Simplify and manipulate algebraic expressions (including those involving surds {and algebraic fractions}) by factorising quadratic expressions of the form x2 + bx + c, including the difference of two squares; {factorising quadratic expressions of the form ax2 + bx + c}.

Practicing to plan and execute studies, make observations and measurements

{describe the changes and invariance achieved by combinations of rotations, reflections and translations}.

Interpret and use fractional {and negative} scale factors for enlargements.

Can solve problems by applying their mathematics to a variety of routine and nonroutine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.

Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

Deduce expressions to calculate the nth term of linear {and quadratic} sequences.

Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (r n where n is an integer, and r is a positive rational number {or a surd}) {and other sequences}.

Solve linear inequalities in one {or two} variable{s}, {and quadratic inequalities in one variable}; represent the solution set on a number line, {using set notation and on a graph}.

Translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution.

{find approximate solutions to equations numerically using iteration}.

Solve two simultaneous equations in two variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph.

Solve quadratic equations {including those that require rearrangement} algebraically by factorising, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph.

{recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point}.

{calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts}.

Plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration.

{sketch translations and reflections of the graph of a given function}.

Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/x with x ≠ 0 {the exponential function y = kx for positive values of k, and the trigonometric functions (with arguments in degrees)y = sin x, y = cos x and y = tan x for angles of any size.

Identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square}.

Use the form y mx c = + to identify parallel {and perpendicular} lines; find the equation of the line through two given points, or through one point with a given gradient.

Where appropriate, interpret simple expressions as functions with inputs and outputs; {interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’}.

Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments {and proofs}.

Simplify and manipulate algebraic expressions (including those involving surds {and algebraic fractions}) bysimplifying expressions involving sums, products and powers, including the laws of indices.

Practicing strategic thinking

Practicing to notice causal connections

Developing problem solving skills

Practicing to use imagination and to be innovative

Practicing to improvise

Practicing creative thinking

Creating requirements for creative thinking

Practicing to evaluate one's own learning

Practicing to take responsibility of one's own learning

Practicing to find ways of working that are best for oneself

Practicing persistent working

Learning to notice causal connections

Practising visual recognition

Practicing categorization and classification

Practicing fine motor skills

Using technology as a part of explorative process

Practicing logical reasoning, algorithms and programming through making

Understanding and practicing safe and responsible uses of technology

Using technological resources for finding and applying information

Using technology as a part of explorative and creative process

Understanding technological system operations through making

Using technology resources for problem solving

Building common knowledge of technological solutions and their meaning in everyday life

Practicing keyboard skills and touch typing

Practicing to find, evaluate and share information

Practicing to use information independently and interactively

Practising to understand visual concepts and shapes and observe their qualities

Understanding and interpreting of matrices and diagrams

Practicing logical reasoning to understand and interpret information in different forms

Realizing the connection between subjects learned in free time
and their impact to skills needed at worklife

Connecting subjects learned at school to skills needed at working life

Practicing versatile ways of working

Practicing decision making

Learning to plan and organize work processes

Learning consumer knowledge and smart economics

Practicing time management

Encouraging positive attitude towards working life

Practicing to give, get and reflect feedback

Learning to understand  the meaning of rules, contracts and trust

Practicing communication through different channels

Learning decision-making, influencing and accountability

Practicing to argument clearly own opinions and reasonings

Encouraging to build new information and visions

Practicing to notice links between subjects learned

Learning to combine information to find new innovations

Learning to build information on top of previously learned

Encouraging the growth of positive self-image

Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems; interpret their solution in the context of the given problem.

Model situations mathematically and express the results using a range of formal mathematical representations, reflecting on how their solutions may have been affected by any modelling assumptions.

Make and use connections between different parts of mathematics to solve problems.

Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial contexts.

Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems.

Assess the validity of an argument and the accuracy of a given way of presenting information.

Explore what can and cannot be inferred in statistical and probabilistic settings, and express their arguments formally.

Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning.

Reason deductively in geometry, number and algebra, including using geometrical constructions.

Make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples; begin to use algebra to support and construct arguments {and proofs}.

Extend their ability to identify variables and express relations between variables algebraically and graphically.

Extend and formalise their knowledge of ratio and proportion, including trigonometric ratios, in working with measures and geometry, and in working with proportional relations algebraically and graphically.

Use mathematical language and properties precisely.

Move freely between different numerical, algebraic, graphical and diagrammatic representations, including of linear, quadratic, reciprocal, {exponential and trigonometric} functions.

Extend fluency with expressions and equations from key stage 3, to include quadratic equations, simultaneous equations and inequalities.

Consolidate their algebraic capability from key stage 3 and extend their understanding of algebraic simplification and manipulation to include quadratic expressions, {and expressions involving surds and algebraic fractions}.

Select and use appropriate calculation strategies to solve increasingly complex problems, including exact calculations involving multiples of π {and surds}, use of standard form and application and interpretation of limits of accuracy.

Consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include powers, roots {and fractional indices}.

Use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing.

Apply statistics to describe a population.

Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency (including modal class) and spread {including quartiles and inter-quartile range}.

Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate graphical representation involving discrete, continuous and grouped data, {including box plots}.

{construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use}.

Interpret and construct tables and line graphs for time series data.

Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling

Set up, solve and interpret the answers in growth and decay problems, including compound interest {and work with general iterative processes}.

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