Estimating sweets and buses

Estimating sweets and buses

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

Question 1Change answer

illustration: sweets

a)  A class of 21 students each bought a packet of sweets.
     Each packet had 38 sweets in it.
i)  An estimate for the total number of sweets is
ii) Explain how you made this estimate.

Question 1Change answer

 
b)  A school has 1217 students to get to a sports ground using buses.
     Each bus can carry 41 students. 
i)  An estimate for the total number of buses needed is
ii)  Explain how you made this estimate.
Task administration: 
This task can be completed with pencil and paper and online.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
estimation, multiplication, division
Description of task: 
Students estimate and explain how they estimated their answer for two number problems: one involving multiplication; and the other division.
Curriculum Links: 
This resource can help to identify students' ability to apply multiplicative strategies flexibly to whole numbers when estimating multiplication problems.
 
Key competencies
This resource involves recording the strategies students use to estimate in multiplication problems. 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
Multiplicative thinking, sets 8-9
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

 

Y10 (11/2000)

a)

i)
 
ii)

760 to 840 [i.e., an accurate estimate]
[do not accept 798]
A description of a reasonable estimation technique is given that is consistent with the answer in a)i) even if it does not give a sufficiently accurate estimate.
Examples:

  • Round 21 to 20 and 38 to 40; then 20 × 40 = 800.
  • 2 × 4 = 8 and then add two zeros.
  • Round to 20 and 30 then 20 × = 600
  • Round (to the nearest 10) and multiply.

moderate
 
moderate

b)

i)
ii)

30 or 31 [i.e., an accurate estimate]
A description of a reasonable estimation technique is given that is consistent with the answer in b)i) even if it does not give a sufficiently accurate estimate.
Examples:

  • Round 1217 to 1200 and 41 to 40; then 1200 ÷ 40 = 30.
  • 12 ÷ 4 = 3 and add one zero.
  • Round 41 to 40 and 1217 to 1000 then 1000 ÷ 40 = 25.

Any 1 of:

  • An incomplete/partially correct explanation.
  • An estimation method is given that uses a method that requires some non-mental calculation.

     Example:
     Round 1217 to 1220 and 41 to 40, then 1220 ÷ 40 = 30.5.
     Round this to 30 or 31.

moderate
2 correct -difficult
 
1 correct - moderate