Formulae and substitution
Algebra
Definition
Algebra uses letters or symbols to represent numbers and quantities in formulae and equations. By using algebra, students learn to apply logical reasoning and develop problem solving skills.
A variable is a symbol, such as x, y or z, used to represent an unspecified member of some set. For example, the variable x could represent the number 5 or 127. It is important for us to think about the reasonableness of our answers when using algebraic skills to solve problems. As algebra is a tool to be used when solving problems it can seem like an abstract concept. (NSW Mathematics K-10 syllabus)
Teaching and learning activities
The resources below provide targeted teaching strategies to support student improvement in this skill.
Each downloadable lesson activity includes:
learning intentions
a list of required resources
a step-by-step lesson sequence
printable classroom materials
Select the download all icon to download all available activities or select each activity separately.
PLAN2 Areas of focus
An Areas of focus template has been created in PLAN2 to support targeted teaching of Text structure in your learning area.
Search for the DoE template titled ‘DoE HSCMinStd Writing: Text structure’ in the Areas of focus template library tab within the Plan menu, and customise it for your students’ needs.
For more information about using PLAN2 Areas of focus templates with this resource, visit the Using this resource with PLAN2 page.
Relevance to the numeracy test marking
The feedback for a Level 3 performance in the HSC minimum standard online numeracy test states:
Individuals performing at this level typically select appropriate strategies from a variety of everyday mathematical processes in familiar and some less familiar contexts. They interpret and comprehend mathematical information in written material, diagrams, charts and tables.
Students are able to interpret and use simple formulae that describes relationships between variables.
Connections with ACSF Level 3 descriptors
The relevant Level 3 ACSF descriptors for numeracy are shown here to demonstrate how simple formulae that describe relationships between variables are assessed in the HSC minimum standard online test. The performance features identified show what a student is able to do in order to achieve at this level and are provided to support teachers to understand what is required to achieve a Level 3 in this skill.
Numeracy Indicator 3.09: Selects and interprets mathematical information that may be partly embedded in a range of familiar, and some less familiar, tasks and texts
Focus area: Explicitness of mathematical information
Level 3 performance features:
interprets and comprehends a range of everyday mathematical information that is embedded in familiar and routine texts
Numeracy Indicator 3.10: Selects from and uses a variety of developing mathematical and problem solving strategies in a range of familiar and some less familiar contexts
Focus area: Problem solving processes including estimating and reflecting
Level 3 performance features:
select appropriate methods of solution from a limited range of mathematical processes Use developing estimation, and other assessment skills, to check and reflect on the outcome and its appropriateness to the context and task
Focus area: Mathematical methods and use of tools
Level 3 performance features:
uses a blend of personal ‘in-the-head’ methods and formal pen and paper methods to calculate and uses calculator/technological processes and tools to undertake the problem solving process
Numeracy Indicator 3.11: Uses a combination of both informal and formal oral and written mathematical language and representation to communicate mathematically
Focus area: Oral mathematical language
Level 3 performance features:
uses a combination of both informal and formal oral mathematical and general language to present and discuss the mathematical and problem solving process and result
Connections with Numeracy Learning Progression:
The progressions describe a typical developmental sequence of literacy and numeracy learning. The numeracy progression sub-elements, levels and indicators relevant to patterns are provided here to assist teachers to identify students’ capabilities and needs to support targeted teaching.
Element: Number sense and algebra
Sub-element: Number patterns and algebraic thinking (NPA)
NPA5 — Generalising patterns
creates and interprets tables used to summarise patterns (e.g. the cost of hiring a bike based on the cost per hour)
identifies a single operation rule in numerical patterns and records it in words (e.g. European dress size = Australian dress size + 30)
relates the position number of shapes within a pattern to the rule for the sequence (e.g. number of counters = shape number + 2)
predicts a higher term of a pattern using the pattern’s rule
NPA6 — Representing unknowns
creates algebraic expressions from word problems involving one or more operations (e.g. when n = number of egg cartons, then the number of eggs can be represented by the expression 12n)
uses words or symbols to express relationships involving unknown values (e.g. number of apples packed = 48 x number of boxes packed; C = 20 + 10h)
evaluates an algebraic expression or equation by substitution (e.g. uses the formula for force ‘F’, F = ma to calculate the force given the mass ‘m’ and the acceleration ‘a’)
NPA7 — Algebraic expression
creates and identifies algebraic equations from word problems involving one or more operations (e.g. if a taxi charges $5 call out fee then a flat rate of $2.30 per km travelled, represents this algebraically as C = 5 + 2.3d where d is the distance travelled in km and C is the total cost of the trip)
identifies and justifies equivalent algebraic expressions
interprets a table of values in order to plot points on a graph