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| == Part II – Negative Numbers == | | == Part II – Negative Numbers == |
− | Objectives | + | === Objectives === |
− | 1. To extend the understanding and skill of representing symbolically numbers and manipulating them
| + | # To extend the understanding and skill of representing symbolically numbers and manipulating them.<br> |
− | 2. To understand tha negative numbers are numbers that are created to explain situations in such a way that mathematical operations hold
| + | # To understand that negative numbers are numbers that are created to explain situations in such a way that mathematical operations hold<br> |
− | 3. Negative numbers are opposite of positive numbers; the rules of working with negative numbers are opposite to that of working with positive numbers
| + | # Negative numbers are opposite of positive numbers; the rules of working with negative numbers are opposite to that of working with positive numbers<br> |
− | 4. Together, the negative numbers and positive numbers form one contiuous number line
| + | # Together, the negative numbers and positive numbers form one contiuous number line<br> |
− | 5. Perform manipulations with negative numbers and express symbolically situations involving negative numbers
| + | # 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''''' |
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− | 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
| |
| 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> |
− | 5. What do I have to add to 15 to make it 7? The answer is (-8).
| + | |
− | 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. |
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