# Equations and expressions units of work

### Level 1 Equations and Expressions

 Achievement Objectives Learning Outcomes Unit title NA1-4NA1-1 draw representations to show simple addition equationswrite 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 symbolsrecognise and use the written and spoken words for addition, with the addition symbolrecognise and use subtraction written and spoken words, with the subtraction symbolrecognise and write addition and subtraction expressions from story contexts Numerals and expressions NA1-4NA2-6 make and recognise combined amounts that have the same valueread and write addition and subtraction equationssolve addition and subtraction balance problems and explain the solutions, using the language of equivalence Equality and equations NA1-4NA2-6 understand the equals symbol as an expression of a relationship of equivalence, and explain thisrecognise 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 subtractionwrite and read sets of related addition and subtraction equationsexplain, in their own words, the inverse relationship between addition and subtractionrecognise that addition is commutative but that subtraction is notsolve number problems that involve application of the additive inverse Number families and relationships NA2-6NA2-8 continue a sequential patterndevelop bar charts to show relationships Staircases NA2-6NA2-8 continue a simple patterngeneralise 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 itread, write and understand the division symbol and the language associated with itrecognise that multiplication is commutative but division is notrecognise 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 divisionrecognise the ambiguity of expressions and equations that include more than one operationunderstand and explain the rules for the order of operations, including explaining the acronym, BEDMASapply 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 operationsunderstand 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 NA3-6NA3-7 consolidate understanding of simple properties of addition, subtraction, multiplication and divisiondiscover and use some more complex properties of addition, subtraction, multiplication and division Properties of operations NA3-6NA4-7 understand that an unknown amount or number can be represented with a symbol: a question mark, a shape or a letterwrite word problems of real life situations and express these with equations that include a variablesolve single step whole number equations that include a variablerecognise that an equation is balanced around the equals symbolformally 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 materialsrepresent number relationships using words, a table and a graph, and recognise the importance of these representationswrite equations, using variables and brackets, to express problem situationssolve equations that have unknown amounts on both sidesunderstand 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 equationsdevelop function rules to describe relationshipsfind specific values for variables from given relationships Balancing acts NA4-7 devise rules based on numerical patterns to solve triangular arithmagonsexplain the condition for the solution of any square arithmagonform and use linear equations to solve triangular arithmagonsdevelop proofs of rules and conditions for the solution of arithmagons Arithmagons NA4-7 understand the concept of Fibonacci numbers and how they are generatedfind factors of a numbermake conjectures and attempt to prove themfind generalisations Fibonacci I NA4-7NA4-9 devise a rule for ensuring that sets of numbers can be arranged into 3-by-3 magic squaresrepresent 3-by-3 magic squares algebraicallydevise rules for determining the Magic Number for magic squaresrepresent magic squares using parametric equationssolve equations that have been formed from magic squares Magic squares NA4-7NA4-9 identify and find values for variables in contextidentify linear relationships in contextrepresent linear relationships using tables, graphs and simple linear equationsdraw strip diagrams to represent linear equationssolve simple linear equations and interpret the answers in context Solving linear equations