# Lower key stage 2

## Place Value

### Year 3

- Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number
- Identify, represent and estimate numbers using different representations
- Read and write numbers up to 1000 in numerals and in words
- Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
- Compare and order numbers up to 1000
- Solve number problems and practical problems involving these ideas

### Year 4

- Count in multiples of 6, 7, 9 25 and 1000
- Count backwards through zero to include negative numbers
- Identify, represent and estimate numbers using different representations
- 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
- Find 1000 more or less than a given number
- Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens and ones)
- Order and compare numbers beyond 1000
- 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

## Addition and Subtraction

### Year 3

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

### Year 4

- Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
- Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

## Multiplication and Division

### Year 3

- 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

### Year 4

- Recall multiplication and division facts for multiplication tables up to 12 x 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, Decimals and Percentages

### Year 3

- 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
- Compare and order unit fractions and fractions with the same denominators
- Add and subtract fractions with the same denominator within one whole (for example 5/7+1/7 = 6/7 )
- Solve problems that involve all of the above

### Year 4

- Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten
- Recognise and show, using diagrams, families of common equivalent fractions
- Add and subtract fractions with the same denominator
- Solve problems that involve increasingly harder fractions to calculate quantities and fractions to divide quantities, including non-unit fractions where the answer is a whole number
- Recognise and write decimal equivalents of any number of tenths or hundredths
- Recognise and write decimal equivalents to 1/4, 1/2 and 3/4
- 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

## Ratio and Proportion, Algebra

### Year 3

- Solve problems, including missing number problems

*Algebraic notation is not introduced until Year 6*

## Measurement

### Year 3

- Measure, compare, add and subtract: lengths (m, cm, mm), mass (kg/g), volume/capacity (l/ml)
- 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 using vocabulary such as o’clock, am/pm, morning, afternoon, noon and midnight
- Know that there are 60 seconds in a minute and the number of days in each month, year and leap year
- Compare durations of events (ie. Time taken by particular events or tasks)
- Measure the perimeter of simple 2D shapes

### Year 4

- Convert between different units of measure (ie. Km to m; hour to minute)
- Estimate, compare and calculate different measures
- Estimate, compare and calculate different measures, including money in pounds and pence
- Read, write and convert between analogue and digital 12 and 24 hour clocks
- Solve problems involving converting from hours to minutes, minutes to seconds, years to months and weeks to days
- Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
- Find the area of rectilinear shapes by counting squares

## Geometry

### Year 3

- Draw 2D shapes
- Make 3D shapes using modelling materials; recognise 3D 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 parallel and perpendicular lines

### Year 4

- Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
- Identify lines of symmetry in 2D shapes presented in different orientations
- Identify acute and obtuse angles and compare and order angles up to two right angles by size
- Identify lines of symmetry in 2D shapes presented in different orientations
- Complete a simple symmetric figure with respect to a specific line of symmetry
- Describe positions on a 2D 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

### Year 3

- Interpret and present data using bar charts, pictograms and tables
- Solve one-step and two-step questions (ie. How many more? How many fewer?) using information presented in scaled bar charts, pictograms and tables

### Year 4

- 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