# YEAR 6 MATHS FOCUS

## NUMBERS AND ALGEBRA

Patterns & Algebra

Learning Experiences

Patterns & Algebra

## PATTERNS & ALGEBRA

OUTCOME

A student:

MA3-8NA:

analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane

Teaching Points | In Stage 2, students found the value of the next term in a pattern by performing an operation on the previous term. In Stage 3, they need to connect the value of a particular term in the pattern with its position in the pattern. This is best achieved through a table of values. Students need to see a connection between the two numbers in each column and should describe the pattern in terms of the operation that is performed on the position in the pattern to obtain the value of the term. Describing a pattern by the operation(s) performed on the ‘position in the pattern’ is more powerful than describing it as an operation performed on the previous term in the pattern, as it allows any term (eg the 100th term) to be calculated without needing to find the value of the term before it. The concept of relating the number in the top row of a table of values to the number in the bottom row forms the basis for work in Linear and Non-Linear Relationships in Stage 4 and Stage 5. |

The notion of locating position and plotting coordinates is established in the Position substrand in Stage 2 Measurement and Geometry. It is further developed in this substrand to include negative numbers and the use of the four-quadrant number plane. | |

The Cartesian plane (commonly referred to as the ‘number plane’) is named after the French philosopher and mathematician René Descartes (1596–1650), who was one of the first to develop analytical geometry on the number plane. On the number plane, the ‘coordinates of a point’ refers to the ordered pair (x,y) describing the horizontal position x first, followed by the vertical position y The Cartesian plane is applied in real-world contexts, eg when determining the incline (slope) of a road between two points. The Cartesian plane is used in algebra in Stages 4 to 6 to describe patterns and relationships between numbers. |

Language | Students should be able to communicate using the following language: pattern, increase, decrease, term, value, table of values, rule, position in pattern, value of term, number plane (Cartesian plane), horizontal axis (x-axis), vertical axis (y-axis), axes, quadrant, intersect, point of intersection, right angles, origin, coordinates, point, plot. |

## Expectations of Attainment

Continue and create sequences involving whole numbers, fractions and decimals; describe the rule used to create the sequence (ACMNA133) | continue and create number patterns, with and without the use of digital technologies, using whole numbers, fractions and decimals, e.g. 14, 18, 116, … or 1.25, 2.5, 5, … {Information and communication technology capability, Critical and creative thinking} |

– describe how number patterns have been created and how they can be continued {Communicating, Problem Solving, Critical and creative thinking} | |

create simple geometric patterns using concrete materials, e.g. △,△△,△△△,△△△△, …{Literacy} | |

complete a table of values for a geometric pattern and describe the pattern in words, e.g. {Critical and creative thinking, Literacy} | |

– describe the number pattern in a variety of ways and record descriptions using words, e.g. ‘It looks like the multiplication facts for four’ | |

– determine the rule to describe the pattern by relating the bottom number to the top number in a table, e.g. ‘You multiply the number of squares by four to get the number of matches’ | |

– use the rule to calculate the corresponding value for a larger number, e.g. ‘How many matches are needed to create 100 squares?’ | |

Complete a table of values for number patterns involving one operation (including patterns that decrease) and describe the pattern in words, e.g. describe the pattern in a variety of ways and record descriptions in words, eg ‘It goes up by ones, starting from four’ determine a rule to describe the pattern from the table, eg ‘To get the value of the term, you add three to the position in the pattern’ use the rule to calculate the value of the term for a large position number, eg ‘What is the 55th term of the pattern?’ {Literacy, Critical and creative thinking} | |

– explain why it is useful to describe the rule for a pattern by describing the connection between the ‘position in the pattern’ and the ‘value of the term’ {Communicating, Reasoning, Literacy, Critical and creative thinking} | |

– interpret explanations written by peers and teachers that accurately describe geometric and number patterns {Communicating, Literacy, Critical and creative thinking} | |

make generalisations about numbers and number relationships, eg ‘If you add a number and then subtract the same number, the result is the number you started with’ {Critical and creative thinking} |

Introduce the cartesian-coordinate-system using all four quadrants (ACMMG143) | recognise that the number plane (Cartesian plane) is a visual way of describing location on a grid |

recognise that the number plane consists of a horizontal axis (x-axis) and a vertical axis (y-axis), creating four quadrants e.g. | |

– recognise that the horizontal axis and the vertical axis meet at right angles {Reasoning} | |

identify the point of intersection of the two axes as the origin, having coordinates (0, 0) {Literacy} | |

plot and label points, given coordinates, in all four quadrants of the number plane {Literacy} | |

– plot a sequence of coordinates to create a picture {Communicating, Literacy} | |

identify and record the coordinates of given points in all four quadrants of the number plane | |

– recognise that the order of coordinates is important when locating points on the number plane, eg (2, 3) is a location different from (3, 2) {Communicating} |

Learning Experiences

To be added