Flower Geometry on Summer Vacation

Summer can be fun Learning Math on your camping trip or at home in your backyard.  An interesting approach to learning geometry in elementary math is by the study of flowers found in your backyard (or schoolyard in Spring or Fall).  Have your class walk around the local grounds, or give them an assignment to go home and document in their notebooks, different flowers, counting the number of petals in the flowers.

A second item, if time permits is to have the Learners identify the flowers as well.  Upon arrival back in the classroom, Learners identify, with their geometry charts, which geometric pattern or shape the flower has grown into.

Materials:

Eyes  (peepers for finding flowers)

Camera, if available

Notebook

Pencil and Good Eraser

Pencil Crayons in various colors

Ruler

Compass (if you wish to measure angles in the shapes)

Glue

String

Next, Learners draw in their notebooks the geometric shape the flower is equated with, and beside the shape, a simple drawing of the flower, coloring the flower drawing with the corresponding color of the petals.  If possible, 3-D forms can be cut out and interlocked together, with a string glued into the top of the start and made into Christmas ornaments.

Example:

Yellow Blue-eyed Grass:  (photo Above) 6-Petaled Yellow Wild Flower (that also grows in Bluish Purple and White); found in tall grasses who / that opens up only with the sun, and closes at the end of the day when the sun sets, or on cloudy days.

Geometric pattern:  6-pointed Star Tetrahedron; Two 3-Dimensional Interlocking Equilateral Triangles with a conjoining dot in the middle.  These 2 photos show the star tetrahedron (6-pointed) both in 2-dimensional form (as it would be if drawn flat on a piece of paper).  The second photo is a rendition of a 3-dimensional form (as if it were hanging as an ornament in a tree).   SourceURL:file:///Users/sheila/Desktop/Summer%20Flower%20Geometry.doc http://en.wikipedia.org/wiki/Star_tetrahedron

When looking, aim for the pattern that is found when counting the Number of Petals in the Flowers.  In the Yellow Blue-Eyed Grass, there are 6 petals which if gazed at in a 3-Dimensional way, one can see the pattern of the 6-pointed star tetrahedron.

This can be a fun activity to do while on summer vacation – or during the schoolyear in Spring and Fall, and depending what climate area your school is, it can be done during winter as well.

For more fun Learning activities on our site, feel free to visit here:

http://www.math-lessons.ca/Decimals/decimal.html

http://www.math-lessons.ca/review/math-review5.html

http://www.math-lessons.ca/worksheets/ttworksheets.html

http://www.math-lessons.ca/activities/FractionsBoard4.html

The Fibonacci Sequence

Fibonacci is a Number / Integer Sequence, that when applied in geometrical form, manifests in a Spiral as in that of a Pine Cone or a SeaShell.  The sequence was named after an Italian mathematician known as Leonardo of Pisa (or Leonardo de Fibonacci).  In 1202, he wrote a book called Liber Abaci in which he gives name to the number sequence.  There are historical examples of the sequence showing up in East Indian mathematics as well.

Add two consecutive numbers from the sequence to equal the next one following.  The basic sequence looks like this:

0,         1,            1,            2,            3,            5,            8,            13,            21,            34,            55,            89,            144,            233,            377, etc., etc.

That is:

0+1=1

1+1=2

2+1 (the “number” before)=3

3+2 (the number before)=5

5+3=8

8+5=13

13+8=21

34+21=55

55+34=89

89+34=144

144+233=377

etc., etc., etc.

In Spiritual Theory, Life must look back on itself before it can move forward.  In Relation to the human species, we must look back toward our Ancestors to learn Wisdom and give Gratitude to Life in the Present in order to move into the Future in the best way and in the Best Direction.  Because in theory the Spiral is not quantifiable in the concrete sense; i.e. it is a sequence that is Infinite (no final end number), mathematicians use straight lines around the spirals to give it as close to a concrete geometric equation as is possible.  Hence, the spiral looks like a spiral of expanding squares as shown here, and is known as the Golden Mean Ratio.  In biological settings, The Fibonacci Sequence can be seen in the Spirals of the Pinecone, in the Branch growth pattern of trees, the mini-fruit pieces of the Pineapple, the Artichoke flower, a Fern during its uncurling, and Seashells.  The sequence can also be seen in Rabbit breeding patterns, and the family tree of Honeybees.

In relation to Rabbits, Fibbonaci posed this question during the middle ages:

Rabbits can mate at the age of one month, a pretty fast breeding cycle for an animal. If a rabbit population was ideal (though not biologically realistic), if one assumed that a new pair of rabbits (one male and one female) were in a field, and after the end of one month, that pair had another pair, and every pair had another pair, how many pairs would there be after one year?

End of First Month:  1 New Pair

End of Second Month:  2 New Pairs

End of Third Month: The Original Female makes a Second Pair, Equaling 3 Pairs in the field

End of The Fourth Month:  First Female makes a Third Pair, The Female born in the Second Month makes Her First Pair, etc., Now Equaling 5 Pairs.

End of “n”th Month, Number of Pairs = The Number of New Pairs (= Number of Pairs in Month “n” – 2 + Number of Pairs alive in Previous Month “n” -1.

This is the “n”th Fibonacci Number, and it looks like this:

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#Rabbits

There are numerous other examples in nature shown in this site, as well as in class activities you can do to demonstrate the Fibonacci.

http://en.wikipedia.org/wiki/Fibonacci_number

And for more of our Fun Learning Math Games, you can visit here:

http://www.math-lessons.ca/activities/index.html

Easter Egg Hunt 100 and Under

Easter is the central feast and holiday in the Christian year representing Jesus’ Ascension.  It culminates the end of 40 days of fasting from the person’s choice.  Some people refrain from eating chocolate for 40 days until Easter weekend! Then they have an Easter Egg Hunt whereby one person hides chocolate eggs and the others have a fun treasure hunt to find the eggs.  For the Unity Spiritual Community, this year’s Easter’s theme is “Release Your Inner Splendor”. http://www.unity.org/publications/free-materials/lent-2012-release-your-inner-splendor

The following is a Fun Easter Egg Hunting Game for Practicing Addition, Subtraction, Multiplication and Division Under 100.  It can be played outdoors or indoors, depending on the weather and environment of the class.

Materials:

Organic Chocolate Eggs with foil covering

Marker

Pencil

Paper

Instructions:

Find a box of Organic Chocolate Easter Eggs.

Unwrap each egg but save the foil covering.

1. Make up a set of Math Problems to Solve, including addition, subtraction, multiplication and division.  At the end of this article, we have included a sample.

2. Wrap each Egg with a problem written on a small piece of paper, and then rewrap the eggs with the foil.  With a marker, number the eggs by groups.

3. Divide Learners into groups of 3, and Assign each group a number.  (In this example, there are 21 students. The class would be divided into 7 groups of 3, and there would be 7 groups of Math Problems).

4.Hide the eggs outdoors and/or indoors, weather permitting.

5. Each group has paper and pencil.  Each group hunts for eggs with their numbers and solves the math problems. As they find the eggs, each group respectively puts them in their basket. Each Learner Individually solves the problem, by first writing the problem on his/her paper and then following with the answer.

6. As each is finished, they bring their sheets to Teacher for checking. If they have any answers wrong, they must redo their answer. When all answers are correct, they can eat the chocolate, and help other groups.

Remember to recycle all the foil and paper wrappings!

http://kidsblogs.nationalgeographic.com/greenscene/2012/03/recycled-kisses.html

http://www.bayroberts.com/green/reduce.htm

Here are some more of our Fun Learning Math Games:

http://www.math-lessons.ca/activities/index.html

http://www.math-lessons.ca/review/math-review4.html

http://www.math-lessons.ca/timestables/times-tables.html

Sample Math Problems:

Group 1:

84 + 11 = 95

88 – 35 = 53

24 */* 3 = 8

8 x 6 = 48

14 */* 7 = 2

88 – 31 = 57

4  x 18 = 72

75 */* 3 = 25

25 – 5 = 20

Group 2:

88 + 12 = 100

25 x 3 = 75

18 */* 2 = 9

22  x  4 = 88

21 */* 3 = 7

55 –11 = 44

23 x 4 = 92

24 */* 12 = 2

45 + 33 = 78

Group 3:

88 – 3 = 85

13 x 4 = 52

100 */*25 = 4

44 x 2 = 88

13 – 1 = 12

44 */* 4 = 11

77 */* 11 = 7

3 x 9 = 27

52 – 23 = 29

Group 4:

44 – 11 = 33

23 x 4 = 92

14 */* 2 = 7

28 + 14 = 42

55 */* 11 = 5

88 – 13 = 75

34 – 17 = 17

22 x 4 = 88

14 + 17 = 31

Group 5:

14 + 5 = 19

33 – 12 = 21

22 x 5 = 77

89 – 17 = 72

34 +55 = 89

33 */* 3 = 11

22 x 4 = 88

100 */* 4 = 25

21 x 4 = 84

Group 6:

19 + 24 =43

47 – 17 =30

88 */* 11 = 8

24 x 3 = 72

90 */* 10 = 9

55 – 23 = 32

17 x 5 = 85

9 */* 3 = 3

100 – 25 = 75

Group 7:

18 */* 9 = 2

7 x 7 = 49

21 x 4 = 84

88 – 55 = 33

21 + 4 = 25

99 */* 3 = 33

22 x 1 = 22

35 – 8 = 27

77 – 22 = 55

Geometry Practice Questions

Geometry questions are very common on high school exit exams, some nursing entrance exams, and college entrance exams.  Topics vary, but most of the following are covered:

– identifying solid figures
– solving problems with solid and plane figures
– solving problems using Pythagorean principles
– solve problems using scale drawings
– calculating area, circumference, volume and perimeter
– solve problems using geometric transformations

Basic Algebra Practice Test Questions

Basic Algebra questions are common on most College Entrance exams, High School exams, Nursing Entrance Exams and High School Equivalence exams.

Fractions for Christmas, Hannukah and Solstice!

This Holiday season, you can have fun both learning about Holiday Celebrations and Learning Fractions in a Fun way!  Here are 3 different Holiday Celebrations that occur in December that have specific special numbers of Days to count for Fractions – Christmas, Hannukah and Winter Solstice.

8 Days of Hannukah

What Fraction is the 3rd Day of The 8 Days of Hannukah?

1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8

Hannukah (sometimes pronounced Chanukah) is known as The Festival of Lights, and this practice is celebrated by the Jewish Peoples of The Earth.

http://www.chabad.org/holidays/chanukah/article_cdo/aid/605036/jewish/Chanukah-FAQs.html.  It is a remembrance of The Miracle of The Holy Olive Oil lasting for 8 days (i.e.) There was only enough oil to last for one day, but through the Miracle of The Holy Spirit during Beit Hamikdesh, it lasted 8 days and 8 nights, for the entirety of The Celebration of Chanukah.  Hannukah is celebrated starting the 25th Day of Kislev (this corresponds to around the 21st-28th of December in the Gregorian calendar).

The typical Menorah consists of 8 branches with an additional raised or lowered branch in the middle to light the candles from, as there is a candle in each branch lit each night of the 8 days.  A fun thing that happens on Hannukah is The Spinning of The Dreidel, a four-sided spinning top that children play with. Each side of The Dreidel is imprinted with a Hebrew letter. http://en.wikipedia.org/wiki/Hanukkah#Dreidel.

Winter Solstice December 21st

What is The Fraction of The Solstices and Equinox Seasonal Cycles, based on The Gregorian and Celtic Calendar Year?

There are 4 quadrants that are the Seasonal Cycles of The Gravitational Cycles of The Earth, Sun and The Moon.  We call them:

Spring Equinox, Summer Solstice, Fall/Autumn Equinox and Winter Solstice.

All fall around the 21st – 23rd of the corresponding month (in general the 21st, depending on where the moon is, every year.

1/4, 2/4, 3/4, 4/4

1. Spring Equinox:  March 21st                        1/4
2. Summer Solstice:  June 21st                          2/4
3. Fall/Autumn Equinox: September 21st      3/4
4. and Winter Solstice: December 21st            4/4

Traditional Song: 12 Days of Christmas

What is the Fraction of the 5th Day of The 12 Days of Christmas?

Here is an example:  If you add together the 3rd Day of Christmas and the 5th Day if Christmas, what Christmas Fraction does this equal? (Answer:  3/12 +5/12 = 8/12)

1/12, 2/12, 3/12, 4/12, 5/12, 6/12, 7/12, 7/12, 8/12, 9/12, 10/12, 11/12, 12/12

Traditional Song:  The 12 Days of Christmas

On the 1st First Day of Christmas,

My true love sent to me

A partridge in a pear tree. (1/12)

On the 2nd Second Day of Christmas,

My true love sent to me

Two turtle doves, (2/12)

And a partridge in a pear tree. (1/12)

On the 3rd Third Day of Christmas,

My true love sent to me

Three French hens, (3/12)

Two turtle doves, (2/12)

And a partridge in a pear tree. (1/12)

On the 4th Fourth day of Christmas,

My true love sent to me

Four calling birds, (4/12)

Three French hens, (3/12)

Two turtle doves, (2/12)

And a partridge in a pear tree. (1/12)

On the 5th Fifth Day of Christmas, (5/12)

My true love sent to me

Five golden rings, (5/12)

Four calling birds, (4/12)

Three French hens, (3/12)

Two turtle doves, (2/12)

And a partridge in a pear tree. (1/12)

On the 6th Sixth Day of Christmas, (6/12)

My true love sent to me

Six geese a-laying, (6/12)

Five golden rings, (5/12)

Four calling birds, (4/12)

Three French hens, (3/12)

Two turtle doves, (2/12)

And a partridge in a pear tree. (1/12)

On the 7th Seventh Day of Christmas, (7/12)

My true love sent to me

Seven swans a-swimming, (7/12)

Six geese a-laying, (6/12)

Five golden rings, (5/12)

Four calling birds, (4/12)

Three French hens, (3/12)

Two turtle doves, (2/12)

And a partridge in a pear tree. (1/12)

On the 8th Eighth day of Christmas,

My true love sent to me

Eight maids a-milking, (8/12)

Seven swans a-swimming, (7/12)

Six geese a-laying, (6/12)

Five golden rings, (5/12)

Four calling birds, (4/12)

Three French hens, (3/12)

Two turtle doves, (2/12)

And a partridge in a pear tree. (1/12)

On the 9th Ninth day of Christmas,

My true love sent to me

Eight maids a-milking, (8/12)

Seven swans a-swimming, (7/12)

Six geese a-laying, (6/12)

Five golden rings, (5/12)

Four calling birds, (4/12)

Three French hens, (3/12)

Two turtle doves, (2/12)

And a partridge in a pear tree. (1/12)

On the 10th Tenth day of Christmas,

My true love sent to me

Ten lords a-leaping, (10/12)

Eight maids a-milking, (8/12)

Seven swans a-swimming, (7/12)

Six geese a-laying, (6/12)

Five golden rings, (5/12)

Four calling birds, (4/12)

Three French hens, (3/12)

Two turtle doves, (2/12)

And a partridge in a pear tree. (1/12)

On the 11th Eleventh day of Christmas,

My true love sent to me

Eleven pipers piping, (11/12)

Ten lords a-leaping, (10/12)

Eight maids a-milking, (8/12)

Seven swans a-swimming, (7/12)

Six geese a-laying, (6/12)

Five golden rings, (5/12)

Four calling birds, (4/12)

Three French hens, (3/12)

Two turtle doves, (2/12)

And a partridge in a pear tree. (1/12)

On the 12th Twelfth Day of Christmas,

My true love sent to me

Twelve drummers drumming, 12/12

Eleven pipers piping, (11/12)

Ten lords a-leaping, (10/12)

Eight maids a-milking, (8/12)

Seven swans a-swimming, (7/12)

Six geese a-laying, (6/12)

Five golden rings, (5/12)

Four calling birds, (4/12)

Three French hens, (3/12)

Two turtle doves, (2/12)

And a partridge in a pear tree! (1/12)

And for some other of our Fun Learning Math Games, you can visit here:

Secret Chocolate Fraction Codes

It is Post-Halloween and we are not quite finished making chocolate FUN just yet!  Here is a fun and easy fractions game to organize that is low-cost and easily teachable, any time of the year.

Supplies:

• Crayola Markers, 3 for each student
• One Organic Chocolate Bar for each student
• Piece of Paper

Have everyone bring in a Whole Chocolate Bar (organic if possible – it is healthier!)  –  One that has an equal number of squares in it.  They do not all have to be the same number of squares, but if they are, it is a bit easier for instructions.

Using a non-toxic marker (Crayola is my favorite), have each Learner draw a gridline across the paper on the outside of the bar in their favorite color. http://www.crayola.com/products/list.cfm?categories=MARKERS,BASICS

Step 1:  Counting 1-12 (usually,  this is the number of squares in a bar.)  If it is different, then  ask the learner to count, respectively re their bar, and write down on paper the basic 12 fractions of their bar:

1/12, 2/12, 3/12, 4/12, 5/12, 6/12, 7/12, 8/12, 9/12, 10/12, 11/12, 12/12

Step 2: Then secretly and individually, each student colors a different amount of squares in each bar, using 3 different colored markers.  Encourage Sharing/Trading markers if there is not enough markers to go around.

Step 3: Then, everyone divides into pairs, and one at a time – without  showing each other what they have colored – each student  guesses what 3 numbered fractions the other one has colored.

Eg/  Susan colored 3 squares in Red, 2 squares in Yellow, and 7 squares in Purple.  Therefore, Susan’s Secret Fraction Codes are:

3/12, 2/12 and 7/12.

Bob colored 3 squares in Blue, 6 squares in Green, and 3 Squares in Orange. Therefore, Bob’s Secret Fraction Codes are:

3/12, 6/12 and 3/12.

Step 4:  After successfully guessing the other’s Secret Fractions, each one guesses the 3 respective Colors – of each Fraction Code.

Step 5: Once they have successfully guessed the other one’s Secret Fraction Codes, have them, TOGETHER then, add all 3 to make the Whole Number One 1.

Eg/ Susan’s Secret Fraction Codes look like this:

3/12 + 2/12 + 7/12 = 12/12 = 1

Bob’s Secret Fraction Codes look like this:

3/12 + 6/12 + 3/12 = 12/12 = 1

Last Step:  Everyone share their Chocolate Bars with The Teacher! lolololololol

Enjoy!  Yum.

Love The Earth!

Remember to Recycle both the paper and the tinfoil or plastic that the bar was wrapped in!  The more Recycling and Care for The Earth, the more Pretty Colored Feathers (or Stars)you receive from The Teacher!

http://iloveloveearth.weebly.com/enter-the-i-love-earth-competition.html

For another one of our fun and affordable Fraction Games, you can visit here: http://www.math-lessons.ca/activities/chocolate.html

Donate a Math Abacus to The Lakota

This month, Math-Lessons.ca are donating a Math Abacus to the Lakota Pineridge Reservation located in South Dakota.  It is home to the Oglala Sioux Tribe, a population of about 40,000.  We like how they have organized their donation drives.  In additional for requesting financial donations, they also have item requests that revolve each week and month.  Last month, the early grade school math classes asked for donations of math abacuses (see picture below if you are not familiar with what an abacus is).

If anyone would like to buy / donate them to the education program there, here is one site they can be purchased on:

http://www.enasco.com/math/Math+Manipulatives/Abacuses/

We found ours in Chinatown in downtown Victoria.  If anyone would like to buy and donate an abacus with us, please let us know, and we can save together on shipping costs.  This photo is Jane Yuan, from China and Victoria ….. and Sheila Hynes (one of our coordinators from math-lessons.ca).  Jane Yuan is a local artist here in Victoria, and is having fun showing us how to use the abacus.

Congratulations Spirit of Math Students!

Congratulations Spirit of Math Students!  Over 2000 kids took part in the 13th Annual Spirit of Math Contest.

There were 742 Placements from Grades 1-4 across Canada, who made the National Mathematics Honour Rolls.  And several others from all grades from other countries, with more details to come, as results roll in.

Categories included Thales; Byron-Germain; Fibonacci; Pythagoras; Math Kangaroo Tournament of Towns; Canadian National Math League; New Jersey National Math League Honour Roll; American Mathematics Competition Honour Roll; Brock University Caribou Math Competition; Centre for Education in Math and Computing Honour Roll (University of Waterloo);

List of Learners’ names to come soon!

http://www.spiritofmath.com

http://www.spiritofmath.com/2011contest/

If you want your class to enjoy one of our Fun Learning Games, downloadable hands-on learning tools, here are a few really great ones:

Race; Fractions Board Game:  http://www.math-lessons.ca/activities/FractionsBoard5.html

Teaching Fractions with Yummy Pizza Pie

The rate of success for learning fractions in elementary class math depend on the teaching method used.  Some of these methods are outlined here – simple to teach, and simple to apply.  Having real life examples for students to connect with makes it easier for the brain to get into the right lane. Learners then have a good foundation in fractions to better understand how to add, subtract, multiply, and divide.

Most kids LOVE pizza, so make it fun and bring REAL pizza into the classroom, several if parents are okay with chipping in on the cost or if the principal authorizes this as a project.  Or, do what we did, and bring in the ingredients, borrow the home economics room, and cook them right there in the classroom. If neither of these possibilities is viable, then divide the kids into groups of different numbers and ask them to draw a simple picture of a pizza on a piece of paper, with the number of slices drawn equal to the number of kids in their group.