Words used across several Curriculum for Excellence levels
| Term | Description | Example |
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| Algorithm | Sometimes known as ‘standard written method’, an algorithm is a step by step process for finding the answer to an adding, subtracting, multiplying or dividing sum that is too difficult to work out mentally. The steps must be carried out in the correct order. | Look at this example: |
| Approximate | To give a ‘rough answer’ that may be slightly more or less than the actual answer (see also estimation and rounding). | Subtraction example: 289 – 42
289 is a bit less than 290 and 42 is a bit more than 40. |
| Area model | An area model (sometimes known as a ‘window array’) is a useful tool for helping us think about multiplication (see also ‘grid partitions’). This song from NUMBEROCK explains the area model method. | A section of fence is 12.4m long. A school needs 38 lengths of fence to enclose their playground. Find the total length of their fence.
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| Associative Law | Addition and multiplication are associative. This means that it doesn’t matter how you group the numbers when adding or multiplying. | Addition:
(6 + 3) + 4 = 10 or 6 + (3 + 4) = 10 Multiplication: (2 x 4) x 3 = 24 or 2 x (4 x 3) = 24 |
| Bar Model | A bar model helps learners to solve maths problems by showing them the parts that make up the whole. By drawing a bar model, pupils can convert the problem into a ‘picture’. Early / 1st level  3rd / 4th level |
2nd level bar model |
| Commutative Law | You can add or multiply numbers together in any order. The answer doesn’t change. Addition and subtraction are commutative – subtraction and division are not. | Addition: 17 + 45 = 45 + 17
Multiplication: 90 x 2 = 2 x 90 |
| Concrete materials | Objects such as cubes and counters that can be used by pupils to help them make more sense of numbers and to understand the relationships between them. |   |
| Denominator | The number under the line is a fraction. The denominator tells us the total number of equal parts that make up the whole. | 
1/4 of the shape is red, 3/4 of the shape is yellow. In both fractions, 4 is the denominator. |
| Difference | The difference between two numbers can be found by comparing objects, counting on from the smaller number or taking away from the larger number. | The difference between 9 and 4 is 5
4 + 5 = 9 9 – 4 = 5
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| Digits | Digits are the symbols used to make numerals (numbers). For example, the numeral 153 is made up of three digits (1, 5 and 3).
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the digits used in our number system. |
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| Empty number Line | An empty number line helps pupils to solve maths problems. One of the numbers is partitioned (broken up) into 1000s, 1000s, 10s and 1s and added or taken away from the starting number in ‘jumps’.
The pupil chooses the size of the jumps that works best for them. These pictures show the ways that two different children have used the empty number line to solve the same problem: There are 46 Primary 3 pupils in a school. 22 are boys. How many girls are there? The empty number line is most often used for adding and taking away but can also be used for multiplying and dividing. |
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| Estimate / Estimation | When we estimate we make a ‘reasonable guess’ about the worth, amount or size of something. | I estimate that the car is worth about £5000
I estimate there are 120 sweets in the jar. I estimate that the room is longer than 9 metres. |
| Equivalent Fractions | Fractions which have equal value are known as equivalent fractions. For example, one half is equivalent to two quarters which is also equivalent to four eighths.
A Fraction Wall is sometimes used to help learners understand equivalent fractions: |
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| Formula | A formula is a mathematical relationship or rule shown in symbols.
To find the volume of a box we multiply the length (l), by the breadth (b), by the height (h). The formula for finding the volume (v) of the box is therefore v = l x b x h |
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| Fraction | A fraction is an equal part of a whole.
The number under the line (denominator) tells us how many equal parts the whole has been split into. The number above the line (numerator) tells us the number of equal parts we are using or referring to. For example, 3/5 means the whole has been split into 5 equal parts (fifths) and we are working with three of these parts (3/5). |
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| Grid Method | The grid method (also known as the area model method) helps learners to understand multiplication by partitioning (breaking up) numbers and dealing with each part one at a time.
For example, learners who have difficulty remembering 6 x 8 (6 rows of 8) can think of it as 5 rows of 8 plus 8 more. |
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| Inverse Relationship | Inverse means the opposite. In maths, an inverse relationship is a relationship between two methods that are opposites but related in some way.
Subtraction is the inverse of addition. |
100 – 40 = 60 because 40 + 60 = 100
There is an inverse relationship between addition and subtraction. 63 ÷ 7 = 9 because 7 x 9 = 63 There is an inverse relationship between multiplication and division. |
| Jottings | Words, pictures or symbols which pupils jot down to help them keep track of their thinking when working mentally, or when solving problems that have more than one step. |  |
| Mental Agility | There is much more to mental maths than being able to recall number facts quickly. Pupils with good mental agility have lots of strategies for solving problems and can choose the best one for the problem.
For example, pupils with good mental agility understand that addition is commutative (the numbers can be added together in any order). They might rearrange the calculation and look for ‘friendly numbers’ (numbers that add together to make ten or a multiple of ten) to find the answer and will not need to use an algorithm. |
16 + 21 + 43 + 14
*Please note that other methods are possible. |
| Million | A million is one thousand thousands. | We say ‘one million‘. We write 1 000 000 |
| Numeral | A symbol that stands for a number | Examples: 3, 49 and twelve are all numerals. |
| Numerator | The number above the line is a fraction. The numerator tells us the number of equal parts we are using to refer to. | 1 of the four equal parts (1/4) is red. 1 is the numerator. 3 of the four equal parts (3/4) are yellow. 3 is the numerator.
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| Numicon | Concrete materials that can help pupils think about numbers in a range of ways. The numbers 1 – 10 each have their own shape, colour and value. |  |
| Ones | The last digit of any whole number with two or more digits.
Our place value system is based on units of one, ten, a hundred, a thousand, a million, a billion… Ten ones equal one ten; twenty ones equal 2 tens (20), thirty ones equal 3 tens (30) etc. One hundred ones equal one hundred (100); two hundred ones equal two hundred (200) etc. One thousand ones equal one thousand (10000) etc. Ten thousand ones equal ten thousands (10 000) etc. |
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| Partition | To split a number into parts to help with adding, subtracting, multiplying and dividing. For example:
10 can be partitioned into 6 + 4, 5 + 5 etc. 138 can be partitioned into 100 + 30 + 8; 130 + 8, 50 + 50 + 30 + 8 etc. 12∙6 can be partitioned into 10 + 2 + 0∙6 3∙542 can be partitioned into 3 + 0∙5 + 0∙04 + 0∙002 |
Click on the image below to watch a video:
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| Place Value | Digits can have different values. The position (place) of a digit tells us its value. For example:
In the number 2 634 634, the 2 has a value of 2 000 000 (2 million) In the number 2634, the 2 has a value of 2000 (2 thousands) In the number 6234, the 2 has a value of 200 (2 hundreds) In the number 6324 the 2 has a value of 20 (2 tens) In the number 2.834, the 2 has a value of 2 (2 ones) In the number 8∙324, the 2 has a value of 2/100 (2 hundredths) |
This song from NUMBEROCK clearly explains the place value system, as well as being fun to listen to with your child. |
| Rounding | Rounding means adding to a number, or subtracting from a number, to make a multiple of ten. Rounding is useful as it allows us to judge whether or not an answer makes sense.
If a number ends in 5, 6, 7, 8 or 9, we usually round up to the next multiple of ten, for example 157 rounded to the nearest ten is 160. If a number ends in 1, 2, 3 or 4 we round down to the previous multiple of ten, for example 223 rounded to the nearest ten is 220. |
To find the approximate answer to 43 + 98, round 43 down to 40 and round 98 up to 100.
40 + 100 = 140 so the answer is approximately 140 (actual answer 141) To find the approximate answer to: 836 – 295, round 836 up to 840 and round 295 up to 300. 840 – 300 = 540 so the answer is approximately 540. (actual answer 541) |
| Sequence | To sequence means to arrange a set of numbers according to a pattern or rule. Sequences can increase (numbers get bigger) or decrease (numbers get smaller). | 2, 4, 6, 8, 10, 12 (going up in twos / increasing in multiples of 2)
25, 23, 20, 18, 15, 13 (take away 2, then 3, then 2, then 3….) 1, 2, 4, 8, 16, 3 (each number is double the one before it) 109, 129, 124, 144, 139, 159 (add 20, take away 5…) |
| Strategy | A way of doing a calculation or solving a problem. As children progress through school they will be encouraged to think about which strategy is best, based on the numbers they are working with. For example, the best way to find the answer to 3000 – 2998 is to count on from 2998 up to 3000. |  |
| Sum | The result of adding two or more numbers together to find a total. The sum of 5, 4 and 2 = 11 |
The sum of 5, 4 and 2 is 11.
The sum of 300, 56 and 221 is 577. |
| Symbol | Shapes, letters or ‘marks’ that are used to stand for something else. Common mathematical symbols are:
= (equals) ≠ (not equal to) ˂ (less than) > (greater than) |
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| Think Board | A tool for showing how we can think about a problem in different ways, for example in words, in symbols, as a picture, as a bar model or on a number line. |  |
| Units | Our place value system is based on units of one, ten, a hundred, a thousand, a million, a billion…Ten ones equal one ten; twenty ones equal 2 tens (20), thirty ones equal 3 tens (30) etc.
One hundred ones equal one hundred (100); two hundred ones equal two hundred (200) etc. One thousand ones equal one thousand (10000) etc. Ten thousand ones equal ten thousands (10 000) etc. |
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| Word Problem | A mathematical puzzle written in words. Pupils must read the question carefully before deciding whether they need to add, subtract, multiply or divide to solve the problem. Some word problems are solved in one step, others require more than one step. Think Boards help pupils to think about word problems. | Example of a second level word problem that requires more than one step:
Jack had £30. After buying a pair of jeans and a shirt he was left with £5.52. His jeans cost £15∙49. How much did Jack’s shirt cost? |
