Estimating scores and crowds

Estimating scores and crowds

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 a way of estimating that you have discussed with your teacher.

Question 1Change answer

cricket-PD-Pxhere-736629-400.jpg
a)  Aramoana wrote down the scores from 6 games of cricket. Here are her results: 
193     156     43     281     120     314
     Make an estimate of about how many runs were scored altogether:
     The number of runs scored is about 

     Show how you made your estimate in this box.

Question 1Change answer

Have a group discussion with your teacher on your ways of estimating for this problem.
 

Question 1Change answer

b)  Tiva wrote down the scores from 7 innings of test cricket. Here are his results:
316     428     630     704     581     283     370
     The total number of runs scored is about .

     Show the nice numbers you would group together.
     

Question 1Change answer

crowd-at-a-stadium-in-johannesburg-south-africa-for-rugby-400-PD.jpg
c)  i)  Make up your own example about crowd sizes at 6 games of rugby so someone could use the method you discussed to get a good estimate of the crowd size.  


, , , , , .
 
     ii)  Make an estimate of the total attendance using your numbers above. 
          Total attendance is 
          Show how the numbers you have chosen group together as nice numbers.
          
Task administration: 
This task is completed with pencil and paper or online.
 
This assessment activity is designed to be carried out with a group of students or a whole class. A suggested lesson sequence:
  1. Give the students the problem of estimating 193 + 156 + 43 + 281 + 120 + 314 to identify whether they use the grouping nice numbers method.
  2. Discuss students' methods. Use the language of estimation in the Computational estimation concept map for each different method.
  3. Introduce the grouping nice numbers method in addition. This use grouping within 100, 1 000, etc.,  i.e., recognising two numbers which approximately sum to 100, 1 000, etc. You may wish to write this example down as you discuss it.
    Example: 193 + 156 + 43 + 281 + 120 + 314
    193 and 314 group to about 500,
    156 and 43 group to about 200,
    281 and 120 group to about 400, so the answer is about 500 + 200 + 400 = 1 100.
  4. Students complete the sentence with the word "grouping nice numbers", and then answer parts b) and c) to assess if they can apply it. Emphasise they are to use grouping nice numbers only.
For more information about discussions see Classroom discourse (Mathematics)
Copyright: 
cricket-PD-Pxhere-736629-400.jpg

Public domain image via Pxhere (https://pxhere.com/)
 
 
crowd-at-a-stadium-in-johannesburg-south-africa-for-rugby-400-PD.jpg
Public domain image via Good freephotos (https://www.goodfreephotos.com)
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
estimation, addition, discussion
Description of task: 
Students estimate an addition problem, share their methods, discuss grouping nice numbers, and then do a problem using this method, then design a question showing how it uses the method.
Curriculum Links: 
This resource can help to identify students' ability to apply additive or multiplicative strategies flexibly to whole numbers to solve addition problems.
 
Key competencies
This resource involves recording the strategies students use to solve 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)

  

Makes a reasonable estimate close to 1 100 and gives a reasonable explanation of their method of estimating it. An example of using grouping nice numbers is: 1 100 because
     190 + 310 = 500 and 160 + 40 = 200 and 280 + 120 = 400
     so it's about 500 + 200 + 400 = 1 100.
(Other nice groupings are possible.)

1 mark
(for both correct)

b)

  

A reasonable estimate close to 3 300 and student working that indicates they can group nice numbers together. An example is 3 300 because
     300 + 700 = 1 000 and 420 + 580 = 1 000 and 630 + 370 = 1 000
     plus about 300 more so it's about 3 300.

1 mark
(for both correct)

c)


i)
ii)

Students ...

  • make an example that grouping nice numbers can be used for and
  • can show how their numbers can be grouped nicely either by writing down the groups or orally describing them.


1 mark
(for both correct)
Diagnostic and formative information: 
  Common error Likely misconception
a)
b)		 1 107
3 312		 Performs the exact calculation.
a)
b)		 1 100
3 310 (or 3 300)		 Performs the exact calculation and then rounds to the nearest 10, 100, etc.
c) Numbers pairs such as
162 + 238 = 400 or
2 372 + 4 628 = 7 000		 Constructs numbers which exactly group to 100, 1 000, etc., rather than ones that roughly group to 100, 1 000, etc. Not using estimation to get roughly 400, 7 000, etc.

Information on grouping nice numbers for estimation.

  • Grouping nice numbers exploits groupings within 100, 1 000, etc., but emphasises approximate groupings rather than exact ones, e.g., 156 + 43  160 + 40 or 223 + 173  230 + 170.

Prior knowledge required

  • A firm base of additive basic facts, especially 7 + 3 = 10, 16 + 14 = 30, etc., (groupings within 10).
  • Good place value concepts.
  • Understanding that estimation is a quick mental way of getting an answer close to the exact one.
  • Knows some computational estimation methods, especially rounding or front-end.
For similar ARB resources about estimation, refer to Estimating sums of money (front-end) and Estimating farm animals (rounding).

For more information about computational estimation see the Computational estimation concept map.

 
Links with Numeracy Project
Grouping nice numbers involves at least early additive part-whole (Stage 5) knowledge and strategies.  The method uses the groupings within 100, 1000 strategy (see The Number Framework, Book 1 (2004, pp.12-13. Wellington: Ministry of Education).