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Challenging all students
Students at all levels of attainment should be challenged in mathematics. The greatest gains in mathematics learning are made when teachers have high expectations of all students. A research project called Effective Teachers of Numeracy in Primary Schools showed this.
The Above and Below the Line activity allows all students to make a contribution at their own level of reasoning by contributing different numbers (e.g. larger, negative or fractional).
Jan's Train is a problem that is easy to adapt for most primary levels — either whole classes or individuals. Variations could be made to the lengths of the train sections and the number of carriages. The open nature of the latter tasks encourages careful listening as well as sharing of reasoning.
Years 5–8 teachers may be interested in an article about challenging mathematics in Singapore.