Worked example · Science and Technology · Year 5
LNF: Numeracy → Understanding the number system helps us to represent and compare relationships between numbers and quantities → The number system
A secure Year 5 response, annotated so you can see which success criterion each part meets. It is also the answer key. Order: Mercury, Mars, Venus, Earth, Neptune, Uranus, Saturn, Jupiter. Differences: 652 km and 22,448 km. Estimate: 143,000 ÷ 13,000 = 11 Earths.
Mars: six thousand, seven hundred and ninety-two.
Neptune: forty-nine thousand, five hundred and twenty-eight.
Jupiter: one hundred and forty-two thousand, nine hundred and eighty-four.
(b) 120,536: Saturn.
Thousands read as a group before the hundreds. Evidences criterion 1.
The 4 next to the 1 is worth 40,000 (4 ten thousands). The 9 is worth 900. In 51,118 the 5 is worth 50,000.
Evidences criterion 2.
| Order | Planet | Diameter (km) |
|---|---|---|
| 1 | Mercury | 4,879 |
| 2 | Mars | 6,792 |
| 3 | Venus | 12,104 |
| 4 | Earth | 12,756 |
| 5 | Neptune | 49,528 |
| 6 | Uranus | 51,118 |
| 7 | Saturn | 120,536 |
| 8 | Jupiter | 142,984 |
Both have 5 digits and the same ten thousands digit (1) and thousands digit (2). The hundreds digit decides it: Earth has 7 hundreds and Venus has only 1, so Earth is bigger.
Compares digits from the left, one place at a time. Evidences criteria 2 and 3.
| Planet | Diameter | Nearest 1,000 | Nearest 10,000 |
|---|---|---|---|
| Mercury | 4,879 | 5,000 | 0 |
| Venus | 12,104 | 12,000 | 10,000 |
| Earth | 12,756 | 13,000 | 10,000 |
| Mars | 6,792 | 7,000 | 10,000 |
| Jupiter | 142,984 | 143,000 | 140,000 |
| Saturn | 120,536 | 121,000 | 120,000 |
| Uranus | 51,118 | 51,000 | 50,000 |
| Neptune | 49,528 | 50,000 | 50,000 |
To the nearest 10,000, Venus, Earth and Mars all become 10,000, and Uranus and Neptune both become 50,000. Mercury becomes 0. Rounding that far is not helpful when the numbers are small or close together, because it hides the differences.
Mercury rounds down to 0 because 4,879 is less than 5,000. Evidences criterion 4.
(a) 12,756 − 12,104 = 652 km.
(b) 142,984 − 120,536 = 22,448 km.
Check by adding: 120,536 + 22,448 = 142,984.
Jupiter is about 143,000 km and Earth about 13,000 km. 143 ÷ 13 = 11, so about 11 Earths.
Check: 13,000 × 11 = 143,000. Using the exact numbers, 12,756 × 11 = 140,316, which is a little less than 142,984, so 11 is a good estimate.
Rounding chosen to make the division easy, then checked. Evidences criterion 5.
(a) 0.382 (Mercury), 0.532 (Mars), 0.949 (Venus), 1.000 (Earth).
(b) Venus, because 0.949 is the closest to 1.000.
(c) No. Half is 0.500, and 0.532 is more than 0.500, so Mars is a bit more than half as wide as Earth.
Compares tenths first, then hundredths. Evidences criterion 3.
About 11 × 13 cm = 143 cm, so a ball about 1.4 m wide.
Uranus and Neptune: 51,000 + 50,000 = 101,000, not close. Saturn and Earth: 121,000 + 13,000 = 134,000. Saturn and Neptune: 121,000 + 50,000 = 171,000. Saturn and Venus: 121,000 + 12,000 = 133,000. The closest is Saturn and Earth (134,000 compared with 143,000).