# Changes

,  18:55, 7 July 2016
Line 31: Line 31:
==Developmental Questions (What discussion questions)==

==Developmental Questions (What discussion questions)==
Discuss a sample problem like this. Ram and his dad are driving to the city. It is 15 kms away. They have already gone 5 kms. How many more kms do they have to drive? <br>
+
*Discuss a sample problem like this. Ram and his dad are driving to the city. It is 15 kms away. They have already gone 5 kms. How many more kms do they have to drive? <br>

After a minute or so, ask for a few children to share with the class. You have to figure out how much farther they have to drive. You could keep going, like count up from 5 to 15. You could go maybe go backwards from 15 down to 5. Students will probably have a variety of ideas for solving the problem, including counting on from, or adding to 5 to reach 15, or counting backwards from 15 to find out how many kms remain. <br>

After a minute or so, ask for a few children to share with the class. You have to figure out how much farther they have to drive. You could keep going, like count up from 5 to 15. You could go maybe go backwards from 15 down to 5. Students will probably have a variety of ideas for solving the problem, including counting on from, or adding to 5 to reach 15, or counting backwards from 15 to find out how many kms remain. <br>
−
Summarize both approaches by writing the following equations below:<br>
+
*Summarize both approaches by writing the following equations below:<br>

5  +  □  = 15 <br>

5  +  □  = 15 <br>

15 –  □  = 5 <br>

15 –  □  = 5 <br>
<br><br>
+
<br>
We could say we just keep going from 5 up to 15, so we wrote 5 + box equals 15. What does the box mean in this equation? The students may say it means  part you have to figure out. It’s where you write the answer. It’s like the problem you have to solve. 5 plus how many more to get to 15? <br>
+
*We could say we just keep going from 5 up to 15, so we wrote 5 + box equals 15. What does the box mean in this equation? The students may say it means  part you have to figure out. It’s where you write the answer. It’s like the problem you have to solve. 5 plus how many more to get to 15? <br>
Another interpretation is that it is like you’re finding out how far you have to go backwards to get down to 5. This is the idea that subtraction is the inverse process of addition.  <br><br>
+
*Another interpretation is that it is like you’re finding out how far you have to go backwards to get down to 5. This is the idea that subtraction is the inverse process of addition.
After taking students’ ideas, it is possible to introduce number lines as a new tool for solving problems like these. Number line can be drawn as a horizontal line across the board. Include an arrow on either end to show that the number line continues indefinitely in both directions. Record the smaller number (5) by marking and labeling a dot on the far left side. Then propose to move along the number line by hops greater than 1 to find the difference between 5 and 15. <br><br>
+
*After taking students’ ideas, it is possible to introduce number lines as a new tool for solving problems like these. Number line can be drawn as a horizontal line across the board. *Include an arrow on either end to show that the number line continues indefinitely in both directions. Record the smaller number (5) by marking and labeling a dot on the far left side. Then propose to move along the number line by hops greater than 1 to find the difference between 5 and 15. <br><br>
This discussion can be extended with the following question.  What if Ram  and his dad drive 2 more kms? How far will they be then?  This can also be shown on the number line.  What if they drove 3 more kms after that? How far would they be? The students should be able to say they are upto 10 miles!
+
*This discussion can be extended with the following question.  What if Ram  and his dad drive 2 more kms? How far will they be then?  This can also be shown on the number line.  What if they drove 3 more kms after that? How far would they be? The students should be able to say they are upto 10 miles!

They have gone 5 miles after the 5 because 2+3=5  and it is possible to know how many more miles they have to go to get to 15!

They have gone 5 miles after the 5 because 2+3=5  and it is possible to know how many more miles they have to go to get to 15!
Ask students to suggest additional hops you could take along the number line to get to 15. <br><br>
+
*Ask students to suggest additional hops you could take along the number line to get to 15. <br>
<br><br>
+
You could keep going by ones, like 1 and then 2and so on more little hop up to 15. <br>
Addition and subtraction are opposite operations
+
[[File:picture5.png|400px]]<br>
+
And this can be generalized for negative numbers also.<br>
+
[[File:picture7.png|400px]]<br>
+
*Addition and subtraction are opposite operations

==Evaluation (Questions for assessment of the child)==

==Evaluation (Questions for assessment of the child)==
3,913

edits