Numeracy Foundation November 2019 Unit 2 Q4
4. Evan wears a fitness watch that shows the time and the number of steps he has taken during the day.
Evan goes for a run one evening.
The displays on his watch at the beginning of the run and at the end of the run are shown below.
Beginning of the run
| TIME | STEPS |
|---|---|
| 19:38 | 2656 |
End of the run
| TIME | STEPS |
|---|---|
| 20:14 | 10538 |
(a) For how long did Evan run?
Circle your answer. [1]
Circle your answer. [1]
24 minutes 22 minutes 52 minutes 36 minutes 76 minutes
(b) Write, in words, the number of steps displayed on Evan’s watch at the end of the run. [1]
(c) Evan wants to know how many miles he has run.
The number of steps taken to complete one mile depends upon the runner’s height.
The table below, taken from the internet, gives this information.
How many miles did Evan run? [4]
The number of steps taken to complete one mile depends upon the runner’s height.
The table below, taken from the internet, gives this information.
Evan is 5 feet 7 inches tall.
| Height | Steps per Mile |
|---|---|
| 5 feet | 2514 steps |
| 5 feet 1 inch | 2473 steps |
| 5 feet 2 inches | 2433 steps |
| 5 feet 3 inches | 2395 steps |
| 5 feet 4 inches | 2357 steps |
| 5 feet 5 inches | 2321 steps |
| 5 feet 6 inches | 2286 steps |
| 5 feet 7 inches | 2252 steps |
| 5 feet 8 inches | 2218 steps |
| 5 feet 9 inches | 2186 steps |
| 5 feet 10 inches | 2155 steps |
| 5 feet 11 inches | 2125 steps |
| 6 feet | 2095 steps |
| Scheme | Marks | Comments |
|---|---|---|
| 36 minutes | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| Ten thousand, five hundred (and) thirty eight | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| Identifying 2252 steps in the table | B1 | May be implied in later working May be identified in the table (must be explicit) |
| (Number of steps = 10538 – 2656) = 7882 (steps) | B1 | |
| (Number of miles =) 7882 ÷ 2252 or equivalent | M1 | FT ‘their 7882’ ÷ ‘their 2252’ Allow sight of 3 × 2252 = 6756 OR 4 × 2252 = 9008 for M1 Award M0 for 10538 ÷ 2252 OR 2656 ÷ 2252 |
| = 3·5 (miles) or 3½ (miles) | A1 | Accept embedded answers 3·5 × 2252 = 7882 Accept answers correct to 1 d.p rounded or truncated on FT |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Identifying 2252 steps in the table | B1 | May be implied in later working May be identified in the table (must be explicit) |
| (10 538 ÷ 2252) - (2656 ÷ 2252) (= 4.679….. – 1.179…..) | M2 | M2 for complete method |
| = 3·5 (miles) or 3½ (miles) | A1 |
Corrected by Westie's Workshop
- The board's mark scheme printed “10 538 ÷ 2252) - (2656 ÷ 2252)”. Changed to “(10 538 ÷ 2252) - (2656 ÷ 2252)” because the opening bracket is missing.
Original: see the board's mark scheme PDF (link above).