Estimation or not?
 select either is or is not estimating and
 explain why they are / are not estimating
 Students correctly identified whether a person was estimating or not, and identified the specific concept targeted by the question.
 Students correctly identified whether a person was estimating or not, but only made a general comment about estimation. See table called Common correct responses, just before Next Steps, for further elaboration.
 Students correctly identified whether a person was estimating or not, but did not give an acceptable explanation.
 Students incorrectly identified whether a person was estimating or not.
Y6 (11/2005)  Y8 (06/2006)  
a) 
Not estimating, and either:

easy very easy 
easy very easy 
b) 
Not estimating, and either:

moderate moderate 
moderate moderate 
c) 
Estimating, and either:

difficult
moderate 
very difficult
moderate 
d) 
Not estimating, and either:

difficult
difficult 
difficult
difficult 
e) 
Estimating, and either:

difficult moderate 
very difficult moderate 
Based on a representative sample of 173 Year 6 and 139 Year 8 students.
NOTE: Responses may be given orally to ensure that writing is not hindering the communication of ideas.
 A firm base of additive basic facts

Good place value concepts
Common error  Likely misconception  
b)  Estimating  Indicates that if numbers are rounded at any stage then it is estimation. 
b) and d)  Estimating  Sees the vertical algorithm or an exact computation as a mental strategy. 
b) and d)  Estimating  Thinks that estimation uses exact working or leads to an exact answer. 
d)  Estimating  Sees rounding 1627 to 1600 as guessing 
d)  Estimating  Believes it is estimation if the answer is close to the exact computation. 
c) and e)  Not estimating  Believes estimation must perform a computation exactly or lead to an exact answer, (or comments that the answer is wrong). 
c) and e)  Not estimating  Believes that no computation can be done in estimation, even an approximate one that can be done mentally. 
e)  Not estimating  Does not see the frontend method as an acceptable way of estimating. 
Common correct responses
Estimation is a quick mental way of getting an answer close to the exact one. It incorporates a wide range of different strategies that depend on the individual person making the estimate, and the particular problem. The following table of responses gives examples of general statements about estimation that are correct, but may restrict students' ability to explore and enhance their range of estimation strategies.
General conception about estimation  Example  
Estimation is guessing. 
"Gina is not estimating because she is not guessing." "Aroha is estimating because she is making an educated guess." 

Estimation uses rounding.  "Gina is not estimating because she is not using rounding."  
Estimation is doing it mentally. 
"Josef is not estimating because he is not using his own brain." "Aroha is estimating because she did it in her mind." 

Estimation is when the answer is close to the real answer but it is not exact. 
"Gina is not estimating because that's the right answer." "Peter is estimating because he is giving a rough answer." 

Estimation is a quick, easy way of way of getting an answer. 
"Aroha is estimating because she did the sum in the shortest possible way." "Peter is estimating because his working out is simple." 
 To encourage students to understand what estimation is and what it is not. A class discussion based upon their responses to each of the examples, with students sharing why they think the student is estimating or not, is one strategy to challenge their ideas. Using the Think, Pair, Share strategy may be a good way of conducting a class discussion.
 Discuss that estimation aims to eliminate exact computation, and is something that can easily be done with mental strategies. Emphasise that estimation is not just a pure guess, but is based on good number sense (i.e. affirm the values in the table of Common correct responses).
 Extend the range of estimation strategies for students who can discriminate between estimation and exact computation (refer to Computational estimation information). This could be through a discussion of the ways different students in the class estimate using a variety of estimation problems.
Comparison between Year 6 and Year 8 students – Research findings
Year 6 and Year 8 students performed at roughly similar levels of achievement on most aspects of these questions, with the Year 6 students outperforming the Year 8 students in the second of the two aspects mentioned below. This is unusual, as generally you would expect Year 8 students to achieve higher success rates than Year 6 students would. It is unclear why this is the case, but it may indicate that little time is spent on aspects of estimation or that it is not looked at in more advanced ways with Year 8 students than it is with Year 6 students. In comparable questions in other areas of mathematics these Year 8 students outperformed the Year 6 students.
 In part a) students were equally likely to identify that estimation was not doing calculations exactly on a calculator. However, Year 6 students were significantly more likely to focus on the fact that the answer was exact and therefore it was not estimation.
 In parts c) and e) Year 6 students were more likely to describe the method of estimation used, whereas Year 8 students were more likely to give a generic description about estimation such as "guessing", "doing it mentally", or "the method of estimating is not exact".
Estimating these numbers with an appropriate estimation strategy involves Advanced additive partwhole (Stage 5) knowledge and strategies.
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