# Mathematics

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Year 3

Number and Place value

Pupils should be taught to:

 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 three-digit number (hundreds, tens, ones)

 compare and order numbers up to 1000

 identify, represent and estimate numbers using different representations

 read and write numbers up to 1000 in numerals and in words

 solve number problems and practical problems involving these ideas.

Number- Addition and Subtraction

Pupils should be taught to:

 add and subtract numbers mentally, including:

 a three-digit number and ones

 a three-digit number and tens

 a three-digit number and hundreds

 add and subtract numbers with up to three 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.

Number- Multiplication and division

Pupils should be taught to:

 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.

Number- Fractions

Pupils should be taught to:  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 [for example, 7/ 5 + 7 /1 = 7 /6 ]

 compare and order unit fractions, and fractions with the same denominators

 solve problems that involve all of the above.

Measurement

Pupils should be taught to:

 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, a.m./p.m., 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].

Geometry- Properties of Shape

Pupils should be taught to:

 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 two right angles make a half-turn, three make three quarters of a turn and four 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

Pupils should be taught to:

 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

Number- Number and place value

Pupils should be taught to

 count in multiples of 6, 7, 9, 25 and 1000

 find 1000 more or less than a given number

 count backwards through zero to include negative numbers

 recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)

 order and compare numbers beyond 1000

 identify, represent and estimate numbers using different representations

 round any number to the nearest 10, 100 or 1000

 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 zero and place value.

Number- Addition and Subtraction

Pupils should be taught to:

 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.

Number- Multiplication and Division

Pupils should be taught to:

 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 three numbers

 recognise and use factor pairs and commutativity 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 one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

Number- Fractions (including decimals)

Pupils should be taught to:

 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 one hundred and dividing tenths by ten.

 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 1/2, 1/4, 3/4

 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 one decimal place to the nearest whole number

 compare numbers with the same number of decimal places up to two decimal places

 solve simple measure and money problems involving fractions and decimals to two decimal places.

Measurement

Pupils should be taught to:

 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, 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.

Geometry- Property of Shape

Pupils should be taught to:

 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 two 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.

Geometry- Position and Direction

Pupils should be taught to:

 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

Pupils should be taught to:

 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.

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