Please place homework on your desk.
8/24
Problem of the Day
Find the missing digits to complete the
problems below.
(a)
63
­ 3,9 9
2,8 3 ∎
(b) 71, 4
­ 4,8 6
6 ,2 7 0
Suppose that in some distant part of the universe there is a star with four orbiting planets. One planet (Esh) makes a trip around the star in 6 Earth years, the second planet (El) takes 9 Earth years, the third (Ma)
takes 15 Earth years, and the fourth (Ans) takes 18 Earth years. Suppose that at some time the planets are lined up. This phenomenon is called conjunction. 1. If planets Esh and El just lined up in conjunction how many Earth years will it take for this phenomenon to happen again?
2. If planets El and Ma just lined up in conjunction how many Earth years will it take for this phenomenon to happen again?
3. If planets Ma and Ans just lined up in conjunction how many Earth years will it take for this phenomenon to happen again?
4. If planets Esh, El, and Ma just lined up in conjunction how many Earth years will it take for this phenomenon to happen again?
5. How many Earth years will it take before all four planets make a conjunction?
One of the most famous Aztec carvings is known as the
Calendar Stone. This beautiful stone is the form of a huge
circular disk, 4 meters across. It was painted with solar symbols and day signs. The stone reminds us that the Aztecs and other Central American Indians developed very accurate calendars, long before the arrival of Columbus. The calendar for religious events was 260 days long. The solar year of 365 days was used as the civil calendar for daily life. This calendar was adjusted, as needed, to agree with the natural seasons. The cycles of the moon were carefully studied so that the Aztecs could predict eclipses of the sun. The 584­
day cycle of the planet Venus was also important in Aztec Astronomy. All these calendars were dated from the same starting day, about 5000 years ago. After many years, the calendars were synchronzied again. Then the 260­day, the 365­day, and the 584­day cycles once again started the New Year on the same day. The coincidences of these cycles were very important dates in Central America. 1. If the 365­day year and the 584­day Venus cycle started on the same day, how long would it take for this to happen again?
2. If the 260­day year and the 365­day year started their New Year on the same day, how long would it take for this to happen again? 260
260 520 780 1040 1300 1560 1820 2080 2340 2600 2860 3120
365
365 730 1095 1460 1825 2190 2555 2920 3285 3650 4015 4380
260
3380 3640 3900 4160 4420 4680 4940 5200 5460 5720 5980 6240
365
4745 5110 5475 5840 6205 6570
260
6430
365
260
365
8/24 Least Common Multiple
multiple: multiplying numbers (many
multiples)
least common multiple: the lowest
multiple that two numbers have in
common (t­chart with multiplication)
LCM 15 and 21
Homework: Least Common Multiple Worksheet
and complete LCM for 260 & 365
TEST ON FRIDAY 31st!