Inspired by Lilavati: Math Poems by Grade 8 Students

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Inspired by Lilavati Math Poems by Grade 8 Students CDNIS 2009-2010

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Inspired by Lilavati Editors: Ms. Hillary Daniels Florence Ho Adrian Tse Gerald Yan

Grade 8 Math Teachers: Ms. Hillary Daniels Mr. Justin Giesbrecht Mr. Michael Luciani

Layout Designers: Florence Ho Ms. Hillary Daniels

Cover Designers: Jessica Xing Ms. Sharon Lacoste

Special thanks to Aaron Metz for the technical support and to Lorraine Ho for the assistance with the bibliography.

Throughout this book you will see the ‘om’ symbol. According to Encyclopaedia Brittanica Online, “The syllable Om is composed of the three sounds a-u-m (in Sanskrit, the vowels a and u coalesce to become o), which represent several important triads: the three worlds of earth, atmosphere, and heaven; the three major Hindu gods, Brahma, Vishnu, and Siva; and the three sacred Vedic

Dedicated to Mr. Pierre Lacoste, for without his ideas and inspiration, this collection would not exist.

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Contents Introduction

Hillary Daniels

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Veronica Dickson LaRotta Ms. Hillary Daniels Christy Lo Andrea Kung Natalee Hung Natalie Leung Sabrina Yang

13 15 17 19 21 23 25

Eunice Lee Jeremy Lai Serene Lam Griffin Hale Arnold Yeung Celine Chan Lorraine Ho Jaime Deverall Ally Lor Mollie Lentchner Jesse Hui

29 31 33 35 37 39 41 43 45 47 49

Florence Ho Halle Hagan Daniel Poon Gerald Yan

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Junior Eleanor’s Plight Dolphins Kittens Ants One Wrong Step Candies Coyotes Intermediate The Stars From Above Wolves An Army of Caterpillars Lions Bees vs. Fleas Fairies How Many Penguins Pandas at the Zoo Children Birds Flying High Advanced How Many Boys The Meadow, Which Bends Yummy Ice Cream Gimme My Gum Solutions

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INTRODUCTION Poetry? In Math?! Yes, indeed! In India, long before there were textbooks, as we now know them, math and astronomy books were written entirely in verse. This comes from an ancient tradition of passing knowledge from generation to generation in spoken, rather than written form in order to prevent the lower castes from learning- text in verse is much easier to memorize.

A fifth part of a swarm of bees came to rest on the flower of Kadamba, a third on the flower of Silinda.

Three times the difference between these two numbers flew over a flower of Krutaja, and one bee alone remained in the air, attracted by the perfume of a jasmine in bloom.

Tell me, beautiful girl, how many bees were in the swarm?

The poem above comes from the Lilavati, the arithmetic portion of the Siddantasiromani, an astronomy text written by Bhaskara (1114-1185), a well-known Indian astronomer and mathematician, for his daughter, Lilavati. Bhaskara, with his astronomical skill, had calculated the perfect time for his daughter to be married, of which she kept careful track with a water clock. Just near the time she was to be wed, she looked over the clock and a pearl from her headdress dropped into it, blocking the flow of the water. Before she realized what had happened, the time for her marriage had passed! Of course, Bhaskara, being the loving father that he was, felt terribly for his beautiful daughter and to console her he named a portion of his book, Lilavati, after her.

Centuries later, how is the Lilavati relevant? Students in the 21st century have been left with big problems, and mathematics offers an approach to finding answers to complex questions. The modern way of doing math - algebra - is extremely powerful but to an eighth grader in math class it can be ‘dry’. To a mathematician it is beautiful. To give students a feeling of how mathematics can be beautiful we have given them the opportunity to return to a more poetic approach to math. It is great fun and hopefully gives them an appreciation for the more logic-based rules of modern algebra.

In Poems in the Style of Lilavati you will find a range of problems and we hope that whatever your ability is in math, in the following pages you too will be able to see the beauty in algebra.

Namaste, Ms. Hillary Daniels

JUNIOR

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ELEANORʼS PLIGHT Veronica Dickson

Eleanor is quite a brainy girl, her hair is just full of bushy curls.

Instead of going out to play, sheʼd stay and study until May. In the lonely summer of ʼ99, Eleanor wished to stay inside.

Her sisters went to play jump rope, but Eleanor had a dreadful stroke.

On the hospital bed she lay as if dead.

The doctor told her she would have to stay until her head had cleared away.

Since several days were needed here, books were provided for poor Eleanor dear.

On the first sickly day, she could not read a book, so tired was she, she could not take a look.

But then on Day 2 she read 3 tomes about magic and mischief and little bearded gnomes.

The Doctorʼd come by, and see her on the bed, as he announced to her that only 10 more days were needed for her head.

Throughout the following 8 days pages turning was the chime.

4 by 12 was the number of books she read in that period of time.

With only a couple of days to go, she read the square of 2, for her little head was churning like a hopping kangaroo.

Now, my dear reader Iʼll give you one last clue: diminish the number by 8, I know how youʼll do.

If you have the skill and the brains and the power, give me the books that Ellie unraveled.

Before I end here, may I please announce that Eleanor is quite fine, her head not hurt an ounce.

Sheʼs living quite well, but thereʼs been one little change, where before she would lay alone on her bed dusting off another novel, she now plays outside with other children, skinning her knee on the gravel.

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DOLPHINS Ms. Hillary Daniels

A pod of dolphins, swimming in the sea, through the water they glide so elegant and free.

The sum of the square of their number and four Gives twenty dear child, not less and not more.

Now say, my student, so smart and so brave, Can you ďŹ nd the number Of dolphins in the waves?

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There are thirty-three kittens dancing on the roof.

Fifteen of them fell down with a single poof!

The owner bought ten more kittens.

All the kittens were wearing mittens!

He separated all the kittens in equal bunch.

Then gave his sisters each a pile after his lunch.

Each of them got seven cute little ones.

Tell me the answer so we are done!

How many sisters does the owner have?

By: Christy Lo

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Ants On the war ground, ants come marching down With different flags of red, black and brown 250 red were given the crown Half of all the ants were black who escaped to town With 150 brown ants lying dead on the ground Would you be so kind And rewind back in time before the war, And count the total number of ants once more.

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One Wrong Step by Natalee Hung

A waddle of penguins Gliding on thin ice, Making every movement So careful, so precise But one wrong motion ends it all, Twenty of them slip And down they fall.

Their number once a product of four, Now dwindled down to twelve, That’s for sure So can you ďŹ nd the number They had in the beginning, Before the tragedy left them all waning?

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Candies Mandy was given candies by her mommy At first, she only got a few.

Then, six more came from granny.

She told a joke to her nanny.

When her nanny thought it was funny, The number of her candies multiplied by seven.

Now she has sixty-three good heavens!

Can you find the original number of candies, That was given by mommy to Mandy?

Natalie Leung 8C

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Coyotes In The Woods

by Sabrina Yang

A pack of coyotes Were speeding through the woods, Running so gracefully Towards the tasty goods.

The sum of the coyotes Was ďŹ ve times two, But three were lost, Due to poachers and zoos.

Now the sum is seven But it multiplies by four, Because there are now Pups ready to explore.

Then ďŹ ve disappeared Into the darkness, And four now belonged to Mr. and Ms.Harkness.

So tell me, How many are left in the pack?

And how many fell back?

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INTERMEDIATE

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The Stars From Above Eunice Lee 8B In the galaxy, stars gleamed from the kiss of god, On the tranquil beach I sat, still in motion, gazing with awe Shimmer and glitter, they were placed on surmount A swish of the wand, it doubled their amount Frisky twinkles continued to flaunt their design, Then, Boom! stars tripled, determined to outshine The jealous demons, stole twenty-nine from display And I, on little earth wept and saw the last star remain Oh how many were there at the beginning of creation?

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Wolves Jeremy Lai Five eagles streaming in the air, Their number squared, good and fair.

Their number squared again, and gives you a scare.

Gives ten hunters and two groups of wolves, on christmas eve Hunting down the eagles, and food they soon will receive.

The ten courageous hunters and the two packs of wolves are multiplied by five, But in the end, five packs of wolves leave, knowing they won’t survive.

Then tell me now, if you won’t take too long, How many wolves are hunting in each group?

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An Army of Caterpillars An army of caterpillars, Was defending their home from killers.

One-sixth of forty-two, Went bravely to their doom in pursuit.

Two multiplied by six, Crawled into a deadly nest of ticks.

Combined with the square root of nine, 10 more caterpillars joined the fight.

There were only 66 caterpillars left in line, Still standing brave and bright.

And so my friends, let me ask you a question.

How many were caterpillars were there in the start of the fight?

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Lions Griffin Hale A zookeeper had some lions; the number was less than ten, If anyone can find how many, he’ll give you one from the den: So now here is the start of the problem, lets lee if you can figure it out.

Times the number of lions by itself, then multiply that by three, this part should be easy, no doubt.

Now take away seventy-two times the number of lions, Then add seven multiplied by the unknown number of lions, And this times the product of three and the lions.

For the last of this side of the equation, take what you’ve got so far, and put that over eight.

This equals to something more simple, just two squared times three.

The answer comes by guess and check, you’ll see.

This problem was fairly basic for me, so I think it will be for thee.

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Arnold Yeung

BEES VS FLEAS Math Poem

V.S THE FIGHT OF BEES AND FLEAS There was a fight between the buzzin bees, And the fiery fleas.

They want to see who is better than the other, So this started the fight between each other.

After their fight they found that they are both the same, The only different thing is their name.

The fleas can run and cover an area of eight decimeter, While the bees can fly and cover an area of three more than A decimeter.

The fleas can jump at ABC meters per hour, While the bees can fly at 30 meters per hour.

The fleas have 42 out of 7 legs, While the bees have C combined with 4 legs.

The fight came to an end.

They both figured out, That they can all do the same.

So my dear child, can’t you see?

What are the numbers of ABC.

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How Many Penguins?

By Lorraine Ho

A group of penguins huddled on an ice shelf, Sliding and bumping amongst themselves.

Fifteen is their number increased by seven, But to get to ďŹ fteen, you have to subtract one.

My fellow Reader, you are now by yourself, Tell me: How many penguins are on the ice shelf?

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Pandas At The Zoo 360 Pandas live at the zoo, Chewing their bamboo through and through.

Say 30 are boy cubs cute and young, And 20 are girl cubs small and fun.

If an unknown number of father pandas live at the zoo, And 2 times the sum of the unknown and 5 represent the number of wives too.

Now handsome young man I ask you, How many father pandas live at the zoo?

Written By: Jaime Deverall

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Children Ally Lor 8B In the classroom the students were playing.

Some were laying, some were greying and some were swaying.

The number of children laying is double the children swaying.

The children swaying is three less than the children greying.

So tell me saying The number of children that are playing When the total children greying Are ďŹ fteen and staying.

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Birds - Mollie Lentchner Thrice a number of birds were flying high, The number of birds then multiplied.

Four times as many are now in the flock, But half are now gone! Oh what a shock!

But the number again grows a bit, It multiplied by the square root of 25, I admit.

Then 21 more decided to join the group, They flew past my eye in one great swoop!

‘How many now?’ I know you might ask.

Well my friend, to find out is your task!

I will give you some hints to move you along.

If you listen to me, you can’t go wrong.

Find the answer to six squared plus three.

Are you still listening closely to me?

Four squared plus three you also most know.

Multiply the two answers and write the number below.

The number of birds that swooped past my eye, Is the number I just told you to write. No lie!

Find the number of birds that started the trend, And this is the end of the poem my friend.

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Flying High Jesse Hui In the stormy, misty sky, Five groups of birds fly up high Forty eight more join the happy flock Cruising together peacefully, without havoc

They grow tired, and rest under the heavens And before you know it, their group multiply by seven They take off as soon as they can As a hurricane comes, and attacks their clan

They find each other, using secret tricks But only to find out their group was divided by six They end up with only ninety one Please tell me, my friends, it may not be fun But how many birds were there in the original group of five You can answer me as you arrive

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ADVANCED

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How Many Boys? Â

By: Florence Ho

A tram slides whistling past on a bumpy track, Sand beneath its wheels and the sun upon its back.

The number of girls in the tram are half the number of boys, As the two genders mix and match their toys.

The number of grandmas are two-thirds of the girls; The wheels of the tram continue to whirl.

The babies are half the number of grandmas, They cooed over their new stuffed llamas.

The number of the passengers is thirty-six; What is the number of boys? Take your pick.Â

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The Meadow Which Bends Halle Hagan

There were many cherry blossom trees in a meadow Their blooms inviting, fragrant and free ‘Twas a lovely place to rest for birds Their nests scattered ‘round Though no one knew how many eggs could be found The number of these a mystery solved by simple curiosity A small girl climbed one tree, The first nest revealing Half of seventy true to the touch, then divided by five gave that number, Though not much The girl then climbed the next tree, But was stung by a bee Once she climbed the third, She was able to see The next nest resting freely Upon a mere leaf Out in the open, Counting the eggs that she found, The square root of sixteen times ‘x’ Combined with half of ‘x’ All divided by three Equals the number of eggs in that third tree You see, my friend Choosing to follow the trend Of counting the eggs in the meadow which bends ‘x’ is five less than the amount in the first nest When you are ready to gather the total eggs in the trees, You must square the sum of nests one and three Diminish by four, Then multiply by three if you so adore, And speak to me this, my wise old friend: How many eggs are present in the meadow which bends?

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Daniel Poon 8D

On a hot summer day, Sam went out to play, Walking towards home on the street, He wanted to taste something sweet!

With a number scoops of ice-cream at first, Sam squared them and added five more, Then the total divided equally among six, With his friends that play with sticks, He multiplied the quotient by four And ice-cream, he didn’t want anymore.

Now with so much ice-cream, He heard a great loud scream, Josh, his brother, saw Sam, And bought ice-cream instead of clams.

Josh started with the same number as Sam, Then he squared it before eating jam.

Four given away, the bullies there to stay, The difference by seven was divided away.

Seventeen was then added to the quotient, When he looked at an advertisement.

At the end, the number scoops they each had was the same, With so many ice-cream they weren’t ashamed.

Their stomachs with ice-cream, about to burst, But how many scoops did Sam have at first?

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Gimme’ my GUM. Gerald Yan Bubblegum, bubble gum, in a dish, So how many pieces do you wish?

Score! Free gum!

Yet before you can give me this delightful treat, You gotta’ figure out just how many I eat.

My real crave, add one, Times the square of their sum, Gives you just the first part, Now isn’t this fun?

All over a dozen (heard chewing gum gets you a date ), It’s gunna’ be sweet, oh I just can’t wait!

‘Free’ really makes it all the more succulent, Now BE-A-MAN and take away five-sixths of the quotient, Tell you what, you ol’ brute.

Square this new number of mine, And it magically gives you the cubed root.

Of? Seven hundred and twenty-nine!

So work this out, and gimme’ my ‘chews’, But if you don’t ‘roll’ with these values…

Just gimme’ my gum.

Dumb dumb…

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SOLUTIONS

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Math 104Q University of Connecticut

Solution to: How Many Bees in Lilavati’s Swarm?

Set x = the number of bees in the swarm. x 5

We have: • over the flower of Kadamba:

x 3

• over the flower of Silinda:

x x 3( − ) 3 5

• over the flower of Krutaja: • in the air:

1 .

TOTAL:

x x x x + + 3( − ) + 1 5 3 3 5

The equation becomes: x x x x + + 3( − ) + 1 = x 5 3 3 5

To solve it we first eliminate parenthesis: x x x x + + 3 − 3 + 1= x 5 3 3 5

LCD = 15 Multiply both sides of the equation by 15: 15 ⋅

x x x x + 15 ⋅ + 15 ⋅ 3 − 15 ⋅ 3 + 15 ⋅ 1 = 15 ⋅ x 5 3 3 5

Reduce all fractions (to get rid of denominators): 3x + 5x + 15x − 9 x + 15 = 15x

Combine like terms: 14 x + 15 = 15x

Subtract 14x on both sides: 15 = 15x − 14 x

Solution: x = 15

Answer: There are 15 bees in Lilavati’s swarm.

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Eleanor’s Plight Let y represent the number of books Eleanor read.

4x + 22 + 3 -8 = y 48 + 4 + 3 - 8 = y 48 + 4 + 3 - 8 = y 48 + 4 + 3 - 8 = 47 Dolphins Let x represent the number of dolphins. x2+4=20 x2=16 x=4 Kittens Find!x!!!!!!

33 " 15 + 10 =7 x

# 33 " 15 + 10 & Multiply!x!to!the!equation!to!get rid of!the!x!from!the!denominator! ! x % (' = 7 ( x ) $ x Do the same thing to the 7, mutiply x to it too.

After you multiply the x for both side you get this ! 33 " 15 + 10 = 7x After you did 33 " 15 + 10 = 7x, you get get ! 28 = 7x Divide 28 by 7 to get what is x !

Answer ! 4 = x

Ants y – (! y +150) = 250 or y – ! y -150 = 250 y-1/2y=400 1/2y=400 y=800 One Wrong Step 4x - 20 = 12 4x=32 x=8 Candies 7(x+6)=63 7x+42=63 7x=21 x=3

28 =x 7

Coyotes Let x represent the number of coyotes that are left in the pack x = {(5 x 2) - 3} x 4-5-4 x = 7 x 4-5-4 x = 28-5-4 x = 19 The number of coyotes that fell back: 3+5+4 12 Stars from Above “A swish of the want, it doubled their amount”—2x “Then Boom! Stars tripled, determined to outshine” 3(2x) “The jealous demons, stole twenty-nine from display” 3(2x)-29 “And I, on little earth wept and saw the last star remain” 3(2x)-29=1 3(2x)-29=1 6x-29=1 6x=30 x=5 Five stars at the beginning of creation Wolves 252 = (10 + 2x)5 - 5x 625 = 50 + 10x - 5x 575 = 5x 115 = x An Army of Caterpillars x-7-12+10+3=66 x=66+7+12-10-3 x=72

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Lions

3x 2 ! 72x + 7x * 3x = 2 2 * 3 3x 2 ! 72x + 21x 2 = 4 * 3 " 24x 2 ! 72x % 8$ ' = 8 *12 8 # & 24x 2 ! 72x = 96 24x 2 ! 72x ! 96 = 96 ! 96 24x 2 ! 72x ! 96 = 0 72 ± 72 2 ! 4 * 24 * !96 x= 2 * 24 72 ± 5184 + 9216 x= 48 72 ± 14400 x= 48 72 +120 x= 48 192 x= 48 x=4 Bees vs Fleas

So, 8 2 = (a + 3)2 8 2 = (a + 3)2 8=a+3 8!3= a 5=a

We already know that a=5 and c =w2

42 = c+4 7 6= c+4 6!4 =c 2=c

So,

So, abc = 30 (5)b(2) = 30 10b = 30 10b 30 = 10 10 b=3

Fairies Let m represent the number of male fairy princes m2+(20/2)-5=30 m2+10-5=30 m2+5-5=30-5 m2=25 m=5 Penguins x + 7 - 1 = 15 Nine penguins Pandas at the Zoo Solution 1 Let x= Total number of father pandas at the zoo 30+20+x+2(x+5)=360 30+20+x+2x+10=360 60+3x=360 3x=300 x=100 Solution 2 Let x= Total number of father pandas at the zoo 360-30-20-x-2(x+5)=0 360-30-20-x-2x-10=0 360-3x=60 -3x=-300 x=100 Children L = laying S = swaying G = greying L = 2s S=G-3 G = 15 2s + (G - 3) + 15 = x 2 (12) + (15-3) + 15 = x 24 + 12 + 15 = x 51 = x

Birds 4(3x) ÷ 2: I multiplied 3x by four, which equals (simplified) to 12x. Then, I divided 12x by 2, which equals 6x.

(6x) • !25: I multiplied the answer to 4(3x) ÷ 2 (which equals 6x) by the square root of 25. The square root of 25 is 5. 6x • 5 equals 30x.

(30x) + 21: After finding the answers to the equation so far (following the BEDMAS rule) I simplify is much as I can on the left side of the equation.

62 + 3: 62 equals 36. 36 + 3 equals 39.

42 + 3: 42 equals 16. 16 + 3 equals 19.

(39) • (19): I simplified what was in the brackets. Now I have to multiply the two answers together. 39 • 19 = 741.

Now I can simplify on the left side of the equation. 30x = 741 – 21 = 720. (30x = 720) X is equal to 720 divided by 30. 720 divided by 30 is 24 so x is equal to 24.

Flying High ! 48 + 5x $ 7# & = 91 " 6 % 336 + 35x = 91 6 91* 6 = 336 + 35x 546 = 336 + 35x 546 ' 336 = 35x 210 = 35x 210

=

35 6=x x=6

35x 35

How Many Boys?

Solution: x 2 x 1 2 x + x + x x 2 3 2 2 3 2 Multiply fractions together (BEDMAS) 36 = x +

x x x + + 2 3 6 Combine like terms 36 = x +

3x 2x x + + 6 6 6 6x 36 = x + 6 Cancel out the 6s 36 = x +

6x 6 36 = x + x 36 = 2x Isolate x by dividing both sides by 2 36 2x = 2 2 18 = x 36 = x +

SOLUTION TO MY POEM HALLE HAGAN (8A)  70 •1 / 2x   4x +1 / 2x  +       ² − 4 ( 3) = n 3 5  Equation: Working out: Let ‘n’ equal the number of eggs in the tree.

Solving for the first nest:

 70 •1 / 2x      = 35/5 = 7 5 So, there were 7 eggs in the first nest.

Solving for the second nest: Following what was stated in the poem, I know that ‘x’ is 5 less than the sum in the first nest. There were 7 eggs in the first nest, and 7 x 5 is 2, so ‘x’ is 2.

Then, we solve the section of the equation for nest 2.

1  ( 4 • 2) +  • 2  8 +1 9  4x +1 / 2x  2      , or 3 3 = 3 = 3 = 3.

Next, we must square the sum of nests 1 & 2.

The word “sum” means the value created when adding a set of numbers together, so in this case I have to find the sum of nests one and two.

So, 7+3 = 10.

Next, we have to square the sum. Squaring means to multiply the number by itself. So, the sum is 10, and 10 x 10 = 100.

Next, we have to “diminish,” or subtract by four. 100 - 4 = 96, so that is the new number.

The last step is to multiply by 3. 96 x 3 = 288.

Therefore, there were 288 eggs in the meadow.

Gimme My Gum Solution

My real crave, add one,

Times the square of their sum,

All over a dozen,

Now BE-A-MAN and take away five-sixths of the quotient,

Square this new number of mine,

And it magically gives you the cubed root of seven hundred and twenty-nine.

Start with:

Combine like terms:

Find the cube root:

Square root both sides:

Take away the second fraction:

Multiply both sides by 6:

Multiply both sides by 12:

Cube root both sides:

Take 1 from both sides:

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