Shopping for vegetables

Shopping for vegetables

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about estimating in division problems.
Broccoli Corn cob Taro
broccoli-IS-300.png Corn-FP.png one taro
$3.85 $0.95 each $9.35

 

a) i)
Billy has $12. How many corn cobs can he buy? __________
  ii)
Show how you did this in the box below.
 
 

 

 

 
 
b)
 
i)
 
Aroha has $20. How many broccoli can she buy? __________
  ii)
Show how you did this in the box below.
 
 

 

 

 
 
c)		  
i)
 
Maraea has $72. How many taro can she buy? __________
  ii)
Show how you did this in the box below.
 
 

 

 

 
Task administration: 
This task is completed with pencil and paper only.
Copyright: 
Image: Corn by brgfx on Freepik
Taro and Brocolli: rica nohara, iStock
Level:
3
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
estimation, division, remainders
Description of task: 
Students use estimation strategies to calculate the number of vegetables they can buy with given amounts of money.
Curriculum Links: 
This resource can help to identify students' ability to apply multiplicative strategies flexibly to whole numbers.

Key competencies
This resource involves recording  strategies  to estimate a division problem. 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 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

 

Y6 (11/2003)

a)

i)
ii)

12 [Do not accept 12.63 or 13.]
Structured working using correct operator:

  • Appropriate exact calculation, e.g., 0.95 × 12 = 11.40, so you can buy 12;
  • Successive addition;
  • Calculates for an initial number and updates;
  • Estimates using rounding (with or without compensation) e.g. 0.95 roughly equals 1.

very easy
easy

b)

i)
ii)

5 [Do not accept 5.19 or 6.]
Structured working using correct operator:

  • Appropriate exact calculation, e.g., 3.85 × 5 = 19.25, so you can buy 5;
  • Successive addition;
  • Calculates for an initial number and updates;
  • Estimates using rounding (with or without compensation) e.g. 3.85 roughly equals 4.

difficult
difficult

c)

i)
ii)

7 [Do not accept 7.70 or 8.]
Structured working using correct operator:

  • Appropriate exact calculation, e.g., 9.35 × 7 = 65.45, so you can buy 7;
  • Successive addition;
  • Calculates for an initial number and updates;
  • Estimates using rounding (with or without compensation e.g. 0.95 roughly equals 1).

very difficult
very difficult

NOTE : The mark for working in a)ii), b)ii) and c)ii) is independent of the answer for the first part being correct.

Diagnostic and formative information: 
 

Student response

Likely misconception

a)   i)
b)   i)
c)   i)

11
4
6

Answer is too small, by 1.

a)   i)
b)   i)
c)   i)

13
6
8

Answer is too big, by 1. This may be because the rounding or compensation was in the wrong direction.

NOTE: The exact calculations (0.95 × 12, 3.85 × 5 and 9.35 × 7) were generally with the correct answer, indicating that this was a check for an initial estimate (12, 5 or 7)

 

 Analysis of student strategies

Used by more able students

  • Estimation based on rounding to the nearest whole number of dollars (with or without compensation).
  • Exact computation based on multiplication (or division) e.g. $3.85 × 5 = $19.25. The choice of what to multiply the price by (e.g. 5) implies mental use of estimation (i.e. they estimated 5 was a good choice).
  • Trial and improvement. They took an initial guess, tried it out, and then made better guesses.

Less able students

  • Gave no strategy.
  • Used successive addition, based on either exact or rounded numbers.
  • Incorrect use of computation.
  • Others, including "I guessed".

NOTE: Within each of these two lists, the strategies are ordered by the frequency of use by students.

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