Q&A #1154

Teachers' Lounge Discussion: Front End Estimation

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From: Xun Chen <chen@dataq.com>
To: Teacher2Teacher Public Discussion
Date: 2001092421:27:50
Subject: Front end estimmation can be very misleading sometimes

Hi, there,

My daughter came home today with the following question:

Use front-end digits to give a range for each sum.

$2909.94 + $14.53 + $3.83

The teacher wrote down the answers to it as:

Range of 2013 to 3024

Where I assume she use 2000+10+3 for the lower rage, and
(2000+1000)+(10+10)+(3+1) for the higher range.

But, on page 24 of her math text book "Exploring Mathematics", about
the front-end digit estimation, it is said that the lower end of the
range is derived from the whole number of the exact number, while the
higher end of the range is from the sum of one and whole number of the
exact number. 

When it mentions whole number, it didní»t say we should round it to a
certain place differently according to each individual number. 

To show an extreme case, considering $100000000.32 + $1, if we use the
teacher's method, we will simple come up with a range of $100000001 as
the lower end, and $200000002 as the higher end. Yes, the real number
is indeed inside this range, but it does not give a suitable picture
of the range.

My believe is that if we have to use this so-called front-end estimate
range, the numbers should be in a same order, or we shouldn't use this
confusing method at all.

Any suggestion on this topic.


Xun Chen	

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