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→Developmental Questions (What discussion questions)
<b>11 + 2 = 13 ( + 2 signifies increase in apples)
<b>11 + 2 = 13 ( + 2 signifies increase in apples)
<br>13 + 2 = 15 Write the expression. Again + signifies increase
<br>13 + 2 = 15 Write the expression. Again + signifies increase
#2. Let us say I ask the question – what should I add to 15 to make the number of apples 10? They will say ”take away”. Let us say we cannot use the word “take away”. <br>
#2. Let us say I ask the question – what should I add to 15 to make the number of apples 10? They will say take away Let us say we cannot use the word “take away”. <br>
Write the expression like this 15 + (-5) = 10.
Write the expression like this 15 + (-5) = 10.
#The numbers that when added to a number increase the original quantity are called positive numbers. The numbers that when added to a number decrease the original quantity are called negative numbers. The negative number is thus an opposite of the positive number.<br>
#The numbers that when added to a number increase the original quantity are called positive numbers. The numbers that when added to a number decrease the original quantity are called negative numbers. The negative number is thus an opposite of the positive number.<br>
*What do I add to 15 to get 9? (-6)
*What do I add to 15 to get 9? (-6)
*What do I add to 15 to get 10? (-5)
*What do I add to 15 to get 10? (-5)
*When I add (-7). I get 8. For me to get 9, I have to add a number greater than (-7) and I have added (-6). Similarly (-5) is greater than (-6). So the larger negative number is actually smaller''.'''<br>
*When I add (-7). I get 8. For me to get 9, I have to add a number greater than (-7) and I have added (-6). Similarly (-5) is greater than (-6). So the larger negative number is actually smaller.<br>
# Now we transition from numbers representing some quantities to numbers being manipulated as numbers.<br>
# Now we transition from numbers representing some quantities to numbers being manipulated as numbers.<br>
===Part 2===
===Part 2===
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>
==Evaluation (Questions for assessment of the child)==
==Evaluation (Questions for assessment of the child)==