Internal assessment resource Mathematics and Statistics 1.1B for
Achievement Standard 91026
PAGE FOR TEACHER USE
Internal Assessment Resource
Mathematics and Statistics Level 1
This resource supports assessment against:
Achievement Standard 91026
Apply numeric reasoning in solving problems
Resource title: Carbon Credits
4 credits
This resource:

Clarifies the requirements of the standard

Supports good assessment practice

Should be subjected to the school’s usual assessment quality assurance
process

Should be modified to make the context relevant to students in their school
environment and ensure that submitted evidence is authentic
Date version published
by Ministry of Education
December 2010
To support internal assessment from 2011
Authenticity of evidence
Teachers must manage authenticity for any
assessment from a public source, because students
may have access to the assessment schedule or
student exemplar material.
Using this assessment resource without modification
may mean that students work is not authentic. The
teacher may need to change figures, measurements or
data sources or set a different context or topic to be
investigated or a different text to read or perform.
This resource is copyright © Crown 2010
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Internal assessment resource Mathematics and Statistics 1.1B for
Achievement Standard 91026
PAGE FOR TEACHER USE
Internal Assessment Resource
Achievement Standard Mathematics and Statistics 91026:
Apply numeric reasoning in solving problems
Resource Reference: Mathematics and Statistics 1.1B
Resource Title: Carbon Credits
Credits: 4
Teacher guidelines
The following guidelines are designed to ensure that teachers can carry out valid and
consistent assessment using this internal assessment resource.
Teachers need to be very familiar with the outcome being assessed by Achievement
Standard Mathematics and Statistics 91026. The achievement criteria and the
explanatory notes contain information, definitions, and requirements that are crucial
when interpreting the standard and assessing students against it.
Context/setting
This assessment activity requires students to reason with linear proportions and
perform operations with fractions, decimals, percentages, and rates.
The context for this assessment is carbon credits purchased at an outdoor music
festival. Students will calculate the minimum number of trees that could be purchased
using carbon credits (or green days).
This activity could be adapted to other contexts that present similar opportunities
to meet the standard, for example, computing exchange rates for different
groups of travellers and destinations.
Conditions
Students work individually to complete this assessment in a one hour session
Resource requirements
Students should have calculators or other appropriate technology, for example,
computer spreadsheets, available.
Additional Information
None.
This resource is copyright © Crown 2010
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Internal assessment resource Mathematics and Statistics 1.1B for
Achievement Standard 91026
PAGE FOR STUDENT USE
Internal Assessment Resource
Achievement Standard Mathematics and Statistics 91026:
Apply numeric reasoning in solving problems
Resource Reference: Mathematics and Statistics 1.1B
Resource Title: Carbon Credits
Credits: 4
Achievement
Apply numeric reasoning in
solving problems.
Achievement with Merit
Apply numeric reasoning,
using relational thinking, in
solving problems.
Achievement with
Excellence
Apply numeric reasoning,
using extended abstract
thinking, in solving problems.
Student instructions
Introduction
The Big Day Out is a three day music festival. At the Big Day Out audience members
can purchase “Green Days”. The organisers will use all the income from these to buy
carbon credits. These carbon credits will be used to purchase trees, which aims to
offset the carbon emissions from the event.
This assessment activity requires you to determine the minimum number of trees that
could be purchased using carbon credits from the Big Day Out.
Task
Use the following information to find out the minimum number of trees that could
be purchased using carbon credits from the Big Day Out for the given year.
In the solution of this problem you should:

Show calculations, as appropriate, that you have used in the solution of the
problem;

Use mathematical statements;

Explain what you are calculating at each stage of the solution.
The quality of your discussion and reasoning and how well you link this to the context
will determine the overall grade.

The audience number at the Big Day Out was 19,000 (to the nearest 1000);

Big Day Out attendees can choose to purchase 0, 1, 2, or 3 ”green days” when
they buy their tickets. 23% of the attendees purchased ”green days”;
This resource is copyright © Crown 2010
Page 3 of 6
Internal assessment resource Mathematics and Statistics 1.1B for
Achievement Standard 91026
PAGE FOR STUDENT USE

Of those who purchase “green days”, one quarter purchase three days, one third
purchase two days and the rest purchase one day;

One “green day” costs NZ$1.34;

A carbon credit costs US$18.

Exchange rate: US$1= NZ$1.33886 (October 2010);

The organisers are able to buy 10 trees with every three carbon credits.
This resource is copyright © Crown 2010
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Internal assessment resource Mathematics and Statistics 1.1B for Achievement Standard 91026
PAGE FOR TEACHER USE
Assessment schedule: Mathematics and Statistics 91026 Carbon Credits
Evidence/Judgements for Achievement
To “Achieve” students will be required to apply
numeric reasoning in solving problems.
Students select and use a range of appropriate
methods in solving problems. This
demonstrates knowledge of number concepts
and terms. Solutions typically require one or two
steps
At least three different numeric methods need
to be used in solving problems
Examples:
Calculating a percentage of a quantity
Evidence/Judgements for Achievement
with Merit
Evidence/Judgements for Achievement
with Excellence
To achieve with “Merit” students will be required
to apply numeric reasoning with relational
thinking in solving problems.
To achieve with “Excellence” students will be
required to apply numeric reasoning with
extended abstract thinking in solving problems.
This involves one or more of:
This involves one or more of
Selecting and carrying out a logical sequence of
steps,
Devising a strategy to investigate or solve a
problem,
connecting different concepts and
representations,
identifying relevant concepts in context,
developing a chain of logical reasoning,
demonstrating understanding of concepts,
forming a generalisation
forming and using a model
and either using correct mathematical
statements or communicate mathematical
insight.
e.g. 0.23 x 19000 = 4370
and either communicating their solutions clearly
or relating their solutions to the context.
Calculating a fraction of a quantity
Audience number of 19000
e.g.
1
x 4370 = 1093
4
23% of 19000 = 4370
Converting using exchange rates from
1
x 4370 = 1092 purchased 3 days
4
e.g. $NZ to $US
1092 x 3 = 3276 days
$NZ10733.40 ÷ 1.33886 = $US8016.82
The student does not have to fully solve the
problem, but there must be evidence of using
three different appropriate methods.
1
x 4370 = 1456 purchased 2 days
3
1456 x 2 = 2912 days
Therefore 1822 purchased 1 day
(Answers should be rounded to the nearest
whole number)
This resource is copyright © Crown 2010
Extended abstract thinking will be evident in the
solution by consideration and discussion
relating to the minimum number of trees.
For example:
Audience number is between 18500 and 19499.
The least number of trees is asked for so the
correct solution involves working with the
minimum possible crowd size.
Number of people who purchased carbon free
days:
Audience number of 18500
23% of 18500 = 4255
Total green days: 8010
1
x 4255 = 1063 purchased 3 days
4
Total carbon credits
1063 x 3 = 3189 days
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Internal assessment resource Mathematics and Statistics 1.1B for Achievement Standard 91026
PAGE FOR TEACHER USE
8010 x 1.34 = $10733.40 ($NZ)
(Answers should be given to the nearest cent)
1
x 4255 = 1418 purchased 2 days
3
$10733.40 ÷ 1.33886 = $8016.82 ($US)
1418 x 2 = 2836 days
(Answers should be given to the nearest cent)
Therefore 1774 purchased 1 day (Answers
should be rounded to the nearest whole
number)
8016.82 ÷ 18 = 445 credits
(Number of credits needs to be truncated to
relate to context)
Total green days: 7799
Total ÷ 3 (As 3 carbon credits buys 10 trees)
Total carbon credits
445 ÷ 3 = 148
7799 x 1.34 = $10,450.66 ($NZ)
Number of trees:
(Answers should be given to the nearest cent)
148 x 10 = 1480 trees
NZ$10,450.66 ÷ 1.33886 = US$7805.64
The student needs to arrive at a solution.
Emphasis is on the sequence of logical
communication of thinking using mathematical
statements. The solution may not be exactly
correct.
(Answers should be given to the nearest cent)
7805.64 ÷18 = 433 credits
(Number of credits needs to be truncated to
relate to context)
Total ÷ 3 = 144.3 recurring
(This answer needs to truncated as there are
not enough credits to buy 145 groups of 10
trees)
Number of trees
144 x 10 = 1440 trees
Note: If students have derived the solution, but
not communicated their ideas clearly or shown
mathematical insight, the maximum grade they
can achieve is “Merit”.
Final grades will be decided using professional judgement based on a holistic examination of the evidence provided against the criteria
in the Achievement Standard.
This resource is copyright © Crown 2010
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