Worked example · Languages, Literacy and Communication · Year 6
LNF: Numeracy → Number system → The number system
A complete, secure Year 6 answer with the full answer key. The figures are real, from the Welsh Government’s report on the 2021 census. The exact answers in Step 4 match the differences the Welsh Government reports (a fall of about 23,700 people since 2011, and 17,600 fewer children aged 5 to 15).
a) five hundred and thirty-eight thousand, three hundred
b) 922,100 c) first 3: 30,000 (thirty thousand); second 3: 300 (three hundred) d) 1,000,000
The same digit has different values in different places. Evidences success criteria 1 and 2.
503,500 < 538,300 < 562,000 < 922,100. The fewest Welsh speakers were in 1981.
503,500 and 538,300 both have 5 hundred thousands, so the pupil must compare the ten thousands (0 and 3). Evidences success criterion 3.
| Number | nearest 1,000 | nearest 10,000 | nearest 100,000 |
|---|---|---|---|
| 538,300 (Wales, 2021) | 538,000 | 540,000 | 500,000 |
| 922,100 (Wales, 1921) | 922,000 | 920,000 | 900,000 |
| 562,000 (Wales, 2011) | 562,000 | 560,000 | 600,000 |
| 134,700 (Children aged 5 to 15, 2021) | 135,000 | 130,000 | 100,000 |
| 73,600 (Gwynedd, 2021) | 74,000 | 70,000 | 100,000 |
| 72,800 (Carmarthenshire, 2021) | 73,000 | 70,000 | 100,000 |
“Rounding to the nearest 1,000 shows the difference: Gwynedd is 74,000 and Carmarthenshire is 73,000. Rounding to the nearest 10,000 makes both 70,000, which hides the difference of 800.”
Look at 538,300 to the nearest 10,000: the thousands digit is 8, so it rounds up to 540,000. And 562,000 to the nearest 100,000 rounds up to 600,000 because the ten thousands digit is 6. Evidences success criterion 4.
| Question | Estimate | Exact answer and method |
|---|---|---|
| a) 2011 to 2021 | 560,000 − 540,000 = 20,000 | 562,000 − 538,300 = 23,700. Count on: 538,300 + 1,700 = 540,000, then + 22,000 = 562,000. 1,700 + 22,000 = 23,700. |
| b) To reach 1 million | 1,000,000 − 540,000 = 460,000 | 1,000,000 − 538,300 = 461,700. Count on: 538,300 + 1,700 = 540,000, then + 460,000 = 1,000,000. |
| c) Children 5 to 15 | 150,000 − 130,000 = 20,000 | 152,300 − 134,700 = 17,600. Count on: 134,700 + 300 = 135,000, then + 17,300 = 152,300. |
“All 3 exact answers were close to my estimates, so they are sensible.”
Estimating first, then counting on in steps to a round number, is efficient and easy to check. Evidences success criterion 5.
a) 64.4% > 55.8% > 17.8% > 12.2% > 6.2%
b) Gwynedd 64 · Anglesey 56 · Wales 18 · Cardiff 12 · Blaenau Gwent 6
c) About 64 people in every 100.
55.8 rounds up to 56 and 17.8 to 18 because the tenths digit is 5 or more. Evidences success criteria 3 and 4.
| Headline | Fair? | Why? |
|---|---|---|
| “Over half a million people in Wales can speak Welsh” | Yes | Half a million is 500,000, and 538,300 is more than 500,000. |
| “Nearly 600,000 Welsh speakers” | No | 538,300 is about 62,000 below 600,000. To the nearest 100,000 it rounds to 500,000, not 600,000. “Nearly 540,000” would be fair. |
| “Almost two thirds of people in Gwynedd speak Welsh” | Yes | Two thirds is about 66.7%. 64.4% is just under that, so “almost” is fair. |
Estimate: 900,000 − 500,000 = 400,000. Exact: 922,100 − 503,500 = 418,600.