When adding two fractions
Take care, delay your actions.
You must allow the whole
To exercise its role.
(Possibly and unwittingly owing something to Ogden Nash)
This is a plug for Jose Vilson, in particular this post:
The comments at the end of this post about the futile nature of current math education by Ted Dintersmith should be posted on the side of the Empire State Building.
Let’s have a number line. We can count up or down by moving to the right or the left, or actually up or down if the number line is drawn vertically.
But what else ?????
The following pictures show how points on the number line which represent fractions can be found exactly by simple geometrical construction, and then how results of multiplication and division of fractions can be found exactly as points on the number line (sorry, the numerical values are however not found).
This arose from a statement in the CCSS math document that the fraction 1/6 could be represented by a point one sixth of the way from zero to one, BUT NOWHERE DOES IT SAY HOW TO FIND THAT POINT.
Being in complete agreement with Dan Meyer on the term “Write an expression” I take exception to the vague instruction “Write a number sentence”.
Multiple choice question – Which of the following is a number sentence?
a) 3 + 2 = 5
b) three + two = five
c) three and two makes five
d) 2 + don’t know = 7
e) seven is 5 more than 2
f) they gave him 20 years
g) Mary gave three of her sweets to Jane and was left with 5
h) none of these, although they all have a verb
Answers on a postcard please, addressed to Santa Claus, North Pole
and next time I have much to say about “equations”