Estimates
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Approach:  Team  
Level: Year 4 and year 8
Focus: Measurement sense; selecting and using devices; number strategy; estimation
172Kb
Resources:
2 cards, 2 calculators, 2 x 250ml marked cups, 2 pair answer sheets, 2 stopwatches, 2 story books, 2 balls
Questions/instructions:  
In this activity you will be working in pairs to estimate the measurements of three different things. You don’t need to try to work out the exact measurement, just a good estimate. You can only work in this room to do this activity. [Student 1] and [Student 2] can work together, [Student 3] and [Student 4] can work together. Here are some things to help you work out your estimates.
Hand each pair a calculator and stopwatch.

With your partner talk about how to do each estimate then write down how you would do it on the answer sheet. After that have a go at using your idea to estimate the measurement.
Hand each pair an answer sheet, a card, a ball, a 250 ml marked cup and a story book.
[Card showed three problems, same as table below.
Year 4 book: Mock-up of book constructed with pages 1 – 31 plus cover only. Bourke, A. & Rendell, J. (2009). Christian The Lion, London.: Red Fox, Random House.
Year 8 book: Johnston, P. (2007). Dead Dan’s Dee. Dunedin, N.Z.: Longacre Press, Random House.]
   
Problem A Way to Estimate This Estimate
The time it would take one of you to bounce a ball 100 times.    
The number of words in the story book.    
The amount one of you would drink in a week    
   
Here are the three things to estimate and your answer sheet. You have up to 15 minutes to work on this activity.
Allow up to 15 minutes. Remind students when five minutes is left.
Bring students back to the team table.
Now it is time to report back. [Student 1] and [Student 2]
can report back first then [Student 3] and [Student 4].
   
 
% responses
2009 ('05)
y4
y8
Let’s start with –    
The time it would take one of you to bounce a ball 100 times.    
1. What did you do to estimate this answer?
2. What was your estimate?
STUDENTS 1 & 2:     
Students did estimate: yes 39 79
Estimation method: attempted to bounce ball by some fraction of
100 and measured time taken, then multiplied
by appropriate ratio for 100 bounces 		14 70
Validity: (time measured × 100 ÷ number of bounces measured)
estimate was in the likely range (40 - 120 secs) 		60 73
STUDENTS 3 & 4:     
Students did estimate: yes 36 73
Estimation method: attempted to bounce ball by some fraction of
100 and measured time taken, then multiplied
by appropriate ratio for 100 bounces 		15 66
Validity: (time measured × 100 ÷ number of bounces measured)
estimate was in the likely range (40 - 120 secs) 		55 80
The number of words in the story book.    
3. What did you do to estimate this answer?
4. What was your estimate?
STUDENTS 1 & 2:    
Estimation method: Figured out words per page by working out words per line, then multiplying by number of lines:    
  counted number of lines and number of words per line and multiplying 3 21
  counting words on a whole page 32 53
  Used estimate of words on a page and multiplied by number of pages:    
  yes, and considered part pages
(Y4 = 27/28 pages, Y8 = 153 pages)		 5 4
  yes, but treated all pages the same
(Y4 = 31 pages, Y8 = 162/170 pages)		 17 40
  yes, counted pages but distinction
between part and whole pages unclear 		14 39
Validity: estimated total was in the likely range 20 63
(Y4 = 3000 – 5500 words / Y8 = 30 000 – 55 000)		    
STUDENTS 3 & 4:    
Estimation method: Figured out words per page by working out words per line, then multiplying by number of lines:    
  counted number of lines and number of words per line and multiplying 4 28
  counting words on a whole page 31 44
  Used estimate of words on a page and multiplied by number of pages:    
  yes, and considered part pages
(Y4 = 27/28 pages, Y8 = 153 pages)		 3 5
  yes, but treated all pages the same
(Y4 = 31 pages, Y8 = 162/170 pages)		 23 36
  yes, counted pages but distinction
between part and whole pages unclear 		14 45
Validity: estimated total was in the likely range
(Y4 = 3000 – 5500 words / Y8 = 30 000 – 55 000)		 21 56
The amount one of you would drink in a week.    
5. What did you do to estimate this answer?
6. What was your estimate?
STUDENTS 1 & 2:      
Students did estimate: yes, as number of cups/glasses 36 58
  yes, as ml or litres 14 26
Multiplied by seven: yes 40 85
  no, took weeks as 5 days 2 3
Validity: estimated total in the range of 7L - 18L
(28 - 72 cups)		 23 57
STUDENTS 3 & 4:      
Students did estimate: yes, as number of cups/glasses 33 63
  yes, as ml or litres 15 22
Multiplied by seven: yes 39 81
  no, took weeks as 5 days 5 2
Validity: estimated total in the range of 7L - 18L
(28 - 72 cups)		 26 80
7. Are any of your estimates similar?    
8. Why is that so?
Discussion:    strong 2 6
moderate 19 50
weak 79 44
9. What things do you think you did well in this activity?    
  not marked here • •
10. If you did this activity again, what would you do differently?    
  not marked here • •
       prompt (Year 4 only): Does anyone else want to say anything?    

Total score:
 21–30
5 40
16–20
11 38
11–15
15 13
6–10
32 4
0–5 37
5
Commentary:
This team task has been released immediately because it appears that the task could be improved if more highly structured. The general approach appears to be worthwhile, but many teams recorded insufficient information to allow full evaluation of their efforts. Because it is a team task, the usual subgroup graphs are not possible.