# 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 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 NA1-4NA2-6 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 NA1-4NA2-6 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 addition and multiplication to find number combinations that 'make' a given result 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 NA2-6NA2-8 continue a sequential pattern develop bar charts to show relationships Staircases NA2-6NA2-8 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 NA3-6NA3-7 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

### Level 4 Equations and Expressions

 Achievement Objectives Learning Outcomes Unit title NA4-7 understand that an unknown amount or number can be represented with a symbol: a question mark, a shape or a letter recognise that to find the value of the missing number, you have to ‘undo’ what has been done to it write word problems of real-life situations and express these with equations that include an unknown recognise that an equation is balanced around the equals symbol formally solve equations, which include unknowns, using inverse operations where needed estimate values for unknown amounts and explain reasoning recognise the calculator is a useful but ‘fallible’ tool, while recognising that the correct choice of operation is critical Food for thought: Using equations 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 NA4-7NA4-9 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 NA4-7NA4-9 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 NA5-7NA5-9 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 NA5-7NA5-9 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 NA5-7NA5-9 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