = 126,000,000 | 126 | ✗ | ✓ | ✓ |
| MP3 at 128 kbps | 16,000 × 3,150 = 50,400,000 | 50.4 | ✗ | ✓ | ✓ |
(c) 907.2 ÷ 4,000 × 100 = 22.7% of the stick. The whole concert at 320 kbps saves (555.66 − 126) ÷ 555.66 × 100 = 77.3%, the same as one piece. That is because both sizes are “bytes per second × seconds”, so the length cancels: the saving is always 1 − 40,000 ÷ 176,400.
Adds minutes and seconds separately, multiplies large numbers accurately, and spots that a percentage of a proportion does not depend on length. Numeracy and DCF evidence. Evidences criteria 1 to 4.
| Format | Email: seconds | minutes | Folder: seconds | minutes |
|---|---|---|---|---|
| WAV, CD quality | 20,000,000 ÷ 176,400 = 113.4 | 1.9 | 500,000,000 ÷ 176,400 = 2,834.5 | 47.2 |
| MP3 at 320 kbps | 20,000,000 ÷ 40,000 = 500 | 8.3 | 500,000,000 ÷ 40,000 = 12,500 | 208.3 |
| MP3 at 128 kbps | 20,000,000 ÷ 16,000 = 1,250 | 20.8 | 500,000,000 ÷ 16,000 = 31,250 | 520.8 |
Only piece 1, the fanfare (100 s), is under 113.4 s, so it is the only piece that could be emailed as a WAV: 176,400 × 100 = 17.64 MB. At 128 kbps the concert is 50.4 MB, and 50.4 ÷ 20 = 2.52, so each family needs at least 3 emails (pieces 1 to 6, 7 to 11 and 12 to 14 fit). That is 3 × 214 = 642 emails.
Uses division as the inverse of the size calculation, rounds up correctly when counting emails, and turns the answer into a real cost (642 emails). Numeracy evidence. Evidences criteria 1, 2 and 4.
| Decision | Choice and justification |
|---|---|
| Archive copy | The recorder-setting WAV (lossless, best quality, 907.2 MB) on the USB stick (22.7% full) and on the staff archive drive. Too big for the 500 MB folder. Two places, so one failure loses nothing. |
| Family copy | MP3 at 320 kbps for quality, plus 128 kbps for listening on phone data. |
| How families get it | One link to the shared folder, set to view only, sent through the school. Switch it off at the end of the summer term. No attachments: 3 emails each would not even fit the 320 kbps copy. |
| Left out | Piece 11, the harp solo: that family did not give consent. |
| File names | year-month_concert_number_title_bitrate, for example 2026-07_concert_04_calon-lan_320.mp3 and 2026-07_concert_14_finale_128.mp3. The number keeps the programme order. |
| Reply to the parent | Thank you, but recordings of pupils must not be posted publicly, and a public site would include piece 11, which has no consent. |
3,150 − 170 = 2,980 s. 320 kbps: 40,000 × 2,980 = 119.2 MB. 128 kbps: 16,000 × 2,980 = 47.68 MB. Together 166.88 MB, and 166.88 ÷ 500 × 100 = 33.4% of the folder.
Every choice is tied to a number or a rule: lossless master in 2 places, view-only link with an end date instead of attachments, a naming convention that sorts in order, and consent respected. Evidences criteria 4, 5 and 6.
I recommend keeping the original recorder WAV as the archive copy, because it is lossless and the best quality we have; at 907.2 MB it is too big for the 500 MB shared folder, so it should go on the USB stick, where it uses only 22.7% of the space, and on the staff archive drive as a second copy. Families should get MP3 files, which are 77.3% smaller at 320 kbps and 90.9% smaller at 128 kbps. Both versions of the family copy together take 166.88 MB, only 33.4% of the folder, so one view-only link can be sent through the school and switched off after the summer. Email would not work: even at 128 kbps the concert is 50.4 MB, so it would take 642 emails to reach 214 families. The harp solo must be left out because that family did not give consent, and the parent’s offer to post the concert publicly should be politely refused because the school’s rules do not allow it.
Quotes more than 8 numbers from the working, compares the sharing options, and keeps the consent and public posting rules. Evidences criteria 4, 5 and 6.