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Fractions differences in algebra

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 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.