Buying electricity

Buying electricity

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about adding and multiplying whole numbers and decimals.
 
For businesses the prices for electricity in the city are:
 
 
Day rate:   8.0 cents per unit of electricity

Night rate: 6.3 cents per unit of electricity
a)
A business in the city used 1 500 units at the day rate, plus 1 000 units at the night rate.
What will the cost of electricity be for ...
 
  i)
their day use? $ ______ . ____
 
  ii)
their night use? $ ______ . ____
 
  iii) both their day and night use together? $ ______ . ____
 
 
The prices for electricity for businesses in the country are:
 
 

 
Day rate:   9.0 cents per unit of electricity

Night rate: 6.5 cents per unit of electricity
 
b)
 
A farm used 2 000 units at the day rate, plus 900 units at the night rate.
 
What will this cost them in total? $ ______ . ____
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
decimals, multiplication, addition, money
Description of task: 
Students carry out calculations involving addition, and multiplication of whole numbers by decimal numbers.
Curriculum Links: 
 
This resource can help to identify students' ability to apply additive or multiplicative strategies flexibly to whole numbers, ratios and equivalent fractions (including decimals and percentages) to solve addition and multiplication problems.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Additive thinking, sets 7-8
Multiplicative thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y9 (04/99)
a) i)
ii)
iii)		 120.00 [Accept 120].
63.00 [Accept 63].
183.00 [Accept 183. Also accept if answer is equal to a)i + a)ii].		 moderate
moderate
easy
b)   238.50 [Accept 238.5] difficult
Diagnostic and formative information: 
  Common error Likely calculation Likely reason
a) i)
    ii) 
    iii)
b)		 12 000
6 300
18 300
23 850		 8 × 1 500
6.3 × 1 000
12 000 + 6 300
9 × 2 000 + 6.5 × 900		 Gives answer in cents rather than dollars.
a) i)
    ii) 
    iii)
b)		 12, 1 200
6.3, 630
18.3, 1 830
23.85, 2 385.0		    Incorrect magnitude of answer (possible place value error).
a) i)
    ii) 
b)		 187.50
158.73
360.68		 1 500 ÷ 8
1 000 ÷ 6.3
2 000 ÷ 9 + 900 ÷ 6.5		 Dividing instead of multiplying by cost of a unit of electricity.
b) 765.00 2 000 × .09 + 900 × .65 Treats .065 as .65