Estimating addition IV

Estimating addition IV

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about estimating the addition of numbers.

An estimate is sometimes called a "good guess" that is easy to do in your head. The following questions are about estimating NOT working out the exact answer.

 

a)
 
i) Estimate the sum of 18 + 23

ii) Show how you estimated the sum.
 
 
 
 
 
 
 
I estimated the sum was about __________
 
 
b)
 
 
i) Estimate the sum of 16 + 27 + 41

ii) Show how you estimated the sum.
 
 
 
 
 
 
 
I estimated the sum was about __________
 
 
c)
 
i) Estimate the sum of 127 + 179

ii) Show how you estimated the sum.
 
 
 
 
 
 
 
I estimated the sum was about __________
 
Task administration: 
This task is completed with pencil and paper only.
Levels:
2, 3
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
estimation, addition
Description of task: 
This task requires students to estimate some addition problems using any appropriate method.
Curriculum Links: 
This resource can help to identify students' ability to use basic addition facts and knowledge of place value and partitioning whole numbers to make estimates of addition problems.
 
Key competencies
This resource involves recording 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, set 5
Additive thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y5 (05/2005)
a)
An acceptable estimation strategy and an appropriate estimate.
For example:
  • 40 (by rounding)
  • 30 (by front-end estimation)
  • 40 (using front-end and final compensation)
very difficult 
(for both estimate & method)
b)
An acceptable estimation strategy and an appropriate estimate.
For example:
  • 90 (by rounding)
  • 70 (by front-end estimation)
  • 81 (using front-end and final compensation)
very difficult
(for both estimate & method)
c)
An acceptable estimation strategy and an appropriate estimate.
For example:
  • 300 (by rounding)
  • 200 (by front-end estimation)
  • 300 (using front-end and final compensation)
very difficult
(for both estimate & method)

These results are based on a trial set of 149 Year 5 students in May 2005.

For more information on estimation, click on Computational estimation concept map.

Teaching and learning: 
Students at this level who are learning to calculate numbers appear to have a reluctance to estimate. If they can work out the answer then they cannot see a reason for estimating. To help students understand the need for estimation encourage discussion about situations when estimation should be used, e.g., for a quick total at the supermarket.

Prior knowledge needed

  • A firm base of addition and subtraction facts.
  • Good place value concepts.
  • Ability to mentally add numbers in tens, hundreds, etc, using standard place value concepts.
Diagnostic and formative information: 
Strategy name Likely calculation Typical estimate(s) % using strategy
Front-end a) 10 + 20
b) 10 + 20 + 40
c) 100 + 100		 30
70
200		 2%
1%
1%
Front end and final compensation a) 30 + (7 + 3)
b) 70 + (5 + 5 + 1)
c) 200 + (30 + 70)		 40
81
300		 1%
2%
4%
Rounding a) 20 + 20 or 2 + 2
b) 20 + 30 + 40 or 2 + 3 + 4
c) 100 + 200		 40
90
300		 3%
1%
2%

NOTE: The percentages include students who attempted that strategy, but did not necessarily come up with an appropriate estimate.

Strategy name Likely calculation Typical answer(s) % using strategy
Exact computation only: using the vertical algorithm. a) 18 + 23
b) 16 + 27 + 41
c) 127 + 179		 41
84
306		 9%
4%
8%
Exact computation only: using place value partitioning.
(see Next steps)		 a) (10 + 20) + (8 + 3)
b) (10 + 20 + 40) + (6 + 7 + 1)
c) (100 + 100) + (20 + 70) + (7 + 9)		 41
84
306		 18%
15%
15%
Exact computation only:
using a method other than vertical algorithm or place value partitioning.		 a) 18 + 23
b) 16 + 27 + 41
c) 127 + 179		 41
84
306		 10%
9%
1%
Total percentage of students computing exact answer a)
b)
c)		 37%
28%
24%

Results are based on a sample of 149 Year 5 students.

Next steps: 
Exact computation based on place-value partitioning is closely linked to front-end estimation with final compensation. The difference is that the student continues to compensate or calculate the next place-value digit until they reach an exact answer. This is effectively a left-to-right addition algorithm. It is important that students recognise that estimation does not need an exact answer. They could work with front-end resources, begin with a single calculation of the largest place value, then perform a single compensation to get a reasonable estimate, and stop. Numbers for an estimation question should be chosen to match students' ability to calculate (i.e., numbers they cannot easily and quickly calculate - more numbers, larger numbers, or less time to work them out).
 
For further information about estimation, refer to Computational estimation concept map.
 
Links with Numeracy framework
Estimating numbers with an appropriate estimation strategy involves early additive part-whole (Stage 5) knowledge and strategies (See The Number Framework: Book 1 (2004) pp.11 & 13. Wellington: Ministry of Education).