# Equations and expressions units of work

### Level 1 Equations and Expressions

Achievement Objectives | Learning Outcomes | Unit title |

NA1-4 NA1-1 | - draw representations to show simple addition equations
- write an equation/number sentence to match their diagram
| Ways to add |

NA1-4 | - understand that written words and oral words can also be represented with numeral symbols
- recognise and use the written and spoken words for addition, with the addition symbol
- recognise and use subtraction written and spoken words, with the subtraction symbol
- recognise and write addition and subtraction expressions from story contexts
| Numerals and expressions |

NA1-4 NA2-6 | - make and recognise combined amounts that have the same value
- read and write addition and subtraction equations
- solve addition and subtraction balance problems and explain the solutions, using the language of equivalence
| Equality and equations |

NA1-4 NA2-6 | - understand the equals symbol as an expression of a relationship of equivalence, and explain this
- recognise situations of inequality and use the inequality (‘is not equal to’) symbol, ≠
- use relationship symbols =, <, > in equations and expressions to represent situations in story problems
| Inequality symbols and relationships |

### Level 2 Equations and Expressions

Achievement Objectives | Learning Outcomes | Unit title |

NA2-6 | - use the mathematical symbols of =, <, >
| Cuisenaire mats |

NA2-6 | - recognise three numbers that are related through the operations of addition and subtraction
- write and read sets of related addition and subtraction equations
- explain, in their own words, the inverse relationship between addition and subtraction
- recognise that addition is commutative but that subtraction is not
- solve number problems that involve application of the additive inverse
| Number families and relationships |

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

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

### Level 3 Equations and Expressions

Achievement Objectives | Learning Outcomes | Unit title |

NA3-6 | - read, write and understand the multiplication symbol, and the language associated with it
- read, write and understand the division symbol and the language associated with it
- recognise that multiplication is commutative but division is not
- recognise the inverse relationship of the operations of multiplication and division
| Multiplication and division symbols, expressions and relationships |

NA3-6 | - understand and explain the relationship between addition and subtraction, and between multiplication and division
- recognise the ambiguity of expressions and equations that include more than one operation
- understand and explain the rules for the order of operations, including explaining the acronym, BEDMAS
- apply the order of operations to solve problems
| The order of operations |

NA3-6 | - recognise that there are number properties and that these describe the behavior of number operations
- understand that a generalisation of an important idea can be expressed using letters (variables)
- recognise representations, using variables, of the commutative, associative, and distributive properties, and write equations to show them in practical contexts
| A study of number properties |

NA3-6 NA3-7 | - 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 |

NA3-6 NA4-7 | - understand that an unknown amount or number can be represented with a symbol: a question mark, a shape or a letter
- write word problems of real life situations and express these with equations that include a variable
- solve single step whole number equations that include a variable
- recognise that an equation is balanced around the equals symbol
- formally solve equations, which include variables and which represent problem situations involving fractional and decimal amounts
| Unknowns and variables: Solving one-step equations |

### Level 4 Equations and Expressions

Achievement Objectives | Learning Outcomes | Unit title |

NA4-7 | - solve two-step equations and represent the solution using materials
- represent number relationships using words, a table and a graph, and recognise the importance of these representations
- write equations, using variables and brackets, to express problem situations
- solve equations that have unknown amounts on both sides
- understand that a variable can be used to represent a quantity that varies in relation to another quantity
| Solving multi-step equations |

NA4-7 | - write and calculate arithmetic expressions precisely using the order of operations.
- realise the importance of the order of operations on a calculator
| Four fours |

NA4-7 | - 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 |

NA4-7 | - 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 |

NA4-7 | - 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 |

NA4-7 NA4-9 | - 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 |

NA4-7 NA4-9 | - 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
- solve simple linear equations and interpret the answers in context
| Solving linear equations |

### Level 5 Equations and Expressions

Achievement Objectives | Learning Outcomes | Unit title |

NA5-7 | - 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 |

NA5-7 | - Represent algebraic expressions as array diagrams.
- Solve for specific unknowns, either areas or side, lengths from array diagrams.
- Expand quadratic expressions with the support of array diagrams.
- Factorise quadratic expressions with the support of array diagrams.
| Array for quadratics |

NA5-7 | - investigate situations involving quadratics
- understand that there are many ways to solve quadratic problems
- solve for unknowns in factorised quadratics
- appreciate the use of algebraic techniques in solving quadratic problems.
| Square Xs |

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 |

NA5-7 NA5-9 | - identify and find values for variables in context
- identify linear relationships in context, including those with negative rates of change
- represent linear relationships using tables, graphs and simple linear equations
- draw strip diagrams to represent linear equations, including those with negative co-efficients of the independent variable
- solve linear equations and interpret the answers in context
| Solving linear equations 2 |

NA5-7 NA5-9 | - Make a table of one variable against another to represent a quadratic relationship.
- Represent a quadratic relationship between two variables in words and as an equation.
- Represent a quadratic relationship as a parabola on the Cartesian Plane.
- Recognise the key features of a parabola, including the vertex and x-intercepts.
- Use graphing software to ‘curve fit’ a quadratic model onto a set of ordered pairs.
- Apply quadratic functions to predict unknown values.
| Quadratics in context |