### Level 1 Patterns and Relationships

Achievement Objectives | Learning Outcomes | Unit title |

NA1-5 NA1-1 NA1-2 | - recognise that counting tells how many objects are in the set irrespective of how they are arranged or the order in which they are counted.
- solve problems involving one more or less to a given set using their knowledge of the forward and backward number sequences
- skip count in 2s
| Counting on counting |

NA1-5 NA1-1 | - see what a number pattern is
- be able to guess and check the next number in a pattern
- skip count in 2s, 5s, and 10s
| Ten in a bed |

NA1-5 NA1-1 | - continue a sequential pattern
- systematically count to establish rules for sequential patterns
- skip count in 2s, 5s and 3s
| The three pigs |

NA1-5 NA1-1 | - continue a skip-counting pattern
- describe skip-counting patterns
- use graphs to illustrate skip-counting patterns
| Beetle wheels |

NA1-5 NA1-6 NA2-7 NA2-8 | - investigate and recognise the results of adding and subtracting combinations of odd and even numbers
- state generalisations about the addition and subtraction of combinations of odd and even numbers
- apply generalisations about odd and even number patterns to problem solving situations
| Early number patterns |

NA1-6 | - describe patterns
- continue a pattern
- create patterns
| Pattern makers |

NA1-6 | - record patterns on grid paper
- make predictions about ‘missing’ sections of a pattern
- use words to describe linear patterns
| Snakes and scarves |

NA1-6 | - "read" a repeating pattern and predict what may come next
- create a repeating pattern with two elements
- create a repeating pattern with three elements
| Mary, Mary quite contrary |

### Level 2 Patterns and Relationships

Achievement Objectives | Learning Outcomes | Unit title |

NA2-7 GM2-2 | - partition numbers less than 10
- know and use "teen" facts
- solve addition problems by making a ten, or making a decade
- solve addition problems involving measurements
| Partitions |

NA2-7 | - draw the next shape in a pattern sequence
- see how the pattern continues from one shape to the next
- draw up a table of values
| Letter patterns |

NA2-7 | - identify patterns in number sequences
- systematically "count" to establish rules for sequential patterns
- use rules to make predictions
| Supermarket displays |

NA2-7 NA2-8 | - create, describe and continue a single-attribute repeating pattern
- identify the unit of repeat in a repeating pattern, and apply known patterning language
- identify and describe the composite pattern
- describe and explain the rule for the pattern in the composite pattern
| Dual patterns |

NA2-7 NA2-8 | - recognise situations in which there is a relationship between two number sets
- transfer mapped values onto a graph (an xy coordinate system)
- explain a simple relationship graph with reference to mapped values
| Mapping relationships |

NA2-8 | - draw the next shape in a pattern sequence
- see how the pattern continues from one shape to the next
- draw up a table of values
| Letter Patterns |

NA2-8 NA2-6 | - continue a sequential pattern
- develop bar charts to show relationships
| Staircases |

NA2-8 NA2-6 | - continue a simple pattern
- generalise the pattern
| Pede patterns |

### Level 3 Patterns and Relationships

Achievement Objectives | Learning Outcomes | Unit title |

NA3-7 NA3-6 | - consolidate understanding of simple properties of addition, subtraction, multiplication and division
- discover and use some more complex properties of addition, subtraction, multiplication and division
| Properties of operations |

NA3-8 | - predict the next term of a spatial pattern
- find a rule to give the number of matchsticks (tiles) in a given member of the pattern
- find the member of the pattern that has a given number of matchsticks (tiles)
| Matchstick patterns |

NA3-8 | - show number patterns using the hundred’s board and other grid arrangements for whole numbers
- find the rule for a pattern of numbers shown on a hundred’s board or for input/output pairs from a calculator;
- relate sequential spatial patterns to how they appear as a number sequence on a hundreds board
| Hundreds of patterns |

NA3-8 | - continue a patterns
- find the recurrence rule of a pattern
- look at relations between two patterns
- have some idea of what a general rule is
| Building patterns incrementally |

NA3-8 | - continue a pattern
- find the recurrence rule of a pattern
- look at relations between two patterns
- have some idea of what a general rule is
| Building patterns constantly |

NA3-8 | - use a "cups and cubes" model to describe relationships
| Cups and cubes |

### Level 4 Patterns and Relationships

Achievement Objectives | Learning Outcomes | Unit title |

NA4-8 NA5-2 | - use powers of two in problem situations
- find number patterns in practical situations
- experiment to find patterns
| Two's company |

NA4-9 NA4-7 | - devise a rule for ensuring that sets of numbers can be arranged into 3-by-3 magic squares
- represent 3-by-3 magic squares algebraically
- devise rules for determining the Magic Number for magic squares
- represent magic squares using parametric equations
- solve equations that have been formed from magic squares
| Magic squares |

NA4-9 GM4-3 | - explore the relationship between rows and columns in finding the areas of rectangles
- calculate the area of rectangles, parallelograms and triangles
| You can count on squares |

NA4-9 | - develop, justify and use rules to solve problems that involve number strips
- identify and clearly articulate patterns, and make generalisations based on these
| Matilda's waltz |

NA4-9 | - find a rule to describe any member of a number sequence and express it in words
| The truth about triangles and squares |

NA4-9 | - find the number of crosses in Tukutuku panels by using areas of squares and rectangles
- find the number of crosses in repeating Tukutuku panels by using linear formulae
| Tukutuku panels |

NA4-9 | - solve problems using linear relationships shown on tables and graphs
| Drive |

### Level 5 Patterns and Relationships

Achievement Objectives | Learning Outcomes | Unit title |

NA5-9 | - 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
| Holistic algebra |

NA5-9 | - devise an algebraic rule to identify tilted squares that can fit on geoboards of different sizes
- devise an algebraic rule to identify the size of the smallest square geoboard on which tilted squares can fit
- devise and use an algebraic rule for Pythagoras’ theorem
- devise algebraic rules to find Pythagorean triples
| Fences and posts |

NA5-9 | - 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
| Linear graphs and patterns |

NA5-7 NA5-9 | - make a table of one variable against another to describe a quadratic relationship
- describe a quadratic relationship between two variables in words and as an equation
- show a quadratic relationship as a parabola on the Cartesian Plane
- recognise the key features of a parabola
- use the graph of a parabola to find unknowns
- find unknowns from a simple quadratic equation.
| Mary's Garden |

### Level 6 and 7 Patterns and Relationships

Achievement Objectives | Learning Outcomes | Unit title |

NA6-7 GM6-6 | - devise an algebraic rule to identify tilted squares that can fit on geoboards of different sizes
- devise an algebraic rule to identify the size of the smallest square geoboard on which tilted squares can fit
- devise and use an algebraic rule for Pythagoras’ theorem
- devise algebraic rules to find Pythagorean triples
| Tilted squares and triangles |

M7-3 | - find the recurrence relation for simple sequences
- construct tables of values for a pattern
- find the value of the general term of a sequence algebraically
- find the value of the general term of a sequence geometrically
| The why and how of general terms |

M7-3 | - find the smaller Fibonacci numbers by using the recurrence relation
- find the initial members of other sequences that can be found using a recurrence relation like the Fibonacci one
- find the general term of these recurrence relations using quadratic equations
- understand the concept of a limit of a sequence
- find various limits relating to sequences
| Fibonacci II |

M7-3 | - find patterns in the lengths of the sides of standard paper formats
- use patterns relating to the lengths of the sides of standard paper formats
- see that fractions can be ‘continued’ in order to calculate basic surds
| All shapes and sizes |