Name: Abacus
Price: 94.89 GBP
Author: Abacus

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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Calcularis

Learning to face failures and disappointments

Recognise and name common 2-D and 3-D shapes, including 2-D shapes [for example, rectangles (including squares), circles and triangles] and 3-D shapes [for example, cuboids (including cubes), pyramids and spheres].

Order and arrange combinations of mathematical objects in patterns and sequences.

Practicing memorizing skills

Given a number, identify one more and one less.

Use place value and number facts to solve problems.

Practicing letters, alphabets and written language

Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change.

Find different combinations of coins that equal the same amounts of money.

Measure and begin to record capacity and volume.

Measure and begin to record mass/weight.

Measure and begin to record heights.

Measure and begin to record the lengths.

Compare, describe and solve practical problems for time [for example, quicker, slower, earlier, later].

Compare, describe and solve practical problems for mass/weight [for example, heavy/light, heavier than, lighter than].

Compare, describe and solve practical problems for    lengths and heights [for example, long/short, longer/shorter, tall/short, double/half].

Recognise and know the value of different denominations of coins and notes.

Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity.

Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Describe position, direction and movement, including whole, half, quarter and threequarter turns.

Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.

Recognise, find and name a half as one of two equal parts of an object, shape or quantity.

Add and subtract numbers using concrete objects, pictorial representations, and mentally, including a two-digit number and ones a two-digit number and tens, two two-digit numbers, adding three one-digit numbers.

Solve problems with addition and subtraction using concrete objects and pictorial representations, including those involving numbers, quantities and measures.

Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = – 9.

Add and subtract one-digit and two-digit numbers to 20, including zero.

Represent and use number bonds and related subtraction facts within 20.

Read easily, fluently and with good understanding.

Learning to find the joy of learning and new challenges

Practicing to set one's own learning goals

Practicing to observe spoken and written language

Learning the basics of spelling

Learning to understand and interpret diverse types of texts

Read and write numbers from 1 to 20 in numerals and words.

Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line.

Naming the letters of the alphabet in order.

Spelling words containing each of the 40+ phonemes already taught.

Form digits 0-9.

Form capital letters.

Continue to apply phonic knowledge and skills as the route to decode words until automatic decoding has become embedded and reading is fluent.

Respond speedily with the correct sound to graphemes (letters or groups of letters) for all 40+ phonemes, including, where applicable, alternative sounds for graphemes.

Apply phonic knowledge and skills as the route to decode words.

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Hi {{firstname}},Thank you for your interest in Mathletics. We will reach out to you from registrations@3plearning.co.uk to get more details on your request. Best regards,The Mathletics Team at 3P Learning

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We aim to transform education through innovative approaches, leveraging technology and collaboration to ensure that every individual, regardless of background or location, has access to world-class educational opportunities.

Hi {{firstname}},Thanks for getting in touch. Please could you email your request to enquiries@whiterosemaths.com, where one of our team will be happy to help.White Rose Education

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Abacus

Abacus is a unique maths toolkit that’s carefully crafted to help you inspire a genuine love of maths and help...

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