Mathematics Developmental Continuum P-10

Making Better Estimates: 1.0

Supporting materials

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Indicator of Progress

Making better estimates involves experience with estimating numbers and quantities, testing the estimate and using the experience to learn how to make better estimates. A key part is knowing when 'close enough' is appropriate and when an exact answer is required.

Prior to this, students will not know the difference between making a guess and making an estimate. As their knowledge and skills develop, students will use estimates as part of problem solving, for example to estimate the size of an answer. Estimating is an important support for computation, to check that the size of the answer is appropriate.

 

Illustration 1: Learning from estimates

Good estimators will be able to estimate how many marbles are here and describe the strategies they use. After they count the marbles, they can discuss whether their estimate was a 'good' one. The students can then estimate how many marbles are in the next container.

Illustration 2: Estimating the answer to computations

On the way to swimming, there are 9 students in one bus and 12 in another bus. How many students are going swimming?

Students who are good estimators might say that the first bus has about 10 students and the other about 10 and estimate the answer as 20. They can then find the exact total by putting out the right number of counters and counting, or by using a calculator.

 

Illustration 3

Examples of the types of tasks that would be illustrative of estimation concepts, aligned from the Mathematics Online Interview:

  • Question 1 - Estimate and count teddies scooped into a cup (at least 20)

 

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Teaching Strategies

Students need to have experiences making and checking estimates. Teachers also need to discuss with students the appropriate times for estimation, compared to a need for an exact answer.

Activity 1: How many marbles? provides practice at estimating numbers and sharing of strategies.
Activity 2: Sharing strategies for checking estimates provides practice at estimating quantities such as capacity, length and time.
Activity 3: Estimating calculations provides practice at estimating quantities and sharing strategies.

 

Activity 1: How many marbles?

Preparation: Put different numbers of marbles into approximately 20 different-sized labeled jars with lids. Label the jars A, B, C etc.

Students estimate how many marbles are in individual jars. They then check their estimates by opening the jars and counting the marbles.

Estimate the number of marbles in the first two jars as a group activity. When each student has made an estimate, count out the number of marbles, checking the estimate.

Next, students make 2 or 3 estimates and discuss the strategies they are using for estimating. In this task, keep the number of actual marbles a secret.

The students then complete the estimates and the checking, recording their results as they go.

Some students' estimating strategies might include:

  • comparing with a known quantity (I know that jar has 10 and I think this one is just a bit less, so I guess 8)
  • building up from simple information (I can see 3 on this side and so there will be about 3 at the back, so guess 6).

The intent is that the students learn about estimating from the experience of estimating and then checking, and then estimating again.

Supplementary activities

The same process can be used for a variety of examples such as:

  • estimating the number of leaves on tree branches
  • estimating how many cups are need to fill different sized jugs
  • estimating how many hand spans long are different lengths of string

 

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Activity 2: Sharing strategies for checking estimates

Pose the problem, preferably at a time when it relates to a classroom event:

How many 2 L bottles of juice do we need for everyone in the class to have a drink?

Preparation: Bring a 2 L bottle to use as a model for the students.

Ask the students to estimate an answer. Next, the students discuss how they might work out an answer. Then they can choose a strategy to check their estimates.

The important features are

  • to build up students' knowledge of ways in which estimates can be checked, and
  • to build up their real-world experience of quantities so that their estimates are better.

Supplementary activities

The same process can be used in many different measurement contexts such as:

  • estimating how much string is needed to tie up a parcel
  • estimating the number of loaves of bread needed to make sandwiches for the class
  • estimating how long it will take to walk to the library from the classroom

 

Activity 3: Estimating calculations

Tens frame estimation

Students are given a Tens Frame and some counters. Teacher says "In one hand I have 4 counters, and in the other hand I have 4 counters. If I put one counter in each box of the frame, will the Tens Frame be completely covered? Ask students to decide, then check. The important step is to share strategies.

Estimating larger sums

The students can be posed many estimation problems in the course of a day at school. For example, approximately how many students are in the library now?

They estimate the answer as a first step. For example, they might say that the two front tables have 5 students each and there are about 5 students looking at the shelves. They can then find the exact total by counting, or by using a calculator to add the components. Again, the important step is to discuss strategies.

It is the experience of estimating for a purpose that is important. Many older students think estimating means work it out exactly then round off the answer so it looks as though they estimated. These students are showing they do not appreciate the usefulness of estimation.

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