# Key Learning in Maths

Number - number and place value

• Count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
• Count forwards and backwards in decimal steps
• Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
• Read, write, order and compare numbers with up to 3 decimal places
• Identify the value of each digit to three decimal places
• Identify represent and estimate numbers using the number line
• Find 0.01, 0.1, 1, 10, 100, 1000 and other powers of 10 more or less than a given number
• Round any number up to 1 000 000 to the nearest 10, 100, 1000,
10 000 and 100 000
• Round decimals with two decimal places to the nearest whole number and to one decimal place
• Multiply/divide whole numbers and decimals by 10, 100 and 1000
• Interpret negative numbers in context, count on and back with positive and negative whole numbers, including through zero
• Describe and extend number sequences including those with multiplication/division steps and where the step size is a decimal
• Read Roman numerals to 1000 (M); recognise years written as such

Solve number and practical problems that involve all of the above

Number - fractions, decimals and percentages

• Recognise mixed numbers and improper fractions and convert from one form to the other
• Read and write decimal numbers as fractions (e.g. 0.71 =
• Count on and back in mixed number steps such as 1
• Compare and order fractions whose denominators are all multiples of the same number (including on a number line)
• Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
• Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
• Add and subtract fractions with denominators that are the same  and that are multiples of the same number (using diagrams)
• Write statements > 1 as a mixed number (e.g.  +  =  =1 )
• Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
• Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal
• Solve problems involving fractions and decimals to three places

Solve problems which require knowing percentage and decimal equivalents of , , , ,  and fractions with a denominator of a multiple of 10 or 25

• Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a known fact, calculate mentally, use a jotting, written method)
• Select a mental strategy appropriate for the numbers involved in the calculation
• Recall and use addition and subtraction facts for 1 and 10 (with decimal numbers to one decimal place)
• Derive and use addition and subtraction facts for 1 (with decimal numbers to two decimal places)
• Add and subtract numbers mentally with increasingly large numbers and decimals to two decimal places
• Add and subtract whole numbers with more than 4 digits and decimals with two decimal places, including using formal written methods (columnar addition and subtraction)
• Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
• Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Solve addition and subtraction problems involving missing numbers

Number - multiplication and division

• Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a known fact, calculate mentally, use a jotting, written method)
• Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
• Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
• Establish whether a number up to 100 is prime and recall prime numbers up to 19
• Recognise and use square (2) and cube (3) numbers, and notation
• Use partitioning to double or halve any number, including decimals to two decimal places
• Multiply and divide numbers mentally drawing upon known facts
• Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes
• Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
• Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
• Use estimation/inverse to check answers to calculations; determine, in the context of a problem, an appropriate degree of accuracy
• Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

Geometry - properties of shapes

• Distinguish between regular and irregular polygons based on reasoning about equal sides and angles
• Use the properties of rectangles to deduce related facts and find missing lengths and angles
• Identify 3-D shapes from 2-D representations
• Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
• Draw given angles, and measure them in degrees (°)
• Identify:

- angles at a point and one whole turn (total 360°)

- angles at a point on a straight line and half a turn (total 180°)
- other multiples of 90°

Geometry - position and direction

• Describe positions on the first quadrant of a coordinate grid
• Plot specified points and complete shapes

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

Statistics

• Complete and interpret information in a variety of sorting diagrams (including those used to sort properties of numbers and shapes)
• Complete, read and interpret information in tables and timetables
• Solve comparison, sum and difference problems using information presented in all types of graph including  a line graph

Calculate and interpret the  mode, median and range

Measurement

• Use, read and write standard units of length and mass
• Estimate (and calculate) volume ((e.g., using 1 cm3 blocks to build cuboids (including cubes)) and capacity (e.g. using water)
• Understand the difference between liquid volume and solid volume
• Continue to order temperatures including those below 0°C
• Convert between different units of metric measure
• Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
• Measure/calculate the perimeter of composite rectilinear shapes
• Calculate and compare the area of rectangle, use standard units square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes
• Continue to read, write and convert time between analogue and digital 12 and 24-hour clocks
• Solve problems involving converting between units of time

Use all four operations to solve problems involving measure using decimal notation, including scaling