Question
A jar contained some pebbles. Nigel took out
half of them plus 2 more for display. Jenny took out half of the remaining
pebbles plus 1 more. Finally,

Solution
We can trace what happens to the remaining pebbles at each stage, and represent the information given in a sequence as above. Note that when “Nigel took out half of them plus 2 more for display”, we would have half and then two less the number of pebbles. Similary for the Jenny’s and Alice’s stages.
Now we just do the
opposite of all the operations. The
inverse operation of ‘–5’ is ‘+5’, the inverse operation of ‘´ ½’
is ‘´
2’ and so on. Working our way backwards,
we arrive at 112.
Ans: There were 112 pebbles at first.
Commentary
Remember: In mathematics, there is no such thing as "the only way" to solve problems. There are many ways to skin the cat, as they say. Other methods to solve this question include: using algebra, and “the branching method” (taught by some tutors/teachers) which tracks
both the remaining pebbles as well as the ones taken away.
If you do use algebra (of some sort), remember to use different letters e.g. v, w, ... etc to refer to different things. Likewise, do not just write ‘½’ to represent ½ a unit, otherwise it could be misinterpreted as literally the number ½. I suggest you can surround the ‘½’ with different shapes (e.g. circle, square, triangle) .
H05. Work backwards
Suitable Levels
* Primary School Mathematics
* other syllabuses that involve whole
numbers and fractions
* any learner who is up for a challenge
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