Understanding sequencing and fraction differences.
Context: It would normally follow on from work on sequences and fractions
Question: Ruth was investigating fraction differences. She wrote down this sequence of fractions:
1/1, 1/2, 1/3, 1/4, 1,5 1,6 ... ...
Then she worked out the difference between the consecutive fractions:
1/2, 1/6, 1/12, 1/20, 1/30, .. ..
She Then worked out the differences between the Fractions in her second series.
1/3, 1/12 ... ...
When doing this question make sure your look at these three things,
1. Making and monitoring decions to solve problems.
3.Developing skills of mathematical reasoning.
... 4,6,8,10,... is easily seen and can be continued to produce the next numbers in the sequence
<br>1/2, 1/6, 1/12, 1/20, 1/30, 1/42, 1/56,...
<br>by adding in the denominator, without using the more difficult method of subtracting the elements from the first sequence.
<br>The next sequence,
<br>1/3, 1/12, ...
<br>is too short to draw conclusions. I might guess that, since the difference between the denominators is 12-3=9, the next denominator might be 12+(9+4) or something like that, but I will have to make the ...