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Equations and expressions units of work

Level 1 Equations and Expressions

Achievement ObjectivesLearning OutcomesUnit title
  • draw representations to show simple addition equations
  • write an equation/number sentence to match their diagram
Ways to add
  • 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
  • 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
  • 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 ObjectivesLearning OutcomesUnit title
  • use the mathematical symbols of =, <, >
Cuisenaire mats
  • 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
  • continue a sequential pattern
  • develop bar charts to show relationships
  • continue a simple pattern
  • generalise the pattern
Pede patterns

Level 3 Equations and Expressions

Achievement ObjectivesLearning OutcomesUnit title
  • 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
  • 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
  • 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
  • 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
  • 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 ObjectivesLearning OutcomesUnit title
  • 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
  • write and calculate arithmetic expressions precisely using the order of operations.
  • realise the importance of the order of operations on a calculator
Four fours
  • 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
  • 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
  • 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
  • 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

Level 5 Equations and Expressions

Achievement ObjectivesLearning OutcomesUnit title
  • 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
  • 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
  • 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