Number

Outcomes

Number & Place Value
Pupils now use multiples of 2, 3, 4, 5, 8, 10, 50 and 100. They use larger numbers to at least 1000, applying partitioning related to place value using varied and increasingly complex problems, building on work in year 2 (for example, 146 = 100 + 40 and 6, 146 = 130 + 16). Using a variety of representations, including those related to measure, pupils continue to count in ones, tens and hundreds, so that they become fluent in the order and place value of numbers to 1000
- Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number
  
  Play Activities 64
  
  Examples
- Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
  
  Play Activities 42
  
  Examples
- Compare and order numbers up to 1000
  
  Play Activities 10
  
  Examples
- Read and write numbers up to 1000 in numerals and in words
  
  Play Activities 29
  
  Examples
- Solve number problems and practical problems involving these ideas
  
  Play Activities 43
  
  Examples
Addition & Subtraction
Pupils practise solving varied addition and subtraction questions. For mental calculations with two-digit numbers, the answers could exceed 100. Pupils use their understanding of place value and partitioning, and practise using columnar addition and subtraction with increasingly large numbers up to three digits to become fluent (see Mathematics Appendix 1)
- Add and subtract numbers mentally, including:
  - A three-digit number and ones
    
    Play Activities 12
    
    Examples
  - A three-digit number and tens
    
    Play Activities 22
    
    Examples
  - A three-digit number and hundreds
    
    Play Activities 15
    
    Examples
- Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction
  
  Play Activities 133
  
  Examples
- Estimate the answer to a calculation and use inverse operations to check answers
  
  Play Activities 24
  
  Examples
- Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction
  
  Play Activities 330
  
  Examples
Multiplication & Division
Pupils continue to practise their mental recall of multiplication tables when they are calculating mathematical statements in order to improve fluency. Through doubling, they connect the 2, 4 and 8 multiplication tables. Pupils develop efficient mental methods, for example, using commutativity and associativity (for example, 4 x 12 x 5 = 4 x 5 x 12 = 20 x 12 = 240) and multiplication and division facts (for example, using 3 x 2 = 6, 6 Ã· 3 = 2 and 2 = 6 Ã· 3) to derive related facts (for example, 30 x 2 = 60, 60 Ã· 3 = 20 and 20 = 60 Ã· 3). Pupils develop reliable written methods for multiplication and division, starting with calculations of two-digit numbers by one-digit numbers and progressing to the formal written methods of short multiplication and division. Pupils solve simple problems in contexts, deciding which of the four operations to use and why. These include measuring and scaling contexts, (for example, four times as high, eight times as long etc.) and correspondence problems in which m objects are connected to n objects (for example, 3 hats and 4 coats, how many different outfits?; 12 sweets shared equally between 4 children; 4 cakes shared equally between 8 children).
Fractions
Pupils connect tenths to place value, decimal measures and to division by 10. They begin to understand unit and non-unit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. They should go beyond the [0, 1] interval, including relating this to measure. Pupils understand the relation between unit fractions as operators (fractions of), and division by integers. They continue to recognise fractions in the context of parts of a whole, numbers, measurements, a shape, and unit fractions as a division of a quantity. Pupils practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency.