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The way we learn best in Mathematics


The best learning in Mathematics comes when we revisit earlier work to reinforce new concepts – that is, a spiralling curriculum; somewhat like this unusual cloud effect. For example, we learn our times-tables and later apply this knowledge to solving equations; then we apply our knowledge of equations to calculus, etc. So, we are always revisiting our earlier work but at a higher level as we progress through each year level. Like a tradesman, we use our simpler tools to help us handle more complex problems. That is what is great about Mathematics – even the work we did in elementary is useful in high school. Check out some more unusual cloud shapes by clicking on the pic below;

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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