 ## Year 3 Areas of Study

Number and place value – students 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

Addition and subtraction – students 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 column 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 and division – students should be taught to:

• Recall and use multiplication and division facts for the multiplication tables for 3, 4 and 8 timetables
• 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 – students 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, 5/7 + 1/7 = 6/7)
• Compare and order unit fractions, and fractions with the same denominators
• Solve problems that involve all of the above.

Measurement – students 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

• 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

• 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 Areas of Study

Number and place value – students should be taught to:

• Count in multiples of 6, 7, 9, 25 and 100
• 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

Addition and subtraction – students 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

Multiplication and division – students 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

Fractions (including decimals) – students 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 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 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 – students 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 – properties of shape – students 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 – students 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 – students 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 