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How can mathematical thinking support and enhance children’s reasoning…

- - - - count up and down in tenths, recognise that 1 / 10 = 0.10
      - recognise, find and write fractions
      - recognise and use fractions as numbers
      - recognise and show, using diagrams, equivalent fractions with small denominators.
      - add and subtract fractions with the same denominator
      - compare and order unit fractions and fractions with the same denominator
      - solve problems that involve all of the above
  - - - 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 one hundred and dividing tenths by ten.
      - solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities
      - add and subtract fractions with the same denominator
      - recognise and write decimal equivalents of any number of tenths or hundredths
      - recognise and write decimal equivalents to 1/4, 1/2, 3/4
      - 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 one decimal place to the nearest whole number
      - compare numbers with the same number of decimal places up to two decimal places
      - solve simple measure and money problems involving fractions and decimals to two decimal places.
  - - - Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity.
      - Write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2.
  - - - compare and order fractions whose denominators are all multiples of the same number.
      - identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
      - recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number.
      - add and subtract fractions with the same denominator and denominators that are multiples of the same number.
      - multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
      - read and write decimal numbers as fractions
      - recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents.
      - round decimals with two decimal places to the nearest whole number and to one decimal place
      - read, write, order and compare numbers with up to three decimal places
      - solve problems involving number up to three decimal places
      - recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred' and write % as fractions with 100 of a denominator and as a decimal.
      - solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those with a denominator of a multiple of 10 or 25.
  - - - use common factors to simplify fractions; use common multiples to express fractions in the same denomination.
      - compare and order fractions, including fractions > 1
      - add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
      - multiply simple pairs of proper fractions, writing the answer in its simplest form
      - divide proper fractions by whole numbers
      - associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 ]
      - identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places