Mathematics Steps to Success. Number. Problem solving with these skills increases the step depending on the complexity of the question.

Transcription

1 Problem solving with these skills increases the step depending on the complexity of the question Mathematics Steps to Success Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Number I can add, subtract, divide, multiply whole numbers and use the order of operations (BIDMAS) I can understand and use place value and order positive and negative numbers and fractions and decimals I can recognise factors, multiples, prime numbers, squares and cubes I can use equivalent fractions I can add, subtract, multiply and divide decimals I can find the LCM and HCF from a venn diagram and use set notation I can can order and convert between fractions and decimals I can understand and use prime numbers I can round to 1 and 2 decimal places I can use a calculator to investigate roots, powers and functions I can add, subtract, multiply and divide negative numbers I can convert between improper and mixed fractions I can simplify fractions fully I can divide decimals I can calculate a percentage increase and decrease I can use negative numbers with power and time I can simplify powers with negatives and use fractional powers I can identify and work with fractions into ratio problems Number I can use BIDMAS to solve multistep calculations I can add, subtract, multiply and divide fractions I can round numbers to 1 and 2 significant figures and estimate solutions to calculations I can find product of prime factors I can manipulate calculations using inverse operations and powers of 10 I can use, simplify and estimate powers and roots of any given positive number I can apply systematic listings to problem solving including use of the product rule for counting I can convert between fractions and decimals I can multiply and divide with directed numbers and substitute directed numbers into formula I can convert between standard form and ordinary numbers and can simplify and compare expressions in standard form I can use the multiplication and division indices rules and evaluate indices I can find an original amount from a percentage change I can change between units of mass, length, time, money and other measures I can find the next terms and the nth term of a sequence and use the nth term to find any number in the sequence I can problem solve with percentages and calculate compound interest I can use positive fractional and negative powers I can adjust a number into correct standard form and can multiply and divide 2 or more standard form numbers I can apply and interpret limits of accuracy including calculating upper and lower bounds with measures I can evaluate indices using fractions and negatives I can change recurring decimals into their corresponding fractions and vice versa I can calculate with surds including simplifying, expanding brackets, rationalising the denominator and problem solving with area and perimeter Algebra I can recognise and name lines parallel to the x-axis and y-axis I can read and interpret conversion graphs I can find the function which gives a set of outputs from a given set of inputs I can calculate the midpoint of a line I can plot points using positive and negative coordinates and join to show special quads on a coord grid I can express formulas in words and symbols I can use and interpret line graphs and conversion graphs and read and interpret coordinates I can simplify expressions with like terms I can expand a single bracket and factorise into a single bracket I can construct a formula from words and recognise and use position to term rules I can simplify fractions with one unknown using multiplication or division I can distinguish between formulae, expressions, equations and identities I can generate and describe a sequnce using the term to term rule I can use formulas with two operations and substitute numerical values into formulae I can read and interpret straight line graphs and recognise how and where graphs are used in finance I can expand and factorise a single bracket with more than one algebraic term I can collect like terms including expansion of single brackets I can recognise inequality signs and use a number line to represent inequalities I can use a table of values and y=mx+c to draw a straight line graph I can calculate the gradient of a straight line I can use scientific formulae including SUVAT equations

2 Algebra Proportion I can expand and factorise a double bracket I can solve one and two step linear inequalities I can read and use inequalities with algebra I can derive quadratic sequences from the nth term I can use inequality symbols with algebra I can solve linear inequalities with a variable on both sides and represent the solution on a number line I can expand products of two or more binomials I can factorise and expand quadratic expressions using the difference of 2 squares I can solve an equation with one and two operations and simplify an expression I can use y=mx+c to write the equation of a straight line from a graph I can write the nth term of a quadratic sequence I can solve linear equations containing brackets and fractions I can recognise and use gradients of parallel and perpendicular lines I can read and plot coordinates and draw the curve of a quadratic graph I can solve equations algebraically I can explain the role of m and c in the linear function y=mx+c I can recognise that functions with the same gradient are parallel I can solve a linear equation with a single unknown and brackets I can use the nth term expression to generate terms in a sequence I can use the difference of 2 squares I can find parallel and perpendicular lines through a point I can find error intervals and percentage errors I can plot speed, distance time graphs and acceleration graphs I can find the equation of the line through two given points and through one point with a given gradient I can sketch and interpret a linear, quadratic and cubic graph I can solve equations by trial and improvement with integer and non-integer solutions I can solve simultaneous equations graphically, by elimination and by substitution I can simplify surds in algebraic expressions I can solve a quadratic equation from a graph I can factorise a quadratic equation where the coefficient of x 2 is greater than 1 I can solve linear and quadratic simultaneous equations graphically and algebraically including forming equations and interpreting the solution I can sketch and interpret a reciprocal and exponential graph and solve a quadratic equation by completing the square I can solve an equation with fractional coefficients and variables on both sides I can use the curve of a function to solve an equation and I can find turning points and roots of a quadratic graph I can change the subject of a formula I can plot and recognise a linear, quadratic, cubic, reciprocal and exponential graph I can match graphs and equations using the properties of each graph and state turning points and roots of each graph I can factorise and solve a quadratic equation algebraically for coefficient of x 2 is equal to and greater than 1 I can solve a cubic equation I can interpret kinematic graphs and plot and use reciprocal and trigonometric graphs I can use SUVAT equations to problem solve I can use function notation and find composite functions and inverse functions I can understand the effect of translating, stretching and reflecting on the function of a graph I can sketch and interpret trigonometric graphs of y = sin x, y = cos x and y = tan x I can solve a quadratic equation by using the quadratic formula Ratio & Proportion I can explain what a percentage is I can simplify ratio, use ratio notation, express a ratio as a fraction and use unitised ratio form I can use map ratios I can change between units of time and metric units I can express a relationship in a ratio, and turn fractions into ratios I can use compound units for speed calculations, rates of pay, unit pricing, density and pressure I can calculate a percentage of an amount - Non Calc I can divide a quantity into a given ratio I can use a ratio table and calculate best value I can change between imperial and metric units I can solve best buy problems I can calculate a percentage of an amount and find simple interest I can find a fraction of an amount and express one quantity as a fraction of another I can express the division of an amount into a ratio and can use proportion in context I can use and interpret conversion graphs I can enlarge a shape by a given scale factor and calculate the scale factor of an enlargement I can apply scale factors to scale drawings and develop understanding of scale factors in the context of maps I can calculate compound interest I can write an amount as a percentage of another and express a quantity as a fraction of another

3 Ratio & P Geometry & Measures I can convert between fractions, decimals and percentages I can convert between lengths and volume/ capacity units I can understand the gradient of conversion graphs I can express absolute increase/decrease in a quantity as a fraction I can use ratio and proportion to solve problems I can calculate a percentage increase and decrease I can use the density formulae I can explain exponential growth I can use compound units in algebraic contexts I can find compound interest, reverse percentages and an amount after repeated percentage changes I can set up, solve and interpret the answers in growth and decay problems incl compound interest I can interpret the gradient of a straight line graph as a rate of change I can explain exponential decay I can evaluate indices using fractions and negatives I can use scale factors for length to solve problems for area and volume I can use proof with similarity I can use direct and inverse proportion to solve problems including the use and interpretation of graphs I can solve quadratic equations using an iterative process I can solve cubic equations using an iterative process Geometry & Measures I can measure different types of units and convert between metric units I can tell the time, convert between 12 and 24 hour and calculate amount of time elapsed I can understand compass directions and draw and measure angles accurately I can recognise acute, obtuse, reflex and vertically opposite angles I can use angles on a straight line, angles around a point, and angles in a triangle I can recognise and calculate the perimeter and area for triangles, quadrilaterals and compound shapes I can find lines of symmetry and order of rotational symmetry I can use the notation of points and line and recognise parallel and perpendicular lines I can recognise and use regular polygons and demonstrate tessellation I can label parts of a circle and recognise the hypotenuse in right angles triangles I can plot points in all 4 quadrants I can convert between metric and imperial units I can calculate missing angles in a quadrilateral I can recognise cubes and cuboids and I can recognise faces, edges, vertices and nets of 3D shapes I can use reflection, translate a shape, rotate a shape and use rotational symmetry I can recognise and apply properties of quadrilaterals I can problem solve with area and perimeter I can find missing angles in a triangle, quadrilateral and an isosceles triangle I can find the perimeter of a triangle and calculate the volume of a cube and cuboid I can convert between units for capacity I can use the sum of the interior angles and the sum of the exterior angles in a polygon I can justify whether two shapes will tessellate I can use a scale factor to enlarge a shape, find the centre of enlargement and find the scale factor of an enlargement I can construct triangles, a perpendicular bisector, an angle bisector and a bisector from a point I can recognise angle sums and exterior angles of triangles including proofs I can recognise congruent shapes using sides and angle notation I can calculate the area and circumference of circles I can find similar sides using enlargement I can enlarge a shape using positive, negative and fractional scales factors I can find the area of a triangle and the perimeter of a trapezia I can find the radius of a circle given the circumference I can recognise the rules for trigonometry and identify the different parts of a triangle used in trigonometry I can construct a loci I can identify the midpoint of a line I can use properties of triangles in quadrilaterals with problem solving I can calculate the circumference given the radius and the area given the diameter of a circle incl problem solving can draw and describe a translation, a reflection, a rotation and an enlargement I can calculate the area and perimeter of compound shapes including circles I can formulate a proof of congruency or similarity using properties I can identify the properties of the faces, surfaces, edges and vertices of cubes and cuboids I can draw the plan, side and front elevation of a 3D solid and can draw a 3D solid from plans and elevations I can read and interpret maps including scales and use and interpret 3 figure bearings I can use scale drawings and bearings I can prove interior and exterior sum expressions I can problem solve with loci I can understand property angles in parallel lines and complementary and supplementary angles

4 Probability I can identify the properties of the faces, surfaces, edges and vertices of prisms, cylinders, pyramids, cones and spheres I can use similar triangles to work out lengths in real life I can identify the midpoint of a line in 3d I can prove two shapes are congruent I can use a compass, ruler and protractor to construct a triangle I can find the volume of any prism given its cross-section incl triangular and trapezoidal prisms and cylinders I can identify and recall the trigonometric ratios I can apply Pythagoras Theorem to find a missing side of a right angled triangle and problems involving quadrilaterals and triangles I can calculate the volume and surface area of prisms, cones, pyramids, cylinders and spheres I can find heights and radius of shapes in exact form using Pi I can calculate arc length, the angle of a scetor and the area of a sector I can use the link between linear scale factor and area scale factor to solve problems I can use trigonometry to find a missing angle and a missing side in a right angled triangle I can solve elevation and depression problems I can describe a translation using a vector and I can add, subtract and multiply vectors using a scalar I can use vectors in geometry and with the origin, I can find the midpoint of a route and use vectors with proof I know the exact values of sin Ɵ and cos Ɵ for Ɵ = 0 0, 30 0, 45 0, 60 0 and 90 0 I know the exact values of tan Ɵ for Ɵ = 0 0, 30 0, 45 0, and 60 0 I can use the links between scale factors for length, area and volume to solve problems I can use trigonometry the sine and cosine rule with non-right angled triangles I can solve problems involving circle theorems Probability I can express the chance of an event and list outcomes of an event I can calculate the probability of an event and state a probability I can calculate relative frequency I can draw and use Venn diagrams I can calculate the probability of an event from a sample space and tree diagram I can draw and use sample space diagram s I can recall how to calculate the probability of a single event and I can use the sum to one for probability I can compare relative frequency and probability I can use and interpret the probability of an event I can use and interpret relative frequency I can use the probability of not I can describe sets I can state the outcome of experiments I can recall how to multiply two fractions I can calculate the expected results for experimental and theoretical probabilities I can compare relative frequency and theoretical probability I can calculate probability of an event which can happen more than once I can apply randomness to expected outcomes I can compare real results with theoretical expected values to decide if a game is fair I can use set notation including union and intersection I can draw and use tree diagrams I can find the probability of 2 independent events I can understand that unbiased samples tend towards theoretical probability distributions I can use conditional probability I can start to use probability trees to calculate probability I can construct a tree diagram to solve a probability problem can use and/ or rules for independent and dependent events Statistics I can collect and represent data using a table I can draw, use and interpret a bar chart I can draw, use and interpret a pictogram I can group information using a tally chart/frequency table I can display grouped data in a bar chart I can draw, use, read and interpret pie charts I can understand the difference between discrete and continuous data I can recognise mean median and mode are types of averages I can understand bias and random samples I can read and draw comparative pie charts I can analyse and select the correct method of displaying data I can understand the concept of a population when collecting/analysing data I can calculate the range, mode, median and mean from a set of data I can draw and interpret a scatter graph I can present statistical data graphically using a stem and leaf diagram I can understand the advantages and drawbacks of each type of average

5 Statistics I can understand the effects of outliers on choosing which measure to choose I can calculate the mean and median from a frequency table I can intepret a scatter graph and draw and use a line of best fit I can draw and interpret a frequency polygon I can compare populations using summary statistics I can draw a boxplot I can use the mean and range to compare two distributions I can draw bar charts for continuous data and I can draw and interpret frequency tables for continuous data I can apply skills and criticise questionnaires and secondary data (census) I can use a scatter diagram to predict values I can intepret a boxplot I can understand the meaning of bivariate data I can understand how to compare 2 sets of data I can draw a cumulative frequency curve I can construct and interpret cumulative frequency graphs and know their appropriate use I can tell the difference between random and stratified sampling and recognise the advantages and disadvantages of both I can find summary statistics from a cumulative frequency curve I can draw and interpret box plots for continuous and grouped data I can use appropriate measures of central tendancy and spread including inter-quartile range Can interpret, analyse and compare the distribution of data sets using MMMR and IQR I can construct and interpret histograms with equal class intervals and know their appropriate use I can draw and interpret tables and line graphs for time series data I can use and understand the terms interpolation and extrapolation I can construct and interpret histograms with unequal class intervals and know their appropriate use Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9