# Number & Calculation

Word/Theme | Meaning |

Addition | Finding the total value of two or more numbers. Denoted by the symbol ‘+’. |

Arithmetic | Maths which deals with the properties of numbers and how to manipulate numbers using the four operations. |

Array | A pictorial representation to help children understand multiplication and division. Typically shown as rows of dots, for example, 2 x 3 would be shown as two rows of three dots. |

Arithmetic | Maths which deals with the properties of numbers and how to manipulate numbers using the four operations. |

Bridging through 10 |
A mental method of adding two numbers whose total is greater than 10. Pupils are taught to count on to 10 and then add the remainder of the number to 10. For example: 7 + 9 – bridging from 7 to 10 requires 3, which leaves 6 (from the original 9), 10 + 6 = 16. |

Column method | A method of calculation where the numbers to be added or subtracted are set out above one another in columns. The calculation is done by ‘carrying’ and ‘borrowing’ numbers from column to column. |

Commutativity | Addition and multiplication have the property of commutativity – when two numbers are added or multiplied, this can be done in any order and the same answer will be obtained: 3 + 2 = 5, 2 + 3 = 5; 4 x 6 = 24, 6 x 4 = 24. Subtraction and division are not commutative. |

Complementary addition | Also known as the ‘jump method’. A method of addition using a number line where children are taught to start with the largest number in the calculation and count on along the number line to find the total. |

Denominator | In a fraction, the number below the line. |

Division | The process of dividing a number up into equal parts, and finding how many equal parts can be made and whether there is a remainder. It is represented by the symbol ‘÷’ or sometimes ‘/’. |

Division fact | A division number sentence related to the times tables. For example, the division fact 16 ÷ 4 = 4 is related to the 4x table. |

Even numbers | All numbers that are exactly divisible by 2. Even numbers always end with 0, 2, 4, 6 or 8. |

Finding the difference | A way of carrying out subtraction calculations by finding the numerical difference between two numbers. So to solve the number sentence 47 – 34, find the difference between 34 and 47. Most often taught by using a number line to count on from the smaller to the bigger number. See also jump method. |

Fraction | A fraction is a number which represents part of a whole. It can be represented using a numerator and denominator e.g. 1/2, or as a decimal e.g. 0.5. |

Greater than (>) and less than (<) |
Symbols used to show the relative size of numbers. The wide end of the symbol always faces the larger number, e.g. 25 > 10. |

Inverse operation |
The calculation which is opposite to a given calculation, and effectively reverses it. Addition is the inverse of subtraction, multiplication is the inverse of division. So for the calculation 4 + 3 = 7, the following calculations also apply: 3 + 4 = 7 ( x 3 = 6 ( |

Jump method | See complementary addition. |

Mental method |
Calculations and problem solving carried out mentally, without the need to write down any working out. |

Multiple | A multiple is a number that can be divided by another number a certain number of times without a remainder. In the number sentence 4 x 5 = 20, 20 is a multiple of 4 and a multiple of 5. |

Multiplication | Finding how many altogether in a given number of equal sized groups. Represented by the symbol ‘x’. |

Multiplication fact | The answer to a multiplication calculation. For example in 3 x 3 = 9, the multiplication fact is 9. |

Multiplication tables | The multiplication calculations for all numbers from 1 x 2 to 12 x 10. Usually grouped by the number being multiplied. Children begin by learning the 2x, 5x and 10x tables, and the English curriculum requires that multiplication tables and the related division facts are known by heart by the end of Year 6. |

Number bonds |
Pairs of numbers that add up to a specific number. For example, the number bonds to 10 are 10 + 0, 9 + 1, 8 + 2 and so on. Children are taught these bonds early on, as they help calculation skills and also show patterns that are repeated for other number bonds, for example to 20 or 100. |

Number facts | Basic addition, subtraction, multiplication and division facts that children should learn to recall instantly to support more complex calculations. Examples include number bonds and multiplication tables. |

Number sentence | An arrangement of numbers and symbols. 3 + 4 = 7 is an addition number sentence, 7 – 3 = 4 is a subtraction number sentence. 3 x 5 = 15 is a multiplication number sentence, 15 ÷ 3 = 5 is a division number sentence. |

Numerator | In a fraction, the number above the line. |

Odd numbers | All whole numbers which are not exactly divisible by 2. Odd numbers always end in 1, 3, 5, 7 or 9. |

Operation |
The four mathematical operations are addition, subtraction, multiplication and addition. |

Ordering | Putting numbers in the correct order according to size. Ascending order goes smallest to largest, descending order from largest to smallest. Ordering also involves using the greater than, less than and equals symbols (<, > and =). |

Ordinal numbers | Numbers which indicate order – 1st, 2nd, 3rd and so on. |

Partitioning | See also recombining. Partitioning is dividing a number into the individual values of its digits, and helps children to understand the values of these digits. For example 782 can be partitioned into 700 + 80 + 2. |

Place value | The value of all the digits in a number. For example, in the number 627, the digit ‘2’ is worth 20, the digit ‘6’ is worth 600. |

Remainder | The amount left over when a number cannot be exactly divided by another number. For example, if we divide 10 by 3, we get three groups of 3 with a remainder of 1. |

Repeated addition | A way of teaching about multiplication as the repeated grouping of the same number. For example, 4 x 2 is the same as four groups of 2, or 2 + 2 + 2 + 2. |

Repeated subtraction |
A way of teaching about division as the repeated subtraction of the same number down to zero. For example 15 ÷ 3 is the same as 15 shared into 3 groups of 5, or 15 – 5 – 5 – 5 = 0. |

Sharing | Children learn early on how to share a number of objects into equal groups. This develops an early understanding of division. |

Subtraction | Taking one number away from another, finding the difference between the two. Denoted by the symbol ‘-‘. |

Subtraction on a number line | See also finding the difference. Children are taught to use a number line to carry out subtraction calculations, either by counting back from the starting number or by finding the difference between the smaller and greater number in the calculation. |

Sum | The result of adding two numbers together. |

Times tables | See multiplication tables. |

Two-step and multi-step problems | Word problems which require pupils to work out more than one step in order to find the eventual answer. Answering the second part of the question requires information derived from the first part, etc. |

Unit fractions | A fraction where the numerator is 1 and the denominator is a whole number. |

Word problem |
A mathematical calculation presented in words. Pupils are taught to find the key information, work out what type of calculation is needed and then work out the answer. |

Working | Written work which supports finding an eventual answer to a calculation or a problem. Important as it shows how a pupil tackled the problem and the skills they used to work out the problem. |

Written method | A way of carrying out a calculation which is done on paper rather than entirely mentally. |