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Understanding sequencing and fraction differences.

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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 ... ...

Investigate Further:

When doing this question make sure your look at these three things,

1. Making and monitoring decions to solve problems.
2.Communicating mathematically.
3.Developing skills of mathematical reasoning.

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Solution Preview

The first thing I look at is the differences between numbers appearing in the sequence. Since these are fractions with 1 as the numerator, the easiest thing to look at is the differences in the denominators. For the first sequence, the difference in the denominators, 2-1=1, 3-2=1, 4-3=1, etc., is 1 and the pattern is obvious. For the second sequence, found by taking the differences between the elements of the first sequence, the difference in the denominators is:
<br>6-2=4, 12-6=6, 20-12=8, 30-20=10
<br>and the ...

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