count backwards through 0 to include negative numbers
recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s)
order and compare numbers beyond 1,000
identify, represent and estimate numbers using different representations
round any number to the nearest 10, 100 or 1,000
solve number and practical problems that involve all of the above and with increasingly large positive numbers
read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place value
Pupils should be taught to:
add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
estimate and use inverse operations to check answers to a calculation
solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
Pupils should be taught to:
recall multiplication and division facts for multiplication tables up to 12 × 12
use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 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 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects
Pupils should be taught to:
recognise and show, using diagrams, families of common equivalent fractions
count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10
solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
add and subtract fractions with the same denominator
recognise and write decimal equivalents of any number of tenths or hundreds
recognise and write decimal equivalents to , ,
find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
round decimals with 1 decimal place to the nearest whole number
compare numbers with the same number of decimal places up to 2 decimal places
solve simple measure and money problems involving fractions and decimals to 2 decimal places
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