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ESTIMATING
Introduction
Sample Activities

 

Estimating is the process of producing an answer that is not exact but is sufficiently close to allow decisions to be made. In the age of computers and calculators, estimation skills are crucial for the recognition of reasonable answers and for solving problems in which an exact answer is not needed, or is impossible to compute.

Almost everyone uses estimation in day-to-day living, whether it be in computation or in estimating a measurement or a quantity. In fact, survey reports suggest that estimates probably represent as much as 80% of all real-world uses of mathematics.

Research has confirmed that children can develop estimation skills, but they must be given the opportunity to do so. The development of estimation skills is a lengthy process that can be accomplished only over a period of many years.

From children's earliest experiences with numbers and measurement, estimation should be an ongoing part of their mathematical experiences. Instruction should emphasize the development of an estimation mind-set. If children are encouraged to estimate, they will accept estimation as a legitimate part of mathematics.

Through instruction children should develop an understanding of the following:

Estimation skills fall into three distinct categories:

Each of these estimation skills, along with strategies that can be used in association with them is described below.

Estimating Quantities

Estimating the number of items in a given display without counting can be accomplished by using the following strategies:

Using a Referent

Children can learn to estimate quantities through visual inspection by internalizing an experiential base that can be used as an anchor or referent.

The overhead projector can be used to help children to develop referents for estimating the number of items in a set. The children should be provided with twosecond exposures to sets of 10 (and later 20, 50 and 100) objects in a variety of different configurations and asked to classify the sets as "less than 10 (20, 50, 100)", "about 10(20, 50, 100)" or "more than 10 (20, 50, 100)"


Less than 10, or about 10?

Through frequent experiences of this nature, the children will eventually acquire a holistic sense of 10 (20, 50, 100) which can then be used as a referent in later estimation activities.

Using Sampling

Sampling techniques can be used to obtain estimates when dealing with large quantities. In sampling, the number of items in a part of the entire set is counted, and this number is then multiplied by the number of parts.

e.g., In estimating the number of dried beans in a jar, the children count the number in a handful, count the number of handfuls and multiply.

Estimating Measurements

Several strategies can be presented to children to help them to arrive at a measurement through visual inspection (i.e. without the aid of measuring instruments). They are described below.

Using a Referent

Children should be helped to establish referents to assist in estimations involving standard units of measurement:. e. g.,

Chunking

In this process, the whole is broken into subparts, an estimate is given for each part, -and the estimates are then totalled.

e.g., To estimate the length of a room, you could estimate the distance from the corner to the door, the door to the window, and the window to the far corner, and then total.

Unitizing

In this strategy, the whole is broken into approximately equal parts, an estimate is given for one part, and then multiplied by the number of parts.

e.g., If asked to cut a string that is 3 metres long, you could estimate 1 metre and take 3 of these.

In estimating quantities and measurements, it is important that children learn to check their initial estimates and then make additional ones so that they can use the feedback to refine their estimating skills.

Computational Estimation

Computational estimation is a mental process that is performed quickly without any recording tools and results in answers that are reasonably close to a correctly computed result.

Computational estimation is an important and practical skill because of its usefulness and convenience. The problems presented below illustrate a few examples of how it is used in our daily lives.

Many children are accustomed only to exact answers in mathematics and must be helped to feel comfortable with the idea that an estimate is not an exact amount. Developing an awareness of what computational estimation is about and highlighting everyday uses of it will help children to acquire a tolerance for approximations and recognize computational estimation as an essential and practical skill.

Research suggests that unless computational estimation strategies are taught, most children will neither learn nor use them. Specific instruction should be followed by opportunities to practise the strategies introduced. Short practice sessions of five to ten minutes each week are recommended.

There are no rules for estimating, but teaching children a variety of strategies to use can help them to make reasonable estimates. The following strategies are suitable for presentation to Junior Division children provided they possess the necessary prerequisite skills:

Front-End Truncating

2446
4219
+ 7112

Add the thousands
Estimate about 13000

Front-End and Adjust

426
275
+ 126
The hundreds total 700
The tens and ones total about 125.
Estimate: 825

 

Front-End Rounding

43
x88
Round to give mentally manageable numbers: 40x90
Estimate: 3600

 

Look for Compatible Numbers

1) 26+79+49+38+56+60=
There are three groups that each total about 100 - 100 100 100
Estimate: 300

2) $8.69 divided by 24=
Change to compatible numbers which are easier and more mentally manageable.
e.g., $8.80 / 22 or $8.00 / 20
Estimate: $0.40

Use Easier Numbers
7/8 + 2/3 =
Each fraction is a little less than 1.
Estimate: a little less than 2.

Look for Clustering
275+314+294+325+264=
All numbers cluster around 300.
Estimate: 5 x 300 = 1500.

Compensating
12.3 + 25.8 =
Round 12.3 down and round 25.8 up
Estimate: 12 + 26 = 38

The development of estimation strategies cannot be accomplished in a single unit. Instruction should be systematic and ongoing, and teachers should look for ways to incorporate estimation into other subject areas and into the everyday happenings of the classroom.

The following suggestions are given to assist teachers in developing effective estimation skills with their children:

Estimating Activity #1:

1) Estimate how much candy there is in total in the bag. Record your individual answers. What strategies did you use to estimate? RECORD your strategies on the CHART PAPER AS A GROUP.

2) AS A GROUP, estimate and divide the candy so that there is approximately the equal amount of candy distributed on 5 paper napkins. RECORD your estimation strategies for dividing the candy on the CHART PAPER AS A GROUP. Don't eat the candy!

3) Estimate how many candies each person would get if we shared them with the rest of the South Option. NOTE: There are 60 people in the South Option. Record your individual answers and RECORD your estimation strategies for this problem on the CHART PAPER AS A GROUP.

Estimating Activity #2:

1) Estimate the perimeter of Canada without using a map. Record your answer individually. What strategies did you use to estimate? RECORD your strategies on the CHART PAPER AS A GROUP.

2) NOW, Use the map of the World to estimate the perimeter of Canada as a group. RECORD your estimation strategies for estimating the perimeter of Canada on the CHART PAPER AS A GROUP.

Estimating Activity #3:

1) Conduct an experiment in which each member of the group estimates how long one minute is by closing their eyes and opening them when they think one minute is up. A chosen recorder of the group records the number of seconds that pass one minute or the seconds less than 1 minute.

2) AS A GROUP, discuss the strategies used to estimate one minute and RECORD your strategies on chart paper AS A GROUP.

3) REPEAT THE EXPERIMENT. On the second try, do you get better at estimating how long one minute is? RECORD why this is so on chart paper as a group.

Estimating Activity #4:

Use only 1 Strawberry Lace Candy Strip.

1) Estimate how many paper clips it would take to measure the length of the strawberry lace candy strip. Record your individual answers. What strategies did you use to estimate the length? RECORD your strategies on the CHART PAPER AS A GROUP.

2) Estimate the length of the strawberry lace candy strip in centimetres. Record your individual answers. What strategies did you use to estimate the length? RECORD your strategies on the CHART PAPER AS A GROUP.

YOU MAY DIVIDE YOUR ONE STRIP OF CANDY SO THAT THERE IS ENOUGH FOR ALL THE MEMBERS OF YOUR GROUP TO EAT. WHAT STRATEGIES DID YOU USE TO DIVIDE? RECORD YOUR ANSWERS ON CHART PAPER.

Estimating Activity #5:

1) Estimate the sum or difference of these two calculation problems:

$1.42 + $3.67 AND $4.85 - $2.65

RECORD THE ESTIMATING STRATEGIES YOU USED TO CALCULATE THE ANSWER. RECORD ON CHART PAPER AS A GROUP.

2) The school library has 894 novels and 649 non-fiction books. Estimate how many more novels than nonfiction books the library has. Estimate the total number of books the library has.

RECORD THE ESTIMATING STRATEGIES YOU USED TO CALCULATE THE ANSWER. RECORD ON CHART PAPER AS A GROUP.