Sums and Differences on a Number Line

Transcription

1 Math Lessons for the Classroom Sums and Differences on a Number Line Lessons for Grade 2 Overview of Lesson Students will add and subtract using a number line. Students will also draw their own number lines making equal intervals and labeling the tick marks. Mathematical Goals Students will: Add on a number line. Subtract using a number line. Label a number line with equal intervals. Label a number line with intervals of 1, 5, or 10, depending on the numbers. Vocabulary Number Line Interval Tick Marks Distance Materials Tiles Rulers Number lines drawn on paper Cut-out arrows of lengths to fit number line intervals 1

2 Math Lessons for the Classroom Sums and Differences on a Number Line Lessons for Grade 2 Teaching Directions Day 1 Introduce and add using the number line. Today we will use number lines. Let me show you what I mean. A number line has tick marks to show the distance between the numbers. Display a number line with 0 to 10. Point out the tick marks. Display an arrow from 0 to 6. I can also draw a number line with equal intervals of 5. Intervals are the spaces between the tick marks. Draw a number line from 0 to 40. To show the number 15, I can draw an arrow from 0 to 15. When we draw a number line we first draw a little line called a tick mark. We label it zero. The numbers start with 0 and as you move to the right, they get bigger. What is the distance between these tick marks? (1) When we draw number lines the intervals must all be the same. I drew arrows on the ends to show that the numbers can go on forever. I can represent numbers on a number line with an arrow. This is how I can show the quantity of 6. I start at 0 and end at 6. 6 is six intervals from 0. It s distance from 0 is 6. We can draw number lines with the numbers we need. We just have to remember to evenly space the tick marks and numbers. In this number line I counted by 5s as I wrote the numbers. Okay, now that we know something about number lines, let s use one to add. Let s add The distance from 0 to 10 is 10. I can draw an arrow from 0 to 10 to represent that distance. (Alternatively: tape cut-out arrows to the number line.) 2

3 I can also draw an arrow to represent the distance from 0 to 15 on the number line. Adding means joining together. I want to know the total distance from 0 if I join them together. So I ll slide one arrow over to the end of the other. The arrow ends at plus 15 is 25. Write the equation on the board If I want to add using a number line, what intervals could I use? (10) Have students draw a number line. Guide them to use a straight edge to draw a line. Then provide a tile to each student. Demonstrate how to draw a tick mark for 0 and then use the tile to make evenly spaced tick marks. Have them label their number lines 0 to 100 by 10s. After students have drawn their number lines, say: The first addend is 30. Let s draw an arrow from 0 to 30. Observe that students are beginning at 0 and ending at the tick mark for 30. How many intervals is it from 0 to 30? (3) What is the distance between each tick mark? (10) Now draw a second arrow a little above the first from 0 to the second addend, 40. Give time for students to draw their arrows. To add, we slide one arrow over to the end of the other one. We can t actually slide our arrow, so we ll think the second arrow is 4 intervals, so I ll start at the end of the first arrow and draw an arrow from the end and to the right four intervals. Draw the arrow from the end of the arrow for 30. Where does the second arrow end? (70) What is ? (70)

4 Write the equation on the board Day 2 Subtracting with a number line. Let s think about subtraction on a number line We know that 8 minus 3 is 5. I can show this on the number line. I first draw an arrow for 8. Then I draw an arrow from the end of 8 in the opposite direction for a distance of 3. I end up at What do I do to start? (draw an arrow to 22) Instead of drawing one arrow that is 9 intervals, I am going to draw an arrow to 20 first. That s a distance of 2. Then I ll draw a second arrow that is 7 intervals because with the arrow of 2 intervals there are 7 left to go 9 intervals. Where do I end up? (between 12 and 14) What is between 12 and 14? (13) Let s check. Is 13 plus 9 equal to 22? (Yes) Record 22 9 = 13. Present a third subtraction equation Present a second subtraction I can draw a number line using intervals of 2 or 5. Why don t I want to use intervals of 1? (the number line would be too long) I will use a number line with intervals of 5. I ll draw an arrow to 50 to start. I ll draw an arrow of 30 because I know that 50 minus 30 is 20. Then I ll draw a second arrow to go back 5 more to find the difference. The arrow ends at 15 so 50 minus 35 is

5 Extensions Use Do The Math Addition & Subtraction B to introduce subtracting with an open number line and then to introduce finding the distance from the number being subtracted to the number you are subtracting from : 48 to 50 is 2, 50 to 60 is 10, 60 to 63 is 3. So the difference is = ( ) Have students draw open number lines for these examples: