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Heavenly Stems & Earthly Branches: Why Only 60 of 120 Pairs Exist

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Ten Stems × Twelve Branches = One 60-Year Loop Ten stems and twelve branches pair up to make exactly 60 combinations. The 61st year brings you back to the first pair. Each combination is called a *ganji*. The same pairs are attached to years, months, days and hours. You might expect 10 × 12 = 120 pairs. Only 60 are ever used, because both lists move forward one step at a time, so odd-numbered stems always meet odd-numbered branches. Stem 1 meets branch 1, 3, 5 and so on, never branch 2. That halves the count to 60. The same number comes out of the arithmetic. Stems repeat every 10 steps and branches every 12. The two lists line up again after 60 steps, the least common multiple of 10 and 12. The cycle starts at Gap-Ja, runs in order through Eul-Chuk, Byeong-In, Jeong-Myo and so on, and ends at Gye-Hae. The 10 Stems, the 12 Branches, and the Five Elements The ten stems run in this order: Gap, Eul, Byeong, Jeong, Mu, Gi, Gyeong, Sin, Im and Gye. They are grouped in pairs under the...
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Multi Digit Multiplication: 3 Slips Behind Wrong Answers

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Lost Steps Happen in 3 Predictable Places Three slips are common, and each leaves a clear mark in the answer to 347 × 26 (correct answer: 9,022). The first is the carry. In 347 × 6, the first multiplication is 7 × 6 = 42. You write the 2 and carry the 4. Next comes 4 × 6 = 24, and the carried 4 must be added to make 28. If the child forgets the carry, the row comes out as 2,042 instead of 2,082. If they add the same 4 twice, it comes out as 2,122. The second is the missing zero. When you multiply by the 2 in 26, you are really multiplying by 20, because each place in a number is worth 10 times the place to its right. That is what place value means: a digit's worth depends on where it sits. A placeholder zero holds the ones spot so the other digits land in the right columns. So the second row must start with a 0 in the ones column. Skip it, and 694 gets added to 2,082 to give 2,776, far from the right answer of 9,022. The same rule shows in 67 × 12: the rows are 134 (67 × 2) an...
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Korean Zodiac Compatibility: 2 Best Matches and 1 Clash for Each Sign

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Each Sign Has 2 Best Matches and 1 Clash In the traditional Korean system, every animal sign has 2 best matches and 1 clash. Put the 12 animals on a clock face in their fixed order: Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog, Pig. After Pig the cycle starts again with Rat, so your animal returns every 12 years. Two simple distances then do most of the work. Animals 4 places apart form a "triangle of harmony" (called samhap in Korean). Counting the order above from 1, Rat (1), Dragon (5) and Monkey (9) are each 4 places from the next, so they make one triangle. There are four triangles in all: Rat, Dragon, Monkey Ox, Snake, Rooster Tiger, Horse, Dog Rabbit, Goat, Pig Animals 6 places apart sit directly opposite each other on the clock. Tradition calls this a clash (chung in Korean). Rat (1) sits directly across from Horse (7). The six clash pairs are Rat–Horse, Ox–Goat, Tiger–Monkey, Rabbit–Rooster, Dragon–Dog and Snake–Pig. There is a...
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Addition Facts Within 20: How 4 Strategies Beat Memorizing 100 Sums

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Teach Strategies First, Then Speed Children reach instant recall by learning a few ways to think about each fact. Repeating a list of sums doesn't get them there. Recall comes after the thinking has become automatic. U.S. first-grade standards name counting on, making ten and building an easier sum among the strategies for adding within 20. In this article, "within 20" means the facts from 0 + 0 up to 10 + 10, so no answer is above 20. If you leave out the zeros, there are 100 ordered facts, from 1 + 1 to 10 + 10. The turn-around rule says you can add two numbers in either order and get the same answer. Since 3 + 8 and 8 + 3 both make 11, a child only has to learn one of each pair. That leaves 55 facts: 10 doubles (like 4 + 4) and 45 pairs of different numbers. If you count the zero facts, 121 ordered facts become 66. Let your child check this by hand. Write 4 + 7 = 11, then ask what 7 + 4 must be. Repeat with 2 + 9 and 6 + 8. Four Bridges From Fingers to Memory F...
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Day Master Saju: How to Find Your 1 of 10 Stems in 4 Steps

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Your Day Master Is the Top Character of Your Day Pillar Your Day Master is a single Chinese character, and it is one of only 10. Saju, also called Four Pillars or BaZi, describes a birth with four pillars: year, month, day and hour. Each pillar has two characters. The top one is a "heavenly stem" and the bottom one is an "earthly branch". Four pillars with two characters each make 4 × 2 = 8 characters in all, which is why the system is also called "eight characters". Your Day Master is the stem of the day pillar, meaning the top character of that pillar. In a Saju reading it stands for you, and the other seven characters are read in relation to it. So finding it means working out one character, not all eight. The 10 stems come from 5 elements: Wood, Fire, Earth, Metal and Water. Each element has a Yang form and a Yin form, and 5 × 2 = 10. Your Day Master therefore has only 10 possible answers. The next section shows how to narrow them to one with simp...
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Two Digit Addition With Regrouping: Why 45 of 100 Pairs Carry

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Carry Only When the Ones Add Up to 10 or More Regrouping and carrying mean the same thing. When the ones column adds up to 10 or more, you trade 10 ones for 1 ten and move that ten to the tens column. This article uses "carry" from here on. The test is one question: is the ones sum 10 or more? 7 + 8 = 15. That is 10 or more, so you carry. 3 + 4 = 7. That is 9 or less, so nothing moves. Take every pair of ones digits, 0 to 9 for each. That gives 100 pairs. Of these, 45 add up to 10 or more and 55 do not. The 45 comes from counting: a pair with a ones digit of 1 has 1 partner that reaches 10, a digit of 2 has 2 partners, and so on up to 9 with 9 partners. Adding these gives 1 + 2 + … + 9 = 45. Almost half of all ones-digit pairs need a carry, so a child who has only practiced the no-carry kind has met just 55 of the 100 possible pairs. Common Core standard 1.NBT.C.4 says the same thing in its own words: when adding two-digit numbers, "sometimes it is necessary to ...
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Five Elements Saju: How to Count Your 8 Characters

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Your Strongest Element Sets the Tone Count the 8 characters in your chart and note which element shows up most. That element has the largest share of your chart. An element at 0 does not appear in any of the 8 characters. Saju (四柱) means "four pillars." The pillars are the year, month, day, and hour of your birth. The name comes from a house, with each of the four pillars holding up the structure. Each pillar is written with 2 characters, so a full chart has 4 × 2 = 8 characters. That is why saju is also called palja (八字), "eight characters." The two characters in a pillar come from two different lists. One is one of 10 heavenly stems. The other is one of 12 earthly branches. Every stem and every branch belongs to one of five elements: Wood, Fire, Earth, Metal, or Water. So each of your 8 characters carries one element, and counting them is simple arithmetic. The Five Elements and the Traits Linked to Each The link between element and character traces back to...
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