Why do we learn maths?
At Franklin, our mathematics curriculum is designed to ensure that every pupil builds competence, confidence and curiosity in Mathematics and experiences a guarantee of long-term learning. Ark Franklin utilises the Maths Mastery curriculum as the foundation of this work which is then adapted to fit with our wider curriculum vision and the needs of our cohort. Our curriculum is anchored in the following principles:
- Sequencing and content for long-term learning
- Problem-solving skills built on proficiency
- Prioritising core knowledge in younger year groups
- Building a foundation for future learning
Our approach
We use a concrete, pictorial and abstract (CPA) approach giving pupils the opportunity to ‘master maths’ - acquiring a deep, long-term, secure understanding in range of topics within the subject. ‘Conceptual understanding’, ‘Mathematical thinking’ and ‘Language and communication’ are continuously embedded and sequentially built upon, allowing children to progress year-on-year. Lessons from Reception to Year 6 follow a familiar 6-part sequence so that children feel comfortable in maths and know what to expect taking fear away from mathematics and enabling children to thrive.
We know that the way children talk about their learning is a vital element in the retention of knowledge and so children are deliberately taught to use mathematical language to articulate concepts and connections. Every maths lesson from nursery to year 6 includes Talk Tasks to enable children to explain and reason orally and bring clarity to their own learning. Children are challenged to think mathematically during the reasoning element of each lesson so that children are challenged to develop deep understanding of concepts answering questions such as ‘Why is this wrong? Describe the pattern. What is the same, what is different?’
Each year group at Franklin has at least two Maths Meetings per week. Our Maths Meetings play a crucial role in developing pupils' mathematical fluency and confidence while ensuring that key knowledge remains accessible and well-practiced.
Year 1
| Place value |
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Count to and across 100 from any given number. |
| Addition & Subtraction | Multiplication & Division |
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Read, write and interpret mathematical statements involving addition, subtraction and equal signs. Add and subtraction within 100. |
Solve one step problems involving multiplication and division using concrete objects, pictorial and arrays. Double numbers within 20. Finding fractions of an object and number. Counting 2,5 and 10. Recognise odd and even numbers. |
| Fractions, percentages and decimals |
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| Recognise, find and name a half one of two equal parts of an object, shape or quantity. Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity. |
| Measurement, time and money |
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Compare, describe and solve practical problems for length, heigh, mass/weight and capacity. |
| Shape and Geometry |
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Recognise and name 2D and 3D shapes. Properties of 2D and 3D shapes e.g vertices, edges and faces. Sort and compare shapes. Describe, complete and create patterns using shapes. Describe position, direction and movement including whole, half, quarter, and three-quarter turns. Use positional language such as left, right, above, between, in front of. |
| Statistics |
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Interpret and construct simple pictograms, tally charts, block diagrams and simple tables. Answer simple questions by counting and sorting objects in categories. Counting and sorting objects |
Year 2
| Place value |
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| Count forwards and backwards across 100 from any given number. Count in multiples of 2,3, 5 and 10 forward and backwards. Compare and order number using ><= Read and write numbers to 100 in numerals and words To use place value and number facts to solve problems To recognise the place value of each digit in a 3 digit number. Compare and order numbers up to 1,000 |
| Addition & Subtraction | Multiplication & Division |
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| Solve addition and subtraction problem using concrete and pictorial manipulatives. Recall and use addition and subtraction facts to 20 and 100. Add 2 digit numbers and ones and tens. Add 2 two digit numbers and 3 one digit numbers. To use commutativity to solve equations. To use the inverse to check calculations and solve missing number problems. |
Count in multiples of 2,3, 5 and 10 forward and backwards. Recognise odd and even numbers. Recognise the multiplication and division symbol and solve problems using concrete objects, pictorial and arrays. |
| Fractions, percentages and decimals |
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| Recognise, name and write fractions of a length, shape, objects and quantity. Write simple fractions Recognise equivalent fractions |
| Measurement, time and money |
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Measure length (m/cm); mass (kg/g) and volume/capacity (l/ml).
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| Shape and Geometry |
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Identify and describe 2D and 3D shapes. Describe position, direction and movement including movement in a straight line and rotation (clockwise and anticlockwise ½ and ¾ turns). |
| Statistics |
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| Interpret and construct simple pictograms, tally charts, block diagrams and simple tables. Answer simple questions by counting, sorting, totalling, and comparing objects in categories. |
Year 3
| Place value |
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| Count from 0 in of 4, 8, 50 and 100; find 10 or 100 more or less than a given number Recognise the place value of each digit in a 3-digit number (100s, 10s, 1s) Read, write, compare and order numbers up to 1,000 in words and numerals Identify, represent and estimate numbers using different representations Solve number problems and practical problems involving these ideas |
| Addition & Subtraction | Multiplication & Division |
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Add and subtract numbers mentally, including:
Add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction |
Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects |
| Fractions, percentages and decimals |
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| Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10 Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators Recognise and show, using diagrams, equivalent fractions with small denominators add and subtract fractions with the same denominator within one whole 5/7 + 1/7 = 6/7 Compare and order unit fractions (when the numerator is 1), and fractions with the same denominators Solve problems that involve all of the above |
| Measurement, time and money |
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Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml) Learn to use and read a ruler Measure the perimeter of simple 2-D shapes Add and subtract amounts of money to give change, using both £ and p in practical contexts Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o’clock, am/pm, morning, afternoon, noon and midnight Know the number of seconds in a minute and the number of days in each month, year and leap year Compare durations of events (for example, to calculate the time taken by particular events or tasks) |
| Shape and Geometry |
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Make 2-D and 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them Recognise angles as a property of shape or a description of a turn Identify right angles, recognise that 2 right angles make a half-turn, 3 make three-quarters of a turn and 4 a complete turn; identify whether angles are greater than or less than a right angle Identify horizontal and vertical lines and pairs of perpendicular and parallel lines |
| Statistics |
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Interpret and present data using bar charts, pictograms and tables Solve one-step and two-step questions (for example ‘How many more?’ and ‘How many fewer?’) using information presented in scaled bar charts and pictograms and tables |
Year 4
| Place value |
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| Count in multiples of 6, 7, 9, 25 and 1,000 Find 1,000 more or less than a given number Count backwards through 0 to include negative numbers Recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s) Order and compare numbers beyond 1,000 Identify, represent and estimate numbers using different representations Round any number to the nearest 10, 100 or 1,000 Solve number and practical problems Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place value |
| Addition & Subtraction | Multiplication & Division |
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Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate Estimate and use inverse operations to check answers to a calculation Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why |
Recall multiplication and division facts for multiplication tables up to 12 × 12 Use place value, known and derived facts (5x 4 =20 so 6 x 4 = 24) to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers ( 3 x 4 x 2) Recognise and use factor pairs (3 & 5 for 15) and commutativity (2 x 3 = 6, 3 x 2 = 6) in mental calculations Multiply two-digit and three-digit numbers by a one-digit number using formal written layout Solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects |
| Fractions, percentages and decimals |
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Recognise and show, using diagrams, families of common equivalent fractions Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10 Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number Recognise and write decimal equivalents of any number of tenths or hundreds Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths Round decimals with 1 decimal place to the nearest whole number Compare numbers with the same number of decimal places up to 2 decimal places Solve simple measure and money problems involving fractions and decimals to 2 decimal places |
| Measurement, time and money |
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| Convert between different units of measure (for example, kilometre to metre; hour to minute) Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres Find the area of rectilinear shapes by counting squares Estimate, compare, and calculate different measures, Estimate, compare and calculate different measures, including money in pounds and pence Read, write and convert time between analogue and digital 12- and 24-hour clocks Solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days |
| Shape and Geometry |
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Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes Describe positions on a 2-D grid as coordinates in the first quadrant |
| Statistics |
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Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables, and other graphs |
Year 5
| Place value |
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| Read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000 Interpret negative numbers in contexts (like thermometers), count forwards and backwards with positive and negative whole numbers, including through 0 Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 Solve number and practical problems Read Roman numerals to 1,000 (M) and recognise years written in Roman numerals |
| Addition & Subtraction | Multiplication & Division |
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Add and subtract whole numbers with more than 4 digits, including using formal written methods Add and subtract numbers mentally with increasingly large numbers Use rounding to check answers to calculations and determine if the answer is accurate. Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why |
Identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers Establish whether a number up to 100 is prime and recall prime numbers up to 19 Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers Multiply and divide numbers mentally, drawing upon known facts divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context Multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000 Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³) Solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates |
| Fractions, percentages and decimals |
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| Compare and order fractions whose denominators are all multiples of the same number Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [ 2/5 + 4/5 = 6/5 = 1 1/5 Add and subtract fractions with the same denominator, and denominators that are multiples of the same number Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams Read and write decimal numbers as fractions [for example, 0.71 = 71/100 ] Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents Round decimals with 2 decimal places to the nearest whole number and to 1 decimal place Read, write, order and compare numbers with up to 3 decimal places Solve problems involving number up to 3 decimal places Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fraction solve problems which require knowing percentage and decimal equivalents of 1/2 , 1/4 , 1/5 , 2/5 , 4/5 and those fractions with a denominator of a multiple of 10 or 25 |
| Measurement, time and money |
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| Convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre) Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres Calculate and compare the area of rectangles (including squares), including using standard units, square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapes Estimate volume (for example, using 1 cm³ blocks to build cuboids) and capacity Solve problems involving converting between units of time Use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling |
| Shape and Geometry |
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Identify 3-D shapes, including cubes and other cuboids, from 2-D representation
Use the properties of rectangles to deduce related facts and find missing lengths and angles Identify, describe, and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed |
| Statistics |
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Solve comparison, sum and difference problems using information presented in a line graph Complete, read and interpret information in tables, including timetables |
Year 6
| Place value |
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Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit Round any whole number to a required degree of accuracy Use negative numbers in context, and calculate intervals across 0 Solve number and practical problems |
| Addition & Subtraction | Multiplication & Division |
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| Perform mental calculations, including with mixed operations and large numbers Use knowledge of the order of operations to carry out calculations involving the 4 operations Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why Solve problems involving addition and subtraction Use estimation to check answers to calculations and determine accuracy |
Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context Perform mental calculations, including with mixed operations and large numbers identify common factors, common multiples and prime numbers Solve problems involving, multiplication and division |
| Fractions, percentages and decimals |
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Use common factors to simplify fractions; use common multiples to express fractions in the same denomination Use written division methods in cases where the answer has up to 2 decimal places |
| Measurement, time and money |
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| Solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3 decimal places (5.425L) Convert between miles and kilometres Recognise that shapes with the same areas can have different perimeters and vice versa Recognise when it is possible to use formulae for area and volume of shapes Calculate the area of parallelograms and triangles Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units (for example, mm³ and km³) |
| Shape and Geometry |
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Draw 2-D shapes using given dimensions and angles Describe positions on the full coordinate grid (all 4 quadrants) Draw and translate simple shapes on the coordinate plane, and reflect them in the axes |
| Statistics |
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| Interpret and construct pie charts and line graphs and use these to solve problems Calculate and interpret the mean as an average |
| Algebra |
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| Use simple formulae Generate and describe linear number sequences Express missing number problems algebraically Find pairs of numbers that satisfy an equation with 2 unknowns Enumerate (work out) possibilities of combinations of 2 variables |
| Ratio and Proportion |
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| Solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts Solve problems involving the calculation of percentages (for example, of measures and such as 15% of 360) and the use of percentages for comparison Solve problems involving similar shapes where the scale factor is known or can be found Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples |