KS4 Progression Ladders: Foundation Tier

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1 Name: KS4 Progression Ladders: oundation Tier xam Results and Target rades Year 9 Level Year 11 xam Year 10 xam S Target rade NUMBR ALBRA SHAP, SPA AN MASUR HANLIN ATA ecimals, Place value and Rounding ractions Percentages P, Ratio and Proportion Powers, Indices, Standard orm and Surds Properties of Number alculations and Negative Numbers xpressions, quations and ormulae Sequences raphs Perimeter, Area and Volume Angles Properties of Shapes & Objects and onstruction Speed, istance, Time Transformations ollecting ata and Sampling onstructing and Interpreting harts and raphs Averages Probability Page: Madeley High School KS4 oundation Progression Ladder

2 School login: madeley Password: maths Individual login: Password: Madeley High School KS4 oundation Progression Ladder

3 rade ecimals, Place value and Rounding Round to the nearest integer Write an integer correct to the nearest 10 or the nearest 100 stimate answers to problems involving decimals Round numbers to given powers of 10 and to given numbers of decimal places Write down the place value of a digit, for example, what is the value of the 4 in 0 24? Order decimals, for example, which is bigger, 0 24 or 0 3? ate Multiply whole numbers and decimals by 10, 100 and 1000 ivide whole numbers and decimals by 10, 100 and 1000 Add decimals to two places Subtract decimals to two places Multiply decimals to two places ivide decimals to two places Round a number to one significant figure Add and subtract decimals stimate answers to calculations involving division Multiply two decimals such as stimate answers to calculations ind minimum and maximum values Understand the effects of multiplying by numbers between 0 and 1 ivide a number by a decimal such as and 2 8 divided by 0 07 Recognise accuracy in measurements given to the nearest whole unit Madeley High School KS4 oundation Progression Ladder

4 rade ractions ind equivalent fractions Simplify fractions such as Arrange fractions in order of size ate Work out fractions of quantities such as 3 of 20 ind one number as a fraction of another o calculations with simple fractions involving addition o calculations with simple fractions involving multiplication o calculations with simple fractions involving subtraction o calculations with mixed numbers o calculations with simple fractions involving division 5 rade Percentages Understand that percentage means out of 100 Work out a percentage of a given quantity Increase or decrease a quantity by a given percentage Work out a percentage increase or decrease xpress one quantity as a percentage of another ate Madeley High School KS4 oundation Progression Ladder

5 rade P, Ratio and Proportion ate ecide which metric unit to use for everyday measurements hange a percentage to a fraction or a decimal and vice versa Solve simple ratio and direct proportion problems onvert one metric unit to another onvert between imperial and metric units ompare percentages, fractions and decimals Use map scales to find distance onvert decimals to fractions and fractions to decimals Solve more complex ratio and proportion problems, such as sharing out money between two groups in the ratio of their numbers Solve ratio and proportion problems using the unitary method rade Powers and Indices ate stimate square roots alculate squares and square roots (with and without the use of a calculator) alculate cubes and cube roots (with and without the use of a calculator) Use function keys on a calculator for powers and roots Use the terms square, positive and negative square root, cube and cube root Recall integer squares from 2 2 to and the corresponding square roots Recall the cubes of 2, 3, 4, 5 and 10 Use index notation and index laws for positive and negative powers Madeley High School KS4 oundation Progression Ladder

6 rade Properties of Number ind the factors of a number ind the least common multiple (LM) of two simple numbers ind the highest common factor (H) of two simple numbers Write a number as a product of prime factors ind the reciprocal of a number ate rade alculations and Negative Numbers Understand positive and negative integers Add and subtract negative integers Multiply any three digit number by any two digit number without a calculator ivide any three digit number by any two digit number without a calculator Make sensible estimates of a range of measures in everyday settings Multiply and divide negative integers Solve numerical problems involving multiplication and division with numbers of any size using a calculator efficiently and appropriately ate Madeley High School KS4 oundation Progression Ladder

7 rade xpressions, quations and ormulae ate Use a formula written in words, such as cost = 20 x distance travelled Simplify expressions with one variable such as a + 2a + 3a Use a simple formula such as P = 2w + 2h Substitute positive numbers into a simple formula Solve equations such as 4x = 24 and x 3 = 7 Simplify expressions with more than one variable such as 2a + 5b + a 2b x Solve equations such as 9 2 = or 4x 2 = 22 Write an expression from a problem Substitute negative numbers into a simple formula Use formulae from mathematics and other subjects Multiply out expressions with brackets such as 5(3x 2) actorise expressions Solve linear equations with unknowns on each side such as 3x 4 = 5 + x Solve linear equations with brackets such as 2(5x + 1) = 28 Substitute numbers into more complicated formulae such as ( A + 1) = 9 Multiply out expressions with brackets such as y(3y 8) xpand and simplify two expressions of the form (x + n) Solve more complex linear equations such as 3x 12 = 2(x 5) Solve linear equations involving fractions such as 7 x = 2 or x x 3 2 = ind a solution to a problem by forming an equation and solving it orm and solve equations such as x 3 + x = 12 using trial and improvement methods Rearrange linear formulae such as s = 4q - 7 Solve inequalities such as 3x < 9 and 12 3n < 20 Solve linear inequalities such as 4x 3 < 10 and 4x < 2x + 7 Represent sets of solutions on the number line Madeley High School KS4 oundation Progression Ladder

8 rade Sequences ate ontinue a sequence of numbers or diagrams Write down terms of a simple sequence ind a particular term in a sequence involving positive numbers Write the term-to-term rule in a sequence involving positive numbers escribe number patterns and relationships including multiple, factor and square ind a particular term in a sequence involving negative or fractional numbers Write the term-to-term rule in a sequence involving negative or fractional numbers Write the terms of a sequence or a series of diagrams given the nth term Write the nth term of a sequence or a series of diagrams rade raphs ate Use coordinates in the first quadrant, such as plot the point (3, 2) Use coordinates in all four quadrants Plot points of a conversion graph and read off positive values raw lines such as x = 3 and y = x + 2 Read from a conversion graph for negative values Interpret distance time graphs Plot the graphs of straight lines such as x = 3 and y = 4 omplete a table of values for equations such as y = 3x + 3 and draw the graph raw lines such as y = 2x + 3 Solve problems involving straight lines Solve problems involving graphs, such as finding where the line y = x + 5 crosses the line y = 1 raw graphs of simple quadratic functions such as y = 2x 2 and y = x Recognise the equations of straight-line graphs such as y = 3x - 5 ind the gradients of straight-line graphs raw graphs of harder quadratic functions such as y = x 2 + 3x -5 ind the points of intersection of quadratic graphs with lines Use graphs to find the approximate solutions of quadratic equations Madeley High School KS4 oundation Progression Ladder

9 rade Perimeter, Area and Volume ind the perimeter of a shape by counting sides of squares ind the area of a square by counting squares stimate the area of an irregular shape by counting squares and part squares ind the volume of a solid by counting cubes and stating units Work out the perimeter of a simple rectangle Work out the area of a simple rectangle ind the perimeter of compound shapes ind the area of compound shapes ind the volume of a cube or cuboid ind the height of a cuboid, given volume, length and breadth ind the area of a triangle, parallelogram, kite and trapezium ind the area and perimeter of more complex compound shapes alculate the circumference of a circle to an appropriate degree of accuracy alculate the area of a circle to an appropriate degree of accuracy Solve problems involving circles such as finding the perimeter of a semicircle Solve problems involving circles such as finding the area of a semicircle alculate volumes of triangular prisms, parallelogram-based prisms and cylinders Solve problems involving surface areas of prisms and cylinders onvert between measures of area onvert between measures of volume ate Madeley High School KS4 oundation Progression Ladder

10 rade Angles xpress fractions of full turns in degrees and vice versa Recognise acute, obtuse and reflex angles stimate angles Measure and draw angles accurately to the nearest degree Understand the terms perpendicular lines and parallel lines Know angles on a straight line add up to 180, and angles at a point add up to 360 Know angles in a triangle add up to 180 Show that the angles of a triangle add up to 180 and use this to find angles Show that an exterior angle of a triangle is equal to the sum of the interior opposite angles Use angle properties of isosceles, equilateral and rightangled triangles alculate interior and exterior angles of a quadrilateral Solve problems using angle and symmetry properties of polygons and properties of intersecting and parallel lines alculate exterior and interior angles of a regular polygon Use Pythagoras theorem to find the hypotenuse of a rightangled triangle Use Pythagoras theorem to find any side of a right-angled triangle Use Pythagoras theorem to find the height of an isosceles triangle Use Pythagoras theorem in practical problems ate rade Speed, istance, Time ate Solve simple speed problems alculate simple average speeds from distance time graphs Solve more difficult speed problems Understand and use compound measures such as speed and density alculate complex average speeds from distance time graphs Madeley High School KS4 oundation Progression Ladder

11 rade Properties of Shapes & Objects and onstruction Identify isosceles, equilateral and right-angled triangles Use the word congruent when triangles are identical Name the parts of a circle Recognise and name shapes, such as isosceles triangle, parallelogram, rhombus, trapezium and hexagon Measure a line accurately to the nearest millimetre Recognise the net of a simple solid such as a cuboid Recognise and name three-dimensional (3-) solids Sketch three-dimensional (3-) solids raw the net of a simple solid such as a cuboid Investigate tessellations raw a triangle given three sides, or two angles and a side, or two sides and the included angle raw a cuboid on an isometric grid and mark its dimensions raw a quadrilateral such as a kite or a parallelogram with given measurements Understand that the lengths of two sides & a non-included angle do not define a unique triangle onstruct and recognise the nets of 3- solids such as pyramids and triangular prisms raw plans and elevations of 3- solids Understand the idea of a locus lassify a quadrilateral by geometric properties ind the midpoint of a line segment Use and understand coordinates in three dimensions onstruct the perpendicular bisector of a line onstruct the perpendicular from a point to a line onstruct the perpendicular from a point on a line onstruct angles of 60 and 90 onstruct the bisector of an angle Match one side and one angle of congruent triangles, given some dimensions onstruct accurately loci, such as those of points equidistant from two fixed points Solve loci problems, such as identifying points less than 3 cm from a point P ate Madeley High School KS4 oundation Progression Ladder

12 rade Transformations ate raw the reflection of a shape in a mirror line raw a line of symmetry on a 2- shape raw all the lines of symmetry on a 2- shape ive the order of rotations symmetry of a 2- shape Name, draw or complete 2- shapes from information about their symmetry raw the line of reflection for two shapes ive a scale factor of an enlarged shape Reflect shapes in the axes of a graph nlarge a shape by a positive scale factor ind the measurements of the dimensions of an enlarged shape Reflect shapes in lines such as x = 2 or y = 1 Rotate shapes about the origin escribe fully reflections and rotations about the origin Identify reflection symmetry in 3- solids Translate a shape using a description such as 4 units right and 3 units down nlarge a shape by a positive scale factor from a given centre Reflect shapes in the lines y = x and y = x Rotate shapes about any point escribe fully reflections and rotations about any point ind the centre of a rotation and describe it fully ombine reflections and rotations Translate a shape by a vector such as 4 3 Transform shapes by a combination of translation, reflection and rotation ompare the area of an enlarged shape with the original shape nlarge a shape by a positive whole number or fractional scale factor Madeley High School KS4 oundation Progression Ladder

13 rade ollecting ata and Sampling ate lassify and know the difference between various types of data esign and use data collection sheets and questionnaires Use a variety of different sampling methods Identify possible sources of bias in the design and use of data collection sheets & questionnaires Specify hypotheses and test them rade onstructing and Interpreting harts and raphs onstruct and interpret a pictogram ate Interpret a pictogram onstruct and interpret a bar chart Interpret a bar chart esign and use tally charts for discrete data esign and use tally charts for grouped data Interpret a pie chart onstruct a pie chart Interpret a stem-and-leaf diagram esign and use two-way tables for discrete and grouped data onstruct a stem-and-leaf diagram (ordered) onstruct a frequency diagram Interpret a time series graph raw a scatter graph by plotting points on a graph Interpret the scatter graph raw a line of best fit on the scatter graph by inspection Madeley High School KS4 oundation Progression Ladder

14 rade Averages ind the mode for a set of numbers ind the median for an odd set of numbers Work out the range for a set of numbers alculate the mean for a set of numbers ind the median for an even set of numbers Write down the mode from a graph ompare two distributions using the range and one of the mode, median or mean ompare the mean and range of two distributions alculate the fx column for a frequency distribution alculate the mean for a frequency distribution ind the mean for grouped data ind the median class for grouped data ind the modal class for grouped data Use measures of average and range to compare distributions and make inferences ate Madeley High School KS4 oundation Progression Ladder

15 rade Probability Understand and use the vocabulary of probability Understand and use a probability scale xpress a probability as a fraction isplay outcomes systematically Understand the difference between experimental and theoretical probabilities Understand and use relative frequency Use a two-way table to find a probability Understand mutually exclusive events Use the fact that the probabilities of mutually exclusive events add up to 1 Understand relative frequency as an estimate of probability Use relative frequency to compare outcomes of experiments ate Madeley High School KS4 oundation Progression Ladder

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