Key Stage 2 | Step 1- Step 2 | Key Stage 2 |
Key Stage 3 | Step 3 - Step 4 | Key Stage 3 |
Key Stage 4 | Step 5 - Step 6 | ≈ GCSE grade 3 - 4 |
Key Stage 4 | Step 7 - Step 8 | ≈ GCSE grade 4 - 7 |
Key Stage 4 | Step 9 - Step 12 | ≈ GCSE grade 7 - 9 |
Step 1
Topic: | Lesson: | Topic: | Lesson: |
Number | Read and write large numbers | Number | Indentify numbers |
Number | Round positive whole numbers to the nearest 10, 100 or 1000 | Number | Round using decimal places |
Number | Round using significant figures | Number | Estimate numbers |
Number | Using an empty number line | Number | Use standard column procedures to add and subtract whole numbers |
Number | Multiply and divide integers by 10 and 100, and explain the effect | Number | Long and short multiplication |
Number | Long and short division | Number | Know and use the order of operations |
Number | Apply simple tests of divisibility | Number | order positive and negative integers |
Statistics | Find range from a set of ordered data | Geometry and measures | Know the names of 2d shapes |
Geometry and measures | Identify and name common solids: cube, cuboid, cylinder, prism, pyramid, sphere and cone | Geometry and measures | Know the terms face, edge and vertex |
Geometry and measures | Use a protractor to measure acute angles to the nearest degree | Geometry and measures | Distinguish between acute, obtuse and reflex angles |
Geometry and measures | Know the sum of angles on a straight line | Geometry and measures | Find the perimeter of a square/rectangle by counting |
Geometry and measures | Identify complex arrangements of a net of a cube | Geometry and measures | Work out time intervals |
Geometry and measures | Read and interpret scales on a range of measuring instruments | Geometry and measures | Suggest suitable units to estimate or measure length, mass and capacity |
Geometry and measures | Identify all the symmetries of 2-D shapes |
Step 2
Topic: | Lesson: | Topic: | Lesson: |
Number | Understand addition and subtraction as they apply to whole numbers and decimals | Number | Be able to use > or < correctly between two positive decimals. Decimals should be to 4 or 5 significant figures |
Number | Be able to order positive decimals. Decimals should be to 4 or 5 significant figures | Geometry and measures | Know the sum of angles round a point |
Geometry and measures | Explain why some shapes tessellate and why other shapes do not | Geometry and measures | Find the perimeter of a shape |
Geometry and measures | Choose suitable metric units to estimate length and area | Geometry and measures | Identify quadrilaterals from their properties |
Geometry and measures | Know the sum of angles in a triangle is 180° | Geometry and measures | Know the sum of angles in a quadrilateral is 360° |
Geometry and measures | Translate a shape on a square/coordinate grid | Geometry and measures | Recognise and visualise the reflection in a mirror line of a 2-D shape |
Ratio, proportion and rates of change | Read and construct scale drawings | Statistics | Calculate Mode |
Statistics | Calculate Median | Statistics | Calulate mean |
Step 3
Topic: | Lesson: | Topic: | Lesson: |
Number | Understand multiplication as it applies to decimals | Number | Understand division as it applies to decimals |
Number | Recognise and use multiples | Number | Recognise and use factors |
Number | Identify numbers with exactly 2 factors (primes) | Number | Understand how to find common multiples |
Number | Understand how to find the common factors | Number | Knowing simple Fraction, Decimal and Percentage equivalents |
Number | Convert percentages to fractions out of 100 | Number | Convert percentage to decimals |
Number | Convert terminating decimals to fractions, e.g. 0.23 = 23/100 | Number | Calculating simple percentages without a calculator |
Number | Find roots of square numbers upto 100 (i.e. roots upto 10) | Algebra | Find outputs and inputs of more complex functions expressed in words (e.g. add 6 then multiply by 3) |
Algebra | Use function machines to find coordinates | Algebra | Read values from straight-line graphs for real-life situations |
Algebra | Drawing straight-line graphs for real-life situations | Algebra | Read and plot co-ordinates in all four quadrants |
Algebra | Be able to interpret inequalities and show on a number line | Algebra | Generate terms of a simple sequence using term to term rule |
Algebra | Generate and describe simple integer sequences – square and triangle numbers | Algebra | Generate terms of a simple sequence arising from practical contexts (Pictorial) |
Probability | Use a probability scale with words | Probability | Mark events and/or probabilities on a probability scale of 0 to 1 |
Statistics | Represent data in a table (Tally chart) | Statistics | Extract data and interpret discrete bar charts |
Statistics | Construct simple bar charts to represent discrete data | Statistics | Produce dual bar charts |
Statistics | Produce pictograms | Statistics | Find the mode and range from a bar chart |
Statistics | Interpret simple pie charts using simple fractions and percentages | Geometry and measures | Using correct notation to label lines, angles and triangles |
Geometry and measures | Use the formula for the area of a rectangle/square | Geometry and measures | Use the formula for the area of a triangle |
Geometry and measures | Calculate the surface area of cubes with a net | Geometry and measures | Calculate perimeter and area of compound shapes made from triangles, rectangles |
Geometry and measures | Identify simple angle, side and symmetry properties of triangles | Geometry and measures | Identify angle, side and symmetry properties of simple quadrilaterals |
Geometry and measures | Recognise and visualise – rotation about a given point (rotation point must be outside the shape) | Geometry and measures | Begin to estimate the size of angles |
Ratio, proportion and rates of change | Use fraction notation to describe parts of shapes | Ratio, proportion and rates of change | Recognise the equivalence of percentages, fractions and decimals |
Step 4
Topic: | Lesson: | Topic: | Lesson: |
Number | Multiply three-digit by two-digit whole numbers | Number | Begin to add and subtract simple fractions and those with simple common denominators |
Number | Add and subtract positive integers from negative integers | Number | Multiply and divide negative integers by a positive and negative numbers |
Number | Add and subtract integers - positive and negative numbers | Number | Use inverse operations |
Number | Simplify fractions by cancelling all common factors | Number | primes factor decomposition |
Number | Calculate simple fractions of quantities and measurements (whole-number answers) | Number | Extend the percentage calculation strategies with jottings to find any percentage, e.g. 17.5% by finding 10%, 5% and 2.5%, and adding |
Number | Use index notation for squares and cubes and for positive integer powers of 10 (e.g. write 27 as 3³ and 1000 as 10³) | Number | Be able to order negative decimals with the smallest on the left. Decimals should be to 2 or 3 significant figures |
Number | Order fractions, decimals and percentages | Algebra | Substitute positive integers into simple formulae expressed in letter symbols, e.g. a+/- b, a × b |
Algebra | Substitute integers into more complex formulae expressed in letter symbols, e.g. a/b, ax +/- b | Algebra | simplify algebraic expressions by collecting like terms |
Algebra | Form expression from words | Algebra | Plot a simple distance-time graph (straight-line graphs) |
Algebra | Plot and draw vertical and horizontal line graphs | Algebra | Generate terms of a linear sequence using term-to-term using positive or negative integers |
Algebra | Multiply together two simple algebraic expressions, e.g. 2a × 3b | Probability | Apply the property that the probabilities of an exhaustive set of outcomes sum to 1 |
Probability | Identify all possible mutually exclusive outcomes of a single event | Probability | Know that if the probability of an event is p, the probability of it not occurring is 1-p |
Probability | Compare experimental and theoretical probabilities | Statistics | Extract data and interpret frequency tables |
Statistics | Find the modal class for a small set of grouped discrete data | Statistics | Use information provided to complete a two-way table |
Statistics | Produce pie-charts | Statistics | Compare two simple distributions using the range and the median |
Statistics | Calculate the mean from a simple frequency table | Statistics | Compare two simple distributions using the mean |
Statistics | Interpret data from simple compound and comparative bar charts | Statistics | find the range and modal class interval from grouped data |
Statistics | Calculate the interval from grouped data containing the median | Statistics | Estimate the mean from a grouped frequency table |
Geometry and measures | Identify interior and exterior angles in a shape | Geometry and measures | Recognise and use vertically opposite angles |
Geometry and measures | Derive and use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles | Geometry and measures | Calculate the surface area of simple cuboids (without use of nets) |
Geometry and measures | Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) | Geometry and measures | Begin to use plans and elevations |
Geometry and measures | Solve simple problems involving units of measurement in the context of length and area | Geometry and measures | Draw or complete diagrams with a given number of lines of symmetry |
Probability | Mutually exclusive outcomes | Ratio, proportion and rates of change | Recognise and visualise the rotational symmetry of a 2-D shape |
Geometry and measures | Solve geometric problems using side and angle properties of equilateral and isosceles triangles | Geometry and measures | Solve simple geometrical problems using properties of quadrilaterals |
Geometry and measures | Give a bearing between 2 points | Ratio, proportion and rates of change | Express the division of a quantity into a number of parts as a ratio |
Ratio, proportion and rates of change | Convert between simple metric units | Ratio, proportion and rates of change | Express one number as a fraction of another |
Ratio, proportion and rates of change | Divide a quantity into two parts in a given ratio, where ratio given in ratio notation | Ratio, proportion and rates of change | Use percentages to compare simple proportions |
Ratio, proportion and rates of change | Express one given number as a percentage of another | Ratio, proportion and rates of change | Find a percentage of a quantity using a multiplier |
Ratio, proportion and rates of change | Interpet percentages and percentage change as a fraction or a decimal | Ratio, proportion and rates of change | Use ratio notation |
Ratio, proportion and rates of change | Reduce a ratio to its simplest form |
Step 5
Topic: | Lesson: | Topic: | Lesson: |
Number | Add and subtract simple fractions with denominators of any size | Number | Multiply a fraction by an integer |
Number | Be able to multiply any number by 0.1 and 0.01 | Number | Be able to divide any number by 0.1 and 0.01 |
Number | Add and subtract up to 3 fractions mixing both addition and subtraction into the calculation, with denominators less than or equal to 12 and using the LCM denominator in the calculation - the answer can be a mixed number | Number | Add mixed number fractions without common denominators, where the fraction parts add up to more than 1 |
Number | Subtracting mixed fractions | Number | work interchangeably with terminating decimals and their corresponding fractions ( such as 3.5 and 7/2 or 0.375 or 3/8) |
Number | Learn fractional equivalents to key recurring decimals e.g. 0.333333..., 0.66666666..., 0.11111... and by extension 0.222222... | Number | Calculate fractions of quantities and measurements (fraction answers) |
Algebra | Substitute positive and negative integers into simple formulae | Algebra | Write expressions to solve geometric problems |
Algebra | use graphs to solve distance-time problems | Algebra | Interpret information from a complex real life graph (fixed charge/unit cost), read values and discuss trends |
Algebra | Find the coordinates of points identified by geometrical information in 2D ( all four quadrants) for simple shapes e.g. squares and rectangles | Algebra | Plot and draw graphs of straight lines using a table of values |
Algebra | Begin to use linear expressions to describe the nth term in a two-step arithmetic sequence (e.g. nth term is 3n + 1 or n/2 − 5) | Probability | Estimate the number of times an event will occur, given the probability and the number of trials |
Probability | Apply probabilities from experimental data to a different experiment in simple situations (only looking at one outcome) - how many successes would you expect? | Probability | Identify all mutually exclusive outcomes for successive events |
Probability | Record outcomes of events in tables and grids | Probability | Find the probability of an event happening using relative frequency |
Probability | Write probabilities in words, fractions, decimals and percentages | Probability | Work out probabilities from frequency tables |
Probability | Work out probabilities from two-way tables | Statistics | Interpret and/or compare bar graphs and frequency diagrams which are misleading (with false origins, different scales etc.) |
Statistics | Design a question for a questionnaire and critiques | Statistics | Produce grouped frequency tables for continuous data |
Statistics | Construct complex bar graphs (should be compound) | Statistics | Interpret a scatter graph |
Geometry and measures | Identify alternate and corresponding angles on parallel lines and their values | Geometry and measures | Solve harder problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons - by looking at several shapes together |
Geometry and measures | Know the formulae for the volume of cube and a cuboid | Geometry and measures | Use a formula to calculate the area of parallelograms |
Geometry and measures | Use straight edge and compasses to construct the mid point and perpendicular bisector of a line segment | Geometry and measures | Know the names of parts of a circle |
Geometry and measures | Draw a circle given the radius or diameter | Ratio, proportion and rates of change | Use the unitary method to solve simple word problems involving ratio and direct proportion |
Ratio, proportion and rates of change | Divide a quantity into more than two parts in a given ratio | Ratio, proportion and rates of change | Use a ratio to find one quantity when the other is known |
Ratio, proportion and rates of change | Use proportional reasoning to solve a problem | Ratio, proportion and rates of change | Find the percentage profit or loss |
Step 6
Topic: | Lesson: | Topic: | Lesson: |
Number | Identify upper and lower bounds for rounding of discrete and continuous data | Number | Write numbers as a decimal number of millions or thousands, e.g. 23 600 000 as 23.6 million |
Number | Divide an integer by a fraction | Number | Understand which part of an expression is raised to a power by knowing the difference between 3 × (7 + 8)² and 3² × (7 + 8) and (3 × (7 + 8))² |
Number | Calculate average speed, distance, time - in mph as well as metric measures | Number | Understand the effect of multiplying or dividing any number between 0 and 1 |
Number | Multiply simple fractions (proper and improper) - | Number | Divide simple fractions (proper and improper) |
Number | Use halving and doubling strategies on fractions to find decimal equivalents of other fractions, e.g. 1/4 = 0.25 so 1/8 is half of 0.25 etc. Original fact is given | Number | Establish multiplying and dividing index laws |
Number | index laws for powers of 1 and 0 | Number | Use an extended range of calculator functions, including +, -, x, , x², √x, memory, xy, x1/y, brackets |
Algebra | Substitute positive integers into expressions involving small powers (up to 3) | Algebra | Expand single brackets |
Algebra | Expand two single brackets and simplify | Algebra | Manipulate expressions by taking out common factors, not necessarily the highest e.g. 4x + 8 = 2(2x + 4) |
Algebra | Change the subject of a formula in one step e.g. y = x + 4 | Algebra | Begin to consider the features of graphs of simple linear functions, where y is given explicitly in terms of x, e.g. y = x, y = 2x, y = 3x are all straight lines that pass through the origin, vary in steepness depending on the function |
Algebra | Draw velocity-time graphs | Algebra | Find the coordinates of the midpoint of a line from a given graph |
Algebra | Recognise that equations of the form y = mx + c correspond to straight-line graphs in the coordinate plane | Algebra | Write down whole number values that satisfy an inequality |
Algebra | Find a specific term in the sequence using position-to-term rules | Probability | complete a probability tree diagram based on given information (no more than 3 branches per event) |
Probability | Use tree diagrams to calculate the probability of two independent events | Statistics | Produce ordered back-to-back stem and leaf diagrams |
Statistics | Recognise when it is appropriate to use mean, median or mode in more complex cases (put in extreme values) | Statistics | Construct and use frequency polygons to compare sets of data |
Statistics | Identify and explain anomalies (outliers) in a data set | Statistics | Recognise types of quantitative and qualitative data |
Statistics | Understand what is meant by a sample and a population | Statistics | Understand primary and secondary data sources |
Geometry and measures | Identify co-interior angles and their values | Geometry and measures | Calculate exterior angles of any polygon using the sum is 360° |
Geometry and measures | Calculate the interior angles of polygons | Geometry and measures | Use a formula to calculate the area of trapezia |
Geometry and measures | Use the formula for the circumference of a circle | Geometry and measures | Use the formulae for area of a circle, given the radius or diameter |
Geometry and measures | Use straight edge and compasses to construct the bisector of an angle | Geometry and measures | Use straight edge and compasses to construct a triangle given three sides (SSS) |
Geometry and measures | Construct an equilateral triangle | Geometry and measures | Construct a regular hexagon inside a circle |
Geometry and measures | Begin to use the trigonometric ratios to find the size of an angle in a right-angled triangle | Geometry and measures | Enlarge 2-D shapes, given a centre of enlargement and a positive whole number scale factor |
Geometry and measures | Find the centre of enlargement | Ratio, proportion and rates of change | Write ratios in the form 1: m or m: 1 |
Ratio, proportion and rates of change | Know rough metric equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons) | Ratio, proportion and rates of change | Convert between area measures (e.g. mm² to cm², cm² to m², and vice versa) |
Ratio, proportion and rates of change | Convert between metric measures of volume and capacity eg 1 cm³ = 1 ml | Ratio, proportion and rates of change | Use a unitary method, e.g. if £40 is 60%, find 1% by dividing by 60 and then 100% by multiplying by 100. Give them the scaffolding to answer the question |
Ratio, proportion and rates of change | Use percentages in real life simple interest, income tax calculations | Ratio, proportion and rates of change | Use and interpret maps, using proper map scales (1 : 25 000) |
Step 7
Topic: | Lesson: | Topic: | Lesson: |
Number | Find the reciprocal of simple numbers/fractions mentally, e.g. 10 and 1/10, 1/3 and 3 etc. Know that a number multiplied by its reciprocal is 1 | Number | Understand and use compound measures: density; pressure; speed |
Number | Use the index laws to include negative power answers | Number | Convert between currencies |
Number | Write numbers greater than 10 in standard index form | Algebra | Use systematic trial and improvement to find the approximate solution to one decimal place of equations such as x³ = 29 |
Algebra | solve equations that involves multiplying out brackets by a negative number (e.g. 4(2a - 1) = 32 - 3(2a - 2)) | Algebra | Multiply out double brakets and collect like terms |
Algebra | Substitute positive and negative integers into linear expressions and expressions involving powers | Algebra | Factorise to one bracket by taking out the highest common factors for all terms e.g. 2x²y + 6xy² = 2xy(x + 3y) |
Algebra | Find an unknown where it is not the subject of the formula and where an equation must be solved | Algebra | Identify parallel lines from their equations |
Algebra | Generate points and plot graphs of simple quadratic functions | Algebra | Construct a table of values, including negative values of x for a function such as y = ax² |
Algebra | Recognise that linear functions can be rearranged to give y explicitly in terms of x e.g. rearrange y + 3x - 2 = 0 in the form y = 2 - 3x | Algebra | Solve simple linear inequalities in one variable and represent the solution on a number line |
Probability | Record outcomes of events in a Venn Diagram | Statistics | Find the median, mode and range from a stem and leaf diagram |
Statistics | Understand that the frequency represented by corresponding sectors in two pie charts is dependent upon the total populations represented by each of the pie charts | Statistics | Know the definition and methods of random sampling |
Statistics | Scattergraphs - Use a line of best fit, or otherwise, to predict values of one variable given values of the other variable | Geometry and measures | Calculate the volume of prisms |
Geometry and measures | Calculate the surface area of prisms | Geometry and measures | Calculate the lengths and areas given the volumes in right prisms |
Geometry and measures | Calculated volumes in cylinders | Geometry and measures | Find the perimeters and areas of semicircles and quarter circles |
Geometry and measures | Use the information given about the length of sides and sizes of angles to determine whether triangles are congruent | Geometry and measures | Use straight edge and compass to construct the perpendicular from a point on a line segment |
Geometry and measures | Understand loci about a point, line and corner | Geometry and measures | Construct angles of 60°, 90°, 30°, 45° |
Geometry and measures | Know the formula for Pythagoras' theorem and use to find the hypotenuse | Geometry and measures | describe and Use vector notation for translations |
Geometry and measures | describe an enlargement | Geometry and measures | Describe a rotation transformation |
Geometry and measures | Describe reflections transformaion | Ratio, proportion and rates of change | Use algebraic methods to solve problems involving variables in direct proportion |
Ratio, proportion and rates of change | Use expressions of the form y α 1/x | Ratio, proportion and rates of change | Calculate compound interest |
Ratio, proportion and rates of change | Use measures in ratio and proportion problems (best value) |
Step 8
Topic: | Lesson: | Topic: | Lesson: | |
Number | Multiply and divide simple fractions (mixed) - | Number | Calculate with roots (surds - exact values) | |
Number | Write numbers less than 10 in standard index form | Number | Order numbers written in standard index form | |
Number | Add and subtract in standard form | Number | Multiply and divide numbers in standard form | |
Algebra | Find the equation of a straight-line from its graph | Algebra | Recognise that when the linear and inverse of a linear function such as y = 2x, y = 3x are plotted, they are a reflection in the line y = x | |
Algebra | Interpret distance-time graphs and calculate the speed of individual sections, total distance and total time | Algebra | Interpret gradient as rate of change in distance-time and speed-time graphs, containers emptying and filling and unit price graphs | |
Algebra | Identify and interpret roots, intercepts and turning points of a quadratic graph | Algebra | Given the coordinates of points A and B, calculate the length of AB | |
Algebra | Plot and draw graphs of straight lines WITHOUT using a table of values (use intercept and gradient) | Algebra | Recognise a quadratic function from its equation and explain the shape of it's graph | |
Algebra | Solve more complex linear inequalities in one variable and represent the solution on a number line | Algebra | Use algebra to support proofs e.g. show that the volume of a cube with side lengths of (2x - 1)cm is (8x³ - 12x² + 6x - 1)cm³ | |
Algebra | Identify which terms cannot be in a sequence | Algebra | Recognise and use simple geometric progressions (rn where n is an integer and r is a rational number number | |
Algebra | By looking at the spatial patterns of triangular numbers, deduce that the nth term is 1/2n(n + 1) | Algebra | Solve linear/linear simultaneous equations graphically | |
Algebra | Solve simultaneous equations where neither or one equation needs multiplying | Algebra | Set up and solve a pair of simultaneous equations in two variables | |
Algebra | Solve simultaneous equations representing a real-life situation | Probability | Use tree diagrams to calculate the probability of two dependent events | |
Statistics | Construct cumulative frequency tables and draw the graph | Statistics | Interpret box plots to find median, quartiles, range and interquartile range | |
Statistics | Produce box plots from raw data and identify outliers when given quartiles and median | Geometry and measures | Find the surface area and volumes of compound solids constructed from cubes, cuboids, cones, pyramids, spheres, hemispheres, cylinders | |
Geometry and measures | Recognise the formulae for length of arcs in a circle | Geometry and measures | Recognise the formulae for area of sectors in a circle | |
Geometry and measures | Use simple examples of the relationship between enlargement and areas and volumes of simple shapes and solids | Geometry and measures | Know the formula for Pythagoras' theorem and use to find a shorter side | |
Geometry and measures | Use Trigonometry to find unknown sides of a right angled triangle | Geometry and measures | Use Trigonometry to find missing angles of a right angled triangle | |
Geometry and measures | Add and Subtract vectors |
Step 9
Topic: | Lesson: | Topic: | Lesson: |
Algebra | Change the subject of a complex formula that involves fractions, e.g. make u or v the subject of the formula 1/v + 1/u =1/t | Algebra | Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function |
Algebra | Recognise, sketch and interpret graphs of simple cubic functions | Algebra | Recognise, sketch and interpret reciprocal graphs |
Algebra | Solve linear inequalities in two variables graphically | Algebra | Answer simple proof and 'show that' questions using consecutive integers (n, n+ 1), squares a², b², even numbers 2n, and odd numbers 2n + 1 |
Algebra | Continue a quadratic sequence and use the nth term to generate terms | Algebra | Cube a linear expression and simplify |
Statistics | Interpret cumulative frequency graphs | Statistics | Compare the measures of spread between a pair of box plots/cumulative frequency graphs |
Geometry and measures | Prove and use the fact that the angle in a semicircle is a right angle ; | Geometry and measures | Prove and use the fact that opposite angles of a cyclic quadrilateral sum to 180° |
Geometry and measures | Prove and use the fact that angles in the same segment are equal | Geometry and measures | Prove and use facts about the angle subtended at the centre and at the circumference; |
Geometry and measures | Know that the tangent at any point on a circle is perpendicular to the radius at that point | Geometry and measures | Find angles of elevation and angles of depression |
Ratio, proportion and rates of change | Use expressions of the form y α x² |
Step 10
Topic: | Lesson | Topic: | Lesson: |
Number | Use the product rule for counting (i.e. if there are m ways of doing one task and for each of these, there are n ways of doing another task, then the total number of ways the two tasks can be done is m × n ways) | Number | Convert a recurring decimal to a fraction in simple cases |
Algebra | Deduce turning points by completing the square | Algebra | Sketch a graph of a quadratic by factorising, identifying roots and y-intercept , turning point |
Algebra | Find the equation of the line through two given points | Algebra | Find the equation of the line through one point with a given gradient |
Algebra | Know that a line perpendicular to the line y = mx + c, will have a gradient of -1/m | Algebra | Finding the equation of a circle on a graph |
Algebra | Simplify and manipulate algebraic expressions involving surds and algebraic fractions | Algebra | Find approximate solutions to simultaneous equations formed from one linear function and one non-linear ( quadratic or circle) function using a graphical approach |
Probability | Use Venn diagrams to calculate conditional probability | Statistics | Stratified sampling - know the definition and state in terms of proportion, fraction, percentage or ratio |
Geometry and measures | Prove and use the alternate segment theorem | Geometry and measures | Understand, recall and use Pythagoras' theorem in 3-D problems |
Geometry and measures | Enlarge 2D shapes, given a negative, fractional scale factor | Geometry and measures | Know and apply the sine rule a/sin A = b/sin B = c/sin C to find unknown lengths and angles |
Geometry and measures | know and apply the cosine rule a² = b² + c² – 2bc cos A to find unknown lengths | Geometry and measures | Calculate the area of a triangle given the length of two sides and the included angle |
Geometry and measures | Work out the magnitude of a vector | Algebra | Solve a quadratic equation by completing the square |
Algebra | Solve quadratic equations using the formula |
Step 11
Topic: | Lesson: | Topic: | Lesson: |
Number | Calculate the upper and lower bounds of 2-D measurements e.g. area | Number | Write (3 - √3)² in the form a + b√3 |
Number | Rationalise a denominator | Algebra | Apply to the graph of y = f(x) the transformations y = f(x) + a y = f(ax) y = f(x + a) y = af(x) for linear, quadratic |
Algebra | Apply to the graph of y = f(x) the transformations cubic, sine and cosine functions f(x) | Algebra | Find the gradient of the radius that meets the circle at a given point |
Algebra | Find the nth term of a quadratic sequence of the form n² ,an², an² ± b, an² ± bn ± c, | Algebra | Solve exactly, by elimination of an unknown, linear/x² + y² = r² simultaneous equations |
Statistics | Construct and interpret histograms from class intervals with unequal width and From a histogram complete a grouped frequency table | Geometry and measures | know and apply the cosine rule a² = b² + c² – 2bc cos A to find unknown angles |
Step 12
Topic: | Lesson: | Topic: | Lesson: |
Algebra | Interpret the gradient of linear or non-linear graphs, and estimate the gradient of a quadratic or non-linear graph at a given point by sketching the tangent and finding its gradient | Algebra | Interpret coodinates for trigonometric graphs |
Algebra | Plot graphs of the exponential function y = abx for integer values of x and simple positive values of a and b | Algebra | Use iteration with simple converging sequences |
Algebra | Recursive Iteration | Geometry and measures | Solve problems involving more complex shapes and solids, including segments of circles and frustums of cones |
Geometry and measures | Find the area of a segment of a circle given the radius and length of the chord | Geometry and measures | Solve problems for areas and volumes of similar shapes and solids |
Geometry and measures | Use the trigonometric ratios to solve 3-D problems | Geometry and measures | Apply vector methods for simple geometrical proofs |