The power of estimation
Sandhya Singh
What is measurement? What is measurement for children?
If you ask children to measure an empty bucket, the first thing they will need to know is what about the bucket is to be measured. Children need opportunities to explore how an object can have many different measurable attributes. For example, let’s take an ice cream cone. What questions are children likely to ask?
1. How long will it take me to eat the ice cream cone?
2. How much ice cream will I need to fill the cone?
3. How high can I pile the ice cream before it falls over?
4. Will my hand fit around the cone?
Children construct the meaning of measurement in terms of length, weight, volume, capacity, time and money. According to the constructivist approach children construct knowledge using their immediate environment. So to help children understand a concept we must build their knowledge of the concept using familiar contexts and objects. For example, to measure length (approximately) they can use hand or foot span, duster, books, sticks, etc. For weight, they can use food packets, vegetables, fruits, etc.
While teaching measurement we generally focus on the units of measurement and their relationship with each other. It is important to understand the need for standard units and their application in daily life. But before children actually learn to measure objects accurately it is important to teach them how to estimate measurement. It is not always that you have the proper tools with you to measure exactly. In fact, more often than not we depend on estimation to carry out activities in our daily lives. For example:
1. In the kitchen we estimate the measure of spices to cook food.
2. We estimate the time to complete household work.
3. We estimate the money to go shopping.
4. Estimate the weight of fruits and vegetables while shopping.
5. Estimate the capacity of a utensil to pour milk.
6. Estimate the time to complete homework.
Building a sense of distance, length, weight, capacity, time or even money is a very important part of measurement which enables children to use their learning in the outside world.
Van se Walle and Folk (2005) in their book Elementary and Middle school mathematics Teaching Developmentally identify four reasons for including estimation in classroom measurement activities:
- Estimation helps children focus on the attribute being measured and on the measuring process. For example, when children measure the weight of a basket, they need to think about what the weight is and how it can be measured.
- Estimation offers intrinsic motivation for measuring. It encourages children to make estimates that are as close as possible to the actual measurement. For example when drinking milk from a glass, a child can estimate whether she has had a half glass of milk, more than half a glass of milk, almost a full glass of milk.
- Estimation helps develop a familiarity with the unit being used, especially when standard units are being used. For example thinking about the size of one centimetre helps estimate a length in centimetres.
- The use of a benchmark to make an estimate promotes multiplicative reasoning and contributes to the understanding of the relationship between numbers. For example, my brother is double my height.
Here are some activities by which you can strengthen estimation skills in children.
Activity: Choose an object. Let’s say a box. Each day select a different attribute or dimension to estimate.
Instructions to give: For example:estimate the length, width, volume, weight. Make sure that children use references (a benchmark or informal measuring units) while estimating.
Activity: Use a transparent jar and marbles. First fill the jar with 10 marbles so that students can observe how much space 10 marbles occupy and then fill the jar.
Instructions to give: How many marbles are there in the jar?
Activity: Have two children of different heights come to the front of the class. Measure one child’s height.
Note: You can use this activity to estimate weight as well.
Instructions to give: Estimate the height of the other child.
There are many strategies to develop estimated measure. Let’s explore them with more activities.
a.
Developing benchmark
Activity : Give a list of some standard measurement and have them find things that are close to these measurements.
Instructions to give: Find objects whose lengths are about 1 m/1 cm. Choose an object whose weight is about half a kilogram.
Children must pay attention to the size of the unit to estimate well. Let the children find the actual measurements of an object and then use this object as a reference to estimate measurements of other objects. You can use the following activity as a startup.
Activity : Measure your body.
Instructions to give: How long is your foot, your stride, your hand span, the width of your finger, your arm span, distance around your wrist and around your waist? How tall are you up to your waist, shoulder, and head? What you find may prove to be useful benchmarks for standard units, and some may be excellent models for single items/objects that are to be measured (the average child’s fingernail width is about 1 cm, and most people can find a 10 cm length somewhere on their hands.)
b.
Chunking
Activity : Use about 20 paper clips to make a chain. Tell the children that the length of one paper clip will be one and a half centimeters.
Instructions to give: What will the length of this chain be?
How did you estimate?
What will be the length now? (Ask this question after you give the actual measurements of the paper clip. This will help children check how close they came in their estimation.)
Here children use the measure of a small part of the whole and estimate the measure of the entire object. In the above activity children estimate the length of the whole string using the length of one paper clip.
Activity : Draw a big line segment on the board. Cut 1 cm paper strips. Tape one strip at one end of the line segment.
Gradually tape as many strips along the length of the line segment so that children can estimate.
Instructions to give: How many strips of paper this length can we tape along the line segment?
Where is the middle of the line segment?
How many paper strips do you think it will take to reach the middle?
c.
Sub division
:
Activity: What is the approximate length of your bench? Ask them to think about the middle of the bench. If children don’t find a measure for half of the bench then try one fourth of the bench.
Instructions to give: Think of something whose length is equal to half the length of the bench.
What was the measure of that object? Now can you estimate the length of the bench?
If not, think of one fourth of the table.
Can you think of an object whose measure is equal to one fourth of the table? And so on if needed.
In the above activity if children want to estimate the whole measure, they can divide the whole into half, or fourths or eights until a more manageable measure is arrived at.
d.
Iteration of a unit
:
Activity: What is the length of your arm? Use toy blocks to measure.
Instructions to give: What is the length now? (Ask after every time they add a few blocks).
If two hand spans equal 10 cm then what will be the length of your arm?
Here children use the iteration of a familiar unit (hand, finger, foot, nail, etc.) and estimate the measure of another object. You can use easily available materials to iterate. For example, book, duster, pencil box, etc.
Now you know different strategies to build estimation skills in children. The more such opportunities you provide them, the better children will get at estimating.
Some classroom tips to estimate
- There is no one right way to estimate. Each student may estimate differently.
- Tell the children how close their estimation is with respect to the actual measure. This helps them to think in relative terms.
- Accept the range of estimation (minimum to maximum) that students give.
- Frequent opportunities to estimate help children understand that experience and refinement of estimation skills will help produce more accurate estimates.
- Vocabulary can cause confusion in children. Do not use measurement and estimation interchangeably.
Note: The author wishes to thank Monica Kochar, mathematics expert, for her editorial help with the article.
The author holds B.El.Ed and M.Ed from the University of Delhi and M.A. Mathematics from SHIATS, Allahabad. She has worked with ‘Currimakers’ as a mathematics content developer and teacher educator. She has conducted workshops in various B.El.Ed colleges to give exposure on ‘Facets of curriculum’. Her areas of expertise are writing elementary mathematics curriculum, teacher training, research on pedagogy of mathematics and development of assessment tools. She can be contacted at sandhyasingh11ms@gmail.com.
