Number: Solve problems using standard form Solve problems including calculating with powers and roots Use upper and lower bounds in calculations


 Cuthbert Knight
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1 Curriculum Tier with Key Questions and action verbs. Excellence Creating working towards grade A* [ new 8/9 ] Can the pupils create a new product or point of view based on internal evidence or external criteria? The pupil appraises, assesses, or critiques on a basis of specific standards and criteria. Comparing and discriminating between ideas; assessing value of presentations; making choices based on reasoned argument; verifying value of evidence; recognising subjectivity. Test, measure, judge, explain, compare, summarise, justify, discriminate, convince, conclude and argue. Albany Learning Tier : Solve problems using standard form Solve problems including calculating with powers and roots Use upper and lower bounds in calculations Substitute fractions, decimals and negatives into formulae Recognise the difference of two algebraic squares Factorise a quadratic expression with an x² coefficient of 1 Sketch and interpret graphs of linear, quadratic, cubic and reciprocal functions Plot quadratic equations Solve simultaneous equations (one linear and one quadratic) graphically Solve quadratics by factorising Solve inverse proportion problems Solve problems involving repeated proportional changes Calculate the original quantity from a proportional change Prove congruence in triangles Use trigonometry in right angled triangles in 2D Calculate the dimensions of a formula; length, area or volume Enlarge 2D shapes, given centre of enlargement and negative scale factor Know and use the formula to calculate the volume of a pyramid Calculate with upper and lower bounds of units to find the minimum and maximum value of the solution Probability Construct and use tree diagrams for dependent events Calculate the probability of dependent events using the AND and OR rule
2 Compare distributions to make inferences Construct and interpret Cumulative Frequency tables and graphs Construct, use and interpret box plots and the IQR Excellence Evaluating working towards grade A [ new 7 ] Can the pupils judge the quality / usefulness of information sources, making decisions based upon agreed criteria? Can they use this to justify a stand or decision? The pupil originates, integrates, and combines ideas into a product, plan or proposal that is new to him or her. Using old ideas to create new ones; generalising from given facts; relating knowledge from several areas; predicting, drawing conclusions. Combine, integrate, substitute, plan, create, prepare, compose, modify, hypothesis, develop and formulate. Understand the effects of multiplying and dividing by numbers between 0 and 1 Estimate calculations by rounding numbers to 1 significant figure Use a calculator efficiently and appropriately to perform complex calculations Solve percentage problems, including VAT, simple and compound interest and successive percentage changes Solve two linear simultaneous equations graphically and algebraically Expand and simplify the product of two linear expressions of the form (x ± n) and simplify the corresponding quadratic expression Find the nth term of a quadratic sequence Solve inequalities in one variable and represent the solution set on a number line Find the equation of a straight line through two given points Use formulae from mathematics and other subjects Substitute numbers into expressions and formulae Change the subject of a formula or expression Solve problems using direct proportion Use multiplying methods for proportional changes Understand and use congruence and similarity Understand and apply Pythagoras Theorem in 2D Calculate volumes of right prisms Enlarge 2D shapes, given a centre of enlargement and fractional scale factor Find the locus of a point using given rules Understand and use compound measures e.g. speed Recognise and identify upper and lower bounds of units
3 Probability Understand relative frequency as an estimate of probability and use to compare outcomes Construct and use tree diagrams for independent events Specify and test hypotheses Justify choices made for statistical decisions Identify possible sources of bias and plan how to minimise this Estimate the mean and median from a grouped frequency table Select, with justification, the most appropriate average to represent a data set Compare distributions using measures of average and spread Find and use the line of best fit on a scatter graph Secure Analysing working towards grade B [ new 5/6 ] Can the pupils break down information sources into key parts, finding a range of differing evidence and break down and distinguish between different parts and find evidence to support conclusion? The pupil distinguishes, classifies, and relates the assumptions, hypotheses, evidence, or structure of a statement or question. Seeing patterns; organization of parts; recognition of hidden meanings; identification of components. Separate, order, explain, connect, divide, compare, select, infer, arrange, classify, analyse, categorise, contrast and extract. Calculate a percentage increase or decrease Calculate the original quantity from a percentage increase or decrease Add and subtract fractions with different denominators Calculate fractions of quantities Multiply and divide any number by a fraction Use prime factor decomposition to determine HCF and LCM Solve problems using HCF and LCM Use systematic trial and improvement methods to find approximate solutions to equations such as x³+x =20 Construct and solve linear equations with unknowns on both sides Factorise a quadratic expression Interpret graphs about real life situations Use index laws to simplify expressions Identify and plot straight line graphs in the form y = mx + c Write an expression to describe the nth term of an arithmetic sequence Write a ratio in the form of 1:n Calculate using ratios
4 Classify quadrilaterals by their geometric properties Solve geometrical problems using properties of angles, parallel and intersecting lines and of polygons Understand a proof that the sum of angles of a triangle is 180 and of a quadrilateral is 360 Enlarge 2D shapes, given a centre of enlargement and positive whole number scale factor Perform and describe translations (vector notation), reflections and rotations Know, understand and use the formulae for the area of a triangle, parallelogram and trapezium Know, understand and use the formulae for the circumference and area of a circle Calculate the area of compound shapes Know and use the formula for the volume of a cuboid Calculate the surface area of a cuboid Use straight edge and compass to do standard constructions Visualise and use 2D representations of 3D objects Probability Know that the sum of probabilities of mutually exclusive outcomes equals 1 Record all possible outcomes for a single or successive events systematically Describe and interpret results of a statistical survey using relevant graphs and diagrams Calculate the mean, median and modal class from a frequency table Construct and use pie charts, frequency diagrams, simple time graphs and scatter graphs Design and use twoway tables Design a survey or experiment to collect large sets of data from different sources, refining when necessary Establish Applying working towards grade C [ new 4 ] Can the pupils use the new or learned information and apply it to different or real situations? The pupil selects, transfers, and uses data and principles to complete a problem or task. Using information; using methods, concepts or theories in new situations; solving problems using required skills or knowledge. Understand and use BIDMAS rules accurately Use the four rules of number to calculate with decimals to two decimal places Round decimals to a fixed number of decimal places Order negative numbers in context Solve problems involving negative numbers Solve problems involving multiplying and dividing a 3 digit number by a 2 digit number Multiply and divide any number by 10, 100 and 1000 Use equivalent fractions to order and compare fractions and decimals Calculate fractional and percentage amounts of a quantity
5 Apply, demonstrate, complete, illustrate, show, examine, modify, relate, change, classify, discover, use, compute, solve, construct and calculate. Use and interpret coordinates in all four quadrants Construct, express in symbolic form, and use simple formula involving one or two operations Multiply together two simple algebraic expressions e.g. 2a x 3b Simplify an algebraic expression by cancelling e.g. 4xx 2 = 2xx Solve simple one and two step equations Simplify expressions by collecting like terms Identify terms in a sequence using the termtoterm rule Use practical sequences Expand a bracket Divide a quantity into a given ratio Solve simple ratio and proportion problems Use a wider range of properties of 2D and 3D shapes and identify all the symmetries of 2D shapes Use angle language Know and use the angle sum of a triangle and that of angles at a point Measure and draw angles to the nearest degree Perform and describe translations (using words) Know, understand and use the formula for the area of a rectangle Read and interpret scales accurately on a range of measuring instruments Convert between a range of metric units Probability Understand and use the probability scale from 0 to 1 Use equally likely outcomes or experiments to find the probability of an event Interpret graphs and diagrams, including pie charts Create and interpret line graphs Understand and use the mean and median of discrete data Compare two simple distributions using range and an average Group data into appropriate intervals Plan how to collect discrete data
6 Establish Understanding working towards grade D [ new 3 ] Can the pupils demonstrate an understanding of the ideas or concepts stated in the text? Can pupils use learned information to build new connections in their minds? The pupil translates, comprehends, or interprets information based on prior learning Understanding information; grasping meaning; translating knowledge into a new context; interpreting facts, comparing, contrasting; inferring causes; predicting consequence. Predict, estimate, differentiate, extend, summarise, describe, interpret, discuss, contrast, explain, paraphrase, illustrate and compare. Use a mixture of mental methods to perform calculations Recognise and describe number patterns and relationships (square, triangular, prime, multiple and factor) Order decimals to three decimal places Use place value to multiply and divide whole numbers by 10, 100 or 1000 Recall multiplication facts up to 12 x 12 and quickly derive corresponding division facts Solve addition and subtraction problems (up to two decimal places) using appropriate written methods Solve multiplication and division problems using appropriate written methods Multiply a decimal by a single digit Reduce a fraction to its simplest form Begin to use simple formulae expressed in words Use and interpret coordinates in the first quadrant Begin to understand simple ratio Simplify a ratio Use properties of 2D and 3D shapes Reflect simple shapes in a mirror line Translate shapes horizontally or vertically Rotate a simple shape about its centre or vertex Find perimeters and areas of simple shapes by counting squares Read and interpret simple scales on a range of measuring instruments Choose and use appropriate units and instruments Probability Use language associated with probability to describe the probability of an event Construct and interpret frequency diagrams and simple line graphs Read from and construct a Venn diagram
7 Group data into equal class intervals Understand and use the mode and range Collect and record discrete data Foundation Remembering working towards grade E [ new 2/1 ] Can the pupils recall or remember previously learned information, for example facts, terms, basic concepts from the text? The pupil recalls or recognizes information, ideas, and principles in the approximate form in which they were learned. Observation and recall of information; knowledge of dates, events, places; knowledge of major ideas; mastery of subject matter. Define, list, label, identify, repeat, who, what, where when, tell, describe, collect, examine, tabulate and quote. Understand place value in numbers up to 1000 Recognise negative numbers in context e.g. temperature Recognise a fraction as part of a whole Recognise when 2 simple fractions are equivalent Use the four rules of number to solve money problems Multiply and Divide by 10 Add and subtract 2 digit numbers mentally Add and subtract 3 digit numbers using a written method Multiply and divide 2 digit numbers by a single digit Interpret and solve worded problems using the four rules of number Recognise a wider range of sequences Begin to understand the role of the = sign Recognise proportions of a whole and use fractions and percentages to describe these Classify 2D and 3D shapes using mathematical properties Recognise nets of 3D shapes Reflect simple shapes in horizontal or vertical mirror lines Describe position and movement Use a wide range of metric measures for length, area, volume and mass Use standard units of time Extract and interpret information presented in simple tables, lists, bar charts and pictograms Collect qualitative data Construct bar charts and pictograms Read information from a simple Venn diagram
8
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