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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 
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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
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