This document outlines algebra skills at different levels. Level 2 skills include continuing patterns, using symbols like = and <, and solving basic addition problems. Level 3 skills build on this with more complex properties of operations, finding rules for patterns, and relating patterns to number lines. Level 4 skills include writing precise arithmetic expressions, developing function rules, representing patterns algebraically like with magic squares, and solving problems using linear relationships and formulas.

1. Algebra
L2 - 4

2. Algebra – Level 2
• What I need to know. • What I can do.
– continue a simple pattern
– generalise the pattern
– use the mathematical symbols of =,
<, >
– 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
– continue a sequential pattern
– develop bar charts to show
relationships
– 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
– identify patterns in number
sequences
– systematically “count” to establish
rules for sequential patterns
– use rules to make predictions

3. Algebra – Level 3
• What I need to know. • What I can do.
– consolidate understanding of simple
properties of addition, subtraction,
multiplication and division
– discover and use some more complex
properties of addition, subtraction,
multiplication and division
– 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)
– 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.
– 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
– use a "cups and Cubes" model to
describe relationships

4. Algebra – Level 4
• What I need to know. • What I can do.
– write and calculate arithmetic expressions precisely using the
order of operations.
– realise the importance of the order of operations on a
calculator.
– 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
– 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.
– use powers of two in problem situations
– find number patterns in practical situations
– experiment to find patterns
– explore the relationship between rows and columns in finding
the areas of rectangles
– calculate the area of rectangles, parallelograms and triangles
– develop, justify and use rules to solve problems that involve
number strips
– identify and clearly articulate patterns, and make
generalisations based on these .
– find a rule to describe any member of a number sequence
and express it in words .
– 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.
– solve problems using linear relationships shown on tables
and graphs.