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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 ... ...

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.

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 ...