Mathematics Student Progress Tracker

Transcription

1 Mathematics Student Progress Tracker Name : Maths Group Date Started : KS2 : MIN : ASP : Yr 7 Result : Yr 8 Result : Yr 9 Result : Yr 10 Result : R E S P O N S I B I L I T Y Your maths, your progress

2 Statistics Geometry Algebra Number Page Section Topic 4 Number Operations 5 Place Value 6 Estimation & Rounding 7 Measures 8 Fractions 9 Decimals 10 Percentages, Ratio & Proportion 11 Integers 12 Indices and Surds 14 Symbols 15 Solving 1 16 Solving 2 17 Graphs 1 18 Graphs 2 19 Graphs 3 20 Sequences & Proof 21 Formulae 23 2D Shapes D Shapes D Shapes D Shapes 2 27 Angles 28 Transformations 1 29 Transformations 2 30 Loci & Constructions 31 Trigonometry 33 Probability 34 Averages 35 Representing Data 1 36 Representing Data 2 37 Collecting Data Contents

3 Number

4 Number Operations Number 3i 18 Add two digit numbers 3ii 19 Subtract two digit numbers 3iii 18 Add three digit numbers 3iv 19 Subtract three digit numbers 3v 10 Multiply and divide using the 2, 3, 4, 5 and 10 times tables 3vi 23 Solve whole number problems involving multiplication and division 3vii 24 Use BIDMAS without indices 4i 10 Times Tables to 12 x 12 4ii 10 Multiplication by a single digit number 4iii 22 Division by a single digit number 5i 21, 144 Multiply three digit number by any two digit number 5ii 145 Divide three digit number by any two digit number 5iii - Check answers by using inverse operations and approximating 5iv 120 Use BIDMAS with indices 6 49 Division resulting in a decimal answer Use a calculator appropriately to perform complex calculations with numbers of any size, knowing not to round during the stages 8 Apply systematic listing strategies, including use the product rule for counting

5 Place Value Number 3i 13 Place value in numbers up to ii 13 Write fiqures into words and vice versa 3iii - Use place value to make approximations Multiply and divide by 10 and Multiply and divide by 10, 100 and 1000 and understand how this affects place value Manipulate given calculations to answer questions 7i - Understand the effects of multiplying and dividing by numbers between 0 and 1 7ii Convert between ordinary numbers and standard form 7iii - Understand the effects of multiplying and dividing by negative powers of Calculate with numbers in standard form

6 Estimation & Rounding Number 3i - Round to the nearest integer. 3ii 17 Write an integer correct to the nearest 10, 100 and i - Estimate answers to problems involving decimals. 4ii 112 Estimate square roots Round to a given number of decimal places. 6i 130 Round a number to one significant figure. 6ii 137 Find minimum and maximum values of a rounded number Use inequality notation to speciy simple error intervals due to truncation or rounding 7i 131 Estimate answers to calculations involving multiplication and division by rounding to 1sf 7ii 131 Estimate answers to calculations involving multiplication and division by numbers less than one. 7iii 130 Round to a given number of significant figures Calculate using upper & lower bounds 9 Apply and interpret limits of accuracy

7 Measures Number 3i 3ii Describe which metric unit to use for everyday measurements. Understand and use time 4 Convert between metric units 5i 5ii 5iii Convert between imperial and metric units. Know the metric equivalents of imperial units still in daily use Make sensible estimates of a range of measures in everyday settings. Use compound units such as speed, rates of pay, unit pricing, density and pressure 6 Solve simple speed & density problems. 7i 7ii Solve more difficult speed & density problems. Recognise accuracy in measurements given to the nearest whole unit. 8 Calculate using upper & lower bounds

8 Fractions Number 3i 59 Find equivalent fractions. 3ii 58 Represent simple fractions with pictures 4i Convert between mixed numbers and improper fractions 4ii 65 Add and subtract fractions with a common denominator 5i 61 Simplify fractions. 5ii 60 Order fractions 5iii 77, 80 Work out fractions of quantities. 6i 62 Find one number as a fraction of another. 6ii 66 Add and subtract fractions 7i Multiply fractions 7ii 70 Divide fractions 7iii - Add, subtract, multiply and divide mixed numbers

9 Decimals Number 3 - Use decimals in money problems 4i 45 Identify place value in decimals 4ii 46 Order decimals 4iii 48 Multiply a decimal by a single digit 5i 47 Add and subtract decimals. 5ii 48 Multiply two decimals 5iii Convert decimals to fractions and vice versa 6 50 Divide a number by a decimal, such as and Write common recurring decimals as fractions 8 54 Convert recurring decimals to fractions and fractions to recurring decimals, using algebra

10 Percentages, Ratio & Proportion Number 4i 81 Understand that percentage means out of 100 4ii Change a percentage to a fraction or a decimal 4iii Calculate a percentage of an amount 5i - Solve simple ratio and proportion problems, such as finding the ratio of teachers to students in a school. 5ii 329 Simplify ratio 5iii - Express one quantity as a percentage of another. 6i 331 Express a ratio in the form 1:n and n:1 6ii 332 Answer questions on amounts with a given ratio 6iii 90 Calculate percentage increase and decrease 7i 89 Calculate proportional changes using a multiplier. 7ii 339 Solve direct proportion problems. 8i 96 Calculate the original quantity given the value after a percentage change 8ii 94 Calculate compound interest Calculate inverse proportion 9 Interpret the gradient of a straight line graph as a rate of change 9 Recognise and interpret graphs that illustrate direct and inverse proportion 9 Set up, solve and interpret the answers in growth and decay problems

11 Integers Number 3 37 Use negative numbers on a number line eg temperature 4i 27 Find all the factors of a number. 4ii 33 Write down multiples of a given number. 5i 41 Order, add and subtract negative numbers 5ii 34 Find the least common multiple (LCM) of two numbers. 5iii 31 Find the highest common factor (HCF) of two numbers. 5iv 28 Recognise prime numbers. 5v Write a number as a product of prime factors. 6i Multiply and divide negative numbers mentally 6ii 32, 35 Find HCF & LCM using product of prime factors 7 71 Find the reciprocal of a number.

12 Indices & Surds Number 4i 99 Use squares and square roots (with and without the use of a calculator). 4ii 100, 101 Use cubes and cube roots (with and without the use of a calculator). 4iii - Use the terms positive and negative square roots. 4iv Recall the square numbers from 2 x 2 to 15 x 15 and the corresponding square roots. 4v 100 Recall the cubes of 2, 3, 4, 5 and 10. 8i Use the rules of indices 8ii 108 Use rules of indices for fractional powers. 8iii 109 Use the rules of indices for complex fractional powers. 8iv 115 Simplify surds 8v 8vi Operations on surds Calculate with roots, and with integer and fractional indices 8vii 118 Rationalise the denominators of surds Simplify surds such as (3-5) 2 in the form a + b Rationalise the denominators of more complex surds

13 Algebra

14 Symbols Algebra Simplify expressions with one variable such as a+2a+3a Simplify expressions by collecting like terms such as 2a+5b+a 2b 5i 160 Expand single brackets. 5ii 161 Expand and simplify more complicated expressions, including those with surds Factorise simple expressions. 7i Expand and simplify quadratic expressions. 7ii 223 Factorise quadratic expressions. (a = 1) 8i 166 Expand and simplify triple brackets. 8ii 172 Operations on simple algebraic fractions 8iii 170 Simplify algebraic fractions by factorising using single bracket 8iv 229 Simplify algebraic fractions by factorising (quadratics a=1) 8v Factorise quadratic expressions. (a 1) 9i 224 Understand and use the difference of two squares 9ii Factorise quadratics by completing the square 9iii 229 Simplify harder algebraic fractions (polynomials)

15 Solving 1 Algebra Solve equations such as 3x = 12 or x + 5 = , 180, 182 Solve equations such as or 3x 1 = 9. 6i - Solve equations with brackets such as 2(5x + 1) = 28. 6ii 184 Solve equations with x on both sides such as 3x 4 = 5 + x 7i Solve equations such as 3x 12 = 2(x 5) 7ii Solve inequalities such as 3x < 9 and 12 3n < 20 7iii Solve linear inequalities such as 4x 3 < 10 and 4x < 2x + 7 7iv Represent inequalities on a number line 7v Solve linear inequalities such as x + 13 > 5x Solve a set of linear inequalities in two variables and represent the solution as a region of a graph.

16 Solving 2 Algebra Solve linear equations graphically Solve a pair of simultaneous equations in two unknowns such as 2x + y = 5 & 3x 27 = 4. 8i 259 Solve a quadratic and straight line graphically 8ii 246 Solve a pair of simultaneous equations where one is linear and one is non-linear such as y = 3x 2 and y = x 2 8iii Solve quadratic equations such as x 2 + bx + c = 0 by factorisation. (a = 1) 8iv Solve equations such as ax 2 + bx + c = 0 by using the quadratic formula 8v 238 Solve quadratic equations such as x 2 + bx + c = 0 by completing the square Solve quadratic equations using iteration 9i 246 Solve a pair of simultaneous equations where one is linear and one is non-linear such as x + 5y = 13 and x 2 + y 2 = 13. 9ii 239 Solve quadratic equations such as ax 2 + bx + c = 0 by completing the square (a 1) 9iii 256 Use completing the square to find the minimum and maximum values of quadratics. 9iv 318 Solve a pair of simultaneous equations where one is linear and one is a circle

17 Graphs 1 Algebra Use and interpret positive coordinates 5i 199 Use and interpret coordinates in all four quadrants 5ii 205 Draw lines such as x = 3 and y = 4. 6i 206, 209 Plot straight line graphs by completing a table of values 6ii 207 Identify the y-intercept and gradient from y=mx+c 6iii 200 Find the midpoint of a line 6iv Find the gradient of a straight line graph 7i - Use and understand coordinates in three dimensions. 7ii Find the equation of a straight line from a graph 7iii 214 Find the equations of parallel lines through any point 7iv - Determining if a point lies on a line (substitution) 8i 210 Identify the y-intercept and gradient from rearranged y=mx+c 8ii 215 Calculate the gradients of perpendicular lines (negative reciprocal) Calculate the equations of perpendicular and parallel lines through a given point

18 Graphs 2 Algebra 5i - Plot and interpret conversion graphs 5ii - Interpret distance time graphs. 7i - Calculate average speeds from distance time graphs. 7ii - Interpret velocity time graphs. 7iii - Discuss and interpret graphs modelling real situations (rates of change) 8 - Interpret Acceleration - time graphs (inc area under graph and gradient)

19 Graphs 3 Algebra 7i 251 Plot graphs of simple quadratic functions such as y = 3x 2 and y = x ii 251 Plot graphs of harder quadratic functions such as y = x 2 2x iii Identify and interpret roots, intercepts, turning points of quadratic functions graphically and deduce algebraically 7iii 260 Use graphs to find the approximate solutions of quadratic equations. 8i Find the points of intersection of quadratic graphs with axes & lines (inc y=o and x=0) 8ii 298, 300 Complete tables for, and draw graphs of, cubic and reciprocal functions 8iii 299, 301 Recognise graphs of cubic and reciprocal functions 9i - Use re-arrangement of quadratic graphs such as y = x 2 2x 4 & y = 2x + 1 to solve equations 9ii - Solve cubic equations by drawing appropriate lines on graphs. 9iii 302 Plot and sketch graphs of exponential & modulus functions. 9iv 9v Transform the graphs of polynomials Transform the graphs of other functions 9vi - Recognise equation of a circle centre (0,0) 9vii 9viii Recognise equation of a circle centre (a,b) Equations of tangent to a circle

20 Sequences & Proof Algebra Continue a sequence of numbers or diagrams. 5i 197 Find the term to term rule for a sequence 5ii 197 Find the terms of a sequence or a series of diagrams given the nth term Recognise and use sequences of fibonacci, triangular, square and cube numbers Recognise the difference between arithmetic and geometric progressions 5iii - Decide with a reason whether a simple statement is true or false. 6i 198 Find the nth term of a sequence or a series of diagrams 6ii - Decide with a reason whether a harder statement is true or false. 6iii 324 Identify a counter example. 7 - Is a value in a sequence (reasoning) 7i Find the terms of a quadratic sequence given the nth term 7ii - Understand how to "show that" 7iii 325 Show step by step deductions in proving a basic algebraic explanation. 8i 248 Find the nth term of a quadratic sequence or series of diagrams 8ii Show step by step deductions in providing a full mathematical explanation 8iii - Derive simple algebraic proofs using reasoning. 9i - Derive harder algebraic proofs using reasoning and logic.

21 Formulae Algebra 4 - Use a formula expressed in words, such as cost = 20 x distance travelled. 5i 155, 189 Substitute numbers into a simple formula. 5ii Write an expression from a problem. 6i 278 Substitute numbers into more complicated formulae 6ii 176 Form an equation from a situation and solve it. 7i Change the subject of a formula 7ii 279 Use and recall complex formulae (inc. quadratic formula & SUVAT) Rearrange formulae that include brackets, fractions and square roots. 9i 9ii 9iii Rearrange formulae where the variable appears twice Inverse functions (reflection in y=x) Composite functions

22 Geometry

23 2D Shapes 1 Geometry 3i _ Naming Polygons 3ii Identify isosceles, equilateral, scalene and right-angled triangles 3iii 611 Use and understand the words congruent and similar 4i Find the perimeter of a shape 4ii 553 Find the area of shapes by counting the squares. 4iii 553 Estimate the area of an irregular shape by counting squares and part squares. 4iv 592 Name the parts of a circle. 4v _ Know the difference between regular and irregular shapes 5i 554 Find the area of a rectangle 5ii _ Investigate tessellations. 6i _ Identify a quadrilateral by geometric properties 6ii Calculate the area of triangles, parallelograms and trapeziums. 6iii 555 Find the area and perimeter of compound shapes. 6iv Calculate the circumference of a circle 6v Calculate the area of a circle

24 2D Shapes 2 Geometry 7i _ Find the perimeter of a semicircle/quarter circle 7ii Find the area of a semicircle/quarter circle 7iii Find sides and angles of similar triangles, given some dimensions. 8i _ Prove that two triangles are congruent. 8ii _ Find the area of a 2 D shape, given the area of a similar shape and the ratio. 8iii Find the length of the major arc of a circle. 8iv Find the area of the major sector of a circle. 8v _ Find the area of a segment of a circle.

25 3D Shapes 1 Geometry 3i _ Recognise and name 3 D solids. 3ii _ Recognise and name the nets of 3D solids 3iii _ Sketch 3 D solids. 4i _ Understand and use faces, edges and vertices 4ii _ Draw the net of a simple solid such as a cuboid. 5i _ Draw a cuboid on an isometric grid and mark its dimensions. 5ii _ Construct and recognize the nets of 3 D solids such as pyramids and triangular prisms. 6i _ Draw plans and elevations of 3 D solids. 6ii Find the volume of a cube or cuboid using dimensions 6iii Find the a missing dimension of a cuboid given the volume and other dimensions

26 3D Shapes 2 Geometry 7i _ Change between area measures such as m 2 to cm 2. 7ii _ Change between volume measures such as m 3 to cm 3 or cm 3 to litres. 7iii Calculate volumes of prisms and cylinders. 7iv Calculate surface areas of prisms and cylinders. 8i _ Distinguish between formulae for perimeter, area and volume 8ii Find the volume and surface area of pyramids, cones and spheres 8iii _ Find the volume of the top cone of a truncated cone. 8iv Find the volume of a 3 D solid, given the volume of a similar solid and the ratio. 8v _ Find the area of a segment of a circle. 9 _ Find the volume of the frustum of a truncated cone.

27 Angles Geometry 3 _ Understand clockwise & anti-clockwise 4i _ Express fractions of full turns in degrees and vice versa. 4ii 455 Recognise acute, obtuse and reflex angles. 5i 457 Estimate angles and measure them accurately. 5ii _ Understand the terms perpendicular lines and parallel lines. 5iii Know and use the sum of angles on a straight line and at a point 5iv , 560 Know and use the sum of angles in a triangle & quadrilateral 5v _ Use angle properties of isosceles, equilateral and right-angled triangles Recognise and use corresponding, alternate and vertically opposite angles. 7i Know how to find the bearing of one point from another 7ii Calculate exterior and interior angles of a regular polygon 8i Solve bearing problems 8ii Use the angle properties of a circle. 8iii Use the angle and tangent / chord properties of a circle. 9i Prove the angle and tangent / chord properties of a circle. 9ii _ Use and prove the alternate segment theorem.

28 Transformations 1 Geometry 3 - Draw the reflection of a shape in a mirror line. 4i - Draw all the lines of symmetry on a 2 D shape. 4ii - Identify the order of rotation symmetry of a 2 D shape. 5i - Give a scale factor of an enlarged shape 5ii - Reflect shapes in the axes of a graph. 5iii - Reflect shapes in horizontal and vertical lines such as x = 2 and y = -1 5iv - Identify reflection symmetry in 3D solids. 6i - Enlarge a shape by a positive scale factor 6ii - Rotate shapes about the origin. 6iii - Describe fully reflections in a line and rotations about the origin. 6iv - Reflect shapes in diagonal lines such as y = x and y = -x. 6v - Enlarge a shape by a positive scale factor from a given centre 6vi - Translate a shape using a description such as 4 units right and 3 units down 6vii - Rotate shapes about any point.

29 Transformations 2 Geometry 7i _ Describe fully reflections and rotations about any point. 7ii _ Transform shapes by a combination of transformations. 7iii _ Enlarge a shape by a fractional scale factor 7iv Translate a shape by a given vector 7v _ Describe transformations that involve a combination Describe the changes and invariance achieved by combinations of transformations 7vi _ Compare the area of an enlarged shape with the original shape. 8i 624 Enlarge a shape by a negative scale factor. 8ii _ Compare areas and volumes of enlarged shapes. 9i Add, subtract and multiply vectors to solve vector geometry problems. 9ii Solve more difficult vector geometry problems.

30 Loci & Constructions Geometry 4i - Measure a line accurately to the nearest millimetre. 4ii - Draw circles of given radius 5 - Draw all points a certain distance from a point 6i - Use map scales to find distances 6ii - Construct the perpendicular bisector of a line. 6iii - Construct an angle bisector 6iv - Construct the perpendicular from a point to a line. 6v - Construct angles of 60 0 and vi - Construct polygons 7i - Understand the idea of a locus. 7ii - Construct the locus of points equidistant from a line 7iii - Construct the locus of points equidistant from a point 7iv - Contruct locus of points (multi stage problem)

31 Trigonometry Geometry 7i 498 Use Pythagoras theorem to find the hypotenuse of a right-angled triangle. 7ii 499 Use Pythagoras theorem to find any side of a right-angled triangle. 7iii _ Use Pythagoras theorem to find the height of an isosceles triangle. 7iv Use Pythagoras theorem in practical problems. 8i _ Find the distance between two points 8ii Use Pythagoras theorem in 3D problems. 8iii Use sine, cosine and tangent to calculate a side in a right-angled triangle. 8iv Use sine, cosine and tangent to calculate an angle in a right-angled triangle. 8v _ Know and apply sin/cos/tan of 30/45/60/90 9i _ Use trigonometry to find sides and angles in 3D problems 9ii _ Find the angle between a line and a plane. 9iii _ Sketch and draw trigonometric graphs. 9iv Know and use the sine rule to find the missing sides and angles in any triangle. 9v Use the cosine rule to find the missing sides and angles in any triangle. 9vi Know and use the formula for the area of a non right-angled triangle. 9vii _ Use graphs to solve trig equations

32 Statistics

33 Probability Statistics Understand and use the vocabulary of probability. 5i 350 Understand and use a probability scale from 0 to 1 5ii Find and express a probability as a fraction. 5iii - Display outcomes systematically. 5iv - Understand the difference between experimental and theoretical probability. 5v - Understand that different outcomes may results from repeating an experiment 6i Identify outcomes of combining events eg rolling a dice and throwing a coin 6ii 354 Understand mutually exclusive events. (Venn Diagrams) 6iii 353 Know that the sum of the probabilities of all the outcomes of an experiment is 1 7i Understand and use relative frequency. 7ii 355 Use probabilities to estimate outcomes for a population. 7iii Complete a frequency tree. 7iii 361 Complete a tree diagram. 8i 360 Understand dependent and independent outcomes. 8ii Use tree diagrams to find probabilities of successive independent events Draw tree diagrams and use them to find probabilities of successive dependent events Venn diagram notation with respect to probability (intersection & union)

34 Averages Statistics 4i 404 Find the mode of a list of numbers. 4ii 410 Work out the range from a list of numbers, a graph and a frequency table 4iii 415 Find the mode from a graph / frequency table 5i Calculate the mean of a list of numbers. 5ii 409 Find the median of a list of numbers. 5iii - Compare an average and range of two distributions. 6i 417 Calculate the mean from a frequency table 6ii 416 Calculate the median from a frequency table 7i - Find the modal class and range for grouped data. 7ii 418 Find the mean from a grouped frequency table 7iii 416 Find the median class from a grouped frequency table 7iv - Use averages and range to compare distributions

35 Representing Data 1 Statistics 3i 426 Construct and interpret a pictogram. 3ii 425 Construct and interpret a bar chart. 4i 425 Construct and interpret line graphs 4ii - Read points on a scale. 5i 429 Interpret a pie chart 5ii 430 Interpret a stem-and-leaf diagram. 6i 6ii Construct a pie chart Construct a stem-and-leaf diagram (ordered). 6iii 441 Construct and interpret frequency polygon 6iv Interpret a time series graph.

36 Representing Data 2 Statistics 6i 453 Plot a scatter graph 6ii 453 Interpret & draw conclusions from a scatter graph. 7i 454 Draw the line of best fit on the scatter graph. 7ii 454 Identify the type and strength of the correlation. 7iii 454 Interpret the line of best fit. 8i 437 Construct and interpret a cumulative frequency graph 8ii 8iii Estimate the median and interquartile range from a cumulative frequency graph Construct and interpret a box plot. 8iv 436 Compare two sets of data using box plots. 8v 9ii Construct and interpret a histogram Use a histogram

37 Collecting Data Statistics 4i Collect and record discrete data 4ii Design and use two-way tables Classify and know the difference between various types of data 6i 403 Collect and record continuous data 6ii Design and use data collection sheet and questionnaires 7i 395 Use a variety of different sampling methods 7ii 394 Identify possible sources of bias in the design and use of data collection sheets and questionnaires Use stratified sampling methods