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![]() Models assist students by providing a tool to support their thinking. 103 take away 90 is 13, then take away another 5 to get 8).Ī good teaching strategy will develop meaning from a model. If they take away 95, it is likely that they have not realised the fact that ‘difference between’ will provide them with an answer to problems like this (e.g. add 5 to get to 100, add 3 to get to 103, altogether I added 8. If they count up from 95, or back from 103, they are using ‘difference between’ e.g. To find out if students can interpret subtraction as 'difference between' observe their responses when they work out 103 − 95. Instead, 25 − (-8) is best interpreted as the difference between 25 and (-8). For example I have 25 objects, but I lose (-8) is an apparently meaningless question and is no help to work out 25 − (-8). If students only have the 'take away' meaning for subtraction, then subtracting a negative number will be meaningless. There is a difference of 17 years between their ages. Then I have 17 left.ĭifference between Example: Kim is 25 and Tim is 8. Take away Example: I have 25 objects, but I lose 8. Illustration 1: Subtraction as 'take away' and as 'difference between'Īll of the arithmetic operations have several real world meanings.įor example, 25 − 8 can be interpreted as: They may see mathematics as arbitrary and unreasonable. Students who do not have a useful model for subtraction of negative numbers will have to focus on memorising rules without understanding, with consequent higher chances of forgetting. ![]() Success depends on being able to give appropriate meanings to the subtraction operation. They interpret subtraction as 'taking away' and it makes no sense to them to 'take away' a negative number of things. Earlier, students can add positive and negative numbers, and subtract positive numbers, but cannot make sense of subtracting negative numbers. The most difficult aspect is to subtract a negative number. Success depends on students being able to add and subtract positive and negative numbers, and to give a meaning to these operations. Lots of practise with various models will support students to develop this understanding. The use of number lines, cartesian planes and extended hundreds charts will help students to understand that both the MAGNITUDE and the DIRECTION of an integer are important to consider to determine which number is larger / smaller than another. Placing integers in order becomes more complex when negative integers are added to the positive. This can be demonstrated through the use of a number line, cartesian plane or extended hundreds chart. Support students to understand the relationship between positive and negative integers of the same magnitude as being 'opposite' numbers in that they are reflected around zero. Will have been introduced to negative integers in Level 6 ( VCMNA210). Negative integers, and to give a meaning to these operations. At this level, students compare, order, add and subtract positive and
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