Equations and expressions units of work

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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 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
NA2-6
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

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
NA4-7
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