# NA4-9: Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.

This means students will describe the function rule for a linear relationship as well as recognise recursive relationships where more complex relationships are involved. For example, given the pattern of fish made with matchsticks and counters below, students should be able to represent the relationships in a table and graph and use these representations to predict the terms in the sequence:

Counters | 1 | 2 | 3 | 4 | 5 |

Matchsticks | 8 | 14 | 20 | 26 | 32 |

Level Four students should be able to:

- give linear rules connecting the variables (for example, "the number of matchsticks is the six times the number of counters plus two", or "take one off the number of fish, multiply that number by six then add eight")
- extend the graph or table of a linear relationship to predict further co-ordinate pairs, recognising that constant difference (add six in the fish pattern) is associated with points that lay on a line
- use recursive methods to predict further members of a sequence where the relationship is non-linear. For example, the sequence of triangular numbers:

| |||||||||||||||||||||

+2 | +3 | +4 | +5 |

Recursive means finding what is added to or subtracted from one term to get the next.

identify a number pattern from the pattern

generalise that repeated addition equates to multiplication

use a rule to describe a pattern

use a diagram or table to find a pattern

use a rule to describe a pattern

explore triangular number patterns

use a table to find a numbr pattern

use an equation to describe a patter

use a table to find a rule for a geometric pattern

write the rule for relationship as a linear equation

continue a pattern

use a table of values

be able to find the general rule for simple patterns

use a table to find a rule for a geometric pattern

write a rule to describe a relationship

Students will:

- measure, record, and average data for 2 variables (number of marbles and bungy cord stretch)
- plot a scatter graph using appropriate scales (independent variable on x-axis [number of marbles]; dependent variable [overall length] on y-axis)
- use tables and graphs to identify patterns/300

use a rule to describe a pattern

use a graph to show a relationship

write a rule to describe a pattern

use a rule to make predictions

**Session One**

Use systematic approaches to find all the possible outcomes, e.g. tree diagrams, organised lists.

**Session Two**

Use tables, graphs, and word rules to represent growing patterns.

**Session Three**

Draw cube models using plan views.

**Session Four**

Draw cube models using isometric300

use a table or double number line to find a linear relationship

complete a table to find a pattern

use a linear equation to describe a relationship

find and use rules in number patterns

- Identify and find values for variables in context.
- Identify linear relationships in context.
- Represent linear relationships using tables, graphs and simple linear equations.
- Draw strip diagrams to represent linear equations and ratios.
- Solve problems in which two or more conditions must be300

draw and interpret graphs of linear relationships.

- Students will be able to identify examples of natural and human made structures that represent the Fibonacci sequence.
- Students will be able to explain the relationship between members of the sequence and how the next number is generated.
- Students will explore the Golden Ratio and the Golden Angle300

use proportions to solve problems (Problem 2)

find patterns in a series of equations (Problem 3)

solve problems using addition facts (Problem 4)

use a formula to continue a pattern