Estimation strategies:

In the next few lessons we are going to have a look at the different estimation strategies (Rounding off strategies)

The first 2 strategies we are going to work through is the traditional and refined rounding off techniques.

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1. Traditional and refined rounding-off techniques

Image source - Rounding down

Traditional rounding off is usually guided by the following:

If the digit you round off to is less than 5, you have to round down. 

If the digit you round off to is 5 or more, you round up. 

Image source - Rounding up

Example: 

If we want to estimate 46 + 33 + 28, we round to 50 + 30 + 30 = 110 

If we had a mathematical problem in which most of the numbers end on a 5, the traditional method will give an estimated answer, which would be too high. 

Example: 25 + 45 + 22 + 96 + 35 + 35 = 258 

If we use the traditional rounding off method, we get an overestimated answer of:

30 + 50 + 20 + 100 + 40 + 40 = 280 

Refined rounding off technique:

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We can now change the traditional rounding off method to the following refined rounding off technique.

If the digit to the left of the 5 is odd, then we round up.  If the digit to the left of the 5 is even, we round down. 

Using this method, we get an estimated answer of: 20 + 40 + 20 + 100 + 40 + 40 = 260 

This estimated answer is much closer, using the refined rounding off technique than the traditional rounding off technique.  

Remember that this “=” means the answer is equal to and it is a definite answer, but the “≈” means to round off or estimate (approximately equal to)   

Activity: 

Use the traditional and refined rounding off techniques to estimate answers for the following.  (State in each case whether you used the traditional or the refined rounding off techniques) 

1. 32 + 89 + 45 + 35 + 21 + 45 =
2. 66 + 34 + 23 + 18 = 
3. 25 + 65 + 75 + 95 + 99 + 24 = 
4. 15 + 12 + 18 + 25 =
5. 45 x 25 =
6. 25 x 25 =
7. 16 x 29 =
8. 5 x 67 =

During the next lesson we will discuss estimating sums and differences of fractions as well as estimating products and quotients of fractions.