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# Maths

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## Year 3 Mathematics

## Year 4 Mathematics

## Year 5 Mathematics

## Year 6 Mathematics

*The National Curriculum for Mathematics.**Blue text** non-statutory***.**

**Number & Place Value**

- Count from 0 in multiples 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)
- Compare and order numbers up to 1,000
- Identify, represent and estimate numbers using different representations
- Read and write numbers up to 1,000 in numerals and in words
- Solve number problems and practical problems involving these ideas.

**Addition & Subtraction**

- Add and subtract numbers mentally, including:
- a three-digit number and 1s
- a three-digit number and 10s
- a three-digit number and 100s

- Add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction

- Estimate the answer to a calculation and use inverse operations to check answers

- Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

**Multiplication & Division**

- 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**

- 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

- Compare and order unit fractions, and fractions with the same denominators

- Solve problems that involve all of the above.

**Measurement**

- Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)

- 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

**Properties of Shapes**

- Draw 2-D shapes and make 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**

Interpret and present data using bar charts, pictograms and tables

Solve one-step and two-step questions using information presented in scaled bar charts and pictograms and tables.

**Number & Place Value**

- 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 that involve all of the above and with increasingly large positive numbers
- 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**

- 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.

**Multiplication & Division**

- Recall multiplication and division facts for multiplication tables up to 12 × 12

- Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers

- Recognise and use factor pairs and commutability 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 (including decimals)**

- 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 a 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

- Add and subtract fractions with the same denominator

- Recognise and write decimal equivalents of any number of tenths or hundredths

- Recognise and write decimal equivalents to ¼; ½; ¾

- 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**

Convert between different units of measure

- 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, 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

**Properties of Shape**

- Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes

- Identify acute and obtuse angles and compare and order angles up to 2 right angles by size

- Identify lines of symmetry in 2-D shapes presented in different orientations

- Complete a simple symmetric figure with respect to a specific line of symmetry.

**Position & Direction**

- Describe positions on a 2-D grid as coordinates in the first quadrant

- Describe movements between positions as translations of a given unit to the left/right and up/down

- Plot specified points and draw sides to complete a given polygon.

**Statistics**

- 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.

**Number & Place Value**

- 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 context, 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 problems and practical problems that involve all of the above

- Read Roman numerals to 1,000 (M) and recognise years written in Roman numerals.

**Addition & Subtraction**

- Add and subtract whole numbers with more than 4 digits,including using formal written methods (columnar addition and subtraction)

- Add and subtract numbers mentally with increasingly large numbers

- Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

- Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

**Multiplication & Division**

- Identify multiples and factors, including finding all factor pairs of a number, and common factors of two 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 (decimals & percentages)**

- 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

- 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

- 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 fractions with a denominator of a multiple of 10 or 25.

**Measurement**

- Convert between different units of metric measure

- 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 (cm
^{2}) and square metres (m^{2}) and estimate the area of irregular shapes

- Estimate volume and capacity

- Solve problems involving converting between units of time

- Use all four operations to solve problems involving measure using decimal notation including scaling.

**Properties of Shape**

- Identify 3-D shapes, including cubes and other cuboids, from 2-D representations

- Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles

- Draw given angles, and measure them in degrees (
^{o})

- Identify:
- angles at a point and 1 whole turn (total 360
^{o}) - angles at a point on a straight line and half a turn (total 180
^{o}) - other multiples of 90
^{o}

- Use the properties of rectangles to deduce related facts and find missing lengths and angles

- Distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

**Position & Direction**

- 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**

- Solve comparison, sum and difference problems using information presented in a line graph

- Complete, read and interpret information in tables, including timetables.

**Number & Place Value**

- 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 that involve all of the above.

**Addition, Subtraction, Multiplication & Division**

- 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

- Use their 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, subtraction, multiplication and division

- Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

**Fractions (decimals & percentages)**

use common factors to simplify fractions; use common multiples to express fractions in the same denomination

compare and order fractions, including fractions >1

add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

multiply simple pairs of proper fractions, writing the answer in its simplest form

divide proper fractions by whole numbers

associate a fraction with division and calculate decimal fraction equivalents for a simple fraction.

identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers are up to three decimal places

multiply one-digit numbers with up to 2 decimal places by whole numbers

use written division methods in cases where the answer has up to 2 decimal places

solve problems which require answers to be rounded to specified degrees of accuracy

recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

**Ratio & Proportion**

- Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

- Solve problems involving the calculation of percentages 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.

**Algebra**

- Use simple formulae

- Generate and describe linear number sequences

- Express missing number problems algebraically

- Find pairs of numbers that satisfy an equation with two unknowns

- Enumerate possibilities of combinations of 2 variables.

**Measurement**

- Solve problems involving the calculation and conversion of units of measure, using decimal notation up to 2 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

- 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 (cm
^{3}) and cubic metres (m^{3}), and extending to other units

**Properties of Shape**

- Draw 2-D shapes using given dimensions and angles

- Recognise, describe and build simple 3-D shapes, including making nets

- Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

- Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

- Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

**Position & Direction**

- 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**

- Iinterpret and construct pie charts and line graphs and use these to solve problems

- Calculate and interpret the mean as an average.

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