Backward Design Plan
Stage 1 - Desired Results
Subject / KLA - Mathematics
Year Level - Year 7
Established Goals (Syllabus / Essential Learnings):
What relevant goals (e.g., content standards, course or program objectives, learning outcomes) will this design
address?
Only list the outcomes you are assessing in your strategy.
Year 7 Mathematics Achievement Standard (Australian National Curriculum)
By the end of Year 7, students solve problems involving the comparison, addition and subtraction of integers.
They make the connections between whole numbers and index notation and the relationship between perfect
squares and square roots. They solve problems involving percentages and all four operations with fractions and
decimals. They compare the cost of items to make financial decisions. Students represent numbers using
variables. They connect the laws and properties for numbers to algebra. They interpret simple linear
representations and model authentic information. Students describe different views of three-dimensional objects.
They represent transformations in the Cartesian plane. They solve simple numerical problems involving angles
formed by a transversal crossing two parallel lines. Students identify issues involving the collection of continuous
data. They describe the relationship between the median and mean in data displays.
Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction
or percentage of another. Students solve simple linear equations and evaluate algebraic expressions after numerical
substitution. They assign ordered pairs to given points on the Cartesian plane. Students use formulas for the area
and perimeter of rectangles and calculate volumes of rectangular prisms. Students classify triangles and
quadrilaterals. They name the types of angles formed by a transversal crossing parallel line. Students determine the
sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes. They
calculate mean, mode, median and range for data sets. They construct stem-and-leaf plots and dot plots.
ACARA (2011). Year 7 Mathematics Achievement Standard. Retrieved January 25, 2012, from
http://www.australiancurriculum.edu.au/Year7
Content Description
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Construct sample spaces for single-step experiments with equally likely outcomes
Assign probabilities to the outcomes of events and determine probabilities for events
Identify and investigate issues involving numerical data collected from primary and secondary
sources
Construct and compare a range of data displays including stem-and-leaf plots and dot plots
Calculate mean, median, mode and range for sets of data. Interpret these statistics in the
context of data
Describe and interpret data displays using median, mean and range
Compare fractions using equivalence. Locate and represent positive and negative fractions
and mixed numbers on a number line
Understandings: Students will understand that . . .
What is your general interpretation of the Broad Statements above?
If you were asked to briefly describe to a parent what you wanted the students to get out of this unit, what
would you say?
In life students need to be aware that not all events are equally likely and that decisions they make (personally,
financially, socially etc) can hinge upon the likelihood that certain events occurs. This unit will assist students
to understand the probability of an event and the process we use to investigate the chances of certain events
occurring. Students will also learn how to collect statistical data and to make calculations to assist them to see
trends. Students will also look at a range of statistical information (data) and analyse this information thus
improving their thinking skills and helping them to make informed choices.
Specific Learning Outcome Statements
(List at least 6 good examples – you don’t need to include every statement)
Students will be able to:
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Carry out mathematical experiments requiring the accurate collection of data (number on die, colour of
counter, student heights etc) and record the data in a Frequency Distribution Table (Headings of Score,
Tally Frequency) using tally marks (grouped in 5s).
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Graph the data contained in a Frequency Distribution Table in the most appropriate forms (pie graph,
column graph, histogram, line graph) ensuring the graph contains a Title, Scale (if applicable) and
Labels.
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Calculate the probability of an event (number of times event occurs / total number of trials) based upon
the data held in the Frequency Distribution Table and convert this to a proper fraction format.
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Construct mathematical spinners (as displayed below) to match the desired probability of events for use
in student constructed games. Eg construct a spinner which would imitate the throwing of a fair die.
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Evaluate the fairness of a game (such as N Counters, roulette, unders and overs etc ) by playing the
game, collecting appropriate data and comparing this data to the expected outcomes if the game was
fair.
Construct and carry out surveys (of other students) to collect data (such as age, pocket money, height,
favourite TV show) and calculate statistical averages (mean, mode, median) and spread (range) of this
data.
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Stage 2 – Assessment Evidence
Through what summative authentic assessment tasks will students demonstrate the desired understandings?
Identify the assessment tool /s you will use (eg portfolio, oral presentation, research assignment, role-play,
news paper article, construction, exam ...)
1. Game Investigation (Fred’s Casino)
 Students will play the Fred’s Casino game making observations about the chances of certain events
occurring. Based upon these observations the students will identify whether they believe the game is fair
or not. The students will then collect data to check on the fairness of the game. The observations,
strategy and data collection and analysis will be recorded in each student’s Learning Log.
 Students will design new rules for the game to make it fair. The students will be required to construct a
new spinner to use with the new game. They will justify the fairness of the game by conducting an
experiment, collecting data etc. The information will be recorded in the individual student’s Learning
Log.
2. Average Year 7 student investigation
 Students (in groups of 3) will construct a survey to be used with all the Year 7 students. The data will be
collected and statistical averages and spread will be calculated. The information will be analysed and the
students will display the information in a creative manner (build an average year 7, poster, video etc)
3. End of Term examination
 The examination will test understanding of probability, calculation of means etc and analysis of data.
Through what formative assessment tasks will students receive feedback to highlight what they have learnt and
how they can improve their future performance?
Identify tasks such as drafting, practice performances, quizzes, observational checklists, peer feedback ...
 The students will be given a timeline for the completion of the main elements of the assessment.
Students will be required to show their progress on a weekly basis to the teacher.
 The Learning Log will be checked after the completion of phase 1 of the Fred’s casino Investigation,
written feedback will be provided to the students.
 The learning log will be checked by the teacher after the completion of Phase 2 of the Game
Investigation. Written feedback will be provided by the teacher.
 The survey questions will be checked by the teacher before the data collection phase. The feedback will
be presented orally to the group of students. Feedback will also be provided by ticking the criteria sheet
to show what standard the survey instrument is at that point in time.
 The average year 7 creative presentation of the survey data will be shared with the class for peer and
teacher feedback before the final submission and public presentation. The students will have a week to
make changes before final submission.
 Students will be given weekly review tests to check their knowledge of the key concepts and prepare
them for the final examination. Groups of students will be identified for specific review activities based
on their results on these review tests.
Stage 3 – The Learning Plan
Identification of activities that scaffold the authentic assessment strategy.
An example would be if you were requiring students to complete an oral presentation, you might include
activities that teach the students what you want them to display in the presentation, give them time to practise
the oral in front of their peers and provide feedback to improve their performance. The actually teaching
strategy you will use does not need to be identified.
The goal of this section of the Backward Design Plan is for you to identify how you can best prepare the
students for the ‘style’ of assessment.
Hidden Skills – skills not obviously part of the unit stated in the National Curriculum
1.Time Management
2. Group-work Skills
3. Journal writing
4. Giving effective and constructive feedback
5. Presentation skills – poster construction, video skills etc
The ‘hidden skills’ will be addressed by:
1. providing a timeline for the completion of activities and drafting, teacher to monitor progress on a
weekly basis and by checking student work in class
2. students will review group skills before the start of the unit and practised in other subjects, group work
skills will be displayed on the wall and monitored by the teacher
3. a practice mathematics investigation will be carried out by the class as a whole and students will give
structured feedback to each other as to strengths and weaknesses as well as get feedback from the
teacher
4. before the feedback on the class investigation students will be taught what constitutes good constructive
feedback and practise this when discussing each other’s learning logs
5. once the groups decide upon the style of presentation they wish to use they will get direct instruction in
Art on the skills needed for the Maths presentation.
Adapted from:
Wiggins, Grant. Understanding by Design (Expanded Second Edition).
Alexandria, VA, USA: Association for Supervision & Curriculum Development, 2005. p 22.
http://site.ebrary.com/lib/unisouthernqld/Doc?id=10081770&ppg=34