Estimation and reasonableness: Year 3: Planning tool

Expected level of development

Australian Curriculum Mathematics V9: AC9M3N05

Numeracy Progression: Number and place value: P6

At this level, students incorporate estimation strategies and use estimation to determine the reasonableness of calculations and detect errors when solving problems. They apply relevant strategies to estimate quantities.
Apply students’ existing number sense and knowledge of place-value to make reasonable estimates when estimating quantities and when checking their solutions to calculation problems. Encourage a habit of defining a range by asking for an estimate that is too high and for one that is too low. Help students see that rounding to near, or convenient, numbers can help to determine the reasonableness of a calculation. For example, when solving 23 + 389, round the numbers to convenient numbers 20 + 400 to determine that 420 is an estimate that is reasonable. Use a similar process when estimating a quantity of objects for example a herd of animals, 100 seems too high, 20 seems too low, 75 seems reasonable.
Make explicit that estimating is not guessing, rather it is a practice of reasoning. When estimating quantities, we know what 10 might look like or 100. We draw on past counting experiences or our visual sense of the comparative size of a collection, and our existing mental objects of number. When estimating the answer to a calculation, existing place value knowledge is often used together with rounding and mental computation.
Estimation can also be applied to measurement for example, recognise and use the relationship between formal units of time including days, hours, minutes and seconds to estimate and compare the duration of events. (AC9M3M03)

Teaching and learning summary:

Give students number problems to solve that encourage them to choose a number operation.
Provide regular opportunities to estimate quantities, including in day-to-day situations.
Explicitly teach and provide meaningful contexts in which to apply rounding up and down when making estimations about the answer to addition problems.

Students:

use estimation to detect and correct computation errors
use what is known, together with rounding to convenient numbers (e.g. multiples of 10 and 100), to make reasonable estimates to addition problems involving two- and three-digit numbers.

Some students may:

lack a mental object of number and/or place value understanding and need to guess rather than use reasoning to make estimates. To address this, support a deeper understanding of one- and two-digit numbers through regular subitising, counting and renaming of the numbers to 10, then 20, then beyond.
think that estimating is simply guessing. To address this, be explicit about how we draw on our existing understanding of number when making estimates (e.g. ‘I know what 5 looks like and this is a lot more than that.’ or ‘I know that 42 is close to 40 and 18 is close to 20.').

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

We are learning to use our number knowledge to make estimates.

Why are we learning about this?

Estimation is used in everyday life and work.

What to do

Explain why making an estimate is not simply guessing. Use an example such as using an estimate to get a rough idea of how many in a collection, a rough idea of how much a grocery bill will cost, a rough idea of how much time until a particular event happens.
Make an estimation before counting a collection. For example:
1. How many pieces of fruit do you think are in the bowl? What number do you think is too low? What number do you think is too high?
2. How many buttons do you think are in the jar? What number do you think is too low? What number do you think is too high?
Use estimation when shopping. For example:
1. How much money to we need to pay for these items? (Round prices up to make calculations easier. Round $2.75 to $3 and $4.50 to $5. Add $3 and $5 together.) $8 will cover it.
Use estimation with time. For example:
1. How long do we have to get ready? It’s about 5:00 pm. We need to be there by 5:30 pm. It takes about 5 minutes to drive there. We’ve got, at most, 20 minutes to get ready.

Success criteria

I can:

make estimates that are reasonable
use what is known together with rounding to convenient numbers (e.g. to multiples of 10) to make reasonable estimates in addition problems.

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