Teachers at this level should take care not to use the word ‘sum’ for anything but addition. Finding the ‘sum’ of two or more numbers means to add them together. This is an inaccurate use of the word ‘sum’. Many years ago students were told to ‘do their sums’ and this could apply to any calculation using any of the four basic operations. It is important that we use the language related to addition correctly. In Latin, less is written as minus, hence our use of the word to mean subtraction. The word ‘sum’ comes from the Latin summus and means highest. Looking at where words come from gives us some indication of what they mean. Often it is desirable to emphasise one term more than others when introducing concepts, however a flexibility with terminology is to be aimed for. It is important that children are exposed to a variety of different terms that apply in addition and subtraction situations and that the terms are used accurately. For example, there is no exact amount of brown sugar that I need to add to my porridge to make it tasty. Some of those words are used imprecisely outside of mathematics. Subtraction − take away, minus, subtract, difference There is a great deal of language related to the concepts of addition and subtraction.Īddition − and, add, plus, put together with, sum If we start with 6 pineapples and take away 2, we are left with 4. So we say there are 6 pineapples altogether and we can write 4 + 2 = 6. For example, in the picture below there are 4 pineapples in the first set and 2 pineapples in the second set, When we combine two or more disjoint collections of objects, the total number of objects is the sum of the numbers in each of the collections. Later, when they have some experience with negative numbers, they will learn that this is not always true. The ability to make a judgment about the relative size of two or more sets of objects as a pre-cursor to finding the difference between them.Ĭhildren’s early experience of addition and subtraction may include an understanding that ‘when I add, I get more’ and ‘when I subtract, I have less than what I started with’.The use of the number line to compare numbers to thirty.The use of the number line to place numbers in relation to other numbers.Counting forwards and backwards by ones and skip-counting.(See the module, Counting and Place Value.) Some ability to decompose small numbers into tens and ones.However, there are some basic skills that are useful foundations necessary for addition and subtraction of whole numbers: The development of solid understanding of addition and subtraction is essential for the development of later concepts including other arithmetical operations, calculations arising from measurements and algebra.Ī child can develop the basic ideas related to addition whilst investigating the place value system. A relatively common example of someone working without a sense of number is the person at the check-out who tries to charge a large sum for an inexpensive item simply because the cash register tells them to, without pausing to think that perhaps the code for the item was incorrect. Once an understanding of numbers has been developed, calculators and computers can be used with some confidence that any data-entry errors that are inconsistent with our number sense will be identified. It is usual for children to develop some basic mental strategies before they are taught formal algorithms.Ī student will not develop a number-sense, or fluency with operations, if they move to calculators too quickly. While there are many ways to calculate with arithmetic, the commonly taught algorithms have remained in constant use because they provide an accurate and efficient means to the answer. The ability to add numbers in your head is used when you play, or watch sport and when you buy a couple of items at the shops.įormal or written algorithms are useful when larger numbers make mental calculations difficult. Subtraction and addition are inverse operations.įor example, 6 = 4 + 2 is equivalent to 6 − 4 = 2 and also 6 − 2 = 4. Of the four arithmetical operations on numbers, addition is the most natural. The word operation comes from the Latin ‘operari’, meaning to work or toil. Addition and subtraction are two of the ways we work with numbers.
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