Who is estimating? Addition

Who is estimating? Addition

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

Your teacher will show you responses from five people who were asked to estimate this sum:

329 + 462 + 836

Some of them were estimating and some were not. For each flash card:

  1. circle either the tick or the cross in the box to show whether that person is / is not estimating; and
  2. explain your answer.
 

Estimating or Not? ( or )    (Circle one)

Explanation why they are estimating or not.
a)  
Sam
       

  
b)  

Aroha
       

  
c)  

Gina
       

  
d)  

Peter
       

  
e)  

Josef
       

  
 
 
Add-est-2.png
 
Add-est-3.png
Task administration: 
This task is completed with pencil and paper, and other equipment.
 
Equipment:
Six flash cards (one with the problem on it, and five each with one person's response on it).
 
Each students needs a copy of just the first page of the printed task.
Only one set of the six flash cards that follow are needed. These could be laminated for future use.
 
This task can be administered to individual students orally, with the teacher recording responses or with small groups of students or a whole class, with students recording their responses on their own worksheets. A suggested lesson sequence:
  1. Show the students the flash card with the original problem. Emphasise that the people have been asked to estimate the answer to the problem.
  2. Show one flash card at a time. For each one ask your students:
       •  Is this person estimating?
       •  Explain why they are estimating or not.
  3. You may lead into a discussion about estimation, why you estimate and what estimation is. For more information about discussions see Classroom discourse (Mathematics)
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
estimation, addition, concept cartoons, discussion
Description of task: 
In this task students decide which people are estimating and which are not, and explain their reasoning.
Curriculum Links: 
This resource can help to identify students' ability to recognise estimation strategies to whole numbers when estimating addition problems.
Key competencies
This resource involves recording the strategies students use to estimate in 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)
ii)

and
Sam has done an exact calculation using a calculator.

1 mark
(for both correct)

b)

  i)
 ii)

and
Aroha has done an exact calculation first, and then rounded.

1 mark
(for both correct)

c)

  i)
 ii)

and
Gina has rounded the numbers to the nearest hundred and then added them together.

1 mark
(for both correct)

d)

  i)
 ii)

and
Peter has done an exact calculation.

1 mark
(for both correct)

e)

  i)
 ii)

and
Josef has added together only the hundreds (front-end method).

1 mark
(for both correct)

NOTE: Responses may be given orally to ensure that writing is not hindering the communication of ideas. See "Working with Students" for other actual examples of student responses.
Diagnostic and formative information: 

Name

Student response

Likely misconception

Aroha 

"Yes ... because she's rounding".

Equates rounding with estimation.

Josef

" ... Everyone else got 16 ... so his is wrong ... I don't think it is estimating"
" ... I don't think so ... 'cause the numbers are too vague"

This estimate is not accurate enough. Does not see front-end estimation as legitimate.

  

Name

Student response

Conception about estimation

Sam

"No, because estimating is guessing."

Estimation is guessing.

Gina

Sam

"I think she is estimating because she rounds them the nearest 100 and she got an answer that might be off but that's how you do it in estimating."
"Yes, that's estimating. She's rounding it to make it easy for herself, and she's not using any paper any calculator or anything. She's just sort of doing it."

Estimation uses rounding.

Gina

"Yes, she was doing it in her head ..."

Estimation is doing it mentally.

Peter

Sam

Aroha

"He's not estimating. He's just adding them all together and gets the exact number."
"No, she's using a calculator."
"Not really, because she did the sum and didn't estimate."

Estimation is neither an exact (right) answer nor using a calculator.

Aroha

"No. She got the sum and found out what it was and then she made it so it looked like an estimate."
"You're not supposed to do the sum straight away in estimating."

Estimation is not an exact answer that is then rounded.

Josef

"Yeah, he's estimating because taking the other numbers off and putting zeros on at the end."
"Yep, he's rounding it to 800, 400, and 300."

Estimation can be front-end (i.e., rounding down). This can look at the left-most digits i.e., face value (8, 4, and 3) or the total value (800, 400, and 300).

Quotes from one-to-one interviews of nine Year 8 students before a unit on estimation.

NOTE:
Students often combine several of these conceptions in the one response; e.g., "I don't think she's estimating. Because she used the calculator she got the right (exact) answer. Usually in estimating you don't (calculate exactly) because you round it to the nearest 10 or 100."

For further information about estimation, refer to Computational Estimation Concept Map.