Review of Kiss My Math and Math Doesn't Suck by Danica McKellar

Recently I had the delight of receiving a review copy of Math Doesn't Suck and Kiss My Math by Danica McKellar. Danica is well-known for her acting career, and her books are best-sellers.

First some basic info. Math Doesn't Suck covers middle school math topics: factors and multiples, fractions, decimals, percents, word problems, and a little algebra.

Kiss My Math covers pre-algebra: integers & negative numbers, variables and working with expressions, solving (linear) equations, word problems, intro to inequalities, exponents, and an intro to functions and graphing lines.

There's a website for each book: KissMyMath.com and MathDoesntSuck.com.

I've split this review into two parts: the pros and the cons. Let's go with the pros first.

Pros:

Danica's writing is excellent. It's conversational and catchy, very friendly. Reminds me of Dr. Math books.

I absolutely adore some of her illustrations that she uses for math concepts.

For example, she tells us to think about positive and negative numbers as breath mints - mint-egers. The positive ones have a good taste, and the negative ones are yucky, getting yuckier as they get more negative. And then she combines the integers as if they were mint-egers in her mouth! It's a fresh, fabulous comparison. You see, that'll stick to your mind for sure... you imagine TASTING something in your mouth, it will SURELY help kids remember.

Another thing I loved about her book were the little motivational "talks" in between the math stuff. For example, on p. 19 she asks, "Ugly Yourself Up?" Since you wouldn't make yourself to appear uglier than you really are, Danica argues, then why do the same as far as your smarts? She is truly encouraging girls to be smart, to study math, to do well in school and even venture into math careers!

It's really hard to put the book down, it's so delightfully written. How about remembering the order of operations by what Pandas Eat? And she goes further than the PEMDAS rule - Multiplication and Division are the main course, while Addition and Subtraction come at dessert.

For EVERY SINGLE topic she's come up with some kind of catchy illustration. For factoring, it's monkeys hanging off of trees. For the x (variable), it's a pearl bag, so 2x + 3 means "2 bags of pearls plus 3 loose pearls" (it's a GOOD illustration, I feel). For inequalities, she talks about how tall you'd want him to be? Perhaps h (his height) should be at least 2 inches taller but no more than 9... For isolating x in equations, she uses the analogy of gift wrapping and unwrapping. For exponents, there's the Ms. Exponent who's a high-powered executive. And so on.

You can see she's given each concept some thought, as to how to present it in a way that helps kids remember it.

She also helps us remember all these difficult math words (such as mean, median, mode, coefficient, variable etc.) with some clever mnemonics. I'll just tell you one. Mode is like "mood", whatever occurs most often, and she gives an example of a person who's iPod playlist contains mostly samba songs: "I guess she's in the mood for samba, huh?" Mode = mood.

The real power of the book is actually in these memorable analogies and in the very friendly tone she uses all through the book. She's talking to a friend, and it makes you to just keep reading!

Now, some might feel that it's all just nonsense. Will it really work to talk about Ms. Exponent being so powerful that all she has to do is say a word and things happen - you know, all she has to do is say "3", and 4 multiplies itself 3 times? Will it help students? Isn't it just silly to do math that way?

I feel it is truly powerful, because it has to do with our EMOTIONS. If it makes you laugh out of silliness, it creates an emotion while studying, and that helps you remember. It's a proven fact from brain research that we remember things better IF they're tied in with some strong emotion, be it fear, embarrassment, joy, surprise, etc.

You can also see from the feedback she's gotten that it IS working. Even math teachers have written to her how good her illustrative ideas are.

Another reason why this approach works is because she starts with the simplest stuff and in a friendly way "lures" you into the more difficult ideas. She basically "bends backwards" in order to not make math intimidating or scary - and that is one of her missions, as she has publicly declared.

I also liked the little "Watch Out!" boxes which contain alerts or explain common errors and misconceptions. Definitions come in "What's It Called?" boxes. Then in between the main text we also find "What's the Deal" boxes, Quick Notes, and Takeaway Tips, all decorated with smart and fashionable looking girl-figures.

Both books have some material on solving word problems. I feel Danica does an excellent job here and has really good common-sense advice AND great example solutions for this difficult topic. And I really liked chapter 12, The Art of Gift Wrapping/Solving Equations in Kiss My Math. It is one of the best "treatises" on solving linear equations that I've seen anywhere! The analogy of wrapping / unwrapping a gift is excellent.

Are the books just collections of tricks and shortcuts?

Some people have characterized Danica's Math Doesn't Suck book as simply a bag of tricks, concentrating on the "how-to" and not on the conceptual understanding. Well, it is written in a "how-to" style. It's like she's talking to you and coaching you through problems — and it's written so interestingly that it's hard to stop reading!

Sometimes she doesn't explain why things work the way they do, but most often she does include something along those lines - usually after the "how-to". So you can't say she's omitting the conceptual side (the why's). The books could use some more explanations on those lines, though.

Cons:

Now, I've checked around on the Internet, and it seems I may be a lone voice in the criticism that follows. However, I do not want to leave this part out so here goes.

You know, there are some of us (and I include myself in this) who don't feel we want our teenage daughters to start thinking about dating at such early ages as what her books audiences are. (Her books often refer to kissing, dating, having crushes, and so on.)

I'll give an example. She talks of integers as "mint-egers", which (like mints) taste like peppermint, spearmint, cinnamon and so on if they're positive. And they taste like vomit & dirt, etc. if they're negative. You combine (add) them in your mouth, and check which kind of taste wins. A great analogy! But right in the midst of several pages of discussing integers there's this one sentence: "These are good before a date, in case, you know, there's going to be kissing involved." To me that felt like a flop in the midst of a great exposition.

Another example: Chapter 9 in Kiss My Math is titled "Do You Like Him Like Him?" This catchy title is used as a mnemonic for the like terms in algebraic expressions — two terms such as 2x and 3x "get full-on crushes".

Her audience for Math Doesn't Suck is 6th-7th graders. Her audience for Kiss My Math is 7th-9th graders. She mentions that after writing Math Doesn't Suck she's been getting emails from 9-13 year old girls. So we're talking about girls 9-15 years old - pre-teens and early teens.

Personally I have a strong opinion against TV shows or teen magazines that give girls this young the idea that they just HAVE to have a boyfriend, go on a date, etc. It becomes a craze, as if a rite of passage that a girl MUST get a boyfriend, dating is cool and not dating is not cool. There's enormous PRESSURE (from peers and especially from those magazines) for teens to do this. And in today's world this pressure is even affecting 9-12 year olds (preteens).

Danica mentions in one of her diary entries in Kiss My Math, "I know the agonizing pain of waiting for a guy to call. This happened to me again and again, from the age of 13 through 17, after which point I got my first "real" boyfriend", who actually loved me and wanted to call me."

So she's experienced herself the pain that this cultural expectation can produce. I would venture to say that most of us adults reading this have, too. So why endorse it so strongly? It is just one more factor adding to the pressure.

Danica probably thinks that she is just going along with what already is there, and using that for math education. But when someone becomes a strong role model (and Danica has), any little hint of something they say carries weight, and just creates another push in that direction, helping along the ideas perpetuated by the TV, the Internet, teen magazines, and peers.

Now, I'm not against girls looking like girls or being savvy shoppers, or aspiring successful careers, or thinking about finding a husband someday. It's just that the cultural norms, the pressure, and downright "obsession" about finding a girlfriend/boyfriend (when you're 12!) have gone way overboard in today's teens' world. I don't want math books pushing in that direction as well.

However, I feel I understand Danica's HEART: she's writing in a very conversational style to an audience she knows how to write to, and she's truly wanting to help girls with math. You know, the teachers that are considered the best are those who are friendly with their students, become as if their friends. So that's what she's trying to be.

Now, she DOES also go against the popular culture in some ways. For example, she strongly encourages girls to study math, to be smart, to work at becoming smarter, not to feel that smart & pretty can't go together, not to underachieve and so on. The Kiss My Math book includes great testimonials from gals who overcame their struggles in math and are now "fabulously successful women".

I just wish she wouldn't go along with the "teen magazine culture" so much when it comes to crushes and boyfriends.

Riding on her fame, these two math books are best-sellers, so Danica has become a powerful role-model for pre-teen and young teen girls. She has influencing power. With power comes responsibility. I feel she is already trying to use that influencing power wisely, and influence girls for the good — to study math and to be smart — but I hope she will be able to use that power even wiser in the future.

Recommendations

Teachers: I can heartily recommend these books for teachers, as they will be able to collect all kinds of ideas for their own teaching, and also learn from Danica's relaxed teaching style.

Parents and students: If you can keep from being influenced further into the boyfriend craze, go for it. If you can't, consider Dr. Math books (I've reviewed them as well). They are written in a somewhat similar, friendly, relaxed manner, though they don't contain nearly as catchy mnemonics and analogies as what Danica's do.

Review by Maria Miller

(The links below go to Amazon)
Math Doesn't Suck and Kiss My Math by Danica McKellar.

---

You may leave comments on this blogpost, but only intelligent discussion, no flaming, please!

Review of Kiss My Math and Math Doesn't Suck by Danica McKellar

Recently I had the delight of receiving a review copy of Math Doesn't Suck and Kiss My Math by Danica McKellar. Danica is well-known for her acting career, and her books are best-sellers.

First some basic info. Math Doesn't Suck covers middle school math topics: factors and multiples, fractions, decimals, percents, word problems, and a little algebra.

Kiss My Math covers pre-algebra: integers & negative numbers, variables and working with expressions, solving (linear) equations, word problems, intro to inequalities, exponents, and an intro to functions and graphing lines.

There's a website for each book: KissMyMath.com and MathDoesntSuck.com.

I've split this review into two parts: the pros and the cons. Let's go with the pros first.

Pros:

Danica's writing is excellent. It's conversational and catchy, very friendly. Reminds me of Dr. Math books.

I absolutely adore some of her illustrations that she uses for math concepts.

For example, she tells us to think about positive and negative numbers as breath mints - mint-egers. The positive ones have a good taste, and the negative ones are yucky, getting yuckier as they get more negative. And then she combines the integers as if they were mint-egers in her mouth! It's a fresh, fabulous comparison. You see, that'll stick to your mind for sure... you imagine TASTING something in your mouth, it will SURELY help kids remember.

Another thing I loved about her book were the little motivational "talks" in between the math stuff. For example, on p. 19 she asks, "Ugly Yourself Up?" Since you wouldn't make yourself to appear uglier than you really are, Danica argues, then why do the same as far as your smarts? She is truly encouraging girls to be smart, to study math, to do well in school and even venture into math careers!

It's really hard to put the book down, it's so delightfully written. How about remembering the order of operations by what Pandas Eat? And she goes further than the PEMDAS rule - Multiplication and Division are the main course, while Addition and Subtraction come at dessert.

For EVERY SINGLE topic she's come up with some kind of catchy illustration. For factoring, it's monkeys hanging off of trees. For the x (variable), it's a pearl bag, so 2x + 3 means "2 bags of pearls plus 3 loose pearls" (it's a GOOD illustration, I feel). For inequalities, she talks about how tall you'd want him to be? Perhaps h (his height) should be at least 2 inches taller but no more than 9... For isolating x in equations, she uses the analogy of gift wrapping and unwrapping. For exponents, there's the Ms. Exponent who's a high-powered executive. And so on.

You can see she's given each concept some thought, as to how to present it in a way that helps kids remember it.

She also helps us remember all these difficult math words (such as mean, median, mode, coefficient, variable etc.) with some clever mnemonics. I'll just tell you one. Mode is like "mood", whatever occurs most often, and she gives an example of a person who's iPod playlist contains mostly samba songs: "I guess she's in the mood for samba, huh?" Mode = mood.

The real power of the book is actually in these memorable analogies and in the very friendly tone she uses all through the book. She's talking to a friend, and it makes you to just keep reading!

Now, some might feel that it's all just nonsense. Will it really work to talk about Ms. Exponent being so powerful that all she has to do is say a word and things happen - you know, all she has to do is say "3", and 4 multiplies itself 3 times? Will it help students? Isn't it just silly to do math that way?

I feel it is truly powerful, because it has to do with our EMOTIONS. If it makes you laugh out of silliness, it creates an emotion while studying, and that helps you remember. It's a proven fact from brain research that we remember things better IF they're tied in with some strong emotion, be it fear, embarrassment, joy, surprise, etc.

You can also see from the feedback she's gotten that it IS working. Even math teachers have written to her how good her illustrative ideas are.

Another reason why this approach works is because she starts with the simplest stuff and in a friendly way "lures" you into the more difficult ideas. She basically "bends backwards" in order to not make math intimidating or scary - and that is one of her missions, as she has publicly declared.

I also liked the little "Watch Out!" boxes which contain alerts or explain common errors and misconceptions. Definitions come in "What's It Called?" boxes. Then in between the main text we also find "What's the Deal" boxes, Quick Notes, and Takeaway Tips, all decorated with smart and fashionable looking girl-figures.

Both books have some material on solving word problems. I feel Danica does an excellent job here and has really good common-sense advice AND great example solutions for this difficult topic. And I really liked chapter 12, The Art of Gift Wrapping/Solving Equations in Kiss My Math. It is one of the best "treatises" on solving linear equations that I've seen anywhere! The analogy of wrapping / unwrapping a gift is excellent.

Are the books just collections of tricks and shortcuts?

Some people have characterized Danica's Math Doesn't Suck book as simply a bag of tricks, concentrating on the "how-to" and not on the conceptual understanding. Well, it is written in a "how-to" style. It's like she's talking to you and coaching you through problems — and it's written so interestingly that it's hard to stop reading!

Sometimes she doesn't explain why things work the way they do, but most often she does include something along those lines - usually after the "how-to". So you can't say she's omitting the conceptual side (the why's). The books could use some more explanations on those lines, though.

Cons:

Now, I've checked around on the Internet, and it seems I may be a lone voice in the criticism that follows. However, I do not want to leave this part out so here goes.

You know, there are some of us (and I include myself in this) who don't feel we want our teenage daughters to start thinking about dating at such early ages as what her books audiences are. (Her books often refer to kissing, dating, having crushes, and so on.)

I'll give an example. She talks of integers as "mint-egers", which (like mints) taste like peppermint, spearmint, cinnamon and so on if they're positive. And they taste like vomit & dirt, etc. if they're negative. You combine (add) them in your mouth, and check which kind of taste wins. A great analogy! But right in the midst of several pages of discussing integers there's this one sentence: "These are good before a date, in case, you know, there's going to be kissing involved." To me that felt like a flop in the midst of a great exposition.

Another example: Chapter 9 in Kiss My Math is titled "Do You Like Him Like Him?" This catchy title is used as a mnemonic for the like terms in algebraic expressions — two terms such as 2x and 3x "get full-on crushes".

Her audience for Math Doesn't Suck is 6th-7th graders. Her audience for Kiss My Math is 7th-9th graders. She mentions that after writing Math Doesn't Suck she's been getting emails from 9-13 year old girls. So we're talking about girls 9-15 years old - pre-teens and early teens.

Personally I have a strong opinion against TV shows or teen magazines that give girls this young the idea that they just HAVE to have a boyfriend, go on a date, etc. It becomes a craze, as if a rite of passage that a girl MUST get a boyfriend, dating is cool and not dating is not cool. There's enormous PRESSURE (from peers and especially from those magazines) for teens to do this. And in today's world this pressure is even affecting 9-12 year olds (preteens).

Danica mentions in one of her diary entries in Kiss My Math, "I know the agonizing pain of waiting for a guy to call. This happened to me again and again, from the age of 13 through 17, after which point I got my first "real" boyfriend", who actually loved me and wanted to call me."

So she's experienced herself the pain that this cultural expectation can produce. I would venture to say that most of us adults reading this have, too. So why endorse it so strongly? It is just one more factor adding to the pressure.

Danica probably thinks that she is just going along with what already is there, and using that for math education. But when someone becomes a strong role model (and Danica has), any little hint of something they say carries weight, and just creates another push in that direction, helping along the ideas perpetuated by the TV, the Internet, teen magazines, and peers.

Now, I'm not against girls looking like girls or being savvy shoppers, or aspiring successful careers, or thinking about finding a husband someday. It's just that the cultural norms, the pressure, and downright "obsession" about finding a girlfriend/boyfriend (when you're 12!) have gone way overboard in today's teens' world. I don't want math books pushing in that direction as well.

However, I feel I understand Danica's HEART: she's writing in a very conversational style to an audience she knows how to write to, and she's truly wanting to help girls with math. You know, the teachers that are considered the best are those who are friendly with their students, become as if their friends. So that's what she's trying to be.

Now, she DOES also go against the popular culture in some ways. For example, she strongly encourages girls to study math, to be smart, to work at becoming smarter, not to feel that smart & pretty can't go together, not to underachieve and so on. The Kiss My Math book includes great testimonials from gals who overcame their struggles in math and are now "fabulously successful women".

I just wish she wouldn't go along with the "teen magazine culture" so much when it comes to crushes and boyfriends.

Riding on her fame, these two math books are best-sellers, so Danica has become a powerful role-model for pre-teen and young teen girls. She has influencing power. With power comes responsibility. I feel she is already trying to use that influencing power wisely, and influence girls for the good — to study math and to be smart — but I hope she will be able to use that power even wiser in the future.

Recommendations

Teachers: I can heartily recommend these books for teachers, as they will be able to collect all kinds of ideas for their own teaching, and also learn from Danica's relaxed teaching style.

Parents and students: If you can keep from being influenced further into the boyfriend craze, go for it. If you can't, consider Dr. Math books (I've reviewed them as well). They are written in a somewhat similar, friendly, relaxed manner, though they don't contain nearly as catchy mnemonics and analogies as what Danica's do.

Review by Maria Miller

(The links below go to Amazon)
Math Doesn't Suck and Kiss My Math by Danica McKellar.

---

You may leave comments on this blogpost, but only intelligent discussion, no flaming, please!

Gyakuten Saiban 4: Mayudzuki Daian

The usually cool and collected detective who specializes in international cases, Mayudzuki Daian, aka Daryan Crescend from Apollo Justice: Ace Attorney, is the bass guitarist of The Gavinners and a close friend of Garyu Kyouya’s. He can be pretty sensitive about certain things like his guitar playing; criticizing on which can make him lose his cool and turn into a jerk.

What can I say? That hair-style is pretty impressive. I doubt that’s actual hair on his head, but it’s pretty accurate to the character. I love his jacket too.

Technorati tags: nanao, research, cosplay, cosplayer, daian, crescend, daryan, mayudzuki, apollo justice, ace attorney, gyakuten saiban 4, gyakuten, saiban, shark, gavinners, kyouya, garyu, klavier, gavin, guitarist, guitar, bass, detective, international, jacket

Rozen Maiden: Shinku 03

This is probably the most unique way to portray Shinku. We’ve had 2 versions so far, but neither of them made Shinku look the way she truly is: a ball jointed doll.

There was an anime episode wherein Shinku had to have her clothes washed, and this is how she looked until she got her clothes back. I can’t remember it too well anymore, but I want to watch the anime again.

Technorati tags: nanao, research, cosplay, cosplayer, shinku, rozen maiden, rozen, maiden, doll, anime, manga, ball, jointed

Chobits: Freya

Now here is a cosplay that I never thought I’d see.

Freya is the first version of the new series of persocoms known as the “Chobit” series. Unlike any other persocom, has the ability to feel emotions, specifically, to love. She was made by Mihara Ichiru to become their “daughter”.

When Hibiya Chitose, Ichiru’s wife, noticed a change in Freya’s attitude, Chitose asked Ichiru to create a younger sister for her, and she was named “Elda“. Freya was happy for a while, but her true sadness was due to the fact that she had fallen in love… with her own “father”. She knew she could never be together with him, and this caused her so much sorrow that she ceased functioning.

Aside from the hair? This is a very impressive cosplay. Great job on this! I really like her ears..!

Technorati tags: nanao, research, cosplay, cosplayer, chobits, chobit, chii, freya, elda, chi, persocom, personal computer, pc, love, daughter, chitose, hibiya, ichiru, mihara, father, sorrow

An AHA! abacus moment in the life of a preschooler

I've been doing math lessons with my 3-year old using the 100-bead abacus. Usually we do a few problems where she tells me a number to make and I tell her a number to make, back and forth. Today she asked me to make 51, and I asked her to make 68. These went smoothly since she's getting pretty good at this now.

Then we did a few "more than" problems. I said, "Let's say your sister has 5 cookies and you have one more than her. How many do you have?" This is a new concept to her so we need to do it slowly and carefully with the abacus: first make her sister's cookies, then let her have the same amount, then give her one more.

Then we do a few subtraction problems such as 7 − 4. She moved 7 beads, then "took away" or moved the other way 4 beads, and how many were left? 3 beads. I showed her also 50 − 10 = 40.

She started doing her own problem, "Let's do 9 − ..." and while she was thinking, I quickly proposed "... minus nine". Nine minus nine. Well, she moved nine beads, then COUNTED the beads one by one moving them the other direction, and was left with none... and what a SURPRISE it was to her! She had to start giggling!

I immediately showed her another one, 4 − 4. She did 10 − 10 herself. And THEN I showed her 100 − 100, which made the greatest giggles of all!

It was just so cute so I had to share. Plus, now you know several ways how to teach math concepts with the abacus.

An AHA! abacus moment in the life of a preschooler

I've been doing math lessons with my 3-year old using the 100-bead abacus. Usually we do a few problems where she tells me a number to make and I tell her a number to make, back and forth. Today she asked me to make 51, and I asked her to make 68. These went smoothly since she's getting pretty good at this now.

Then we did a few "more than" problems. I said, "Let's say your sister has 5 cookies and you have one more than her. How many do you have?" This is a new concept to her so we need to do it slowly and carefully with the abacus: first make her sister's cookies, then let her have the same amount, then give her one more.

Then we do a few subtraction problems such as 7 − 4. She moved 7 beads, then "took away" or moved the other way 4 beads, and how many were left? 3 beads. I showed her also 50 − 10 = 40.

She started doing her own problem, "Let's do 9 − ..." and while she was thinking, I quickly proposed "... minus nine". Nine minus nine. Well, she moved nine beads, then COUNTED the beads one by one moving them the other direction, and was left with none... and what a SURPRISE it was to her! She had to start giggling!

I immediately showed her another one, 4 − 4. She did 10 − 10 herself. And THEN I showed her 100 − 100, which made the greatest giggles of all!

It was just so cute so I had to share. Plus, now you know several ways how to teach math concepts with the abacus.

Naruto: Uchiha Sasuke and Uchiha Itachi

Itachi, the older brother of Sasuke, is the young prodigy of the Uchiha Clan. People looked to him as the future of the Uchiha Clan. This left Sasuke in Itachi’s shadows, craving for the same affection Itachi receives from their parents.

It was during these times, however, that Itachi loved and cared for his younger brother. He was the only one who acknowledge any hard work and effort Sasuke accomplished.

Isn’t this cosplay just too cute for words? Too bad we can’t see their faces, but they both looks so cute. Nice photo!

Technorati tags: nanao, research, cosplay, cosplayer, naruto, uchiha, sasuke, itachi, prodigy, clan, brother, parents, accomplishment, kids, children, umbrella

Are these really parallelograms - answers

These are answers to my earlier post where I asked if certain figures necessarily are parallelograms.

The question was: Does the given information in each diagram guarantee that each is a parallelogram?

Figure 1:
This one you can't get around; it ends up being a parallelogram, actually a dandy rhombus. Let's prove it. You can notice it has lots of sides of the same length. If we draw a diagonal, we get two triangles with all kinds of same sides:

The two triangles ABD and BCD end up having all three sides the same. So by the SSS triangle congruence theorem, they are congruent triangles. Hence, their corresponding angles are the same.

I've marked the corresponding angles with the same colors. Actually the triangles are even isosceles so the blue and purple angles are even congruent... but we don't need that fact.

To prove ABCD is a parallelogram, we need to prove its two sides are parallel. And for that, it's often handy to use the corresponding angle theorem: if corresponding angles are equal, the lines are parallel. So image that we continue the line segment CD. Notice the additional green angle that I've marked:


How do I know it actually is a "green angle" (congruent with the other green angle)? It's because the three angles, being angles of a triangle, add up to 180:
+ + = 180. And the three angles being there along the same line (the continuation of CD), it must be. This sounds a little too complicated as I'm typing it. Perhaps I shouldn't have marked it green. Anyhow, since it IS congruent with the other green angle at C, then the line segments BC and AD must be parallel.

A similar argument would prove the other two sides parallel.

Figure 2: This isn't necessarily a parallelogram, but it IS always a trapezoid:



Figure 3:
This one is trickier, but it isn't necessarily a parallelogram. I used a compass to find a way to make this into a trapezoid:ABCD is a trapezoid with the non-parallel sides 5 units long.

Figure 4: This one is actually a repetition of the Figure 1, because it has the opposites sides of same length. We can use the identical argument to prove it is a parallelogram.

Are these really parallelograms - answers

These are answers to my earlier post where I asked if certain figures necessarily are parallelograms.

The question was: Does the given information in each diagram guarantee that each is a parallelogram?

Figure 1:
This one you can't get around; it ends up being a parallelogram, actually a dandy rhombus. Let's prove it. You can notice it has lots of sides of the same length. If we draw a diagonal, we get two triangles with all kinds of same sides:

The two triangles ABD and BCD end up having all three sides the same. So by the SSS triangle congruence theorem, they are congruent triangles. Hence, their corresponding angles are the same.

I've marked the corresponding angles with the same colors. Actually the triangles are even isosceles so the blue and purple angles are even congruent... but we don't need that fact.

To prove ABCD is a parallelogram, we need to prove its two sides are parallel. And for that, it's often handy to use the corresponding angle theorem: if corresponding angles are equal, the lines are parallel. So image that we continue the line segment CD. Notice the additional green angle that I've marked:


How do I know it actually is a "green angle" (congruent with the other green angle)? It's because the three angles, being angles of a triangle, add up to 180:
+ + = 180. And the three angles being there along the same line (the continuation of CD), it must be. This sounds a little too complicated as I'm typing it. Perhaps I shouldn't have marked it green. Anyhow, since it IS congruent with the other green angle at C, then the line segments BC and AD must be parallel.

A similar argument would prove the other two sides parallel.

Figure 2: This isn't necessarily a parallelogram, but it IS always a trapezoid:



Figure 3:
This one is trickier, but it isn't necessarily a parallelogram. I used a compass to find a way to make this into a trapezoid:ABCD is a trapezoid with the non-parallel sides 5 units long.

Figure 4: This one is actually a repetition of the Figure 1, because it has the opposites sides of same length. We can use the identical argument to prove it is a parallelogram.

Code Geass: Lelouch of the Rebellion: Zero

The mysterious, masked revolutionary who is the leader of the Order of the Black Knights, Zero, the alias Lelouch Lamperouge uses in this guise, wishes to campaign against those who oppress the helpless.

Originally, the rebellion was to seek revenge for his mother’s death, and make a new world for his sister, Nunally. However, as the story progresses, Lelouch’s friends help him realize that the rebellion is no longer just for his sister after she becomes Viceroy of Area 11.

This is really an awesome cosplay. I wonder what the cosplayer looks like behind the mask?

Technorati tags: nanao, research, cosplay, cosplayer, code geass, lelouch, lamperouge, zero, rebellion, order of the black knights, alias, campaign, revenge, nunally, viceroy, area 11

Neon Genesis Evangelion: Ayanami Rei 02

She is the First (Child) Children, the pilot of Unit 00, and the clone who is a vessel for the Angel Lilith. In the beginning of the series, Ayanami Rei seemed like an emotionless puppet who apparently only had a relationship with Ikari Gendo. However, when she met Shinji, something changes, even though Asuka wants little to do with her.

It’s been a long time since I featured a cosplay from Evangelion. I love the wig used for this one, it looks so natural. Great work!

Technorati tags: nanao, research, evangelion, ayanami, rei, angel, lilith, puppet, vessel, clone, first, child, children, pilots, unit 00, ikari, gendo, shinji, asuka, soryu, langley, cosplay, cosplayer, neon, genesis

Multiplication vs. addition once more

Keith Devlin has published another column along the lines of multiplication not being repeated addition. I feel quite honored that he mentions THIS blog in his column (scroll down to the end), referring to what I wrote about the issue.

This time he expounds on research results. The research clearly shows that thinking of multiplication as repeated addition hinders students' further understanding of mathematics. It can lead to the misconception that multiplication always makes things bigger. Children need to acquire multiplicative reasoning, which is different from additive reasoning. And so on. Go read it yourself.

Multiplication vs. addition once more

Keith Devlin has published another column along the lines of multiplication not being repeated addition. I feel quite honored that he mentions THIS blog in his column (scroll down to the end), referring to what I wrote about the issue.

This time he expounds on research results. The research clearly shows that thinking of multiplication as repeated addition hinders students' further understanding of mathematics. It can lead to the misconception that multiplication always makes things bigger. Children need to acquire multiplicative reasoning, which is different from additive reasoning. And so on. Go read it yourself.

Lineage II: Gatekeeper Jasmine

Here is another unknown cosplay I’ve yet to figure out. Looking for her information took up some time, but I still came up with nothing. I can’t remember where I got this image from, but it might have been from Cosplay.com… Or was it Cosplaylab.com?

Not sure, but whoever knows where this character is from, feel free to comment and/or send me an email.

And yes, this is the 6th. The 5th one I’d already found out who she is before I posted it as an Unknown. ;)

EDIT: Thanks you very much to Soyoungim for commenting that this is Gatekeeper Jasmine from Lineage II!

EDIT again: Thanks to anon for directing me where the image came from! The cosplayer's name is Erika Door!

Technorati tags: nanao, reasearch, cosplay, cosplayer, cosplaylab, unknown, character, black

The Ipswich Handmade Expo

The very first Ipswich Handmade Expo, held on Saturday 16th August, saw many BrisStyle members not only making great sales, but getting some fantastic feedback, and even publicity as well!

With close to 2000 people coming through the doors of the 87 stallholder event, various BrisStyle members described the day as huge, wonderfully organised, busy and exhilarating! Some of the BrisStyle members who sold their wares at the expo included:

Michelle from Pedrosprout and Sharon from Shazzabeth Creations, who both had photos of themselves and their stalls featured in the Queensland Times paper (click on the photo to read the whole article).


Michelle's gorgeous booties and other handmade sewn goodies made a beautiful display, and Sharon's original beaded, wirework and chainmaille Jewellery brought lots of crowds, with earrings being her most popular items.


Other BrisStyle members who attented included Jacqui from Bellabijoux, selling beautiful one-of-a-kind jewellery pieces.


Trish from Trishalan Designs, also had a beautiful stall set up, selling wonderfully vibrant hand-dyed fabric and threads, with the threads being a particularly popular item.

Polka dot Rumba pants were the most popular item for Louise from Made by Miffy, who sells boutique wear for kids and the kitchen! And Eliza of Eliza's Art was happy to find customers falling in love with her gorgeous art prints.

All members who attended agreed that the morning was the peak time for crowds, with many stall holders not getting a coffee break until well into the afternoon. They also said that the organisation of the event was superb, as was the publicity leading up to the event, and they are sure that next month's Expo will be even bigger and better, so stay tuned for more information on the next Expo happening in September. We will put the information in our 'What's Happening' section of the blog (in the top right hand column) as details come to hand :)

Bleach: Urahara Kisuke

“Geta-boshi”, meaning “Mister Hat-and-Clogs” is a generally carefree character who mysteriously appears in the scene of some important event, being the catalyst rather than the one who does the actual work. He can be serious when the situation calls for it, but he rarely intervenes in battles unless extremely necessary.

It makes me wonder what this cosplayer really looks like behind the fan. Nice cosplay and posing! I especially like his hat. Good job!

EDIT: Thanks to MelonPlay for letting me know this cosplayer is Scruffy Rebel from Cosplay.com!

Technorati tags: nanao, reasearch, cosplay, cosplayers, bleach, urahara, kisuke, geta, boshi, hat, clogs, sandals, carefree, catalyst, battle, fan, cane, zanpakutou

Gurren Lagann: Yoko Littner

Don’t let her cute looks fool you. Yoko is an extensive wielder of firearms, including the long range sniper rifle she’s holding in the image. She is the mature and rational member of the group, though she badmouths Kamina on occasion.

Yoko also loves children and is seen as a teacher named “Yomako” by the end of the series.

Nice pose, and her boots are pretty cute. I had no idea who this was until I searched the internet for more information. Thanks to Cosholics Cafe for the photo!

Technorati tags: nanao, research, cosplay, cospalyer, yoko, littner, rittona, fireamrs, long range, sniper rifle, mature, rational, kamina, yomako, teacher, children, internet, cosholics, cafe

Air Gear: Noyamano Ringo and Simca

She may look like a simple junior high school girl, but the King Class AT user, Noyamano Ringo, is the current Thorn King (or rather “Queen”) of the Eight Kings in the AT World. She is the successor of the legendary Storm Riders Team Sleeping Forest and Simca’s rival to Minami Itsuki aka “Ikki”.

And of course, I’ve already rambled about Simca here. No need for a repeat, am I right? :D

I do think I like this Simca cosplayer better than the first one though. Then again, maybe that’s just because of the costume?

I first found this on That Girls Site. Thanks for sharing the photo!

Technorati tags: nanao, research, cosplay, cosplayers, air gear, noyamano, ringo, simca, junior, high school, king class, at, thorn king, thorn queen, eight kings, at world, storm riders, sleeping forest, minami, itsuki, ikki, that girls site, genesis, swallow, regalia, trophaeum tower, sky regalia, sky king, kogarasumaru, behemoth, kenjiyo

Final Fantasy X: Auron

This 35-year-old unsent warrior monk for Bevelle whose attack to Yunalesca led to his death, Auron is Tidus‘ Mentor and Yuna’s guardian. He kept his status of being an unsent a secret, although there were a lot of suspicions raised when he refused to enter the farplane at Guadosalam. He was eventually laid to rest when Yu Yevon was finally defeated.

I can’t believe how accurate this cosplay is! I love the costume’s details and the cosplayer’s attitude. Nice job!

Technorati tags: nanao, research, cosplay, cosplayer, warrior, monk, bevelle, yunalesca, auron, tidus, yuna, mentor, guardian, unsent, farplane, guadosalam, yu, yevon, final fantasy x, final fantasy

Tsubasa - Reservoir Chronicle: Fay D. Flourite

I am so annoyed that I can’t see the cosplayer’s face here. But for Fay to now show his face is actually very characteristic.

Fay is one of Syaoran’s allies. He is happy-go-lucky and carefree, but is very mysterious, in the sense that he seems to have little regard for his own life. He can be very perceptive and is considered to be as skillful as Kurogane. He also often hides his own unhappiness with a fake smile.

I’ve been wondering if I should post this or not when I found it on Flickr. Mainly because I seldom feature cosplayers who don’t show their face, give or take a few. I still find this pretty, though!

EDIT: Thanks to MelonPlay for letting me know the cosplayer's name is Naraku from Cosplay.com!

Technorati tags: nanao, research, cosplay, cosplayer, fay, fay d. flourite, flourite, li, syaoran, tsubasa reservoir chronicle, tsubasa chronicle, tsubasa, reservoir, chronicle, kurogane, flickr, clamp, fye, fai

Bar diagram problem

This was asked of me as of today:

Please solve this using the bar/block diagram method. My friends and I are stumped....

Desmond had 480 more oranges than pears. After selling half of his oranges and half of his pears, he had four times as many oranges as pears left. Find the number of pears he had at first.
Thank you!

This problem is from a Primary School Leaving Examination (PSLE) paper. PSLE is the final examination for primary school students in Singapore. So, you would expect to see these kind of problems in Singapore Math.

My first attempt for solving this was like this:

It shows the difference being 480. The red lines are halving the quantities of pears and oranges.

But I quickly noticed this was way off. The amount of pears needed to be way less than the amount of oranges.

My second attempt was like this:
It was a little better, but half the pears looked more like 1/3 of the half the oranges. So the amount of pears needed to still be less.

This is the final diagram that solves the problem. The main idea is that the parts "match" - that you can see the relationship 1 to 4 in the amount of pears versus oranges, or in the halved amounts.

Actually, the CRUCIAL point of this problem - that there are 1/4 as many pears as there are oranges - can be understood without any kind of bar diagrams. You see, if that is true of the halved quantities (4x as many oranges as pears), then the same is true of the original quantities as well!

So without ever drawing anything, one can figure that there are 4 times as many oranges as pears. The DIFFERENCE is 480. The difference is also 3/4 of the oranges. So if 3/4 of the oranges is 480, then 1/4 of the oranges is 480 ÷ 3 = 160 (which is the number of pears). And the total number of oranges is then 4 x 160 = 640. That solves the problem then without the usage of bar diagrams or algebraic equations.

Bar diagrams can be of enormous help in visualizing the relationships between PARTS in the problem. BUT, to draw one is not necessarily easy because to get it right (like in my case) actually REQUIRES understanding something about the problem.

So, let the bar diagrams be a tool that helps you understand the problem ALSO in this sense: while you try to draw one, let the misdrawn ones guide your thinking towards the right ideas.

Bar diagram problem

This was asked of me as of today:

Please solve this using the bar/block diagram method. My friends and I are stumped....

Desmond had 480 more oranges than pears. After selling half of his oranges and half of his pears, he had four times as many oranges as pears left. Find the number of pears he had at first.
Thank you!

This problem is from a Primary School Leaving Examination (PSLE) paper. PSLE is the final examination for primary school students in Singapore. So, you would expect to see these kind of problems in Singapore Math.

My first attempt for solving this was like this:

It shows the difference being 480. The red lines are halving the quantities of pears and oranges.

But I quickly noticed this was way off. The amount of pears needed to be way less than the amount of oranges.

My second attempt was like this:
It was a little better, but half the pears looked more like 1/3 of the half the oranges. So the amount of pears needed to still be less.

This is the final diagram that solves the problem. The main idea is that the parts "match" - that you can see the relationship 1 to 4 in the amount of pears versus oranges, or in the halved amounts.

Actually, the CRUCIAL point of this problem - that there are 1/4 as many pears as there are oranges - can be understood without any kind of bar diagrams. You see, if that is true of the halved quantities (4x as many oranges as pears), then the same is true of the original quantities as well!

So without ever drawing anything, one can figure that there are 4 times as many oranges as pears. The DIFFERENCE is 480. The difference is also 3/4 of the oranges. So if 3/4 of the oranges is 480, then 1/4 of the oranges is 480 ÷ 3 = 160 (which is the number of pears). And the total number of oranges is then 4 x 160 = 640. That solves the problem then without the usage of bar diagrams or algebraic equations.

Bar diagrams can be of enormous help in visualizing the relationships between PARTS in the problem. BUT, to draw one is not necessarily easy because to get it right (like in my case) actually REQUIRES understanding something about the problem.

So, let the bar diagrams be a tool that helps you understand the problem ALSO in this sense: while you try to draw one, let the misdrawn ones guide your thinking towards the right ideas.

Loveless: Aoyagi Seimei

The mysterious older brother of Aoyagi Ritsuka, Seimei’s personality has a lot of different interpretations canonically. To Soubi, who serves as his fighter, Seimei is kind and gentle; to the members of Nanatsu no tsuki, Beloved was cruel and sadistic. Ritsuka could only remember him as the one who protected him from their abusive mother.

What could Seimei be really like? Since the manga is still on going, there’s no real info about him yet. But there was one thing that was apparently confirmed: Seimei is still alive, and the person who died in his place was only identified by his dental records.

I wasn’t too sure if this was Ritsuka or Seimei, but his hair is long enough to be Seimei’s I think. The cat ears are really cute too, don’t you think?

Technorati tags: nanao, research, cosplay, cosplayer, loveless, aoyagi, seimei, ritsuka, agatsuma, soubi, beloved, nanatsu no tsuki, seven moons, manga, dental records, cat ears

Tenchu: Fatal Shadows: Ayame

No Unknown Cosplays for this week, guys. I found out who she’s cosplaying as!

An orphan raised and trained by Master Shiunsai, Ayame (once called “Omon”) posses natural, raw talent as a kunoichi. She never had the patience to master techniques as a child, but she was initiated into the circle of ninja at the age of 14. Ayame is known for her skills with blades, caustic tongue, and speed.

I first thought she was an assassin from Ragnarok, but I was wrong. The symbols on her white belt are definitely from Techu’s 4th Game. The blades of those swords look very sharp. I wonder if they’re real?

Technorati tags: nanao, research, cosplay, cosplayer, tenchu, fatal, shadows, ayame, omon, kunoichi, female, ninja, patience, master, technique, child, circle, skill, blade, caustic tongue, speed, ragnarok, online, shiunsai