Estimating lots

Estimating lots

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

Do NOT use a calculator for these tasks.

              

a)
Each of these 5 pots has 387 gold coins in it.
 
  i) In the box below show how you would ESTIMATE (using simple sums and without using a calculator) the number of gold coins in the 5 pots.
  

 

 

 

 

  
   
ii)		  
My estimate of the number of coins in the 5 pots is ___________.
 

 


 
b)
A telephone book has 502 pages of numbers. Each page has 4 columns and each column has an average of 73 telephone numbers.
 
  i) In the box below, show how you would ESTIMATE (using simple sums and without using a calculator) the total number of phone numbers in the telephone book.
  

 

 

 

 

 

   
   
ii)		  
My estimate of the total number of telephone numbers is ___________.
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
estimation, multiplication
Description of task: 
Students show how they would carry out estimation of multiplication tasks.
Curriculum Links: 
This resource can help to identify students' ability to apply additive or multiplicative strategies flexibly to whole numbers to estimate in multiplication  problems.
 
Key competencies 
This resource involves recording the strategies students use to estimate the answer to multiplication problems. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 
Y9 (04/1999)
a) i)

ii)

 Any working which shows sensible rounding or 
estimation techniques, for example: 
400 × 5 = 2 000
390 × 5 = 400 × 5 - 10 × 5= 1 950
380 × 5 = 400 × 5 - 20 × 5 = 1 900
Accept in range 1 880 - 2 000 if done by estimation technique.
[Do not accept 1 935 unless estimation is clearly used as this is a calculation not an estimate.]
[Do not accept 1 930 or 1 940 which indicates an exact calculation which is then rounded unless estimation is clearly used.]		 difficult

difficult
b) i)

ii)

 Any working which shows sensible rounding or 
estimation techniques, for example:
500 × 70 × 4 = 140 000
300 × 500 = 150 000 ( where 300 = 75 × 4
                     300 is approx 73 × 4 = 292)
500 × 70 × 4 + (500 × 4) × 3 = 146 000
500 × 292 = 150 000 – 8500 = 146 000
146 000 + 2 × 300 = 146 600
Accept in range 140 000 - 151 000 if done by estimation technique.
[Do not accept 146 584 unless estimation is clearly used as this is a calculation not an estimate.]
[Do not accept 146 580 or 146 585 which indicates an exact calculation which is then rounded unless estimation is clearly used.]

very difficult

very difficult
Diagnostic and formative information: 
   Common error Likely calculation Likely reason
a) ii)
b) ii)		 1 935
146 584		    Calculating not estimating.
b) ii) 35 000 500 × 70 Ignores "4 columns per page".
For more information about computational estimation see the Computational estimation concept map.