 # Maths

We are determined to equip the pupils of St Thomas’ with a uniquely powerful set of tools to understand and change the world. These tools include logical reasoning, problem solving skills and the ability to think in abstract ways. We recognise that mathematics is integral to all aspects of life and with this in mind; we endeavour to ensure that our children develop a positive and enthusiastic attitude towards mathematics that will stay with them.

We use the National Curriculum for Mathematics as the basis of our mathematics programme. We are committed to ensuring that all pupils achieve mastery in the key concepts of mathematics, appropriate for their age group, in order that they make genuine progress and avoid gaps in their understanding that provide barriers to learning as they move through their education.

Research around metacognition underpins our mathematical teaching in school. Teachers use precise questioning in class to test conceptual and procedural knowledge and effective modelling of concepts allows our children to view the workings and thinking of the master at work. Children are then given adequate time to practice concepts with scaffolds and supports being withdrawn to ensure the children have opportunity to grapple with new learning in order for it to be committed to long term memory eventually.

A detailed, structured curriculum is mapped out across all phases, ensuring continuity and supporting transition. Effective mastery curricula in mathematics are designed in relatively small carefully sequenced steps, which must each be mastered before pupils move to the next stage. Fundamental skills and knowledge are secured first. This often entails focusing on curriculum content in considerable depth at early stages.

As a school, we are passionate about children acquiring the basic skills of mathematics that will be valuable to them as they move on to further education and beyond.

Reception

 Autumn Spring Summer In Number we will be learning: To use some number names and number language spontaneously. To use some number names accurately in play. To recite numbers in order to 10. To being to represent numbers using fingers, marks on the page or pictures. To sometimes match numeral and quantity correctly. To show an interest in representing numbers. To show an interest in numerals in the environment.   In Shape, Space and Measure we will be learning: 2D shape names and properties. We will look for shapes in our environment and show an interest in shapes by playing with them. To being to talk about the shapes of everyday objects e.g ‘round’ and ‘tall’. To make patterns. To measure using non-standard units To have a sense of time. To identify and write numbers up to 10. To add groups of objects. To find one more and one less than a given number. The names and properties of 3D shapes. Positional language. To understand, recognise and use money. To halve and double. To solve simple addition and subtraction sums using numbers to 20. To apply our knowledge to problem solving.

Year 1

 Autumn Spring Summer Counting and representing numbers to 20 and beyond Addition and subtraction using numbers to 20 and beyond Doubling numbers Recognising and naming some 2D shapes Identifying one more and one less when given a number Knowing and using number bonds to 10 including subtraction facts Using the language of, equal to, more than, less than etc. Counting on and back to 100 Forming numbers correctly Counting in 2s, 5s and 10s Position and direction; length Addition and subtraction using money Estimation Knowing simple directions; right, left, forwards and backwards Showing whole, ½, ¼ and ¾ turns. Measuring and beginning to record length and height Using objects to work out missing numbers Partitioning numbers into Tens and Ones Finding half of an amount and shape Comparing, describing and solving practical problems for measurements of length and time Saying the number one more or less and two more or less using a number line or a 100 grid, writing and saying 2-digit numbers and understanding them as some tens and some ones Recalling number facts and using these to solve simple word problems Using known number facts to add and subtract Naming and identifying 3D shapes and their properties Counting in 2s, 5s and 10s and identifying patterns Telling the time to the nearest half hour Addition and subtraction; counting on and back, sometimes crossing 10. Understanding place value in two digit numbers and then in relation to money Forming numbers correctly Rehearsing the days of the week and months of the year Estimating a number of objects within a range and counting by grouping into 10s or 5s Finding half, quarter and three quarters of shapes Developing an understanding of how long a minute, hour, day, week, etc. are Consolidating understanding of 2-digit numbers, representing these in different ways, and partitioning into 10s and 1s Revision of number facts and using these to solve additions and subtractions involving 1- and 2-digit numbers to 100 Doubling and halving numbers Recognising halves and quarters of shapes. Rehearsing place value in 2-digit numbers Identifying and exploring patterns in multiples of 2, 5 and 10. Relating counting in 2s to doubling and halving Recognise, find and name ½, ¼ of shapes, objects or quantities Telling the time to the quarter hour Comparing and using uniform non-standard units to measure weight and capacity; information is recorded in block graphs for ease and clarity Measuring lengths and heights, mass/weight, capacity and volume. Recording information in pictograms and block graphs Creating repeating patterns using 2D shapes Recognising and using pounds and pence; solving money problems

Year 2

Year 3

Year 4

 Autumn Spring Summer Recall all times tables to 12 x 12 and their linked division facts.  Mentally work with factor pairs 144. Count in multiples of 6, 7, 9, 25, 1000 Order and compare numbers beyond 1000, recognise place value in 4 digit numbers. To round any number to the nearest 10, 100 or 1000. Use the column method when adding or subtracting numbers with up to 4 digits. Solve two-step problems using the 4 main operations. Learn to count back through 0 to include negative numbers. When multiplying 2 or 3-digit numbers by 1-digit, use formal written methods (grid and ladder). When dividing 2 or 3-digit numbers by 1-digit, use formal written methods (chunking method) Divide a 1 or 2-digit number by 10 or 100 to create a decimal number. Identify the value of the digits in the answer. Find the area of straight-sided shapes using your knowledge of multiplication. Relating fraction notation to division. Find common equivalent fractions. Dividing a 1 or 2-digit number by 10 or 100 to create a decimal number. Identify the value of the digits in the answer. Counting up/down in hundredths, know that 1/100 is the same as 1/10/10. Recognising and showing, using diagrams, families of common equivalent fractions. Rounding decimals with one decimal place to the nearest whole number. Compare and order numbers with up to two decimal places. Recognising and writing decimal equivalents to ¼, ½, ¾ and any number of tenths and hundredths. Solve problems that involve converting between different units of measure, including money and time to two decimal places. Find the area of straight-sided shapes by counting squares. Measure and calculate perimeters in centimetres and metres. Identify and compare the sizes of acute and obtuse angles. Identify lines of symmetry in 2D shapes in different orientations. Complete drawings. Compare and classify geometric shapes, including quadrilaterals and triangles based on properties and sizes. Plot specified points and draw sides to complete a given polygon. Describe positions as coordinates in the first quadrant. Describe simple translation. Interpret and present discrete and continuous data in various ways, including bar charts and time graphs. Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs. Consolidate knowledge of the four operations and the different methods we can use.

Year 5

 Autumn Spring Summer Consolidating methods of calculation and considering the most effective methods. Developing reasoning skills in order to explain mathematical work. Using accurate mathematical vocabulary.   Reading, writing and ordering numbers up to 1,000,000 and know the value of each digit. Counting forwards and backwards in steps of 100, 1000, 10,000 to 1,000,000 from any number. Being able to count forwards and backwards through zero and use negative numbers in simple calculations. Solving multi-step problems, choosing the correct operations and explain your methods. Solving problems that involve converting between units of time. Understanding the terms: factor, factor pairs, prime and multiple. Using times tables and related division facts. Comparing and ordering fractions where denominators are multiples of the same number. Finding equivalent fractions. Using understanding of place value to multiply and divide whole and decimal numbers by 10, 100 and 1000. Using formal written methods to multiply up to 4 digits by 1 digit numbers. Using short division to divide up to 4-digit by 1-digit numbers, explaining remainders. Drawing and measuring angles in degrees. Estimating and comparing obtuse, acute and reflex angles. Understanding composite shapes. Knowing that 360 is a whole turn. Rounding any number up to 1,000,000 to the nearest 10, 100, 1000, 10,000, 100,000. Rounding including decimals with two decimal places to the nearest whole number and also to one decimal place. Practising to mentally add and subtract large numbers (10,000). Ordering whole numbers up to six digits and decimals with up to three decimal places. Using formal written methods, multiply up to 4 digits by both one and two digit numbers. Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates. Using times tables and related division facts. Comparing and ordering fractions where denominators are multiples of the same number. Finding equivalent fractions. Using understanding of place value to multiply and divide whole and decimal numbers by 10, 100 and 1000. Using short division, divide up to four digits by one digit and be able to explain any remainders. Compare/order fractions where denominators are multiples of the same number.  Find equivalent fractions. Recognise mixed numbers and improper fractions and be able to convert from one to the other.  Be able to add/subtract fractions with a common denominator. Use this knowledge in problem solving. Multiply proper fractions and mixed numbers by a whole number. Say, read and write decimal numbers, fractions and percentages. Use the relationship to solve problems. Say, read and write decimal fractions and related tenths, hundredths and thousandths accurately. When solving multi-step problems, choose the correct operations and explain methods. Round answers appropriately. Using formal written methods, multiply up to 4 digits by both one and two digit numbers. Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates. Solve problems that involve converting between units of time, including time lapse. Draw and measure angles in degrees. Estimate and compare acute, obtuse and reflex angles. Know that 360˚ is a whole turn. Distinguish between regular and irregular polygons based on reasoning about equal sides and angles.  Match a net to its 3D shape. Describe the position of a shape following a reflection or translation.

Year 6

 Autumn Spring Summer Reading, writing and ordering numbers to 10,000,000. Rounding numbers to any degree of accuracy. Knowing the value of each digit to 3 decimal places. Rapid recall of all times tables. Using estimation to check answers. Using long and short methods of multiplication with numbers up to four digits. Calculating differences between negative numbers. Expressing unknown numbers using symbols or letters. Generating and describing linear number sequences. Comparing fractions with different denominators. Finding fractions of amounts and simplifying fractions. Adding and subtracting fractions with different denominators. Using pictorial representation to understand and explain calculations. Using a variety of methods to show our understanding of number including ‘active maths’. Multiplying one digit numbers with up to two decimal places by whole numbers.   Multiplying pairs of fractions and writing the answer in its simplest form. Multiplying and dividing fractions by whole numbers. Recalling the facts that allow us to identify factors, multiples and prime numbers. Using long division to divide numbers with up to 4 digits.     Solving simple problems involving the calculation of percentages. Solving problems that involve converting between units of time. Converting related units of measure from smaller to larger and vice versa. Comparing and classifying geometric shapes based on their properties and sizes. Knowing that shapes with the same areas can have different perimeters. Calculating area and perimeter of parallelograms and triangles. Finding unknown angles in triangles, quadrilaterals and polygons. Solving multi-step problems by identifying steps needed. Knowing how and when to calculate the mean of a set of data. Constructing, interpreting and solving problems involving pie charts and line graphs.      Describing positions on the full coordinate grid. Translating and reflecting shapes using all four quadrants. Performing mental calculations that include large numbers and mixed operations. Reading, writing, ordering and comparing numbers and knowing the value of each digit. Solving measure problems involving decimal notation up to 3 decimal places. Matching fractions, decimals and percentages. Using both long and short methods of multiplication with numbers up to 4 digits. Using estimation to check answers to calculations. Solving multi-step problems by identifying steps needed.                  Recalling the facts that allow us to identify factors, multiples and prime numbers.                Solving simple problems involving the calculation of percentages. Naming parts of circles, including radius, diameter and circumferences. Reducing ratios to the simplest forms.

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