Estimating sweets II

Estimating sweets II

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

Question


 

There were exactly 47 sweets in each bag of sweets. A group of 91 children had a bag of sweets each, and 8 other children bought a bag each.
Ben, Jess, and Sam were arguing how many sweets there were altogether.
  • Ben said the answer was exactly 4 700.
  • Jess said that she didn't know the answer, but she was sure it was less than 4 700.
  • Sam said that he didn't know the answer, but it was sure to be more than 4 700.

Who was correct? (Select one)

    • Ben

    • Jess

    • Sam

Explain, without doing the exact calculation, how you can tell who is correct.
Task administration: 
This task can be completed with pencil and paper or online (with SOME auto marking).
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
estimation, multiplication
Description of task: 
Students explain multiplication estimation methods used to solve word problems.
Curriculum Links: 
This resource can help to identify students' ability to apply multiplicative strategies flexibly to whole numbers when estimating the products.
Key competencies
This resource involves recording the strategies students use to estimate a multiplication 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 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y9 (04/1999)
a)
b)		 Jess
Indicates estimation using
47 × (91 + 9) = 47 × 99
which is less than 47 × 100 = 4 700
because 99 is less than 100.
or
Other similar explanations.
[Do not accept arguments based on exact calculations.]		 difficult
(for both correct)
Diagnostic and formative information: 
   Common error Likely reason
a) Sam Rounds 99 to 100 and 47 to 50 to get an estimate of 5 000.
b)    Does exact calculation rather than estimation.