This is a level 3 link measurement activity from the Figure It Out series. It relates to Stage 6 and 7 of the Number Framework.
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make estimates of measurements
3 classmates
Estimating is an important skill that can be used in many real-life situations, and it’s one that improves rapidly with practice. This activity gives students opportunities to develop their estimating skills in a variety of different scenarios.
It is useful to recognise three kinds of estimation processes (and skills):
1. Measurement. This kind involves a measurement (continuous) variable and requires the use of suitable benchmarks. See Judgment Calls for examples.
2. Computational. This kind involves simplifying numbers in an appropriate way to reduce the complexity of a calculation, often to the point where it can be done mentally.
3. Numerosity. This kind involves estimating the number of items in a given situation (always a discrete or whole number variable). This is done by benchmarking and often goes hand in hand with computational estimation. Examples include the number of people in a crowd, coins in a stack, or fish in an aquarium.
When tackling the challenges in Eyeball Estimates, students should try and distinguish which of the three kinds of estimation are involved.
Use question 1 as the subject for class discussion or small-group discussion followed by a report back and class discussion. It is important that students understand that estimate and guess are not the same thing (see the introduction to Judgment Calls, pages 23–24) and why they need to know how to estimate.
Estimating is the process of coming up with an approximate answer that is accurate enough for our purpose. Estimates are useful:
After looking at how Lakisoe and Sara estimated the number of people that would fit into their school hall, ask the students to suggest situations where they have used estimation or observed others using estimation.
Ask them why it was more appropriate or useful to estimate in those situations than to make an accurate measurement or do an exact calculation.
Question 2 gives students a number of scenarios and asks them to choose three. This means that they can choose ones that interest them and have an appropriate level of difficulty. They are told to write their methods down; this is part of the learning process, and the written notes are needed for the discussion that takes place in question 3.
In each case, the estimate must be based on some real information with numbers in it; otherwise it is a guess, not an estimate. This information may be a known fact (a benchmark), or it may need to be gathered:
You will need to decide how much help you should give your students before sending them off to make their estimates. One approach is to put them into pairs, give them time to decide which of the estimates they are going to work on, and get them to write down the methods they plan to use. They could then combine with another pair (who may have chosen different challenges) and critique each other’s strategies. Or you could get the whole group together to say which challenges they are taking on and to share plans before putting them into action.
Your students may struggle with some of the calculations if they aren’t allowed to use a calculator, but wherever possible, they should try to cope without. They won’t see the point of simplifying the numbers (for a computational estimate) if they can equally easily work out the exact result. Encourage them to use a pencil and paper to jot down intermediate working stages.
Questions 3 and 4 are for follow-up. Question 3 should highlight the fact that there is normally a variety of different ways of arriving at an estimate and that there is no one “correct” estimate for any given situation.
You will need to make it clear that one estimate may be better than another (because it gives a better approximation of the actual measurement or number) but that both may be completely acceptable estimates. This is not the same as saying that any estimate is OK. (10 is not an acceptable estimate for 27!)
Try these questions to promote reflective thinking:
1. Answers will vary. One possible definition is: “Estimation is when we work out a rough (but good enough) answer.” Some reasons why we estimate:
i. In the circumstances, an estimate may be all we need or want.
ii. For some practical reason, it may be difficult to get exact numbers or measurements.
iii. We don’t have a calculator with us, and the numbers are too difficult to work with in our head.
iv. We’ve worked out the answer on our calculator and want to check if it is sensible.
2. Answers and methods will vary, even for exactly the same challenge (for example, two students estimating the height of the same tall tree).
3. Practical task. The important thing is that you can explain to your classmates how you arrived at your estimates and why you chose the methods you did.
4. Practical task
Printed from https://nzmaths.co.nz/resource/eyeball-estimates at 9:55pm on the 12th May 2024