# Key Learning in Maths

Number - number and place value

• Count from 0 in multiples of 4, 8, 50 and 100
• Count up and down in tenths
• Read and write numbers up to 1000 in numerals and in words
• Read and write numbers with one decimal place
• Identify, represent and estimate numbers using different representations (including the number line)
• Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
• Identify the value of each digit to one decimal place
• Partition numbers in different ways (e.g. 146 = 100+ 40+6 and 146 = 130+16)
• Compare and order numbers up to 1000
• Compare and order numbers with one decimal place
• Find 1, 10 or 100 more or less than a given number
• Round numbers to at least 1000 to the nearest 10 or 100
• Find the effect of multiplying a one- or two-digit number by 10 and 100, identify the value of the digits in the answer
• Describe and extend number sequences involving counting on or back in different steps
• Read Roman numerals from I to XII

Solve number problems and practical problems involving these ideas

Number - fractions

• Show practically or pictorially that a fraction is one whole number divided by another (e.g.  can be interpreted as 3 ÷ 4)
• Understand that finding a fraction of an amount relates to division
• Recognise that tenths arise from dividing objects 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,  +  = ]
• Compare and order unit fractions, and fractions with the same denominators (including on a number line)
• Count on and back in steps of  ,  and

Solve problems that involve all of the above

• 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
• Understand and use take away and difference for subtraction, deciding on the most efficient method for the numbers involved, irrespective of context
• Recall/use addition/subtraction facts for 100 (multiples of 5 and 10)
• Derive and use addition and subtraction facts for 100
• Derive and use addition and subtraction facts for multiples of 100 totalling 1000
• 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
• 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

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)
• Understand that division is the inverse of multiplication and vice versa
• Understand how multiplication and division statements can be represented using arrays
• Understand division as sharing and grouping and use each appropriately
• Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
• Derive and use doubles of all numbers to 100 and corresponding halves
• Derive and use doubles of all multiples of 50 to 500
• 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
• Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

Solve problems, including missing number problems, involving multiplication and division (and interpreting remainders), including positive integer scaling problems and correspondence problems in which n objects are connected to m objects

Geometry - properties of shapes

• 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

Geometry - position and direction

Describe positions on a square grid labelled with letters and numbers

Statistics

• Use sorting diagrams to compare and sort objects, numbers and common 2-D and 3-D shapes and everyday objects
• 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

Measurement

• Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
• Continue to estimate and measure temperature to the nearest degree (°C) using thermometers
• Understand perimeter is a measure of distance around the boundary of a shape
• Measure the perimeter of simple 2-D shapes
• 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/read time with increasing accuracy to the nearest minute
• Record/compare time in terms of seconds, minutes, hours; use vocabulary such as o’clock, a.m./p.m., morning, afternoon, noon, 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]
• Continue to recognise and use the symbols for pounds (£) and pence (p) and understand that the decimal point separates pounds/pence
• Recognise that ten 10p coins equal £1 and that each coin is  of £1
• Add and subtract amounts of money to give change, using both £ and p in practical contexts

Solve problems involving money and measures and simple problems involving passage of time