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From Karnataka Open Educational Resources
Series of Activities on Number Systems (view source)
Revision as of 03:51, 29 January 2013
, 03:51, 29 January 2013→Lesson 1 : The idea of negative numbers and operations on negative numbers
*Two boxes – one of negative numbers and the other of positive numbers<br>
*Two boxes – one of negative numbers and the other of positive numbers<br>
'''How to do the activity'''<br>
'''How to do the activity'''<br>
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'''''Part 1'''''
'''''Part 1'''''
6. Now we transition from numbers representing some quantities to numbers being manipulated as numbers.<br>
6. Now we transition from numbers representing some quantities to numbers being manipulated as numbers.<br>
'''Part 2'''
'''Part 2'''<br>
1. We have seen what negative numbers are. We will see how to work with them. <br>
1. We have seen what negative numbers are. We will see how to work with them. <br>
2. We have seen that negative numbers are such that when we add them the quantity decreases. What happens when we subtract them?<br>
2. We have seen that negative numbers are such that when we add them the quantity decreases. What happens when we subtract them?<br>
*-3 x -3. How do we do this? <br>
*-3 x -3. How do we do this? <br>
Let us look at the table below.<br>
Let us look at the table below.<br>
- 3 x 3 = -9<br>
- 3 x 3 = -9<br>
- 3 x 2 = -6<br>
- 3 x 2 = -6<br>
- 3 x 1 = -3<br>
- 3 x 1 = -3<br>
- 3 x 0 = 0<br>
- 3 x 0 = 0<br>
- 3 x-1 = -3<br>
- 3 x-1 = -3<br>
- 3 x-2 = -6<br>
- 3 x-2 = -6<br>
- 3 x-3 = -9<br>
- 3 x-3 = -9<br>
Extend the pattern above. By simple pattern evaluation we see it is 3, 6 and 9. We have shown the number line above. It makes sense logically that the next number is 3 and that it becomes positive. The best way to extend this to division is to treat this as multiplication by fraction and extend these rules.<br>
Extend the pattern above. By simple pattern evaluation we see it is 3, 6 and 9. We have shown the number line above. It makes sense logically that the next number is 3 and that it becomes positive. The best way to extend this to division is to treat this as multiplication by fraction and extend these rules.<br>
Yet another way of explaining could be like this. When we add -3, -3 times we are actually operating with two opposites. The (-3) times signifies the opposite of the repeated addition, think of it as repeated subtraction. I am subtracting -3 once (in effect, adding 3); -(-3) second time (adding another 3) and -(-3) for the third time -(-3) (adding one more 3). We get 9. Hence -(-) is positive.<br>
Yet another way of explaining could be like this. When we add -3, -3 times we are actually operating with two opposites. The (-3) times signifies the opposite of the repeated addition, think of it as repeated subtraction. I am subtracting -3 once (in effect, adding 3); -(-3) second time (adding another 3) and -(-3) for the third time -(-3) (adding one more 3). We get 9. Hence -(-) is positive.<br>
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'''Evaluation activities'''
'''Evaluation activities'''
