1. Open Number Line

2. Strategies for Addition

3. Addition – Can someone explain what is happening here? 36 + 24 +10 36 +10 +4 36 + 24 = 60 4656 60

4. Addition – Can someone explain what is happening here? 36 + 24 +4 36 +10 36 + 24 = 60 4050 60

5. Addition – Can someone explain what is happening here? 36 + 24 36 +20+4 36 + 24 = 60 56 60

6. Strategies for Subtraction

7. Subtraction – Can someone explain what is happening here? 53 - 37 +10 37 +3 53 - 37 = 16 4750 53 Strategy: count up from the smallest number 10 + 3 + 3 = 16

8. 53 - 37 -3 37 -3-10 53 - 37 = 16 4043 53 Strategy: count back from the largest number 3 + 3 + 10 = 16 Subtraction – Can someone explain what is happening here?

9. Subtraction – Student 3 53 - 37 -4 16 -3-10 53 - 37 = 16 3343 53 Strategy: count back from the largest number -10 20 23

10. Using Benchmarks

11. How long is the movie? I started watching a movie at 3:30 pm and it ended at 4:45 pm.

12. Elapsed Time The movie started at 3:30 and ended at 4:45. How long was the movie? +30 min 3:30 30 + 30 + 15 = 75 minutes = 1 hour 15 minutes 4:004:30 4:45 +30 min +15 min Strategy: Start at 3:30 and add time increments to the hour or ½ hour, (benchmarks), then continue until end time.

13. How much time is there between school and bedtime? How much time is there between the time school is out (3:40 pm) and bedtime (8:15 pm)?

14. Elapsed Time – using benchmarks How much time is there between 3:40 and 8:15? +20 min 3:40 4 hours + 20 min. + 15 min.= 4 hours 35 minutes 4:008:00 8:15 +4 hours +15 min Strategy: Start at 3:40 and add time increments to the ½ hour benchmarks, then continue increments.

15. Time over the 12:00 hour How much time is there between 10:30 am and 2:45 pm?

16. Elapsed Time – over 12 o’clock hour How much time is there between 10:30 am and 2:45 pm? +30 min. 1 hr. + 2 hr. + 30 min. + 45 min. = 3 hr. 75 min. = 4 hr. 15 min. 12:00 noon 2:00 2:45 +2 hours +45 min 11:00 10:30 +1 hour Strategy: Add increments to 12:00, then continue benchmark increments.

17. Find the ending time What time is 4 hours and 30 minutes from 6:55?

18. Finding the ending time – What time is it 4 hours and 30 minutes from 6:55? The time is 11:25, which is 4 hrs. and 30 min. after 6:55. 11:0011:25 +25 min 7:00 6:55 +4 hr. +5 min Strategy: Add minute increments to the ½ hour benchmark, then hours, then minutes.

19. Finding the ending time – What time is it 4 hours and 30 minutes from 6:55? The time is 11:25, which is 4 hrs. and 30 min. after 6:55. 11:00 11:25 +25min 7:55 6:55 +1 hr. +5 min 9:55 8:5510:55 Strategy: Add hour increments until close, then minutes to the ½ hour, then minutes.

20. Find the start time What time did we start on our trip if we arrived at 8:17 and it took 3 hours and 10 minutes?

21. Finding the start time What time did we start on our trip if we arrived at 8:17 and it took 3 hours and 10 minutes? -10 min.-3 hr. The start time is 5:07. 5:075:17 8:17 Strategy: Subtract the hours then minutes.

22. Find the start time What time do I need to wake up if I have to be at school at 8:15 am and it takes me 1 hour and 45 minutes to get ready?

23. Finding the start time What time do I need to wake up if I have to be at school at 8:15 am and it takes me 1 hour and 45 minutes to get ready? -15 min. -1 hr. I have to wake up at 6:30 AM. 6:457:15 8:15 6:307:00 -15 min. Strategy: Subtract the hour, then minute benchmarks.

24. References Teaching Student-Centered Mathematics Grades K-3, John A. Van de Walle, LouAnn H. Lovin, Pearson Publishing, 2006 Teaching Student-Centered Mathematics Grades 3-5, John A. Van de Walle, LouAnn H. Lovin, Pearson Publishing, 2006 Tracking Time – Representing Elapsed Time on an Open Timeline, Juli K. Dixon, Teaching Children Mathematics, NCTM, August 2008