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Line 97: − + − 1. To extend the understanding and skill of representing symbolically numbers and manipulating them+ − 2. To understand tha negative numbers are numbers that are created to explain situations in such a way that mathematical operations hold+ − 3. Negative numbers are opposite of positive numbers; the rules of working with negative numbers are opposite to that of working with positive numbers+ − 4. Together, the negative numbers and positive numbers form one contiuous number line+ − 5. Perform manipulations with negative numbers and express symbolically situations involving negative numbers+ − + − + + + + + + + + + + + + − Objectives of the activity − 1. Develop an idea that negative numbers are part of a type of numbers − 2. That negative numbers are continuous − 3. Repesent the number line with zero as a place holder − Materials needed − 1. More apples (or any other fruit) − 2. Small cards for writing down the numbers as well as for writing the operations − 3. Pencils, etc − 4. Two boxes – one of negative numbers and the other of positive numbers − How to do the activity − Part 1 + − + − + − + − 5. What do I have to add to 15 to make it 7? The answer is (-8). + − + − + − + − + + + + +
Series of Activities on Number Systems (view source)
Revision as of 15:59, 28 January 2013
, 15:59, 28 January 2013→Part II – Negative Numbers
== Part II – Negative Numbers ==
== Part II – Negative Numbers ==
Objectives
=== Objectives ===
# To extend the understanding and skill of representing symbolically numbers and manipulating them.<br>
# To understand that negative numbers are numbers that are created to explain situations in such a way that mathematical operations hold<br>
# Negative numbers are opposite of positive numbers; the rules of working with negative numbers are opposite to that of working with positive numbers<br>
# Together, the negative numbers and positive numbers form one contiuous number line<br>
# Perform manipulations with negative numbers and express symbolically situations involving negative numbers<br>
Lesson 1 : The idea of negative numbers and operations on negative numbers
(Similar to the first part, there could be many more activities and lessons here- this is just an illustration)
'''Lesson 1 : The idea of negative numbers and operations on negative numbers'''<br>
'''Objectives of the activity'''
#Develop an idea that negative numbers are part of a type of numbers<br>
#That negative numbers are continuous<br>
#Repesent the number line with zero as a place holder<br>
'''Materials needed'''
*More apples (or any other fruit)<br>
*Small cards for writing down the numbers as well as for writing the operations<br>
*Pencils, etc<br>
*Two boxes – one of negative numbers and the other of positive numbers<br><br>
'''How to do the activity'''
'''''Part 1'''''
1. By the previous activity we have 11 apples. Now we add a few more. Let us say we add 4 more. We have 15 apples.
1. By the previous activity we have 11 apples. Now we add a few more. Let us say we add 4 more. We have 15 apples.
11 + 2 = 13 + 2 signifies increase in apples
11 + 2 = 13 + 2 signifies increase in apples
13 + 2 = 15 Write the expression. Again + signifies increase
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?
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”.
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.
3. 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.
4. Now frame the question as follows – what do I
3. 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 8? (-7)
4. Now frame the question as follows
What do I add to 15 to get 9? (-6)
*What do I have to add to 15 to make it 7? The answer is (-8).
What do I add to 15 to get 10? (-5)
*What do I add to 15 to get 8? (-7)
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.
*What do I add to 15 to get 9? (-6)
*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>
6. Now we transition from numbers representing some quantities to numbers being manipulated as numbers.
6. Now we transition from numbers representing some quantities to numbers being manipulated as numbers.