Throughout all the strands of this curriculum emphasis has been placed on the development of estimation strategies. Estimation is the process of taking an existing problem and changing it into a new form that is easier to compute mentally and gives an approximate answer. This skill is essential for real-life mathematics, for example shopping or measuring time and distances.
From the very early days at school children need to be encouraged to estimate. The young child finds it difficult to differentiate between 'estimate' and 'answer'. The teacher will have to lead the work by encouraging them to make a sensible 'guess', to test their guess and revise it where needed. Estimation is a help towards finding a solution but need not in itself be the solution. This is important in measurement activities, where the children can be encouraged to compare objects as being 'a good bit longer than ...' or 'only a little heavier than ...'
Children must also be taught to investigate the reasonableness of their results. They can be encouraged to develop their own ways of deciding when an answer is reasonable. They can be presented with a problem and several solutions, from which they select the most reasonable solution.
Estimation is also necessary for work with calculators so that the child can evaluate the validity of the result given by the machine. Quick recall of number facts and a strong number sense are important for efficient estimation. There are many different approaches to computational estimation, and good estimators use a variety of strategies.
Front-end strategy
This strategy has its strongest application in addition. The left-most digits (front-end) are the most significant in forming an initial estimate and can be used on their own in the earlier stages to establish a rough estimate:
€
1.54
6.35
0.99
2.51 +
front-end process:
add the front-end amounts: €1 + €6 + €2 = €9
adjust by grouping the pennies to form euro 54c + 35c makes €1 approx.
99c is nearly €1
51c is nearly 50c
cents estimate: €2.50 overall estimate is €11.50 (€9 + €2.50).
This strategy can be introduced by using money initially but works equally well with whole numbers, fractions and decimals. The adjustment stage can be introduced gradually as the children become familiar with the concept of 'nearly €1' or 'nearly 50c'. It can also be accomplished with multiplication for example,
369 x 6
300 x 6 = 1800
70 x 6 = 420 Estimate is 2220
Clustering strategy
This is best suited to groups of numbers that 'cluster' around a common value, for example
Numbers of people who came to our concert
Monday 425
Tuesday 506
Wednesday 498
Thursday 468
Friday 600
The average attendance was about 500 per night.
500x5 nights = 2500.
Rounding strategy
Numbers can be rounded in many different ways. The choice of rounding process will produce different but reasonable results, and this can be refined according to the child's ability to compute mentally. It is necessary to give children plenty of mental practice
with this method and demonstrate how it can be refined by choosing closer rounding factors. Using this strategy can generate plenty of discussion about why one child's answer is different from that of another.
37 x 59: in this case it would be best to round both numbers up:
40 x 60 = 2400
51 x 22: here we would round both numbers down to 50 and 20:
50 x 20 = 1000
24 x 65: they are both close to the middle so you can try rounding one
down (20) and one up (70):
20 x 70 = 1400
Rounding can be used with the four operations but is very useful in division. In division it is often better to round up:
419 ÷ 65 could be rounded to
420 ÷ 70.
Special numbers strategy
This strategy looks for numbers that make patterns, for example tens or hundreds
(a)
3
5
7
4
6 +
(b)
37
54
71
42
69+
(a) 3 and 7 are ten, 6 and 4 are ten, that's 20; add the 5, this totals 25
(b)older children could group the tens using a mixture of rounding and compatibility, for example 37 and 42 is about 80 ...
Estimation skills are essential throughout the strands and at all class levels. These skills can be used in Measures in conjunction with using a known unit, for example nearly a metre, less than a litre, about half a kilogram and in fractions and decimals: close to 0, close to a half, close to 1.