The year 8 project: A great start to high school mathematics
Rationale
Students enter high school with a variety of skills and experiences in mathematics. This is sometimes
seen as an issue to be overcome, typically addressed by revision of number work as the initial
topic(s) in secondary school. The focus on number skills is accompanied by skill-based assessments
and grouping of students on the basis of perceived need. For many students such an approach is
likely to reinforce negative stereotypes about mathematics and negative perceptions of themselves
as learners.
On the other hand the diversity of students entering year 8 can be seen as a resource. When
students’ initial experiences of high school mathematics are engaging and successful, they are more
likely to develop skills and dispositions that will enable them to be successful in mathematics in
secondary schools. Commencing year 8 with a rich and challenging activity that has a variety of levels
of challenge and support can both engage students in mathematics and provide teachers with
valuable data about students’ current levels of fluency and understanding.
Proposal: Implement a common unit of work and assessment to be used at the commencement of
year 8 mathematics.
Counting Trees: http://map.mathshell.org/materials/download.php?fileid=1239
For teachers the activity enables them to promote the development of students as
powerful learners of mathematics by:
 Providing a structure for teaching and learning that incorporates formative assessment and
differentiation within a flexible classroom setting;
 Challenges existing textbook-dominated paradigms of teaching and learning in mathematics;
 Offers opportunities to use ICT in productive and innovative ways;
 Highlights a bank of expert-designed freely available concept development activities and
assessment tasks that can be used in a variety of topics at different year levels;
 Links to content descriptions of the Australian Curriculum: Mathematics;
 Enacts the proficiencies of the Australian Curriculum: Mathematics.
For students the activity promotes powerful learning in high school mathematics by:
 Providing an accessible, engaging, contextually and mathematically rich introduction to high
school mathematics;
 Engaging them in both individual and collaborative work;
 Introducing important mathematical concepts and skills;
 Developing skills of reasoning and problem solving including estimation, communication,
justification, and the valuing of alternative solution methods;
 Encouraging risk-taking in a safe environment.
Suggested implementation
Trial phase (2013)
 Term 3, Weeks 1 to 10: Development of proposal, presentation to numeracy expert group,
identify pilot schools (Steve Thornton)
 Term 4, Weeks 1 and 2: Use the task with current year 8 teachers in three schools. Obtain
feedback from teachers and students (teachers in pilot schools supported by Steve
Thornton)
 Term 4, Weeks 3 to 5: Analyse feedback, prepare report for DECD, modify activity as
necessary (Steve Thornton)
 Term 4, Week 6: Disseminate to schools for implementation in 2014 (Steve Thornton with
DECD support).
 Term 4, Weeks 6 to 8: Set up shell for teacher discussion blog, set up shell for student
exchange of solutions and methods (Steve Thornton with DECD support).
Implementation (2014)
 Term 1, Weeks 1 and 2: Implementation across school, region or system (Teachers, school
leaders, numeracy coaches)
 Term 1, Weeks 3 to 8: Evaluation, reporting, further recommendations to DECD L&N team,
numeracy expert group, Region Directors (DECD L&N team)
Cost
2013 costs covered by existing contractual arrangements with Steve Thornton. Evaluation of 2014
activity and further development will need to be arranged internally, or with an external consultant
or a University school of education.
The task—Estimating: Counting Trees
Students are asked to estimate the number of old and new trees in a forest. They are provided with
a stylised diagram of a forest in which trees are planted in a square arrangement.
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Stage 1: Students complete as much of the task as possible as formative assessment. The
teacher asks written questions of each student’s work according to the guidelines provided.
Stage 2: Students collaborate to design a poster detailing their best estimate of the number
of old and new trees and the most efficient method.
Stage 3: Students discuss different approaches, analyse three sample responses provided
and reflect on their learning.
Possible technological approach: Copy the stylised forest onto a blank Geogebra screen and
use a rectangular screen that can be positioned over the grid in various places to generate
random samples.
Features of the task include:
(1) It is mathematically rich, directly addressing Australian Curriculum content descriptions
ACMSP284 and ACMSP206, while indirectly addressing parts of ACMNA187 and ACMNA188.
(2) It is both accessible and challenging, offering opportunities for teachers to identify student
needs and for students to monitor their own knowledge.
(3) It is relatively short, however could easily be extended to a much longer and more
challenging unit of work.
(4) Formative assessment is built into the task.
(5) It is part of a freely available suite of concept develop activities and tasks at the
Mathematics
Assessment
Resource
Service
(MARS)
website
at
http://map.mathshell.org/materials/index.php. The activities give extensive detail for
teachers and can be used with minimal additional preparation. Hence teachers wishing to
use similar tasks and activities throughout the year are able to do so. The website also
contains professional development resources for staff discussion and/or personal learning.
The tasks have a sound research and development base, having been designed by leading
mathematics educators at the Shell Centre for Mathematics Education at the University of
Nottingham and Michigan State University.
(6) The follow up activities integrate the use of technology and can be used with laptop
computers, tablets or an Interactive whiteboard. They engage students in distributed
learning within and across schools through sharing solution methods and their estimations.
However similar activities could also be used without extensive technology if necessary.
Follow-up activities/assessment
(1) Use the random point generator at Geomidpoint at http://www.geomidpoint.com/random/
to generate some random points on the surface of the earth. Use this to estimate the
percentage of the earth’s surface that is land or water. Discuss the number of points needed
and assumptions made. Discuss other possible uses for random point sampling.
(2) Use a spreadsheet to generate some random pairs of numbers, each between 0 and 1. Plot
them as points on a coordinate grid and print the page. Use the page as a method for
estimating the area of an irregular shape such as a map of Australia. Or superimpose the
graph on a map. Discuss the advantages or disadvantages of this method of estimating area
compared to counting squares. A similar method can be used to estimate π.
(3) Use a Gigapan picture from http://www.gigapan.com/ and a sampling method to estimate
the size of a crowd at an event. Some possible crowd pictures are:
 Melbourne Boxing Day Test: http://www.gigapan.com/gigapans/39511
 CHOGM Perth barbecue: http://www.gigapan.com/gigapans/91196
 Rutgers University student convocation: http://www.gigapan.com/gigapans/139414
 Melbourne Anzac Day dawn service: http://www.gigapan.com/gigapans/48607
 Swedish Royal Wedding: http://www.gigapan.com/gigapans/52304
 Colorado v San Diego baseball: http://www.gigapan.com/gigapans/127025
 North Carolina State University insect museum: e.g. http://www.gigapan.com/gigapans/34377
Students exchange answers and solution methods within and across schools. For (1) and (2) they
enter their data into a shared spreadsheet which automatically updates and records moving average
as more data is added. This enables them to observe the effect of sample size on the accuracy of the
answer. For (3) they share solutions methods via an interactive discussion board.