Numeracy Foundation November 2017 Unit 2 Q2
2. Declan has two pet rabbits.
He wants to buy a new rabbit hutch.
Declan finds a rule to work out the amount of floor space that each rabbit should have in the hutch.
Floor space needed = mass of rabbit × 1800
Floor space is measured in cm2.
Mass is measured in kg.
(a) Declan’s larger rabbit weighs 3·2 kg.
What floor space should this rabbit have in the hutch? [2]
What floor space should this rabbit have in the hutch? [2]
(b) Declan works out that his smaller rabbit needs 4860 cm2 of floor space.
What is the mass of the smaller rabbit? [2]
What is the mass of the smaller rabbit? [2]
(c) Declan sees a hutch with a rectangular floor that measures 150 cm by 80 cm.
Show that this hutch has enough floor space for the two rabbits.
You must show all your working. [3]
Show that this hutch has enough floor space for the two rabbits.
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 3·2 ×1800 5760 (cm2) | M1 A1 | Mark final answer. |
| Scheme | Marks | Comments |
|---|---|---|
| 4860 ÷ 1800 2.7 (kg) | M1 A1 | Allow embedded answer |
| Scheme | Marks | Comments |
|---|---|---|
| (area of hutch 150 ×80 =)12 000(cm2) | B1 | Ignore irrelevant calculations |
| (area needed=) 4860 + 5760 OR (area left for large rabbit =)12000 – 4860 (=7140) OR (area left for small rabbit =)12000 – 5760 (=6240) OR (area left over =)12000 – 4860 – 5760 (=1380) | M1 | FT ‘their 5760’ FT ‘their 12 000’ where subtraction leads to a positive answer. |
| 10620(cm2) (so the area is smaller than 12 000cm2) OR 7140 is greater than 5760 OR 6240 is greater than 4860 OR 1380 (is left over) | A1 | FT ‘their 12 000’ if greater than 10620 |
Alternative methods
| Scheme | Marks | Comments |
|---|---|---|
| (area of hutch 150 ×80 =)12 000(cm2) | B1 | |
| (3.2 + 2.7) ×1800. | M1 | FT their ‘2.7’ |
| 10620(cm2) (smaller than 12 000cm2) | A1 | FT 'their 12 000’ if greater than 'their 10620' |
| OR | ||
| (area of hutch 150 ×80 =)12 000(cm2) | B1 | |
| (mass of rabbit allowed =)12000 ÷ 1800 | M1 | |
| = 6.6(6….) and comparison with 3.2 + ‘their 2.7’ | A1 |