Learning Sequence 
Curriculum Achievement Objectives 
Specific Learning Outcomes
The students will be able to: 
Algebra Units of Work 
Level One
Exemplar Link
Link to Learning Objects 
Level 1 Patterns and relationships AO1

Level 1 Number Strategies AO1
 
Number Knowledge AO1


 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 
Level 1 Patterns and relationships AO1

Level 1 Number Strategies AO1
 

 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 
Level 1 Patterns and relationships AO2

 describe patterns
 continue a pattern
 create patterns

Pattern Makers 
Level 1 Patterns and relationships AO2

 record patterns on grid paper
 make predictions about ‘missing’ sections of a pattern
 use words to describe linear patterns

Snakes and Scarves 
Level 1 Patterns and relationships AO2

 "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 1 Patterns and relationships AO1

Level 1 Number Strategies AO1
 

 continue a sequential pattern
 systematically count to establish rules for sequential patterns
 skip count in 2s, 5s and 3s

The Three Pigs 
Level 1 Patterns and relationships AO1

Level 1 Number Strategies AO1
 

 continue a skipcounting pattern
 describe skipcounting patterns
 use graphs to illustrate skipcounting patterns

Beetle Wheels 
Level 1 Number strategies AO1

Level 1 Equations and expressions AO1
 

 draw representations to show a simple addition equations
 write an equation/number sentence to match their diagram

Ways to Add 
Level Two
Exemplar Link

Level 2 Equations and expressions AO1

Level 2 Patterns and relationships AO2
 

 continue a simple pattern
 generalise the pattern

Pede Patterns 
Level 2 Equations and expressions AO1

 use the mathematical symbols of =, <, >

Cuisenaire Mats 
Level 2 Patterns and relationships AO1

Level 2 Measurement AO2:
 

 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 
Level 2 Patterns and relationships AO2

Level 2 Equations and expressions AO1:
 

 continue a sequential pattern
 develop bar charts to show relationships

Staircases 
Level 2 Patterns and relationships AO2

 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 
Level 2 Patterns and relationships AO2

 identify patterns in number sequences
 systematically “count” to establish rules for sequential patterns
 use rules to make predictions

Supermarket Displays 
Level Three
Exemplar Link
Link to Learning Object

Level 3 Patterns and relationships AO1

Level 3 Equations and expressions AO1
 

 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 
Level 3 Patterns and relationships AO2

 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 
Level 3 Patterns and relationships AO2

 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 
Level 3 Patterns and relationships AO2

 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 
Level 3 Patterns and relationships AO2

 use a "cups and Cubes" model to describe relationships

Cups and Cubes 
Level Four
Exemplar Link
Link to Learning Object

Level 4 Equations and expressions AO1


 write and calculate arithmetic expressions precisely using the order of operations.
 realise the importance of the order of operations on a calculator.

Four Fours 
Level 4 Equations and expressions AO1

 predict further members in patterns of equations using relationships within the equations
 develop function rules to describe relationships
 find specific values for variables from given relationships

Balancing Acts 
Level 4 Equations and expressions AO1

Level 4 Patterns and relationships AO2
 

 devise a rule for ensuring that sets of numbers can be arranged into 3by3 magic squares
 represent 3by3 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 
Level 4 Patterns and relationships AO1

Level 5 Number strategies and knowledge AO2
 

 use powers of two in problem situations
 find number patterns in practical situations
 experiment to find patterns

Two's Company 
Level 4 Measurement AO3

Level 4 Patterns and relationships AO2
 

 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 
Level 4 Patterns and relationships AO2


 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 
Level 4 Patterns and relationships AO2


 find a rule to describe any member of a number sequence and express it in words .

The Truth about Triangles and Squares 
Level 4 Patterns and relationships AO2


 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 
Level 4 Patterns and relationships AO2


 solve problems using linear relationships shown on tables and graphs.

Drive 
Level Five
Exemplar Link
Exemplar Link
Link to Learning Object

Level 5 Equations and expressions AO1


 devise rules based on numerical patterns to solve triangular arithmagons
 explain the condition for the solution of any square arithmagon
 form and use linear equations to solve triangular arithmagons
 develop proofs of rules and conditions for the solution of arithmagons

Arithmagons 
Level 5 Equations and expressions AO1


 investigate situations involving ratios
 understand that there are many ways to solve ratio problems
 solve simple equations of the form ax = b
 see the relevance of algebra to ratio problems.

Beanies 
Level 5 Patterns and relationships AO1


 infer the precise limit as a fraction from the limit inferred as a decimal number
 set up a spreadsheet to explore the convergence of certain sequences

What happens on Average? 
Level 5 Patterns and relationships AO2


 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 
Level 5 Patterns and relationships AO2

Level 5 Transformation AO2 

 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 Sqaures and Triangles 
Level 5 Patterns and relationships AO2


 understand the concept of Fibonacci numbers and how they are generated
 find factors of a number
 make conjectures and attempt to prove them
 find generalisations

Fibonacci I 
Level 5 Patterns and relationships AO2


 find pairs of whole number coordinates 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 axby=c

Linear Graphs and Patterns 
Level Six

Level 6 Equations and expressions AO1


 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 
Level 6 Equations and expressions AO1


 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 
Level 6 Patterns and relationships AO2


 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 