By Henry Joseph Monck Mason
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Extra resources for A grammar of the Irish language
If they are introduced as a way to record relations between quantities, and this use is enculturated, over time, into the regular work of mathematics lessons. On entry to new schools in early adolescence, therefore, students may have significant knowledge about relations between quantities. Some students may have expressed these algebraically, or may have met algebraic formulae such as l × b for area of a rectangle of length l and breadth b. The use of conversions and formulae for area, perimeter, and volume, are useful pre-cursors for algebra (NMAP, 2008).
It helps to know what an expression means. Possibilities of this approach Programmed learning packages, or ‘teach the computer’ tasks, can be effective learning tools. Colouring, underlining, or circling particular terms can help distinguish ‘like’ from ‘unlike’ terms. Fluency with procedures can develop if exercises are well-designed and students can deal with negative signs. Students can learn about uses of algorithms and come to recognise equivalent expressions. They can learn how to ﬁnd unknowns in fully-deﬁned equations; to ﬁnd where some functions cut the x-axis; and to transform expressions into more useful forms.
In each case we evaluate their possibilities and limitations. The limitations of each method might prompt teachers to devise tasks to find out if their own students exhibit these problems. 30 | key ideas in teaching mathematics Create a need for algebra to express equivalent arithmetical relations E x amples Equivalent expressions 4a + 4 ≡ 4(a + 1) ≡ 2(a + 2) + 2a ≡ 4(a + 2) − 4 can arise from counting paving slabs round an a by a square in different ways. Equivalent equations x = 3; x + 2 = 5; 2x – 3 = 3; 7 = 2x + 1 can arise from classroom games to ‘hide the number’.
A grammar of the Irish language by Henry Joseph Monck Mason