Algebra



|Algebra |Numbers and the number system |Calculating | |

|8 |I can factorise quadratic expressions including the |I understand the equivalence between recurring decimals and |I understand compound interest. |

| |difference of two squares, |fractions. | |

| |e.g. x2 – 9 = (x + 3) (x – 3) | | |

| |I am able to manipulate algebraic formulae, equations and | |I can solve problems involving powers, roots and numbers |

| |expressions, finding common factors and multiplying two | |expressed in standard form, checking for correct order of |

| |linear expressions | |magnitude and using a calculator as appropriate |

| |I can use more complex formulae and change the subject of a | | |

| |formula | | |

| |I am able to evaluate algebraic formulae by substituting | | |

| |fractions, decimals or negative numbers | | |

| |I can solve inequalities in two variables and find the | | |

| |solution | | |

| |I confidently sketch, interpret and identify graphs of | | |

| |linear, quadratic, cubic and reciprocal functions. | | |

| |I understand the effect on a graph of addition (or | | |

| |multiplication) with a constant | | |

|7 |I can multiply together and simplify two sets of brackets. |I can understand and use proportionality. |I understand the effects of multiplying and dividing by |

| | | |numbers between 0 and 1 |

| |I can use algebraic and graphical methods to solve | |I always make estimates and approximations of calculations |

| |simultaneous linear equations with two variables | |by rounding numbers to multiply and divide mentally |

| |I am able to solve inequalities with one variable and | |I use a calculator to perform complex calculations with |

| |represent the solution on a number line. | |numbers of any size, knowing not to round until the end. |

| |I can use formulae from mathematics and other subjects; | |I am confident at adding, subtracting, multiplying and |

| |substitute numbers into expressions; in simple cases | |dividing fractions |

| |rearrange. | | |

| |I can find the next term and nth term of quadratic sequences| | |

| |and functions. | | |

| |I know how to plot graphs of simple quadratic and cubic | | |

| |functions, e.g. y = x2, y = 3x2 + 4, y = x | | |

|6 |I can use trial and improvement to find approximate |I understand the equivalence of fractions, decimals and |I can calculate percentages including increases and |

| |solutions to equations such as x3 + x = 20 |percentages. |decreases |

| |I can construct and solve linear equations |I can use to compare proportions |I can multiply and divide an integer by a fraction. |

| |I am able to generate terms of a sequence using term-to-term| |I can divide a quantity in a given ratio and solve problems |

| |and position-to-term definitions; on paper and using ICT | |involving ratio. |

| | | |I am able to solve more difficult percentage problems such |

| | | |as – if a computer is on sale at 30% off, and is priced at |

| | | |£600. What is its original price? |

| |I know how to write an expression to describe the nth term | | |

| |of a sequence. | | |

| |I can plot the graphs of linear functions, where y=mx + c, | | |

| |and recognise that | | |

| |equations of this form correspond to straight-line graphs. | | |

| | | |I can add and subtract fractions by writing them with a |

| | | |common denominator and also |

| | | | I know how to calculate fractions of quantities |

| |I can construct and interpret graphs arising from real-life | | |

| |problems and situations. | | |

|5 |I can construct sequences with two operations. E.g. x3 +2. |I can use place value to multiply and divide numbers |I can use brackets in my sums, and I understand order of |

| |5, 8, 11, 14, … |including decimals by 10, 100 and 1000 |operations. |

| | | |I can do sums with decimals |

| |I can read and plot co-ordinates in all 4 quadrants |I can round decimals and order negative numbers |I can use a calculator to do sums with fractions, decimals |

| | | |and percentages. |

| | |I can recognise and use number patterns | I know a written method for multiplying and dividing three |

| | | |digit numbers by two-digit numbers |

| | |I understand equivalent fractions and I know how to order |I am able to solve problems involving ordering, adding and |

| | |fractions and decimals |subtracting negative numbers |

| | |I am able to reduce a fraction to its simplest form |I have started to solve simple problems involving ratio |

| | |I understand simple ratio |I use inverse operations and approximations to check answers|

|4 |I can use word formulae such as if I buy 6 apples at 30p |I can recognise and describe number patterns |I use mental methods involving all operations |

| |each, how much do I spend? | | |

| |I can read and plot co-ordinates on a grid. |I understand the difference between multiples, factors and |I can recall my multiplication facts up to 10 × 10 and the |

| | |square numbers. |related division facts |

| | |I can use place value to multiply and divide by 10 or 100 |I am getting good at written methods for addition and |

| | | |subtraction, and multiplication and division |

| | |I can use simple fractions and percentages to describe parts|I can multiply a decimal number by a single digit |

| | |of a whole | |

| | |I can order decimals to three decimal places |I am starting to check if my answers are sensible |

|3 |I can recognise more sequences such as 4, 8, 12, 16, … |I can understand place value up to 1000 |If I know 3 x 5 is 15, I also know that 15 ÷ 3 is 5. |

| | |I can use place value to make approximations |I can add and subtract two-digit numbers mentally |

| | |I recognise negative numbers such as temperatures |I can add and subtract three digit numbers using a written |

| | | |method |

| | |I can recognise simple equivalent fractions |I can multiply and divide two digit numbers by 2, 3, 4 or 5 |

| | | |as well as 10 |

| | |I can use decimal notation for money |I know my addition and subtraction facts to 20 |

|2 |I can recognise sequences of numbers, such as odd and even. |I understand the place value of each digit up to hundreds, |I know that subtraction is the opposite of addition and that|

| | |tens, units |halving undoes doubling |

| | |I can order numbers up to 100. |I know my addition and subtracting facts up to 10 |

| | |I can count sets of objects reliably |I can mentally solve number problems |

| | | |I can choose the correct method when solving addition and |

| | | |subtraction problems |

| |Using and applying Mathematics |Shape, Space and measure |Handling Data |

| |I am able to develop alternative methods to solve problems |I understand congruence and similarity |I can estimate and find the median, quartiles and |

| | | |interquartile range for large data sets using a cumulative |

| | | |frequency diagram |

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|8 | | | |

| |I frequently select and combine known facts and problem |I understand and use trigonometrical relationships in | |

| |solving strategies to solve problems of increasing |right-angled triangles, and use these to solve problems, | |

| |complexity |including those involving bearings | |

| | | |I can compare two or more distributions and make inferences,|

| | | |using measures of average and spread including median and |

| | | |quartiles. |

| |I examine generalisations or solutions reached in an |I understand the difference between formulae for perimeter, | |

| |activity, commenting constructively |area and volume by | |

| | |considering dimensions | |

| | | |I know when to add or multiply two probabilities |

| |I convey mathematical meaning through precise and consistent| | |

| |use of symbols | | |

| |on the reasoning and logic used | | |

| | | |I can use tree diagrams to calculate probabilities of |

| | | |combinations of independent events |

| |I reflect on lines of enquiry when exploring mathematical | | |

| |tasks | | |

| |I am beginning to distinguish between practical | | |

| |demonstration and proof. | | |

| |I understand the importance of assumptions in proofs. | | |

| |I am solving increasingly demanding problems and evaluating |I understand and can apply Pythagoras' theorem when solving |I am able to suggest a problem to explore using statistical |

| |the solutions. |problems in 2-D |methods. |

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|7 | | | |

| |I am exploring connections in |I calculate lengths, areas and volumes in shapes and prisms |I understand how to identify sources of bias and plan how to|

| |mathematics across a range of contexts | |minimise them. |

| | I feel confident enough to justify generalisations, |I can enlarge 2-D shapes, given a centre of enlargement and |To progress an enquiry, I can construct and modify, on paper|

| |arguments or solutions |a fractional scale factor. |and using ICT, frequency polygons and lines of best fit on |

| | | |scatter graphs |

| |I appreciate the difference between mathematical explanation|I recognise the similarity of the resulting shapes | |

| |and experimental evidence | | |

| | |I am able to find the locus of a point that moves according |I am able to estimate the mean, median and range of a set of|

| | |to a given rule, both by reasoning and using ICT |grouped data and determine the modal class. |

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| | |I understand that measurements given to the nearest whole | |

| | |unit may be inaccurate by up to one half of the unit in | |

| | |either direction | |

| | | |I can compare two or more distributions using measures of |

| | | |average and range |

| | | |I understand relative frequency as an estimate of |

| | | |probability and use this to compare outcomes of an |

| | | |experiment |

| | |I understand and use measures of speed, density, or | |

| | |pressure, to solve problems. | |

| | | |I examine critically the results of a statistical enquiry, |

| | | |and justify the choice of statistical representation. |

| |I know how to solve problems by breaking them into smaller |I can classify quadrilaterals by their geometric properties |I can design a survey or experiment and complete it. |

| |tasks, using a range of methods and resources, including | | |

| |ICT. | | |

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|6 | | | |

| | |I know how to solve geometrical problems using properties of|I am able to construct tables for large discrete and |

| | |angles, parallel and intersecting lines, triangles and other|continuous sets of raw data, choosing suitable class |

| | |polygons |intervals. |

| |I can interpret, discuss and use information presented in a | | |

| |variety of mathematical forms | | |

| | | |I can design and use two-way tables |

| | | |I can construct and modify, on paper and using ICT: |

| | | |. pie charts for categorical data |

| | | |. bar charts and frequency diagrams for discrete data and |

| | | |continuous data. |

| | | |. simple time graphs for time series |

| | | |. scatter graphs |

| | | |and identify which are most useful in the context of the |

| | | |problem |

| | |I can identify alternate and corresponding angles. | |

| |I can present a concise and reasoned argument, using | | |

| |symbols, diagrams, graphs and explanatory texts | | |

| | |I understand a proof that the sum of the angles of a | |

| | |triangle is 180° and of a quadrilateral is 360° | |

| |I use logical argument to establish the truth of a statement|I can visualise and use 2-D representations of 3-D objects | |

| | |I can enlarge 2-D shapes, given a centre of enlargement and |I can find and record all possible mutually exclusive |

| | |a scale factor |outcomes for single events and two successive events in a |

| | | |systematic way |

| | |I know that translations, rotations and reflections preserve| |

| | |lengths and angles | |

| | | |I am able to use the fact that, the sum of probabilities in |

| | | |mutually exclusive events is 1, to solve problems |

| | |I can use a straight edge and compasses to create | |

| | |constructions | |

| | |I can deduce and use formulae for the area of a triangle and| |

| | |parallelogram, and the volume of a cuboid. | |

| | |I am able to calculate volumes and surface areas of cuboids | |

| | |I know and can use the formulae for the circumference and | |

| | |area of a circle | |

| |I can identify the necessary information to carry through a |I know and use a wider range of properties of 2-D and 3-D |I ask questions, plan how to answer them and collect the |

| |task and solve mathematical problems |shapes and identify all the symmetries of 2-D shapes |data required |

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|5 | | | |

| | | |I understand and use the probability scale from 0 to 1 |

| |I always check results, considering whether they are |I know angle vocabulary (e.g. acute, obtuse) and I know the |I can calculate the mean, and compare two sets of discrete |

| |reasonable |sum of angles in a triangle, at a point, and on a straight |data using the range and one of mode, median or mean |

| | |line. | |

| |I am able to solve word problems and investigations from a | | |

| |range of contexts | | |

| | |I’m able to reason about position and movement, and |I understand that different outcomes may result from |

| | |transform shapes. |repeating an experiment |

| |I show understanding of situations by describing them |I will measure and draw angles to the nearest degree. |I can interpret graphs and diagrams, including pie charts, |

| |mathematically using symbols, words and diagrams | |and draw conclusions |

| | |I read and interpret scales on a range of measuring |I am able to create and interpret line graphs for continuous|

| | |instruments, explaining what each labelled division |data. |

| | |represents | |

| |I can draw simple conclusions of my own. | | |

| | |I’m able to solve problems involving the conversion of units| |

| | |and make sensible estimates of measures | |

| | |I can use the formula for the area of a rectangle | |

| | |I can distinguish area from perimeter | |

| |I develop my own strategies for solving problems |I can use the properties of 2-D and 3-D shapes |I can collect and record discrete data |

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|4 | | | |

| | | |I know how to group data |

| |I use these strategies when applying mathematics to |I can make 3-D models from nets. |I continue to use Venn and Carroll diagrams to sort and |

| |practical contexts | |classify information |

| |I present information and results in a clear and organised |I can reflect shapes in a mirror line, translate shapes |I can construct and interpret frequency diagrams and simple |

| |way |horizontally or vertically and begin to rotate a shape |line graphs |

| |I search for a solution by trying out ideas of my own |I can choose appropriate units. I can use a range of |I can use the mode and range to describe sets of data |

| | |measuring instruments | |

| | |I can find perimeters of simple shapes and find areas by | |

| | |counting squares | |

| |I will try different approaches and ways of solving problems|I can classify 3-D and 2-D shapes using mathematical |I am able to gather information |

| | |properties such as reflective symmetry | |

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|3 | | | |

| |I’m beginning to organise my work and check my results |I have begun to recognise nets of familiar 3-D shapes, e.g. |I can construct bar charts and pictograms. |

| | |cube, cuboid, triangular prism, square-based pyramid | |

| |I can use and interpret mathematical symbols and diagrams |I can recognise shapes in different orientations and reflect|I know how to use Venn and Carroll diagrams to sort and |

| | |shapes horizontally or vertically |classify information |

| | |I can use a wider range of measures for length, capacity and|I can extract and interpret information presented in simple |

| | |mass using both metric, and imperial units. |tables, lists, bar charts and pictograms |

| | |I can describe position and movement | |

| | |I am using standard units of time | |

| |I can discuss my work using mathematical language |I use mathematical names for common 3-D and 2-D shapes; and |I can sort objects |

| | |describe their properties, including numbers of sides and | |

| | |corners | |

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|2 | | | |

| |I’m beginning to represent my work using symbols and simple |I understand angles as a measurement of turn |I understand the vocabulary relating to handling data |

| |diagrams | | |

| |I can predict what comes next in a pattern or sequence and |I begin to use a limited range of measures for length and |I can collect and sort data. |

| |give reasons |mass, understanding that there are imperial and metric | |

| | |units. | |

| |I am able to explain why an answer is correct |I begin to understand the difference between discrete |I am able to record and discuss results in simple lists, |

| | |objects and continuous measures |tables, pictograms and block graphs |

| | |I can describe the position of objects | |

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