An ordered collection of counters in rows or columns, showing multiplication facts.

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2 Commutative When we add or multiply, we can swap the order of the digits and the answer will remain the same. E.g = 8 and = 8 The answer is the same whichever order the numbers are. 2 x 5 = 10 and 5 x 2 = 10 Again, the answer is the same whichever order the numbers are. Subtraction and division are not commutative 6-3 does not give the same answer as 3-6 Common factor A number which is a factor or two or more other numbers. E.g. 3 is a common factor of 9 (3 x 3 = 9) and 30 (3 x 10 = 30). Common multiple An integer (whole number) which is a multiple of a set of other whole numbers E.g. 12 is a common multiple of 2 (2 x 6 = 12), 3 (3 x 4 = 12), 4 (4 x 3 = 12) and 6 ( 6 x 2 = 12). Complement In addition, a number and its complement have a given total. E.g. When considering complements to 100, 65 has the complement 35 as = 100. Consecutive Following in order. Consecutive numbers are adjacent when counting. E.g. 5, 6, 7, 8 are consecutive numbers. Cube numbers A number multiplied by itself 3 times gives a cube number. E.g. 3 x 3 x 3 = 27. This can also be written 3 3 = 27 Decimal A number that contains a decimal point and tenths, hundredths thousandths etc. are represented by the numbers to the right of the decimal point. E.g has 3 decimal places 2 tenths, 7 hundredths and 5 thousandths. Decimal fraction When a decimal is represented as a fraction rather than using a decimal point. E.g equivalent to 2 / 10, 7 / 100 and 5 / 1000 or 275 / 1000 Denominator Difference When using fractions, the denominator is the number on the bottom of the fraction. E.g. In the fraction 3 / 4, the denominator is 4. In maths, the difference is the numerical difference between the quantities of one set of objects compared to another E.g. The difference between 5 and 9 is 4; 9 is 4 more than 5; 9 is 5 more than 4. Difference is one way of thinking about subtraction e.g. 9 5 = 4.

3 Digit Each symbol of the number system is a digit The digits are: is a 2-digit number; there are 3 digits in 2.95 The position or place of a digit conveys its value. The value of the 3 in 38 is 30 Divide Dividend To split a number into equal groups or parts. It is fair sharing. The or / symbol are used to show division. In division, the dividend is the number that is being divided. E.g. In the calculation 20 5 = 4, 20 is the dividend. Divisibility Divisible Divisor The property of being divisible by a given number with no remainder. E.g. the number 12 is divisible by 6, 4, 3 and is not divisible by 5 as 12 5 = 2 remainder 2. In division, the number by which another is being divided. In the calculation 35 7 = 5, 7 is the divisor. Double To multiply by 2. Double 4 is 8 (2 x 4 = 8); double 11 is 22 (2 x 11 = 22) See also near double Efficient methods Equal = A means of a calculation which achieves the correct answer in as few steps as possible. This may be a mental or written method. The symbol = is read as equal to or equals and means is the same as. E.g. In the calculation 7-2 = 4 + 1; 7 subtract 2 is 5 which is the same as 4 add 1 which also equals 5. Or 7 = Equivalent fractions Fractions with the same value as another. E.g. 2 / 4 is equivalent to ½ : Estimate To arrive at a rough or approximate answer by calculating using approximate terms e.g is approximately equal to = 60. In measurement, an estimate might be made from previous experience. Evaluate Even number To solve a calculation. A whole number that is divisible by 2, leaving no remainder.

4 Exchange Change a number or expression for another of equal value. (This was previously known as borrowing.) E.g. in subtraction, we might exchange a ten for ten ones in order to carry out the calculation. Please see Calculation Policy for further explanation. Factor Factors are numbers we multiply together to get another number. In the calculation 3 x 2 = 6; 3 and 2 are factors of 6. A number can have many factors: 1, 2, 3, 4, 6 and 12 are all factors of 12. Factorise Facts To find all the factors of a given number. The word fact is related to the four operations (+ - x and ) and the instant recall of knowledge about a number i.e. addition facts for 20 could be 11+9, and so on. A multiplication fact for 20 could be 5 x 4 or 2 x 10. Fluency Formal written methods Four Operations To be mathematically fluent there must be a solid understanding, be competent at using a method, a solid knowledge of facts and use all these to tackle problems appropriate to stage of development. Setting out calculations using the column form see Column Method for Addition and Subtraction. Addition, subtraction, multiplication and division. Fraction The result of dividing one whole number by another whole number (not 0). E.g. 1 2 = ½ Hundred square A 10 by 10 grid numbered 1 to 100 or Inequality Infinite Where a number or quantity is not equal to another. An infinite number sequence is one which continues forever. Numbers are infinite. Integer Any whole positive or negative number or 0. E.g. -4, 16, 0. Inverse operation The opposite operation. + and are inverse operations: = 9 and 9 5 = 4. x and are inverse operations 3 x 2 = 6 and 6 2 = 3

5 Long division A column division method which divides by a 2 (or more) digit number e.g Please see Calculations Policy for further explanation. Long multiplication A column multiplication method for multiplying by a 2 (or more) digit number: 37 x 3 = x (3 x 37) (20 x 37) Please see Calculations Policy for further explanation. Mental calculation Missing number problems Mixed fraction Mixed number Multiple Calculations that are solved mentally or supported by a few jottings. A type of problem where a missing number must be calculated. These are often used as an introduction to algebra. E.g. 7 = - 9 A whole number and a fraction e.g. 1 3 / 4. Also known as a mixed number. See mixed fraction above. We get a multiple of a number when we multiply it by another number. E.g. 8, 12 and 16 are multiples of 4 Multiplication x Denoted by the sign x. Repeated addition: = 12 which is the same as 4 lots of 3 = 12 so 4 x 3 = 12 We can multiply by whole number, fractions and decimals. Multiply To carry out the process of multiplication Near doubles A near double is one away from a double. E.g. 27 is a near-double of 13 and of 14. (Spotting near doubles is a good mental strategy e.g = double 13 add one more.) Negative numbers A number less than zero e.g. -2 Commonly known as minus

6 Number bond A pair of numbers with a particular total e.g. all the pairs of numbers that add together to make ten are known as the number bonds to 10 (1 + 9; 2 + 8; 3 + 7; 4 + 6; 5 + 5; 6 + 4; 7 + 3; 8 + 2; ( + 1; ) or number bonds to 20 (1 + 19; ; and so on) These number facts can be transferred to larger numbers e.g. if we know that = 10, we know that = 100. Number line A line where numbers are represented by points upon it Number sentence Any mathematical sentence involving numbers E.g = 9 is a number sentence; 3 < 8 is a number sentence. Numeral A symbol used to denote a number. E.g. Roman numerals are I V X L C D and M. Numerator Odd number The top part of a fraction. In the fraction ¾ 3 is the numerator. A number that is not divisible by 2 a remainder of 1 will always be left. E.g. 1, 3, 5, 7, 9 Ordinal number A word that describes a position within an ordered set E.g. first (1 st ), second (2 nd ), third (3 rd ), fourth (4 th ).. fifteenth, sixteenth etc. Partition To partition a number means to separate it into parts. E.g. to partition 38 we could get 30 and 8 or 19 and 19. Every number can be partitioned in many different ways. Percentage % An amount shown as a part of 100. The symbol is %. E.g. 1% means 1 out of % means 45 out of 100. Place value The value of a digit that relates to its position or number E.g. in the number 1483 the values of the 1 is 1000; the 4 is 400; the 8 is 80 and the 3 is 3 ones. A place value chart: Thousands Hundreds Tens Ones Plus + A name for the symbol + (addition)

7 Positive number A number greater than zero (0) Prime factor The factors of a number that are also prime numbers. E.g. the factors of 12 are 1, 2, 3, 4, 6 and 12. The prime factors are 2 and 3. Prime Number A whole number greater than 1 that has exactly two factors, itself and 1. E.g. 2 (factors are 1 and 2); 3 (factors are 1 and 3); 13 (factors are 1 and 13). One (1) is not a prime number because it only has one factor (1). Product Proper fraction The result of multiplying one number by another number. The product of 3 and 4 is 12 (3 x 4 = 12) A fraction where the denominator is larger than the numerator E.g. ½ is a proper fraction because 2 is larger than 1, whereas 3 / 2 is an improper fraction because the numerator is larger than the denominator. Quotient The answer from a division calculation e.g = 5 so 5 is the quotient. Remainder When dividing, the remainder is what is left over E.g = 5 remainder 1 Repeated addition Repeated subtraction Roman Numerals The process of adding the same number or amount = 20 is an example of repeated addition (Links to multiplication: 4 x 5 = 20) The process of subtracting the same number or amount = 0 is an example of repeated subtraction (links to division: 20 5 = 4) The Romans used a set of capital letters to denote cardinal numbers. I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000 And all other numbers are built up using these letters. Round To round a number to the nearest whole number / ten / hundred. 5 and above are always rounded up. 0-4 are rounded down. E.g. 45 rounded to the nearest 10 is rounded to the nearest 10 is 30.

8 Sequence A succession of numbers formed according to a rule. E.g. 2, 4, 6, 8, 10 is a sequence of even numbers. 2, 4, 9, 16 is a sequence of square numbers. Set Share Short division A well-defined group of objects To share equally is to split a group of objects into equal groups (division) A compact method of division E.g = Please refer to Calculation Policy for further explanation. Short multiplication A compact method of multiplication E.g. 136 x 4 = x Simple fraction Simplify (a fraction) Please refer to Calculation Policy for further explanation. Where both the numerator and the denominator are whole numbers, also known as a common fraction. To reduce a fraction to its simplest form. E.g. 5 / 10 can be simplified to ½ Subtract - Subtraction Subtraction by decomposition To carry out the process of subtraction The inverse operation to addition take away. When you need to exchange within a subtraction calculation E.g = For further explanation, please see the Calculation Policy.

9 Sum The sum of addition the sum of 4 and 5 is 9. Take away Total Zero To remove a number of items from a set (subtraction) The sum found when adding Nought or nothing. It is neither positive nor negative. It is even (rather than odd)

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