There are three steps outlined below. Each step should be introduced separately, practiced and then combined with the steps learned previously.

Step 1 – Use benchmarks – Using benchmarks of 0, 1 and greater than 1 (improper fractions) help students get a general idea of the size of the fraction.

Example – Put the following fractions in order from least to greatest:

Encourage students to find those fractions that are equivalent to 0, 1 and greater than 1 first. Then identify if any of the fractions are exactly  Compare the numerator and denominators on the remaining fractions to determine if they are less than  or more than  Try to relate the fraction to real life examples. (“If I received 11 out of 12 on a test, did I get more than half the questions correct or fewer than half the questions correct?”)

Provide a simple table for those students who have trouble organizing their work.

Step 2 – Use Common Denominators – Many students think ordering fractions with common denominators is even easier than using benchmarks. Since each fraction will have the same number of parts to make the total, comparing is easy. Again, present fractions in real life situations that allow students to visualize them. For example, if you took a math quiz worth 25 points, who would get more of the quiz correct: the student who gets 24 questions correct (  ) or the student who gets 13 questions correct (  )?

Step 3 – Use Common Numerators – This strategy is a bit more difficult for students to grasp. The use of fraction towers, fraction circles and/or drawings helps students grasp this concept.

When the numerators are the same, you are receiving the same number of pieces of the object. However, since the denominators are different, the whole will be cut into a different amount of pieces. For example, imagine you are eating a candy bar. You receive one piece (the numerator), no matter what. If you are all by yourself, you get the whole candy bar. Now imagine one of your friends comes by. You want to share the candy bar; so you split it into 2 pieces (in half). What happens to the size of your one piece as you share with more and more friends?

For a pie version of this, Birmingham Learning Resources shows us:  http://www.bgfl.org/custom/resources_ftp/client_ftp/ks2/maths/fractions/numerators.htm

And: http://www.freemathhelp.com/numerator-denominator.html

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

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

Materials: Attribute blocks(these are our ingredients) and a hula hoop (this is our pot in which to cook).

How to Play the Game:

1)    Have your students sit around the outside of the hula hoop so that they can all see and reach it. The teacher begins the game by creating a rule for the “soup” (e.g. square soup). Without telling the students the rule, the teacher places one attribute block into the center of the hula hoop, saying “This piece belongs in my soup today.”

2)    The first student in the circle chooses any other piece, places in in the “pot” and asks, “Does this belong in your soup today?” If the piece matches the rule, the teacher says, “Yes it does,” and the student gets another turn. If it does not, the student removes that piece from the center, and her turn is over.

3)    Students continue to take turns going around the circle. A student may guess the rule only during her turn. (e.g. “I think you are making blue soup.”) If the student is wrong, her turn is over. If she is correct, she wins the game.

4)    You can continue to play the game by creating a new rule or allowing the winning student to create a new rule for her classmates to figure out.

Notes:

1)    Attribute blocks are excellent tools for this game because they contain four different attributes (color, shape, size and thickness). When I play with very young students, I choose only one attribute (e.g. red soup or triangle soup). However, when I play with older students, I use several attributes (e.g. thick yellow soup or small red triangle soup).

2)    When allowing students to create the rule and start the game, it is a good idea to have them whisper their “soup recipe” in your ear. They tend to forget their rule and provide false information at times!

3)    I find that continuing around the circle after a game is won keeps students from arguing about whose turn it is and gives everyone a chance to play. For example, if the sixth child in the circle correctly guessed the soup recipe, the next game starts with the seventh child in the circle.

For more fun and interesting Learning Math Games, you can visit us here:
http://www.math-lessons.ca/activities/FractionsBoard5.html
http://www.math-lessons.ca/timestables/times-tables.html
http://www.math-lessons.ca/activities/FractionsBoard4.html
http://www.math-lessons.ca/index.html

Start the project by having students take digital pictures of solid figures in their everyday lives. They can either do this at home or (if they do not have a digital camera) at school. The following chart lists the common solids primary students learn about and some everyday items children would be familiar with. Hopefully, your students will find numerous examples of each.

Once students have taken their pictures, visit the computer lab so students can create their “Book of Geometric Solids.” Students can organize their books in a variety of ways. However, each picture should have one to three sentences to serve as a caption. Captions must identify the type of solid the object is and must tell something about that object. For example, the student inserts a picture of a soccer ball. He then writes, “A soccer ball is an example of a sphere. I play soccer every Saturday morning. It is my favorite sport.”

This activity not only allows students to discover math in their everyday lives, but it also helps develop multiple academic skills.

For more fun and interesting Learning Math Games, you can visit us here:
http://www.math-lessons.ca/activities/FractionsBoard5.html
http://www.math-lessons.ca/timestables/times-tables.html
http://www.math-lessons.ca/activities/FractionsBoard4.html
http://www.math-lessons.ca/index.html

Base-Ten Blocks – Yes, everyone uses base-ten blocks (units [1], longs [10] and flats [100]) with primary students to help them learn place value, counting and operations.

However, base-ten blocks are the perfect tool to teach decimal places as well. Simply reversing the value of each piece (flats [1]; rods [ ]; units [ ]) allows students to explore smaller numbers in a hands-on fashion.

Fraction Towers– Fraction towers are possibly the best manipulative for middle school students. Fractions are often the most challenged of all middle school math concepts, usually because students do not understand fractions. They are taught to memorize rules, which make no sense to them. Towers allow students to easily compare fractions and complete various operations. Working with fractions in a concrete, visual and hands-on way makes fractions less intimidating for students.

Color Chips – Color chips are most often used for statistics and data analysis topics. They are wonderful tools for those topics. However, another great way to use them is with integers. The red side is negative, while the yellow side is positive. You can even take a permanent marker and draw + and – signs on the chips. Students can model adding, subtracting, multiplying and dividing using the chips.

You don’t always need to have the physical materials. Visit the National Library of Virtual Manipulatives at: http://nlvm.usu.edu/en/nav/vlibrary.html to see online versions of these and many other math manipulatives.

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

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

http://www.math-lessons.ca/activities/FractionsBoard5.html

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

Materials Needed:

Colored Markers or Crayons

Glue or Scotch Tape

Scissors

Colored Yarn or String

Sparkles

Colorful Recycled Paper (tissue boxes, flyers, old wrapping, etc.)

Directions for Christmas Star Cutout:

1.Cut out the outline.

2.Cut along all heavy lines.

3.Score plain lines on the front.

4.Score dotted lines on the back.

5.Fold triangles upword along plain lines.

6.Fold triangles downword along dotted lines.

7.Glue or tape tabs to form small tetrahedrons.

8.Continue until you have your Geometry Christmas Star Tetrahedron.

Everyone has their own Star!  Everyone has their own Inner Light!  With Favorite colors, draw your stars, or print this page and cut the pattern of the star out.

Inside each shape on the side of the star, write your name and birthday.  Or – write the names of each member of your family (If you Wish, your family / family Tree Star can be made of relatives (close or extended), friends and/or adopted family – as long as you write each name on each.  You could make many stars – a pretty star for each member of your Christmas Tree, or write everyone’s name on the same Star.

Color and Decorate each one with colored markers, crayons, sparkles, gluing pieces of recycled Christmas paper from last year.  You can also write happy words all over your star like Love, Divine Wisdom, Infinity, Pure Spirit, Fun and Harmony!

Remember to Decorate your Stars!

Glue Yarn / Strong at the top  into a 2 inch loop and tie a knot at the end

Hang your Christmas Geometry Math Stars and Decorate your Tree at Home or in your Classroom!

Have a Merry Christmas and Happy Holiday!

For more of our Fun Learning Math Games:

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

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

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

Reference for Star Tetrahedron Geometry Template: “The Ancient Secret of the Flower of Life,” Vol. 2, by Drunvalo Melchizedek

The Pythagorean Theorem is named after the Greek mathematician Pythagoras. Many believe the first discovery and proving of this ancient math theorem came before Pythagoras, but since no tangible account of this has yet been documented, it is named as such. If that was true, however, we wonder what another name of the theorem would have been, and from what country and nation? (a fun question to ponder).  The Pythagorean Theorem can be used with any shape and for any formula that squares a number. And, in fact, the area of any shape can be computed from any line segment squared.  http://en.wikipedia.org/wiki/Pythagorean_theorem  (reference also for Diagram Above).   Apparently, even the teenage Brainiac Lisa Simpson from The Simpsons television series knows all about Pythagoras.  On this site, there are some cool diagrams showing the differences of Lines (Segments / Legs), Radius, and Area: http://betterexplained.com/articles/surprising-uses-of-the-pythagorean-theorem/.  And, to assist in figuring out these math scenarios, this site offers tabs for entering in numbers to calculate the square root of the numbers in question: http://www.math.com/students/calculators/source/square-root.html.

Finally, here are a few Real Life Examples:

Meet Me at The Corner:
Let’s say Stephanie and Maria are meeting at the Hiking Trail Entrance on the corner of Saanich Rd. and Cedar Rd. One phones the other on her mobile phone and asks, “How long will it be before you arrive at the entrance?”… “Well, let’s estimate by first finding out how far away we are from each other.” In present time, Stephanie is on Saanich Rd. to and is 10 miles away. Meanwhile, Maria is on Cedar Rd. and is 4 miles away.  How far away from one another are Stephanie and Maria?  The distance between them = a^2 + b^2 = c^2 or, respectively: 10^2 (10 squared) + 4^2 (4 squared); or respectively, 100 +16 = 116 miles. The square root of 116 is 10.77. Thus, Stephanie and Maria are 10.77, almost 11 miles away from one another. Hence, they figure they will be another hour on their bicycles to meet one another to go hiking.

Firefighters Needing to Know Height of a Building:
3 Firefighters receive a call to help Ann rescue her cat Tia from the Oak Tree outside her window. The tree is about 3 stories tall, and the Tia, after chasing a squirrel, is stuck on a branch at about the height of 2 stories of her house. The height to the branch may be 20 feet, and the firefighters have to put the ladder about 10 feet away from the Oak Tree in order to go around Ann‘s shed. How long of a ladder do the firefighters need in order to rescue Ann‘s cat? a^2 + b^2 = c^2 or, respectively: (20)^2 + (10)^2 = 2^2, the length of ladder required. 400 + 100 = 500. The square root of 500 is approximately 22.37. The firefighters extend their expandable ladder to be approximately 23 feet, whereas they need at least 22.37 feet to safely reach the Oak branch. Ann’s cat Tia is rescued and All are Happy!

For more fun and interesting Learning Math Games, you can visit us here:
http://www.math-lessons.ca/activities/FractionsBoard5.html
http://www.math-lessons.ca/timestables/times-tables.html
http://www.math-lessons.ca/activities/FractionsBoard4.html
http://www.math-lessons.ca/index.html

Then, as the year progresses, if a student is having a challenge learning a particular new math lesson, Teachers can refer to the student’s personal file of “Favorites Activities List”.  At this time, then, introducing the association and how that interest relates to the new lesson.

Example No. 1:  Young Matthew enjoys playing or watching the game of baseball. That is included in their list of favorite activities.  November rolls around, and the lesson of drawing shapes in geometry arises, but Matthew is not grasping the concepts.  If looking down onto a Baseball Diamond from an aerial perspective, the shape of Square is easily seen in the formation of the 4 bases on the ball field.  As well, the shape of the bases individually, is a square.

Then show in sequence what happens when the player runs to first base, second, third and fourth, demonstrating the making of a Straight Line 4 times, and in consecutive order. Within each corner, while the player stands on the base, the player looks down at both straight lines that connect, and the player can then see a perfect Right Angle of 90 degrees.  Drawing a line across from the base to the left to the base t the right demonstrates a perfect Right Triangle.

Suddenly a light is switched on in the child’s brain, and Matthew is on the way to understanding the concept of geometry.  Not only do they understand it on paper in 2-D form, but now in 3-D form, in the context of a baseball game, in a real life scenario.

Example No. 2:  Ashley likes archery.  Archery is included in her favorite activities list.  While imaging and practicing her archery skills, she sees concentric circles – one inside the other.  When a line is drawn from her bow to the target, she demonstrates a perfect straight line.  Hence, she has a different yet equally effective association of a favorite interest to relate to the concepts in geometry -  as Mathew’s love of baseball.  Imagine now that Susie, not only is attaining the required skills the in geometry lesson, but is also having fun while doing it, and has developed self-motivation and interest in learning math.

In these examples, both sides of the Brain are exercised, (Left Right Brain Learning and Thinking) new neural connectors and dendrites grow, and you have encouraged the growth of a healthy developing young brain.

http://www.funderstanding.com/brain/right-brain-vs-left-brain/.

http://www.oecd.org/edu/ceri/neuromyth6.htm.

Start the school year off right, and find out what your students’ favorite activities are. Keep the lists on file, and refer to them from time to time during the school year.  You may be surprised at the effectiveness of this subtle teaching tool.

For one of Our Fun Learning Math Games, feel free to visit here:

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

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

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

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

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

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

Small Easter Baskets

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