Mathematics — numeracy (Year 10)
Example short assessment
In the Australian Curriculum, numeracy is one of the general capabilities embedded across all
learning areas.
Students become numerate as they develop the knowledge and skills to use mathematics
confidently across all learning areas at school and in their lives more broadly. They need to
recognise that mathematics is constantly used outside the mathematics classroom and that
numerate people apply mathematical skills in a wide range of familiar and unfamiliar situations.
“Numeracy involves students in recognising and understanding the role of mathematics in the
world and having the dispositions and capacities to use mathematical knowledge and skills
purposefully.” 1
Assessment technique
Short response
Targeted indicator
Recognising and using patterns and relationships
PR 10 ii
Solve, with or without technologies, problems involving:
• line of best fit
• linear equations including simple algebraic fractions and those derived from formulas
• linear inequalities, including graphing solutions on a number line
• linear simultaneous solutions
• simple quadratic equations
Context
This short response provides opportunity to monitor each student’s ability to use linear equations
and simultaneous solutions to solve problems involving revenue and expenses when planning a
dance.
This assessment could be linked to Australian Curriculum content:
• Algebra — Linear and non-linear relationships
- Solve linear simultaneous equations, using algebraic and graphical techniques including
using digital technology (ACMNA237).
Australian Curriculum v5.0, accessed 8 July 2013,
<www.australiancurriculum.edu.au/GeneralCapabilities/Numeracy/Introduction/Introduction>.
13487 R1
1
Teacher information
This assessment is an example of one way that teachers may gather evidence of a student’s
ability to demonstrate the highlighted sections of the targeted indicator.
Students should have access to graphing technology (computer programs or graphical
calculators) to help them complete the task.
This assessment may be differentiated by:
• having further discussion to allow some students to clarify and question
• providing extra time for some students who are reluctant readers and need adjusted time.
Implementation
Modelling
The teacher:
• models
- the process of graphing linear functions on a Cartesian plane
- writing linear functions to represent the relationship between variables
• guides discussion of
- factors that have an impact on the organisation and costs associated with planning a dance
- terminology such as:
 revenue
 break even
 profit/loss
 constants
 variables.
Gathering evidence
The students:
• view and read the resource Financial analysis graph
• interpret the graph to answer the questions.
Evidence of student achievement of each indicator can be recorded in the Class monitoring
record provided. Teachers analyse the evidence to inform decisions about ongoing numeracy
teaching and learning.
2
|
Mathematics — numeracy (Year 10) Example short assessment
Resource: Financial analysis graph
To raise $150 for a new banner for softball team events, a Year 10 HPE class suggested holding
a dance in the school hall.
A group of students researched the costs of holding a dance and the revenue that could be
raised from ticket sales. They summarised their results in the graph below.
Use the Financial analysis graph to answer the following questions (show your working):
1.
What is the proposed price of a ticket? Do you think this is a reasonable price?
2.
The dance can go ahead if it breaks even.
3.
a.
What is meant by break-even?
b.
How can you determine this from the graph?
c.
How many tickets must be sold to break even?
If the running costs can be summarised by the equation y = mx + c where m is the price of
refreshments per ticket sold and c is the price of the entertainment, find the values for:
a.
c
b.
m
c.
How did you find the values for m and c from the graph?
4.
Approximately how much profit will be made if 40 tickets are sold?
5.
Approximately how much money will be lost if only 10 tickets are sold? Show your working.
6.
Approximately how many tickets must be sold to raise the $150 needed? Show your working.
Queensland Studies Authority
|
3
Class monitoring record
Teacher
4
|
Class
Term
Indicator
PR 10 ii
Solve, with or without technologies, problems involving:
• line of best fit
• linear equations including simple algebraic fractions and those derived from
formulas
• linear inequalities, including graphing solutions on a number line
• linear simultaneous solutions using a variety of techniques and technology
simple quadratic equations using a range of strategies
Student names
Evidence
Mathematics — numeracy (Year 10) Example short assessment