Mathematics

Threshold Concepts

Knowledge Categories

The Number System Representation; Properties; Manipulation Space, Shape and Measure Shapes and Solids; Transformation; Measurement; Position Data Data Representation; Data Interpretation; Probability Abstraction Algebraic Manipulation; Pattern; Algebraic Solving; Functions

Milestone 1 [Nursery; Reception; Year 1]

The Number System Representation Identify and represent numbers to at least 50 using objects and pictorial representations, including the number line. Recall number bonds to 10 fluently; represent and use number bonds and related subtraction facts within 20. Properties Recognise the place value of digits in a 2-digit number up to 50. Compare and order numbers to 100 and with a given number identify one more and one less. Count, read and write numbers to 100 in numerals and to 20 in words. Recognise and find a half/ a quarter of two/ four equal parts of an object, shape or quantity. Manipulation Read, write and interpret mathematical statements involving addition (+), subtraction () and equals (=) signs. Add and subtract 1-digit and 2-digit numbers to 20, including zero. Count forwards in multiples of 2, 5 and 10s. Solve one step problems involving multiplication and division. Solve addition and subtraction problems involving missing numbers. Space, Shape and Measure Shapes and Solids Recognise and name common 2D and 3D shapes in different orientations and sizes. Measurement Compare, describe and solve practical problems for measuring: lengths/ heights, mass or weight, capacity/ volume and time. Measure and begin to record lengths and heights (in cm). Tell the time to the hour and half past the hour on analogue and digital clocks. Tell the time to the hour and half past the hour Recognise and know the value of different denominations of coins and notes. Position Describe position, direction and movement, including whole, half, quarter and threequarter turns.

Data Data Interpretation Ask and answer simple questions by counting the number of objects in different categories and sorting the categories by quantity.

Milestone 2 [Year 2; Year 3]

The Number System Representation Read and write numbers up to 1000 in numerals and in words. Identify, represent and estimate numbers using different representations. Recognise and show, using diagrams, equivalent fractions with small denominators. Properties Recognise the place value of digits in a 3-digit number. Reason about the location of any 3-digit number in the linear number system, including identifying the previous and next multiple of 100 and 10. Compare and order numbers to 1000. Count up and down in tenths and understand how tenths arise. Manipulation Add and subtract mentally, including addition of numbers up to 3 digits. Add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction. 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 2-digit numbers multiplied by 1-digit numbers, using mental and formal written methods. Recognise, find and write fractions of a discrete set of objects and amounts (unit and non-unit fractions with small denominators). Space, Shape and Measure Shapes and Solids Identify, draw/make and describe properties of 2D and 3D shapes with relevant vocabulary. Identify right angles. Identify horizontal and vertical lines and pairs of perpendicular and parallel lines. Transformation Recognise angles as a property of a shape or a description of a turn. Measurement Measure the perimeter of simple 2-D shapes. Measure, estimate, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml).

Data Data Representation Data Interpretation Present data in bar charts, pictograms and tables.

Interpret bar charts, pictograms and tables. Solve problems with one or two steps using scaled bar charts, pictograms and tables.

Milestone 3 [Year 4; Year 5]

The Number System Representation Round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000. Read and write decimal numbers as fractions. Read, write, order and compare numbers with up to three decimal places. Compare and order fractions whose denominators are all multiples of the same number. Solve problems which require knowing key percentage and decimal equivalents. Manipulation Add and subtract numbers mentally with increasingly large numbers. Add and subtract whole numbers with more than 4 digits, including using column method. Solve addition and subtraction multi-step problems in contexts, deciding which operations to use and why Multiply numbers up to 4 digits by a 1 or 2-digit number using a formal written method, including long multiplication for 2-digit numbers. divide numbers up to 4 digits by a 1-digit number using a formal written method of short division and interpret remainders appropriately for the context. Solve calculation problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes. Space, Shape and Measure Shapes and Solids Distinguish between regular and irregular polygons based on reasoning about equal sides and angles. Draw rectilinear shapes to given dimensions. Transformation Understand congruence. Measurement Convert between different units of metric measure. Calculate the perimeter and area of composite rectilinear shapes. Position Identify angles around a point and on a straight line; recognise 1/4, 1/2, 3/4 and one whole turn as multiples of 90º. 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. Describe positions on a coordinate grid (first quadrant).

Data Data Representation Data Interpretation Present data in more complex tables, including timetables.

Read and interpret more complex tables, including timetables. Interpret line graphs. Solve comparison, sum and difference problems using information presented in a line graph.

Milestone 4 [Year 6 to Year 7]

The Number System Representation Round numbers to a given degree of accuracy. Properties Know and be able to find key types of numbers including factors, multiples, and primes. Manipulation Perform calculations using the order of operations and directed numbers. Understand the equivalence of fractions and ratios and convert between fractions, decimals, percentages, and ratios. Perform calculations using fractions, decimals, percentages, and ratios. Space, Shape and Measure Shapes and Solids Classify two-dimensional shapes and describe their properties. Measurement Use properties of angles (for example, angles on a straight line, around a point, vertically opposite, and in polygons). Find the area and perimeter of two-dimensional shapes. Convert between common units of measure. Position Represent location on a coordinate grid (with 4 quadrants). Data Data Representation Represent data using simple statistical diagrams. Data Interpretation Interpret data using statistical diagrams. Calculate measures of location and spread. Probability Use and apply the probability scale. Abstraction Algebraic Manipulation Form and manipulate algebraic expressions. Evaluate algebraic expressions by substituting directed numbers and using order of operations. Pattern Generate and describe sequences. Algebraic Solving Form and solve linear equations. Functions Plot coordinates that follow a pattern which is expressed algebraically. Describe a line by referring to its gradient.