NA5-9: Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
This means students will recognise the features of tabular, graph and equation representations of linear and quadratic relationships. This includes connecting constant first or second order difference in tables with linear and quadratic relations respectively, with the graph (linear and parabolic) and standard equation forms (y = mx + c and y = a x 2 + bx + c) for such relations. For example, given the spatial pattern below students can use a table, graph or equation to represent the relation and solve problems.
This includes finding both a recursive and direct (functional) rules and using them to find further terms using a spreadsheet or calculator, for example:
Students should also use these tabular and graphic representations for other relationships, such as simple exponential and step relations, but it is acceptable for them to use recursive rules for these more difficult relations.
use a table to find a pattern
write a quadratic equations to describe the relationship
- use rates, ratios, and reasoning with linear proportions to solve a problem.
- make connections between representations of linear data in tables and graphs.
find a rule to describe a geometric pattern
- Find the rule for summing consecutive numbers.
- Identify the pattern of triangular numbers.
- Devise and use problem solving strategies to explore situations mathematically (be systematic, use algebra).
- use algebra to generalise the results of a practical investigation.
- apply knowledge of circuits, power, voltage, currents, and resistance to problem solving.
- use graphical techniques to identify and describe a linear relationship found in a practical investigation.
- Name the fraction for a given Cuisenaire rod with reference to one (whole) and with reference to another rod.
- Fluently multiply two or more fractions.
- Divide a fraction by another fraction, including when the divisor is greater than the dividend.
usea table to continue a pattern
use a rule to describe a prediction
write a rule as a quadratic equation
- Find areas of shapes.
- Find simple two-variable linear patterns relating to areas.
use a graph to find a pattern for a non linear relationship
- Solve linear equations.
- Describe a linear relationship between two variables in words and as an equation.
- Make a table of one variable against another.
- Use a graph to find the value of y, given x, and x, given y.
interpret a relationship shown by a graph
- Find pairs of whole number co-ordinates and use them to draw graphs in problem contexts.
- Link the graphs to formulae of the kind ax±by=c
- Find the nth whole number pairs in a context that solve ax-by=c
- Make a table of one variable against another to represent a quadratic relationship.
- Represent a quadratic relationship between two variables in words and as an equation.
- Represent a quadratic relationship as a parabola on the Cartesian Plane.
- Recognise the key features of a parabola, including the300
use a table to find a rule for a geometric pattern
write the rule for a relationship as a linear equation
use rules that describe quadratic relationships
- Continue multiplicative sequences.
- Find connections between numbers in a table.
- Use Pythagoras’ theorem in a general algebraic form.
- Measure accurately from a scale drawing.
- devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).
- Make a table of one variable against another to represent a quadratic relationship.
- Represent a quadratic relationship between two variables in words and as an equation.
- Represent a quadratic relationship as a parabola on the Cartesian Plane.
- Recognise the key features of a parabola, including the300
make a graph from a data table
interpret a relationship shown on a graph
- Generate patterns from a structured situation.
- Find a rule for the general term (extension problem).
- Devise and use problem solving strategies to explore situations mathematically (be systematic, guess and check, make a table, look for a pattern).