Estimating team scores

Estimating team scores

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about using different estimation strategies.

Question 1Change answer

Liam wanted to get a quick first estimate of some team scores. His first estimate was too low so he then adjusted it to make a better estimate.
For each of these scores:
  • Make a first estimate of what the total score is at least.
  • Improve your estimate (it still does not need to be exact).

Question 1Change answer

a)  Team Beta's scores were as follows: 246,  327 and 283.
 
     Beta's total score is at least       This is because ...
 
     A closer estimate of Beta's score is       This is because ...

Question 1Change answer

b)  Team Omega's scores were as follows: 2317, 6574, 5769 and 1368.
 
     Omega's total score is at least       This is because ...
 
     A closer estimate of Omega's score is       This is because ...
Task administration: 
This task can be complete with pencil and paper or online.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
estimation, addition, front-end
Description of task: 
Students discuss making an initial estimate in addition problems using the front-end method followed by compensation to get a more accurate estimate. They then use this method on two addition problems.
Curriculum Links: 
This resource can help to identify students' ability to apply additive ideas flexibly to combine or partition whole numbers to make sensible estimates of addition problems.
 
Key competencies
This resource involves explaining how they performed estimates of several addition problems. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Additive thinking, sets 7-8
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

a)

i) 700
ii) 200 + 300 + 200 = 700 or other acceptable explanations (including rounding).
iii) 840
iv) 40 + 20 + 80 = 140 so add 140 to 700 or other compensation and explanation (see notes).
[Conditional marking: accept either part iii) or iv) if it is consistent with part i)]
b)
i) 14 000
ii) 2 000 + 6 000 + 500 + 1 000 = 14 000 or other acceptable explanations (including rounding).
iii) 15 800
iv) 300 + 500 + 700 + 300 = 1 800 so add 1 800 to 14 000 or other compensation and explanation (see notes).
[Conditional marking: accept either part iii) or iv) if it is consistent with part i).]

 
 
NOTE:

  • If students don't use front-end methods you may conference them to see if they can, even if they prefer other methods.
  • Students may use rounding at the compensation stage rather than front-end. This is an excellent idea, getting the best from both strategies.
  • Students may use a combination of estimation and computation (i.e., computations that they cannot easily do in their heads and may need to write down).
  • Do not accept the exact answers (841 and 16 028) unless they have first made a front-end estimate and then used compensation sequentially to get the exact answer. Highlight this as computation rather than estimation.
Teaching and learning: 

Prior knowledge needed

  • A firm base of additive basic facts.
  • Good place value concepts.
  • Understanding that estimation is a quick mental way of getting an answer close to the exact one.

Information on front-end with compensation in estimation

  • Front-end is sometimes called truncation (cutting off all but the first number) or rounding-down.
  • Front-end addition always underestimates the exact answer because all the numbers being added are smaller than the numbers in the original sum.
  • Front-end is not usually as accurate as other methods but is very easy to learn and apply. It is very easy to use compensation with front-end because all numbers are being added on to the original estimate. Compensation after rounding is harder as some numbers need to be added on and some subtracted off.
Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
a) i)
b) i)		 841
16 028		 246 + 327 + 283
2 317 + 6 574 + 5 769 + 1 369		 Performs exact calculation rather than estimation.
a) i)
b) i)		 800
16 000		 200 + 300 + 300
2 000 + 7 000 + 6 000 + 1 000		 Uses rounding rather than front-end so the estimate can be bigger or smaller than the exact answer.

Links with Numeracy Project
Using front-end estimation with compensation involves at least early additive part-whole (Stage 5) knowledge and strategies (Book 1: The Number Framework (2004, pp.10 & 13). Wellington: Ministry of Education).
 
Other resources
For a similar ARB resource about front-end estimation, refer to Estimating sums of money (front-end without compensation).
For further information about estimation, refer to Computational Estimation Information.