TPS1 | TPS2 | TPS3 | TPS4 | TPS5 | TPS6 | |
Number | Read, write & order numbers to 1000.
Read & write whole numbers to 10 million. Use < & > to compare whole numbers. Multiply & divide mentally drawing upon known facts. Count backwards & forwards in whole numbers through zero. Recognise factor pairs. Order fractions of the same denominator. |
Round whole numbers to the nearest 10, 100 or 1000.
Add & subtract whole numbers with more than 4 digits. Multiply 2 digit by one & two digit numbers using a formal write method. Divide numbers up to 4 digits by a single digit using a formal written method of short division. Recognise negative numbers in context Solve two step problems using different operations. Recognise square numbers. Recognise factor pairs. Recognise equivalent fractions. Order fractions of different denominators. Change mixed numbers to improper fractions & vice versa. |
Round numbers to powers of 10.
Use all four operations with positive integers & decimals. Multiply & divide by powers of 10. Round to a given number of decimal places. Estimate answers by rounding to 1 significant figure. Solve problems involving money Use a calculator. Order directed numbers. Use all four operations with directed numbers. Use the order of operations BIDMAS. Recall square & cube numbers & their roots. Determine prime numbers. Find factors, multiple & prime factors. Identify HCF & LCM. Prime factorization. Add & subtract fractions including mixed numbers. Find fractions of amounts. |
Round to a given number of decimal places.
Round to a given number of significant figures. Read numbers of any form written in standard from. Write numbers of any form in Standard Form. Use efficient methods to apply the four operations to calculations with decimals. Multiple & divide by 0.1 & 0.01. Use a calculator, interpreting a sensible degree of accuracy. Use BIDMAS with negative values, indices & roots. Use prime factorisation. Use index notation x^{0}, x^{1}, x^{n} with whole numbers. Use Venn Diagrams to find HCF & LCMs Multiply & divide proper fractions. |
Write numbers in terms of their factors, LCM, and HCF. Write ordinary numbers in standard form and vice versa. Round numbers to 1 significant figure and perform estimations and approximations. Work out upper and lower bounds of given quantities. Multiply and divide fractions and mixed numbers. Apply the laws of indices. Simplify surds. | Round numbers to given degree of accuracy.
Work out problems involving upper and lower bounds. Change fractions to decimals and write them in order of size. Add, subtract, multiply, and divide decimals and solve word problems. Convert recurring decimals into fractions using algebra. Efficiently to answer mathematical problems. |
Algebra | Recognise that different symbols & letters can be used to represent variables & unknowns.
Find missing numbers, lengths, co-ordinates & angles. Solve number puzzles e.g. what two different even numbers add up to 12, a + b = 12. Describe & continue number sequences. |
Express missing number problems algebraically.
Recognise equivalent expressions e.g. a+b = b+a. Complete function machines & work inversely. Recognise algebraic notation. Substitute positive values into simple formulae. Substitute positive & negative values into expressions. Find pairs of numbers that satisfy an equation with two unknowns. Solve one-step equations. Generate terms of a sequences from a term-to-term rule. Generate terms of a sequence from a position-to-term rule. |
Change the subject of a formula.
Derive algebraic formulae and plot them on a graph. Work out the gradient of a straight-line graph. Draw quadratic and cubic graphs from a table of values. Expand double brackets. Factorise algebraic expressions with double brackets. Solve linear equations which involve brackets and fractions. Solve simultaneous equations with one of the variables having equal coefficients. Solve inequalities. work out the nth term of an arithmetic sequence. |
Identify & use expression, equation, formula & identity.
Simplify expressions involving indices & brackets. Use the laws of indices. Explore powers of powers. Substitute & simplify algebraic fractions. Expand & factorise a single bracket. Expand two or more binomials. Plot graphs y = n, x = n, y = nx, y = x + n, y = mx + c. Work out position to term rules of sequences. Recognise geometric sequences & special sequences. |
Change the subject of a formula.
Derive algebraic formulae and plot them on a graph. Work out the gradient of a straight-line graph. Draw quadratic and cubic graphs from a table of values. Expand double brackets. Factorise algebraic expressions with double brackets. Solve linear equations which involve brackets and fractions. Solve simultaneous equations with one of the variables having equal coefficients. Solve inequalities work out the nth term of an arithmetic sequence. |
Write down equations of straight lines parallel and perpendicular to a given line.
Solve simultaneous equations with both variables having unequal coefficients. Work out the nth term of quadratic sequences. Work out terms of a recursive sequence |
Geometry and Measures | Convert between different units of metric measures.
Calculate area of rectangles using cm^{2 }. Estimate area of irregular shapes. Estimate volume by counting cm^{3} or other cubes. Identify 3D shapes from 2D representations. Know angles are measured in degrees Estimate & compare acute, obtuse & reflex angles. Draw angles & measure them in degrees. draw the plan, front, and side elevation of 3D shapes. |
Measure & calculate the perimeter of composite rectilinear shapes.
Calculate the volume of cuboids. Distinguish between regular & irregular polygons based upon reasoning about equal lengths & sides. Identify, describe & represent the position of a shape following a reflecting or translation. Recognise that the shape has not changed after a reflection or translation. Describe co-ordinate positions in all four quadrants. Reflect simple shapes on & away from the mirror line. Identify angles at point total 360°(whole turn). Identify angles on a straight line total 180° (½ turn). |
Work out interior and exterior angles in a polygon.
Calculate the arc length and area of a sector. Solve problems that involve bearings and parallel line. Perform and specify translations, rotations, reflections of 2D shape.s enlarge a 2D shape with a centre of enlargement. Calculate the surface area and volume of a prism. |
Recognise & use geometric notation.
Find the area of a trapezium. Calculate the circumference of a circle. Find the area of a circle. Calculate the area of compound shapes. Find the surface area of cuboids & cylinders. Explore the properties of the diagonals of quadrilaterals. Enlarge simple shape by scale factors. Reflect shapes in a given line. Rotate points about a given point. Calculate & give reasons for angles in parallel lines. Know simple angle proofs. Find & prove simple geometric proofs. |
Work out interior and exterior angles in a polygon.
Calculate the arc length and area of a sector. Solve problems that involve bearings and parallel line. Perform and specify translations, rotations, reflections of 2D shapes Enlarge a 2D shape with a centre of enlargement. Calculate the surface area and volume of a prism. |
Convert metric units including those of area and volume.
Work out problems involving angle facts. show that two triangles are congruent using SAS, SSS, RHS, or ASA. Enlarge 2D shapes with a negative scale factor. Solve problems that involve similar shapes. Construct triangles. Solve loci problems. Solve problems that involve Pythagoras’ Theorem. Use Trigonometry to calculate acute angles of right- angled triangles. |
Handling Data and Statistics | Use tally charts to collect data.
draw pictograms to represent statistical data. draw bar charts & vertical line charts to represent statistical data. Solve comparison sum & difference. problems use line graphs & bar charts Recognise the mode & range of a set of data. Use the language of probability Draw a describe a probability line. |
Solve comparison sum & difference. problems use line graphs & bar charts Recognise the median of a set of data. Place events accurately on a probability line. Sort objects & numbers in a Venn Diagram. |
Calculate the mean from grouped data.
Interpret scatter graphs and describe correlation. Draw cumulative frequency curves and estimate quartiles from them. Draw box plots. Estimate quartiles from box plots and describe their distribution. Represent probabilities on a tree diagram. Calculate probabilities from tree diagrams. |
Organise data into the following: categorical data, discrete data, continuous data.
Compare & interpret multiple & composite bar charts. Draw frequency polygons and interpret them. Calculate missing values with mean, median & mode Construct & interpret frequency tables using grouped & ungrouped data. Find the mean from an ungrouped frequency table. Read from two-way tables. Calculate the probability of equally likely outcomes. Use sample space diagrams for more than one event. Use simple probability trees. |
Calculate the mean from grouped data.
Interpret scatter graphs and describe correlation. Draw cumulative frequency curves and estimate quartiles from them. Draw box plots. Estimate quartiles from box plots and describe their distribution. Represent probabilities on a tree diagram. Calculate probabilities from tree diagrams. |
Interpret, analyse, and deduce conclusions from time series graphs.
Compare the distribution of two box plots. Draw histograms and interpret them. Calculate the probability of two independent events. Calculate experimental probabilities. Draw Venn diagrams and calculate probabilities from them. |
Ratio and Proportion | Read & write decimal numbers as fractions.
Recognise the % symbol & understand that per cent relates to ‘a number of parts per hundred’. Write % as fractions with denominator of 100. Convert between metric units e.g. km to m, m to cm, cm to mm, g to kg, l to ml. Convert between units of time e.g. how many seconds in two minutes? |
Write % as decimals
Solve problems which require knowing % equivalents of ½, ¼, ,⅕ Know % equivalents of fractions with a denominator of 10 or 25. Convert between units of time e.g. how many seconds in two minutes? Complete diagrams to represent statements such as ‘for every blue square there are 3 red squares’ and explore different representations of this, including multiples. |
Work out percentage increase and percentage decrease.
Solve problems involving ratio. Share a quantity in a given ratio and solve problems. Use direct proportion to answer best buy problems. calculate compound measures (speed, density, and pressure). |
Express one number as a fraction of another.
Explore calculator & non-calculator methods of interchanging fractions & decimals. Find percentage increase & decrease. Use multipliers. Express one quantity as a % of another. Compare quantities using %. Understand and use scale factors in scale diagram and maps. Construct and interpret conversion graphs and currency graphs. Recognise similar shapes. Understand and recognise ratio notation. Divide into a ratio. Work out parts and whole. Use the unitary method to solve problems. Solve problems with compound measures – speed. |
Work out percentage increase and percentage decrease.
Solve problems involving ratio. Share a quantity in a given ratio and solve problems. Use direct proportion to answer best buy problems. calculate compound measures (speed, density, and pressure). |
Work out problems that involve a fraction of a quantity.
Use fractions, decimals, and percentages to describe proportions. Work out problems using reverse percentages. Work out compound interest and depreciation question. Solve problems that involve the application of direct proportion. Interpret and deduce conclusions from distance time graphs. Use maps and scale drawings to represent real life distances. Read and interpret real life graphs. |