Name: …………………………………………………
Class Teacher: ……………………………………..
ORANGE HIGH SCHOOL
MATHEMATICS
YEAR 10 2015 - Assignment 2
TIME ALLOWED - 2 weeks
Due: Monday 3rd August 2015
INSTRUCTIONS

Section 1 – Data and Analysis

Section 2 – Reasoning and Logic

Section 3 - Evaluation

Read all questions carefully and answer each question in the space provided.

All necessary working should be shown in every question.

The mark for each question is indicated.
Data and Analysis:
/33
Reasoning and Logic:
/29
Evaluation:
/15
TOTAL:
/77
DATA AND ANALYSIS
YEAR 10
Aim: Use quartiles and box plots to compare sets of data
and evaluate sources of data.
SECTION 1
Engage
Collect, represent, analyse, interpret and evaluate data.
Time: 15–20 minutes
Explore
Students start the activity by finding the five point summary.
Students can then start investigating petrol prices and
patterns.
Section 1
Explain
Students may have used other methods to achieve their
answer.
Activity recording sheet
Elaborate
Students analyse the spread and mean of the data and make
predictions on the calculated mean and interquartile range.
Students complete the activity and present their work.
Section 1
Evaluate
Reflect using the learning grid and self-assessment.
 What have I learned?
 What did I do well?
 What did not go so well?
 What could I do to improve next time?
Worksheet reflection
Assessment rubric
REASONING AND LOGIC
YEAR 10
Aim: To investigate open ended problems that
involve mathematical thinking.
SECTION 2
Engage
Play the horse race activity.
Time: 30 minutes
Explore
Students try various reasoning and techniques to solve
the problems. They make predictions before exploring
the concept.
Section 2
Explain
Students explain their predictions and how they solved
the problems.
Connect/Extend sheet
Elaborate
Students explain how they reach at their conclusions
and consequently understand how theoretical
probabilities could vary from the experimental
probability.
Section 2
Evaluate
Reflect using the learning grid and self-assessment.
 What have I learned?
 What did I do well?
 What did not go so well?
 What could I do to improve next time?
Worksheet reflection
Assessment rubric
SECTION 1: Data Analysis and Evaluation
Outcomes Addressed: Collect, represent, analyse, interpret data and make sound judgements
Part A - Introduction and representing the data:
In August 2012 the cost (in cents per litre) of unleaded petrol at 11 petrol stations in Melbourne
and Brisbane were as shown in this table.
Melbourne
133.9
125.9
142.9
132.9
144.9
134.9
142.9
160.9
136.9
132.9
139.2
Brisbane
144.9
125.9
142.9
143.5
156.9
144.9
145.3
146.5
147.9
151.9
148.9
1. Record the five-figure summary (minimum, Q1, Q2, Q3, maximum) for each city’s petrol
prices. Also record the outliers for each city.
2. Draw parallel box plots (box and whisker), recording any outliers.
(12 marks)
(6 marks)
3. Calculate the range and interquartile range for each city’s petrol prices.
(4 marks)
4. Record the mean for each city’s petrol prices.
(2 marks)
Part B - Analysing and reporting:
Using the calculations in questions 1, 3 and 4 write a brief report comparing the prices between
the cities in 2012, by interpreting:
1. the spread of the data
(2 marks)
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2. the centre of the data
(2 marks)
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Part C - Research and making judgements:
Use the information on http://www.aip.com.au/pricing/retail.htm to investigate the average
prices of petrol in Australia from 2002 until today. Complete the table below:
(2 marks)
Year
2002
2005
2008
2011
2014
Average Price
1. Which year was the highest average?
(1 mark)
.................................................................................................................................................................
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.................................................................................................................................................................
2. What is the percentage change from 2002 to 2014?
(2 marks)
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3. What’s the trend in the petrol prices? Is it positive or negative? Why?
(2 marks)
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.................................................................................................................................................................
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SECTION 2: Reasoning and Logic (Miscellaneous Problems)
1. a) Count the total number of squares of all sizes on a chess board. Show all the
working out to gain full marks. You can draw the squares to explain your answer. (3 marks)
b) Can you see a pattern in counting all the squares? Show the pattern if you think there is
one.
(2 marks)
2. Rules of Horse Race
Aim - The aim of the game is to pass the finish line first.
Equipment: Two dice, a counter for each row and a flat surface to throw the dice.
How to play:
i. Roll the two dice and add the scores.
ii. The horse with that total moves forward one square on the grid provided below.
iii. Keep rolling the pair of dice.
iv. The horse that is first past the finishing line wins.
a) Before you start the game, write down the order you predict the horses will finish in
on the race result sheet.
Why do you predict this? Write down your reason next to your prediction in the space
provided.
(4 marks)
b) Play the race twice. Record the final positions of the horses each time. (4 marks)
c) Does the outcome vary very much from race to race? What do you think is the
explanation for your answer?
(2 marks)
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d) Which horses are more likely to win? Why?
(2 marks)
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e) Which horses are least likely to win? Why?
(2 marks)
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f) Could the finishing order have been predicted? Why or why not?
(2 marks)
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g) Could the winning distance have been predicted? Why or why not?
(2 marks)
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3. A dartboard is marked as shown.
Josetta is good enough that she always hits the dartboard with her darts but beyond that,
the darts hit in random locations. If a single dart is thrown, calculate the probability of:
(2 marks each)
a) scoring a 1
..............................................................................................................................................................................
b) scoring a 3
..............................................................................................................................................................................
c) scoring a 5
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SECTION 5: EVALUATION (Activity recording sheet)
Name: ...........................................................................................................................................................
Learning obstacle tasks in this assignment:
1.
What were the activities asking you to FIND OUT for both tasks?
2
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..............................................................................................................................................................................
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2.
What STRATEGIES did you use to help solve the problems?
1
 look for a pattern
 guess and check
 work backwards
 draw a picture
 make a list
 make a table or diagram
 use objects to act out the problem
 brainstorm
 use logical reasoning by eliminating some answers
3.
Did you get anyone to help you solve the problems?
1
..............................................................................................................................................................................
..............................................................................................................................................................................
4.
How do you rate the problems?
 The problems were easy to solve.
 The problems needed some brain power.
 The problems were hard to solve and needed lots of brain power.
1
Connect–Extend–Challenge
(6 Marks)
Connect:
Extend:
Challenge:
How are the ideas and
information connected to
what you already know?
What ideas did you get that
extend your thinking in
new directions?
What is challenging or
confusing for you? What
questions do you have?
What puzzles you?
Worksheet reflection
Reflection
 What have I learned? What did I do well?__________________________________________ 2
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________

What did not go so well? What could I do to improve next time?________________________ 2
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
Assessment rubric
Name: ………………………………………………………………………………………………………………………………………………Date: ___/___/20__
Criteria
 Look beyond
 Look within
 Look at
A
B
1.
Above the standard: expert
2.
At the standard: practitioner
E
C/D
3.
Approaching the standard:
moving forward
4.
Ungraded below standard:
travelling required
An efficient strategy is chosen and
progress towards a solution is
evaluated.
Adjustments in strategy, if
necessary, are made along the way,
and/or alternative strategies are
considered.
Note: The expert must achieve a
correct answer.
Deductive arguments are used to
justify decisions and may result in
more formal proofs.
A correct strategy is chosen based
on the mathematical situation in
the task.
Evidence of solidifying prior
knowledge and applying it to the
problem-solving situation is
present.
Note: The practitioner must
achieve a correct answer.
A systematic approach and/or
justification of correct reasoning
are present.
A partially correct strategy is
chosen, or a correct strategy for
solving only part of the task is
chosen. Evidence of drawing on
some relevant previous knowledge
is present, showing some relevant
engagement in the task.
No strategy is evident, or a strategy
is chosen that will not lead to a
solution. Little or no engagement
in the task is present.
Some correct reasoning or
justification for reasoning is
present with trial and error or
unsystematic trying of several
cases.
No correct reasoning or
justification for reasoning is
present.
Communication
 Look beyond
 Look within
 Look at
Precise mathematical language and
symbolic notation are used to
consolidate mathematical thinking
and to communicate ideas.
Communication of an approach is
evident through a methodical,
organised, coherent, sequenced and
labelled response.
No awareness of audience or
purpose is communicated. Little or
no communication of an approach
is evident.
Connections
Mathematical connections or
observations are used to extend the
solution.
Abstract or symbolic mathematical
representations are constructed to
analyse relationships and to extend
thinking.
Mathematical connections or
observations are clearly
recognised.
Appropriate and accurate
mathematical representations are
constructed and refined to solve
problems or portray solutions.
Communication of an approach is
evident through verbal/written
accounts and explanations, use of
diagrams or objects, writing and
mathematical symbols.
Some attempt is made to relate the
task to other subjects or to own
interests and experiences.
An attempt is made to construct
mathematical representations to
record and communicate problem
solving.
Problem solving
 Look beyond
 Look within
 Look at
Reasoning and proof in
support of conclusions,
opinions and claims.
 Look within
 Look at
Representations
Numerical grade [
No connections are made.
No attempt is made to construct
mathematical representations.
/ 77]; Letter grade [___] (A = 90–100%; B = 70–89%; C = 40–69%; D = 10–39%; E = 0-9%)
Comments: ………………………………………................................................................................................................................................