Hopping on Number Line
In this lesson, students generate sums using the number line model. This model highlights the measurement aspect of addition and is a distinctly different representation of the operation from the model presented in the previous discussion. The order (commutative) property is also introduced. At the end of the lesson, students are encouraged to predict sums and to answer puzzles involving addition. Objectives
Represent the number line using objects. Count each group of ones objects. Relate the cumulative total of each group to the number on the number line. Write the cumulative total for each group. Skip count by pointing to each group of objects.
How to do the activity
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?
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.
Summarize both approaches by writing the following equations below:
5 + □ = 15
15 – □ = 5
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? 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. 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!
Ask students to suggest additional hops you could take along the number line to get to 15.
You could keep going by ones, like 1 and then 2and so on more little hop up to 15. Picture5.png And this can be generalized for negative numbers also. Picture7.png
Addition and subtraction are opposite operations
Evaluation (Questions for assessment of the child)
How much farther did Ram and his dad have to drive to get to the city? How do you know? Can you show us on the open number line? Does this give us the answer to the problem? Did we add or subtract to find the answer?