WFIS & Nursery Mathematics Glossary Addend Addition A number to be added to another. For example, 8 + 6, 6 is the addend. This operation adds one number of the set to anther in the set to form a third number. The result of the addition is called the sum or total. The operation is denoted by the + sign. When we write 5 + 3 we mean add 3 to 5; we can also read this as 5 plus 3. In practise the order of addition does not matter; the answer to 5 + 3 is the same as 3 + 5 and in both cases the sum is 8. This is the same for all pairs of numbers and therefore the operation of addition is commutative. To add 3 numbers together, first two of the numbers must be added and then the third added to this intermediate sum. E.g. 5 + 3 + 4 means add 3 to 5 then add 4 to the result to be given an overall total of 12. Addition is the inverse operation to subtraction. There are two models for addition; augmentation and aggregation. Augmentation: one quantity or measure is increased by another quantity, e.g. I had 1.50 and was given 1, then I had 2.50. Aggregation: combining two quantities or measures to find the total. I had 1.50 and my friend had 1. altogether we had 2.50. Algebra Analogue clock Angle Anti clockwise Array The part of mathematics that deals with generalised arithmetic. Letters are used to denote unknown numbers. For example, 2 + 6 = a, 6 + 2 = a, a 6 = 2, a 2 = 6. A clock with 12 equal divisions to represent hours. Commonly each of the 12 divisions is further subdivided into five equal part representing minutes. An angle is a measure of rotation and is often shown as the amount of rotation required to turn one line segment onto another where the two line segments meet at a point. In the opposite direction from the normal travel of the hands of an analogue clock. An ordered collection of counters, numbers etc in rows and numbers. Used as a pictorial representation of repeated addition and multiplication. The rows are the number being repeated added/ multiplied and the number of rows is how many lots of the number there are. For example; This array shows; This array shows; 2 + 2 + 2 = 6 or 2 x 3 = 6 3 + 3 = 6 or 3 x 2 = 6 Children learn that as multiplication is repeated addition it is commutative, a commutative array is a rotation of the other and therefore has a different multiplication statement. Bar chart A format for representing statistical information. Bars, of equal width, represent frequencies and the length of the bars are proportional to the frequencies. The bars can be vertical or horizontal depending on the orientation of the chart.
Block graph A simple format for representing statistical information. One block represents one observation. For example, a birthday graph where each child places one block, or colours one square, to represent himself/herself in the month in which he or she was born. Capacity The volume of a material (usually liquid or air) held in a vessel or container. NB the volume of a cup is the space taken up y the material of the cup. Where as the capacity of the cup is the volume of the liquid or air that the cup can contain. A solid cube has volume but no capacity. Cardinal A cardinal number denotes the quantity of objects in a set. number Carrol diagram A sorting diagram in which numbers or objects are classified as having a certain number of property or not having that Even property. Not even Multiple of 6, 12, 18, 24, 30 3, 9, 15, 21, 27, 33 three Not a multiple 2, 4, 8, 10, 14, 16, 20, 22, 1, 5, 7, 11, 13, 17, 19, 23, 25, 29, of three 24, 26, 28, 32 31 Centi - Centimetre Chart Chronological Clockwise Column graph Commutative Prefix meaning one hundredth of Symbol; cm. A standard unit of measure equivalent to one hundredth of a metre. Another term for a table or graph. Relating to events that occur in a time ordered sequence. In the direction in which the hands of an analogue clock travel. A bar graph where the bars are presented vertically. Addition and multiplication are commutative as the operation can be carried out to the numbers in any order and will equal the same total. Subtraction and division are not commutative. For example, 4 + 5 is the same as 5 + and 4 x 2 is the same as 2 x 4. However, 21 4 is not the same as 4 21 and 21 3 is not the same as 3 21. Composite shape A shape formed by combining two or more shapes.
Concrete objects Cone Continuous data Corner Cube Cuboid Cylinder Denomination Difference Objects that can be handled and manipulated to support understanding of the structure of a mathematical concept. For example, materials such as dienes Tens and Ones, Cuisenaire, Numicon and beadstrings. A cone is a 3-dimensional shape with a circular base, a vertex and Data arising from measurement taken on a continuous variable, for example, length o caterpillars., weight of crisps. A point where two lines or sides of a flat shape meet for example, a rectangle has 4 corners. (see Vertex for 3D shapes) A 3-dimensional shape with 6 square faces, 12 edges and 8 vertices. A 3-dimensionalshape with 6 rectangular faces, 12 edges and 8 vertices. A 3-dimensional shape with 2 circular faces and one curved rectangular face and 2 edges. The face value of coins. The smallest denomination of our currency is 1p and the largest is 50 note. In Maths it is the numerical difference between two numbers or sets of objects found by comparing the two. For example, the difference between 12 and 5 is 7, and the difference between Difference is one way of thinking about subtraction and can be a more helpful image for subtraction than take away e.g. find the difference between 108 and 97. when you subtract 97 from 108 the difference is 11. Digit The symbols of the number system; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. For example, 29 is a two digit number. The digits represent 2 Tens and 9 Ones. Digital clock Dividend A clock that displays the hours and minutes passed since midnight. In division, it is the number that is divided. For example, 15 3. 15 is the dividend. Division Division can be sharing, the number to be shared is divided equally inot a given number of parts. For example, sharing 20 pencils into 5 pots or finding a quarter of a strip of paper. Division can also be grouping, the number of groups of a given size is found. For example, grouping a pile of 10 pencils into piles of 2. Division is the inverse operation to multiplication. Double To multiply by 2. For example, double 13 is 26. The number that is twice another 26 is double 13. A near doubles is one away from a double. For example, 10 + 11 is a near double of 10. Spotting near doubles is a very useful mental calculation strategy, for example, seeing 12 plus 14 as 2 more than double 12. Edge The line where two faces of a 3D shape meet (see Faces). For example, a cuboid has 12 edges, a cylinder has two edges.
Equal The symbol = read as is equal to or equals meaning having the same value as or balances with. For example, 2 + 8 = 10, 10 = 2 + 8, 4 + 6 = 5 + 5 as they both have the same value of 10. It is important to represent the equals symbol on the both the right hand side and the left hand side of the calculation, so that the children do not think it means the answer. Otherwise children will be iunstuck when faced with questions such as + 5 = 18 or 15 + 9 = 17 +? Equivalent Fractions with same value as each other. For example, 2/4 = 1/2 and 4/4 = 2/2. fractions Even number A quantity that is divisible by 2. Face Facts One of the flat surfaces of a solid 3D shape. For example, a cube has 6 faces and the faces are square. A cylinder has 3 faces, 2 circular and one curved rectangular. A sphere has one curved face. i.e. addition/subtraction/multiplication and division facts. The word fact is related to the 4 operations and the instant recall of knowledge about the composition of the number. For example, an addition fact 10 + 20 = 30, a subtraction fact 20 = 30 10, a multiplication fact 10 x 3 = 30, a division fact 30 3 = 10. Fluency Generalised statement To be mathematically fluent one must have a mix of conceptual understanding, procedural fluency and knowledge of facts to enable you to tackle problems appropriate to the stage of development confidently, accurately and efficiently. A statement that applies correctly to all relevant cases. For example, the sum of two odd number is always an even number. All even numbers can be shared equally by 2. Generalise Hundred square Inverse operations To formulate a general statement or rule. A 10 by 10 square grid numbered to 100. Children learn to use this tool to find one more and one less than another number by locating the original number and then moving their finger right or left. Then they progress onto using the grid to find 10 more or 10 less than by moving vertically up or down. Next they progress on finding 9 more or less by moving vertically up or down then adjusting by moving left 1. Then the same method again for finding 11 more or less, moving vertically then adjusting by moving right 1. Operations that perform the opposite calculation to each other. Addition and subtraction are inverse operations. Multiplication and division are inverse operations. Mass Mental calculations Minus Mass differs from weight, mass is a constant measure, whereas weight can change without gravity. The mass of an object is measured by the amount of matter in a given object. We measure mass in grams and kilograms. Referring to calculation that are largely carried out mentally, but may be supported with a few simple jottings. A name for the symbol, representing the operation of subtraction.
Missing number problems A problem such as 12 + = 19 or - 9 = 13 Children use their knowledge of either inverse operations, for example, 12 + = 19 becomes 19 12 = or - 9 = 13 becomes 13 + 9 =. Or as the children understand the equals sign as a balance, then they can work out what needs to be added or subtracted to make the two sides of the equals sign balance. This can lead onto examples such as, 7 + = 10 + 5 or 12 = 4 + 3 as they know the value of one side of the equals sign, the other must be made to balance. Multiple Numbers that are within the times table for a number. For example; 8, 12 and 18 are multiples of 2 as 2 x 4 = 8, 2 x 6 = 12 and 2 x 9 = 18. Multiples of 10 are 10, 20, 30, 40 etc. Multiplicand A number to be multiplied by another number. For example, in 5 x 3, 5 is the multiplicand as 5 is to multiplied by 3. Multiplication Multiplication is the operation denoted by x and is the calculation of scaling one number by another. The calculation is initially taught as repeated addition, as it is scaling one number consistently by another. Then the links are made to connect the two operations. For example, 2 + 2 + 2 + 2 is the same as 4 lots of 2 or 2 x 4. Here 2 and 4 are the factors and 12 is the product. Multiplication is commutative, as it is repeated addition and addition is commutative. For example, 2 x 5 = 5 x 2. (See arrays for drawn representation.) Number bond A pair of numbers with a particular total. For example, number bonds to 10 are pairs of whole numbers with a total of 10 such as 3 + 7 = 10, 6 + 4 = 10. These facts can then be used to work out bonds to 20, 3 + 17 = 20. Then multiples to 100, 30 + 70 = 100 and then in Year 2, any bond to 100, 33 + 67 = 100. Number statement A mathematical statement involving numbers. For example, 9 + 11 = 20, 27 5 = 22, 5 x 5 = 25, 18 3 = 6 Numeral The symbol used to denote a number value. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Octagon Ordinal A polygon with 8 sides. A term that describes the position within a set. For example, first, second, third twentieth. number Partition The method of splitting a number into its component parts. For example, the two digit number 38 can be partitioned into 30 + 8. This method can be used to calculate addition or subtraction once the children are secure with the place value of numbers. For example, 36 + 23 is partitioned into 30 + 20 = 50, 6 + 3 = 9, 50 + 9 = 59. 48 32 is partitioned into 40 30 = 10. 8 2 = 6. Then combine the remaining values 30 + 6 = 36. This is drawn as; 48-32 40 8 30 2 40 30 = 10 8 2 = 6 10 + 6 = 16 48 32 = 16
Pentagon Pictogram A polygon with 5 sides. A format for displaying statistical information. Suitable picture, symbols or icons are used to represent values. Pictures can each represent a value larger than 1 and then a part symbol will represent a proportion of the whole value. In Year 1 pictures can represent 2, 5, and 10 and Year 2 pictures can represent 2, 3, 5, and 10 (in line with the multiples they are expected to count in). Pictorial representation Place value Pictorial representations enable learners to use pictures to represent mathematical structures. Pictorial representations follow on from the learners experience with concrete objects, such as a dienes stick representing 10, can then be drawn as a stick in their jottings. Pictorial representation may be used as ones that have been shown to them to use or the children may create their own. The value of a digit that relates to its position or place in a number. For example, in the number 138 the digits represent 1 hundred, 3 tens and 8 ones. In the number 72 the digits represent 7 tens and 2 ones. It is very important that the children read numbers as both the quantity name such as, 33 as thirty three and also the value that each of the digits represent, 3 tens and 3 ones. As we do not write it as 30 3. Plus A name for the symbol +, representing the operation of addition. Product The result of multiplying one number by another. For example, 5 x 7 = 35, the product is 35. Property Repeated addition Repeated subtraction Rotation Sequence Share equally Standard unit Any attribute. For example, the property of a square is that all the sides are equal length. The process of repeatedly adding the same number or amount. This is a model for multiplication. For example, 5 + 5 + 5 = 5 x 3. The process of repeatedly subtracting the same number or amount. This is a model for division. For example, 35 5 5 5 5-5 5 5 = 0, so 35 5 = 7. A whole flat shape/plane which turns about a fixed point, the centre of rotation. A succession of terms formed according to a rule. There is a definite relationship between one term and the next and between each term and its position in the sequence. For example, 1, 4, 9, 16, 25. One model for the process of division. A recognise unit of measure, for example centimetres, grams, millilitres. Non standard units of measure are also used, such as, hand span or foot length. Which vary from, person to person but are used to introduce the concept of measure.
Subtraction Sum Tally The inverse operation to addition. Subtracting a value from another. Refers to addition number statements only. The sum is the combined total of two or more values. Make marks to represent objects counted. Drawn by counting 4 vertical lines crossed by a diagonal 5th. The counted in 5 s and 1 s. A tally chart is a table representing a tally count. Total Unit Vertex Volume The sum found by adding. A standard used is measuring e.g. the metre is a unit of length, the degree is a unit of turn. The point at which 2or more edges meet on a 3D shape. Plural is vertices. For example, a cube has 8 vertices. A measure of 3 Dimensional space inside an object. Also, the volume of a liquid being measure in Litres and/or millilitres. Zero Nought or nothing. In the Place Value system it is a place holder, for example, 30, 105, 260. Nought show that there is a value to be held until the number is increased. Resources to help with the Concrete to Pictorial to Mental phases of learning in Maths. Dienes hundreds, tens and ones. Bead strings Number line Numicon 100 square Double sided counters Cuisenaire rods Multilink cubes Useful website for printing your own resources! www.twinkl.co.uk www.sparklebox.co.uk