Foundation June 2017 Paper 2 Q3
3
(a) Nathan works out \(23 \times 12.4\) without a calculator.
This is Nathan’s working.
| \(10 \times 12.4 = 12.40\) \(20 \times 12.4 = 24.80\) \(\phantom{2}3 \times 12.4 = 37.2\) \(23 \times 12.4 = 24.80 + 37.2 = 62\) |
Nathan’s working is incorrect.
Explain the error that Nathan has made and work out the correct answer. [3]
(b) Four friends buy cinema tickets using this offer.
Cinema tickets Buy 3 tickets and get a ticket free |
They each pay £6.45.
How much does a ticket cost? [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| When multiplying [12.4] by 10, Nathan has not moved the figures to the left [he has just added a 0] | 1 | Accept \(12.4 \times 10 = 124\) not 12.40 | Condone he has not moved the decimal point to the right soi Accept reference to either first or second line of working See Appendix B |
| 285.2 | 2 | M1 for \(12.4 \times 20 = 248\) or \(124 \times 2 = 248\) | Accept 248 seen If \(12.4 \times 23\) is worked out using grid method, allow M1 if no more than one error. If other long multiplication method used, allow M1 if not more than one arithmetic slip but M0 if error in place value |
Appendix B
Exemplar responses for Q3(a) explanation mark
| Response | Mark |
|---|---|
| For 10 × 12.4 Nathan has only times by 1. For 20 × 12.4 he has only times by 2. 10 × 12.4 = 124. Accept identifying that he has timesed by 1 instead of 10, or by 2 instead of 20. | 1 |
| 10 × 12.4 is not 12.40 it is 124. He didn’t add the 0s onto the numbers. 10 x 124 is not 12.40 it is 124 scores 1, ignore the rest of the explanation because it is unclear rather than being incorrect. | 1 |
| He added 0 to 12.4 Explains what he has done wrong. | 1 |
| He does not move the decimal place when he x by 10 so it should have been 124.0. Doesn’t need to say where | 1 |
| Nathan has got the place value wrong on first answer. They have correctly identified that the error is in the place value | 1 |
| 10 × 12.4 = 124 so 20 × 12.4 is wrong Allow identification of error in second line | 1 |
| Instead of moving the decimal place to the right he just added a zero to the end of the number and instead of multiplying he add. Ignore final part of statement | 1 |
| He hasn’t multiplied it he just added a zero that makes no difference. Error identified and ‘makes no difference’ explains error | 1 |
| He said that 20 × 12.4 is 24.80 when it is 248 which means the answer is 285.2 Accept reference to second line of working | 1 |
| When Nathan done 10 × 12.4 it should equal 124 10 x 12.4 = 124 is not enough. ‘It should equal 124’ is just about enough to identify the error. | 1bod |
| When he multiplied by 10 he didn’t remove the decimal place and same when he multiplied by 20 Multiplying by 10 isn’t the same as removing the decimal place. | 0 |
| Nathan kept the decimal in. When calculating a sum with a decimal you take it out as you do the sum then put it back at the end. Too vague. | 0 |
| Nathan has divided the 12.4 rather than moving the decimal point to the right (positive/multiplying) Moving the decimal point to the right would score 1, but we can’t ignore the rest of the explanation because it is incorrect rather than unclear. | 0 |
| 12.40 is wrong Identifies error but doesn’t explain | 0 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 8.60 | 3 | M2 for \(6.45 \times 4 \div 3\) oe Or M1 for \(6.45 \times 4\) oe or 25.8[0] seen | |