# 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

Number - addition and subtraction

__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 cm^{3}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 (cm__^{2}) and square metres (m^{2}) 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__