Gizmos for United Kingdom Curriculum - Mathematics: Key Stage 3 (Programme of Study adopted 2013)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

WM: : Working mathematically

WM.DF: : Develop fluency

WM.DF.1: : consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots

WM.DF.2: : select and use appropriate calculation strategies to solve increasingly complex problems

WM.DF.3: : use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships

WM.DF.4: : substitute values in expressions, rearrange and simplify expressions, and solve equations

WM.DF.5: : move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]

WM.DF.6: : develop algebraic and graphical fluency, including understanding linear and simple quadratic functions

WM.DF.7: : use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

WM.RM: : Reason mathematically

WM.RM.2: : extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically

WM.RM.3: : identify variables and express relations between variables algebraically and graphically

WM.RM.6: : interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning

WM.RM.7: : explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

WM.SP: : Solve problems

WM.SP.3: : begin to model situations mathematically and express the results using a range of formal mathematical representations

N: : Number

N.1: : understand and use place value for decimals, measures and integers of any size

N.2: : order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, is not equal to,

N.3: : use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

N.4: : use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

N.5: : use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

N.6: : recognise and use relationships between operations including inverse operations

N.7: : use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

N.8: : interpret and compare numbers in standard form A x 10 to the n power 1 is less than or equal to A

N.9: : work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 38)

N.10: : define percentage as 'number of parts per hundred', interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

N.11: : interpret fractions and percentages as operators

N.12: : use standard units of mass, length, time, money and other measures, including with decimal quantities

A: : Algebra

A.1: : use and interpret algebraic notation, including:

A.1.1: : ab in place of a × b

A.1.2: : 3y in place of y + y + y and 3 × y

A.1.4: : a/b in place of a ÷ b

A.2: : substitute numerical values into formulae and expressions, including scientific formulae

A.3: : understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

A.4: : simplify and manipulate algebraic expressions to maintain equivalence by:

A.4.1: : collecting like terms

A.4.2: : multiplying a single term over a bracket

A.4.3: : taking out common factors

A.5: : understand and use standard mathematical formulae; rearrange formulae to change the subject

A.6: : model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

A.7: : use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

A.8: : work with coordinates in all four quadrants

A.9: : recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

A.10: : interpret mathematical relationships both algebraically and graphically

A.11: : reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

A.12: : use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

A.14: : generate terms of a sequence from either a term-to-term or a position-to-term rule

A.15: : recognise arithmetic sequences and find the nth term

A.16: : recognise geometric sequences and appreciate other sequences that arise.

RP: : Ratio, proportion and rates of change

RP.2: : use scale factors, scale diagrams and maps

RP.3: : express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1

RP.4: : use ratio notation, including reduction to simplest form

RP.6: : understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

RP.7: : relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

RP.8: : solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

RP.9: : solve problems involving direct and inverse proportion, including graphical and algebraic representations

RP.10: : use compound units such as speed, unit pricing and density to solve problems.

GM: : Geometry and measures

GM.1: : derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

GM.2: : calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

GM.3: : draw and measure line segments and angles in geometric figures, including interpreting scale drawings

GM.5: : describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

GM.6: : use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles

GM.7: : derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

GM.8: : identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

GM.10: : apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

GM.11: : understand and use the relationship between parallel lines and alternate and corresponding angles

GM.12: : derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

GM.13: : apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras' Theorem, and use known results to obtain simple proofs

GM.14: : use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

GM.15: : use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

P: : Probability

P.1: : record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale

P.2: : understand that the probabilities of all possible outcomes sum to 1

P.3: : enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams

P.4: : generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

S: : Statistics

S.1: : describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

S.2: : construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

Correlation last revised: 9/16/2020

United Kingdom Curriculum - Mathematics: Key Stage 3

Programme of Study | Adopted: 2013