The first thing we noticed was that 137 is one less than 138. We therefore have a difference of one group of 28 between the two calculations. To calculate the answer to 138 x 28, all we have to do is add 28 to 3836 because we know that this is correct.
Therefore, we don't need to use long multiplication or division methods for the inverse; all we need to be able to do is add two numbers, which we can all do!
Kim's answer should be 3864.
The words 'rough estimate' told us that we weren't looking for an exact answer, so we found 'roughly' half of the total number of calls, which was 45-46. We then noted that this phone call would have been the halfway point in the 60-89 seconds interval, meaning that it was approximately 75 seconds long. Therefore, half of the calls took place before this and would have lasted for less than 75 seconds.
Lots of resilience was required, but we got there in the end!
This question required a systematic approach. We had to think of all of the different types of number and try calculations involving them all. E.g. negative numbers, positive integers, decimal numbers, 0 and numbers smaller than 0 such as 0.2 etc.
All we needed was one calculation that proved Alfie wrong, as he said that every calculation proved his point.
E.g. 0 x 7 = 0
0.5 x 6 = 3
-1 x 8 = -8
The list is endless!
Therefore, Alfie is wrong because in all of the above examples, the answer is smaller than or equal to at least one of the numbers in the question.
This week we have been looking at the next method of problem solving, which was spotting patterns. This is yet another area of Maths that we needed our times tables for! We worked our way up to the tricky Level 3 questions by going through levels 1 and 2, which were more straightforward.
We had to work out the difference between the numbers, before identifying how far they had been moved (or 'shifted').
At first, this problem seemed a little daunting. With so many points to meet, it was difficult to know where to start. We knew we were looking at trial and error (guess and check) this week, so that made it a little easier.
As a class, we made a list of all of the pairs that would satisfy the first statement (in red on the photo). We knew we couldn't go beyond 7/8 as the pairs started repeating. Then we did the same for the second statement.
Then the fun started!
We then started putting the different combinations of numbers together using the cards we made ourselves. As soon as we realised a combination wouldn't work, we removed the starting pair from our original list. We continued until we found the correct answers (we found 2).