Monday, 11 June 2018

ALG 18

This week we look at the rules of arithmetic, as expressed through the use of brackets. But we start informally, with a 'real life' task, specifically a sour dough problem, which may not be to everyone's liking....
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MONDAY: A lighthearted story about pizza slices.
TUESDAY: Here we complete some numerical expressions involving brackets to describe a set of dots.
No pizzas.... No pseudo contexts...? Just dots. Simple.
Note: I have curtailed the string of expressions a bit. You might, for example, want to insert the expression 3×5×(20+?), and perhaps also 3×(5×20 + 5×?), between my second and third expressions.
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WEDNESDAY: Here we look at expressions that give the total number of dots in a (recursive) dice pattern.
Note 1: we have used brackets more frequently than is strictly necessary here, so that the order of operations is explicit and unambiguous, ie so that the expressions can be read without knowing the conventional order of operations. Of course, it is important to learn these conventions but it means that the current expressions should be accessible to a high proportion of students. Also, as the expressions refer to familiar, concrete elements that are easy to group and count, the work should help demystify the use of expressions involving brackets - students don't need to refer to rules like 'do the brackets first' to make sense of the notation.
Note 2: you might want to ask students to annotate the diagram, or to draw a revised diagram, to show how the dots are being structured by the various expressions.
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THURSDAY: Here we use expressions to count dots in some partitioned/compound arrays.
Again, it might be helpful to annotate the sets of dots to show how they relate to the expressions.
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FRIDAY: We look at some neat and some not so neat ways of performing the calculation 15 × 22.

This slide is somewhat overloaded. It's really two tasks in one. And for the first task, it would be better to introduce the parts one at a time. Then, having worked through these exemplars, it should prove fruitful to devote time to students' methods of calculating 15 × 22, and to representing these as strings of expressions involving brackets.
The second task should help students take a more conscious, formal view of the distributive law and to think about when it applies.

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