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## Maths

Sankey Valley St James Mathematics Guidance

Introduction

At Sankey Valley St James’ we use the National Curriculum for Mathematics (2014) as the basis of our mathematics programme. We are committed to ensuring that all pupils achieve at least age related expectations 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 education. Assessment for Learning, an emphasis on investigation, problem solving, the development of mathematical thinking and development of teacher subject knowledge are therefore essential components of our approach to this subject.

Aims

The aim of teaching mathematics is based on three key principles:

• To become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understand and the ability to recall and apply their knowledge;
• To reason mathematically by following a line of enquiry, building relationships, developing an argument and using mathematical language;
• To solve problems by applying their mathematics to a variety of routine and non-routine problems with increasingly confidence, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Maths is taught daily to children across the whole school and is usually taught in morning sessions. Throughout the school, a range of teaching styles are adopted to ensure lessons motivate, enthral and inspire our children to want to learn more. The highest standards of planning, preparation and assessment, paying particular attention to individual need, are expected from staff.

Each year group will work towards children being able to achieve a set of end of year objectives based on the new National Curriculum aims.

End of Foundation Stage Objectives

Number

Children count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.

Shape, space and measure

Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them.

End of Year 1 Objectives

Number

• Count to/across 100;
• Count on 1s, 2s, 5s, and 10s to 100;
• Know one more and one less than any numbers to 100;
• Can read and write all numbers to 20 in words and numerals;
• Use objects and pictures to represent numbers;
• Use language of comparison;
• Use +, - and = signs;
• Know number bonds to 20;
• Solve one step problems;
• Recognise and use ½ and ¼.

Measurement

• Compare, describe, measure, record and solve problems for lengths, weights, capacities/volumes and times;
• Recognise coins and notes;
• Sequence events chronologically using ordering language;
• Use language related to dates;
• Tell time to the hour and half hour.

Geometry

• Recognise and name common 2D and 3D shapes;
• Describe position, direction and movement, including ½, ¼ and ¾ turns;

End of Year 2 Objectives

Number

• Count in 2s, 3s, 5s and 10s;
• Use place value;
• Identify, represent and estimate numbers;
• Compare and order numbers 0 – 100;
• Read and write numbers to 100 in numerals and words;
• Rapid recall of all addition and subtraction facts up to 20;
• Add and subtract using concrete, pictorial and mental methods;
• Recognise and apply inverse relationship between addition and subtraction;
• Recognise, find, name and write 1/3, ¼, 2/4, and ¾;
• Recognise equivalence of 2/4 and ½;
• Solve problems related to place value.

Measurement/Geometry

• Recognise and name common 2D and 3D shapes;
• Identify and describe properties of 2D shapes (sides, right angles, lines of symmetry);
• Identify and describe properties of 3D shapes (edges, vertices and faces);
• Compare and sort common 2D and 3D shapes;
• Use vocabulary to describe position, direction and movement including rotation (as a turn and as right angle for quarter and half turns – clockwise and anti-clockwise, and movement on a straight line;
• Arrange shapes in patterns/sequences;
• Choose and use appropriate standard units;
• Compare and order length, mass, volume/capacity;
• Use £ and p signs;
• Solve problems involving adding/subtracting money;
• Compare and order time intervals;
• Tell time to nearest 5 minutes;
• Know the number of minutes in an hour/hours in a day.

Statistics

• Interpret and draw simple pictograms, tally charts, block diagrams and tables;

End of Year 3 Objectives

Number

• Count from 0 in 4s, 8s, 50s and 100s;
• Find 10 or 100 more/less;
• Numbers to 1000:recognise place value of each digit, compare and order, read and write in numerals and words;
• Identify, represent and estimate numbers in different ways;
• Mentally add and subtract ones, tens or hundreds to/from numbers with up to three digits;
• Add and subtract numbers with up to three digits in columns;
• Estimate answers and check using inverse operations;
• Learn 3, 4 and 8 times tables;
• Multiply and divide two digit by one digit numbers;
• Use tenths and count in tenths;
• Recognise, find and write fractions of sets of objects;
• Recognise and use fractions as numbers;
• Recognise some equivalent fractions;
• Add/subtract fractions with the same denominator up to 1;
• Order fractions with common denominator.

Measurement

• Measure and calculate with metric units;
• Measure perimeter of simple 2D shapes;
• Tell analogue time;
• Estimate and read time to nearest minute; record and compare times; use time vocabulary;
• Know the number of seconds in a minute and days in each month/year/leap year;
• Compare durations of events.

Geometry

• Draw 2D and make 3D shapes;
• Recognise angles as a property of a shape or a description of a turn;
• Identify right angles; use them to describe turns and compare other angles;
• Identify horizontal, vertical, perpendicular and parallel lines;

Statistics

• Interpret, draw and answer one and two step questions about bar charts, pictograms and tables.

End of Year 4 Objectives

Number

• Count in multiples of 6, 7, 9, 25 and 1000;
• Find 1000 more/less;
• Count backwards to include negative numbers;
• Recognise place value of each digit in a four digit number;
• Order and compare numbers beyond 1000;
• Identify, represent and estimate numbers in different ways;
• Round numbers to nearest 10, 100 or 1000;
• Solve problems with larger positive numbers;
• Use roman numerals to 100 (C);
• Add and subtract numbers with up to four digits in columns;
• Estimate and use inverse operations to check answers;
• Solve two step addition and subtraction problems;
• Know all tables to 12x12;
• Multiple and divide mentally;
• Use factor pairs and commutatively in mental calculations;
• Use standard short multiplication to multiply two and three digit numbers by a one digit number;
• Solve problems involving multiplying and dividing;
• Recognise common equivalent fractions;
• Count up and down in hundredths;
• Solve problems involving increasingly harder fractions;
• Add and subtract fractions with common denominators;
• Recognise and write decimal equivalent of any number of tenths and hundredths and of ¼ ½ and ¾;
• Find the effect of dividing a one or two digit number by 10 and 100;
• Round decimals with 1dp to whole numbers;
• Compare numbers with same number of decimal places with up to 2dp;
• Solve measure and money problems involving fractions and decimals.

Measurement

• Convert between units of measure;
• Measure and calculate perimeter of right angle shapes;
• Find area of right angle shapes by counting squares;
• Estimate, compare and calculate different measures;
• Read, write and convert times between analogue and digit and between 12 and 24 hour;
• Solve time conversion problems.

Geometry

• Compare and classify 2D shapes including quadrilaterals and triangles;
• Identify, compare and order acute, obtuse and right angles;
• Identify lines of symmetry in 2D shapes;
• Complete a simple symmetrical figure;
• Introduce simple translations;
• Plot points and draw sides to complete a polygon.

Statistics

• Use bar charts, pictograms, tables and time graphs.

End of Year 5 Objectives

Number

• Numbers to 1 million: read, write, order, compare; know place value; round to nearest power of 10; count on/back in powers of 10;
• Use negative whole numbers in context;
• Roman numerals: read numbers to 1000 and years;
• Add and subtract whole numbers with more than 4 digit using column methods;
• Mentally add and subtract increasingly large numbers;
• Use rounding to check answers;
• Identify multiples, factors, prime numbers, prime factors and composite numbers;
• Find primes to 100; recall primes to 19;
• Multiple numbers up to four digits by a one or two digit number using formal written method;
• Multiple and divide numbers mentally;
• Divide numbers up to four digits by a one digit number using formal written method; interpret remainders;
• Multiple and divide by powers of 10;
• Use square and cube numbers and use notation;
• Compare and order fractions;
• Identify, name and write equivalent fractions;
• Use mixed numbers and improper fractions and convert between them;
• Add and subtract fractions with common/related denominators;
• Multiple other fractions by whole numbers;
• Write decimals as fractions;
• Recognise and use thousandths and relate to tenths, hundredths and decimal equivalents;
• Order and round decimal numbers;
• Recognise and understand % sign; link percentages to fractions and decimals;
• Solve problems involving all aspects of number, including multi-step problems.

Measurement

• Convert between metric units and between metric and imperial units;
• Measure and calculate the perimeter of composite right angled shapes;
• Calculate and compare area of rectangles; estimate area of irregular shapes;
• Estimate volume and capacity;
• Use four operations to solve measure problems using decimal notation;
• Solve problems involving converting between units of time;
• Use all four operations to solve measure problems.

Geometry

• Identify 3D shapes from 2D representations;
• Measure, estimate, compare and draw angles in degrees;
• Identify angles: at a point (whole turn); on straight line (half turn); other multiples of 90 degrees;
• Finding missing lengths and angles in rectangles;
• Distinguish between regular and irregular polygons;
• Reflect and translate shapes.

Statistics

• Solve problems based on line graphs;
• Complete, read and interpret information in tables.

End of Year 6 Objectives

Number

• Numbers to 10 million: read, write, order and compare; know place value; round to a given degree of accuracy;
• Use negative numbers in context; calculate intervals across zero;
• Multiple and divide numbers up to 4 digits by a two digit whole number using formal written method; interpret remainders;
• Perform challenging mental calculations;
• Identify common factors, common multiples and primes;
• Use order of operations;
• Use estimate to check answers;
• Simplify, compare and order fractions;
• Use equivalent to add and subtract fractions;
• Multiple simple fractions together and divide fractions by whole numbers;
• Associate a fraction with division and calculate decimal fraction equivalents;
• Know place value to 3dp; multiple and divide numbers by 10, 100 and 1000;
• Multiple 1 digit numbers with up to 2dp by whole numbers;
• Use written division for answers with up to 2dp;
• Recall and use equivalency between simple fractions, decimals and percentages;
• Solve problems involving all aspects of number, including multi-step problems.

Ratio and Proportion

• Solve problems involving: relative sizes of two quantities; percentages, similar shapes, unequal sharing and grouping.

Algebra

• Use simple formulae;
• Generate and describe linear number sequences;
• Express missing number problems algebraically;
• Find pairs of numbers that satisfy an equations with two unknowns;
• Enumerate possibilities of combinations of two variables.

Measurement

• Use a range of measures and conversations using decimals up to 3dp;
• Convert between miles and kilometers;
• Know that shapes with the same area can have different perimeters and vice versa;
• Use area and volume formulae;
• Calculate area of triangles and parallelograms;
• Calculate, estimate and compare volumes of cubes and cuboids.

Geometry

• Draw 2D shapes given dimensions and angles;
• Describe and build simple 3D shapes;
• Classify shapes by properties;
• Understand circle terminology;
• Know and use angle rules to find unknown angles;
• Describe positions on full co-ordinate grid;
• Translate and reflect shapes using all four quadrants.

Statistics

• Use pie charts and line graphs to solve problems;
• Calculate mean averages.    X