Internal assessment resource Mathematics and Statistics 1.7A for Achievement Standard 91032
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Internal Assessment Resource
Mathematics and Statistics Level 1
This resource supports assessment against:
Achievement Standard 91032
Apply right-angled triangles in solving measurement problems
Resource title: The Rugby Posts
3 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
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.
To support internal assessment from 2011
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 1.7A for Achievement Standard 91032
PAGE FOR TEACHER USE
Internal Assessment Resource
Achievement Standard Mathematics and Statistics 91032: Apply
right-angled triangles in solving measurement problems
Resource reference: Mathematics and Statistics 1.7A
Resource title: The Rugby Posts
Credits: 3
Teacher guidelines
The following guidelines are supplied to enable teachers to 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 91032. 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 activity requires students to take measurements and use to find lengths and
angles in right angled triangles. The context is the height of the rugby posts on the
school field, which need to be taken down and transported away for storage.
The measurements of the rugby goal as specified by the RFU are:
The cross bar should be 5.6 m long at a height of 3 m above the ground.
The upright posts should be at least 0.4 m above the crossbar. This height will vary
at schools.
Possible alterations to the task
The dimensions of the trailer in the task have been set so that the upright posts will
not fit in flat along the diagonal for posts that are of height 8 m above the ground. If
the school’s posts are lower than this the dimensions of the trailer will need to be
altered so the school posts do not fit in it.
Conditions
Students will need to work in pairs during one session to take measurements and
record them. A sunny day is required for the shadows.
The students will work individually during a second session to complete the
calculations.
Students may use any appropriate technology.
Resource requirements
Students will need to be provided with a tape measure of length at least 30 m, and a
clinometer to take the measurements. They will also need a pole of at least 1 m length
for measuring the shadow.
This resource is copyright © Crown 2010
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Internal assessment resource Mathematics and Statistics 1.7A for Achievement Standard 91032
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Additional information
The standard identifies measuring at a level of precision appropriate to the task as a
‘method’. For Achieved students must both select and use a range of methods. If there
is assessor confidence that the student has contributed to the selection and making of
the measurements and that the measurements are accurate to a suitable level of
precision then measuring would be acceptable as one of the three methods.
This resource is copyright © Crown 2010
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Internal assessment resource Mathematics and Statistics 1.7A for Achievement Standard 91032
PAGE FOR STUDENT USE
Internal Assessment Resource
Achievement Standard Mathematics and Statistics 91032: Apply
right-angled triangles in solving measurement problems
Resource reference: Mathematics and Statistics 1.7A
Resource title: The Rugby Posts
Credits: 3
Achievement
Apply right-angled triangles in
solving measurement
problems.
Achievement with Merit
Apply right-angled triangles,
using relational thinking, in
solving measurement
problems
Achievement with
Excellence
Apply right-angled triangles,
using extended abstract
thinking, in solving
measurement problems.
Student instructions
Introduction
A set of rugby goalposts has to come down and be transported away for storage. The
groundsman needs to know if he can transport the posts safely using his tractor and
trailer.
The posts are vertical. They are placed in the ground with 0.5 m below the ground (the
dashed part in the diagram.) The cross bar is 5.6 m long.
The groundsman intends to shift the posts using his trailer. On this sunny day use the
shadows, and at least one other method, to find the above-ground height of the posts.
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Internal assessment resource Mathematics and Statistics 1.7A for Achievement Standard 91032
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The trailer has a rectangular base 6 m long, 2.5 m wide and 0.5 m high. The
groundsman thinks that the posts cannot be placed in the trailer along the diagonal of
the trailer without sticking out as shown in the diagram.
He has asked you to confirm this, using the height calculated from one of your
measurements.
The groundsman wants to place the posts in the trailer, as shown in the diagram. For
safety reasons, the horizontal distance that the posts stick out beyond the trailer must
be no more than 1 m.
The groundsman can increase the height of the sides of the trailer. He has asked you
to investigate what height the sides of the trailer will need to be if he is to transport the
posts without exceeding this restriction.
The Task
Session 1
Working with a partner use the equipment provided to make whatever measurements
you require to enable you to calculate the height of the rugby posts on your school field
using the methods you have selected.
Session 2
Use your measurements to:

calculate the height of the rugby posts on your school field using the two different
methods you have selected.

use the height from one of these calculations to determine if the posts can be
carried in the trailer

investigate what height the sides of the trailer needs to be to allow the posts to be
carried safely.
The quality of your reasoning, using a range of methods, and how well you link the
context to your solutions will determine your overall grade.
Round your calculations sensibly, and show units.
Clearly communicate your method using appropriate mathematical statements, so that
the groundsman can verify your calculations.
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Internal assessment resource Mathematics and Statistics 1.7A for Achievement Standard 91032
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Assessment schedule: Mathematics and Statistics 91032 The Rugby Posts
The schedule assumes the following measurements were taken.
Method 1:
Distance from base of post: 30 m
My height: 1.73 m
Angle of inclination of top of the pole: 12º
Method 2:
Height of pole: 1 m
Length of shadow of pole: 2 m
Length of shadow of the posts: 16 m
Evidence/Judgements for Achievement
Evidence/Judgements for Achievement with
Merit
Evidence/Judgements for Achievement
with Excellence
To achieve students will take measurements and
apply right angled triangles in solving these
problems.
To achieve with Merit students apply right angled
triangles using relational thinking in solving these
problems.
To achieve with Excellence, students apply right
angled triangles using extended abstract thinking
in solving these problems.
This will involve selecting and using a range of
methods in solving measurement problems,
demonstrating knowledge of measurement and
geometric concepts and terms, and
communicating solutions which would usually
require only one or two steps.
Relational thinking will involve selecting and
carrying out a logical sequence of steps, connecting
different concepts and also relating findings to the
context or communicating thinking using
appropriate mathematical statements.
Extended abstract thinking will involve devising a
strategy to investigate or solve a problem and use
correct mathematical statements.
Students will use their measurements to make
calculations using at least three different methods.
For example
Height of posts above clinometer = 30 x tan 12 = 6.4 m
(method, side from trig)
Height of post = 16*1/2 = 8 m
(method, side from similar triangles)
Diagonal of the base of the trailer = (62 + 2.52) = 6.5 m
Or diagonal of the trailer = (62 + 2.52 + 0.52) = 6.52 m
(Method, side from pythagoras)
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Students will solve at least one aspect of the
problem correctly and communicate their solutions.
E.g., solve showing length of diagonal of trailer is
less than length of post or find one solution showing
dimensions of trailer that meet the safety
requirements and relate the findings to the context.
For example
Method 1
Height of posts above clinometer = 30 x tan 12 = 6.4 m
Height of posts = 6.4 + 1.7 m = 8.1m
Students will solve both aspects of the problem
correctly and communicate their thinking using
correct mathematical statements.
E.g., solution showing length of diagonal of trailer
is less than length of post AND one solution
showing dimensions of trailer that meet safety
requirements explained with correct mathematical
statements.
For example
Method 1
Height of posts above clinometer = 30 x tan 12 = 6.4 m
Height of posts = 6.4 + 1.7 m = 8.1 m
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Internal assessment resource Mathematics and Statistics 1.7A for Achievement Standard 91032
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If there is assessor confidence that the student has
contributed to the selection and making of the
measurements and that the measurements are
accurate to a suitable level of precision then
measuring would be acceptable as one of the
three methods.
Minor omissions and variations in rounding can be
accepted.
Method 2
Height of post = 16*1/2 = 8 m
Method 2
Height of post = 16*1/2 = 8 m
I will take the height of the posts as 8m
The length of the posts to be transported = 8+0.5 = 8.5 m
I will take the height of the posts as 8 m
The length of the posts to be transported = 8+0.5 = 8.5
m
Diagonal of the base of the trailer = (62 + 2.52) = 6.5 m
Diagonal of the trailer = (6.52 + 0.52) = 6.52 m
The posts are too long to be transported without sticking
out of the trailer by more than 1 m.
Diagonal of the base of the trailer = (62 + 2.52) = 6.5 m
Diagonal of the trailer = (6.52 + 0.52) = 6.52 m
The posts are too long to be transported without
sticking out of the trailer.
Alternative methods for solving these problems are
possible and allowed.
Students should not be penalised for minor errors
(e.g., omitting the 0.5m below ground), running
arithmetic or failing to communicate clearly.
Accept answers (and follow through) to 3 s.f.
Answers must include relevant units. Answers must
be related to the context of the problem.
Minor omissions can be accepted
This maximum horizontal length outside the trailer will
be directly below the post.
This diagram shows the position of the post when the
horizontal distance is 1m. I have to find h.
cos  = 7.5/8.5
 = 280
h = 6.5 tan = 3.46 m
The height of the trailer must be more than 3.46 m
Alternative methods for solving these problems
are possible and should be allowed.
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Internal assessment resource Mathematics and Statistics 1.7A for Achievement Standard 91032
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Students should not be penalised for minor errors
(e.g., omitting the 0.5 m below ground.)
Accept answers (and follow through) to 3 s.f.
Answers must include relevant units. Answers
must be related to the context of the problem.
Students should not be penalised for using an
incorrect answer to one calculation in subsequent
calculations, provided their calculations follow
through correctly.
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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