Draw a digital clock to show each of the following times:

a) quarter to 4	b) 21 minutes after 8
c) 9 minutes to 1	d) 25 minutes before 4

If you have 45 minutes of homework, when is the latest you can start so that you will be finished in time to watch Heros at 8:00 pm. Show your thinking.








If you started this test at 12:15:05 and finished at 12:19:23,
a) how long did it take you? Show your work.








b) how much time do you have until nutrition break at 12:45:00? Show your work.

Name: _____________________________


Remember: 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day.


How to add and subtract time.


Suppose Rilie studies from 3:48 to 7:05, how would you go about calculating how long he studied?
One way is to do addition. He studies 12 minutes to get to 4:00, plus 3 hours to get to 7:00, plus 5 minutes to get to 7:05, for a total of 3:17. This same method can be extended to include seconds, or even days and years.
The other way is to do subtraction, but there's a catch. You have to be careful when borrowing between different units.

7:05	->	6:65
-3:48		-3:48
-------		-------
		3:17

Notice how, when we borrowed from the hour, we only got 60, not 100 as we would have if we were subtracting 348 from 705.


Practice:
4 runners want to recreate the run from Marathon to the Acropolis in Athens. The each leave at 7:45am. Use the runners finish time to calculate the elapsed time

	Finish Time	Elapsed Time
Runner 1	10:52	______________________________
Runner 2	10:34	______________________________
Runner 3	12:14	______________________________
Runner 4	12:05	______________________________

Which runner is the fastest?
Which runners took more that 4 hours?

In your groups, try these activities, and come up with some of your own. Each person in the group should try these and have a partner record the start and end times.

Activity	Estimate	Start time	End time	Elapsed time
1. Sing Jingle Bells
2 10 Jumping Jacks
3. Walk across the classroom
4.
5.
6.
7.
8.

Extend your thinking:
Including washrooms, there are about 7 rooms between us and the office. Calculate how long it would take you to walk to the office.

Name: __________________________________

Purpose

To investigate the relationship between the height of water in a container and how fast if flows out.

Material

1. Prepared Water bottle with hole
2. Graduated cylinder
3. Ruler
4. Stopwatch or Wall clock with second hand

Instructions

Repeat the following steps with the bottle starting with different water levels in the bottle. For example, nearly full, half full, and nearly empty. Collect additional data for other water levels as time permits. The more data the better.

1. Place your finger over the hole in the bottom of the bottle and pour water in it.
2. Keeping your finger over the hole, set the bottle on the edge of a level surface and measure the height of the water from the bottom on the bottle. Record this data.
3. Place the graduated cylinder on a level surface so that it will collect the water that runs out of the hole in the bottle and you can see when the water reaches the 100ml mark. Make sure the cylinder is empty before you start.
4. Hold the bottle upright over the cylinder.
5. If you are using a stopwatch, start it when you take your finger off the hole, and stop it when the water reaches the 100ml line in the cylinder. Record this as the elapsed time. You do not have to fill in the start and stop time.
6. If you are using a wall clock, record the time when you take your finger off of the hole, as well as the time when the water reaches the 100ml line in the cylinder, then calculate the elapsed time.

Ruberic (Formative)

Level 4: with thorough detail and accuracy completes the experiment report
Level 3: with considerable detail and accuracy completes the experiment report
Level 2: with some detail and accuracy completes the experiment report
Level 1: with little detail and accuracy completes the experiment report

Observations

Trial	Water Level	Start time	End time	Elapsed time
1
2
3
4
5
6
7
8
9

Analysis

Create a scatter plot of water height versus time for 100ml to flow out of the bottle. What can you conclude from this experiment (Hint: Look a the purpose).

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Application

What does this relationship mean for a simple water clock?

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How would you change the design of a water clock to account for this relationship?

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This is the basic clepsydra (literally "water thief"). This device can be traced back to nearly 2000 BCE in ancient Egypt. This type of clepsydra was often used to time speakers during debates and trials.

Ctesibius, a Greek inventor and mathematician in Alexandria, Ptolemaic Egypt developed many improvements on the water clock. His clepsydra kept more accurate time than any clock invented until the Dutch physicist Christiaan Huygens detailed the use of a pendulum to regulate a clock in the 17th century.

One of the problems faced by Ctesibius was the one we investigated in our experiment. That is, as the water level in the upper container, (reservoir) goes down, the flow of water slowed down. This problem was solved by having water flow into the reservoir faster thannit was used by the clock, and have an outflow tube to take the extra water away.

Another problem facing clock builders is how the Ancient Greeks counted time. Unlike us, the Greeks divided the time between sunrise and sunset into 12 daytime hours, and the time between sunset and sunrise into 12 nighttime hours. As we are sadly aware, the time between sunrise and sunset is much shorter during the winter than the summer. Ctesibius solved this problem by marking the hours with curved lines on a drum. He then added a mechanism that reset the hour pointer every day and turned the drum so the lines matched the season.

This is a picture of what the Tower of the Winds in the agora would have looked like. It was 12 m tall and about 8 m in diameter. It was supposedly built by Andronicus of Cyrrhus around 50 BC, but according to other sources might have been constructed in the 2nd century BC before the rest of the forum. It was topped in antiquity by a weathervane-like Triton that indicated the wind direction.

Triton was the son of Poseidon and the Amphitrite, goddess of the sea. He was the messenger of the deep and carried a conch shell with which he could raise or quiet the waves.

Around the top is a frieze depicting the eight wind deities — Boreas (N), Kaikias (NE), Eurus (E), Apeliotes (SE), Notus (S), Livas (SW), Zephyrus (W), and Skiron (NW). Below them were eight sundials. You can see the lines marking the hours below the frieze. Inside, there was a clepsydra, driven by water coming down from the Acropolis.