4.1 (a) Generating arithmetic expressions from repeating patterns
Patterns and the rules that govern them; students construct an understanding of a relationship as that which involves a set of inputs, a set of outputs and a correspondence from each input to each output.
4.1 (b) Representing situations with tables, diagrams and graphs
Relations derived from some kind of context – familiar, everyday situations, imaginary contexts or arrangements of tiles or blocks. Students look at various patterns and make predictions about what comes next.
4.1 (c) Finding formulae
Ways to express a general relationship arising from a pattern or context
4.1 (d) examining algebraic relationships
Features of a linear relationship and how these features appear in the different representations. Constant rate of change. Proportional relationships
4.1 (e) Relations without formulae
Using graphs to represent phenomena quantitatively.
4.1 (f) expressions
Evaluating expressions derived from real life contexts.
I should be able to:
Foundation Level
4.1 (a) Generating arithmetic expressions from repeating patterns
– use tables to represent a repeating-pattern situation
– generalise and explain patterns and relationships in words and numbers
– write arithmetic expressions for particular terms in a sequence
4.1 (b) Representing situations with tables, diagrams and graphs
– use tables, diagrams and graphs as tools for representing and analysing linear patterns and relationships
– develop and use their own generalising strategies and ideas and consider those of others
– present and interpret solutions, explaining and justifying methods, inferences and reasoning
4.1 (c) Finding formulae
– find the underlying formula written in words from which the data is derived (linear relationships)
4.1 (d) examining algebraic relationships
– show that relations have features that can be represented in a variety of ways
– distinguish those features that are especially useful to identify and point out how those features appear in different representations: in tables, graphs, physical models, and formulae expressed in words
– use the representations to reason about the situation from which the relationship is derived and communicate their thinking to others
– discuss rate of change and the y-intercept; consider how these relate to the context from which the relationship is derived, and identify how they can appear in a table, in a graph and in a formula
– decide if two linear relationships have a common value
– recognise problems involving direct proportion and identify the necessary information to solve them
4.1 (e) Relations without formulae
– explore graphs of motion
– make sense of quantitative graphs and draw conclusions from them
– make connections between the shape of a graph and the story of a phenomenon
– describe both quantity and change of quantity on a graph
4.1 (f) expressions
– evaluate expressions given the value of the variables