Estimating cards, money and pinecones

Estimating cards, money and pinecones

Auto-markingPencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about estimation with multiplication and division.
An estimate is sometimes called a "good guess".
 
You make an estimate without working out the exact answer.

Question

a)  Phil's grandpa has 805 collector's cards. He wants to divide them equally into 10 albums. 
     About how many cards will go into each album?

    • 8

    • 80

    • 800

    • 8000

Question

b)  18 students in Huia’s class raised $64 each for camp.
     Which of these is the best way to estimate how much money they raised altogether?

    • 10 × $60

    • 10 × $70

    • 20 × $60

    • 20 × $70

Question 1Change answer

c) Zack has collected 9 baskets of pinecones. In each basket there are 53 pinecones.
    What two numbers would you multiply together to estimate the total number of pinecones? 
    You do not have to work out the answer.
 
     × 
Task administration: 
This task can be completed with pencil and paper or online (with SOME auto marking).
Levels:
2, 3
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
estimation, multiplication, division
Description of task: 
Students select the best estimate for division and multiplication problems involving stamps, money, and baskets of pinecones.
Curriculum Links: 
This resource can help to identify students' ability to apply simple multiplicative ideas flexibly to combine or partition whole numbers to make or recognise sensible estimates for multiplication problems.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 3-4
Multiplicative thinking, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 
Y4 (11/2003)
a) B easy
b) C moderate
c) Accept any of the following:

  • 9 × 50 or 50 × 9
  • 10 × 50 or 50 × 10
  • 10 × 53 or 53 × 10
  • Other reasonable estimates.
 very difficult

 

Diagnostic and formative information: 
  Student response Likely misconception
d) 9 × 53 or 53 × 9 Exact calculation rather than an estimate.

NOTE: Many able students calculated exactly - approximately a third of all students trialled calculated exactly rather than estimated.