# Category: Fraction Fun

## Folding Fractions

Supplies Needed:
20 sheets of Blank Paper size: 8 1/2×11
(for approximately 20 students)
Instructions:
1. Break class into 5 groups of 4. Each group has 4 sheets of blank paper.
2. Showing instruction, fold the bottom of the sheet up and to the left creating a right triangle. 3. Cut / tear the top of the folded left over top, removing the top, leaving a perfect square with a fold in it (looking like 2 triangles).
3. Write on each triangle 1/2 and 2/2, denoting the two fractions.
4. With the second sheet of paper, repeat instructions No. 2. This time folding the triangle in the opposite direction. Now there ought to be 4 folds / 4 triangles. Write on each triangle 1/4, 2/4, 3/4, 4/4, denoting the 4 fractions.
5. With the third sheet of paper, repeat instruction No. 2 again. This time folding the paper 3 times. This time there ought to be 8 folds / 8 triangles. Write on each triangle 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8, denoting the 8 fractions.
6. With the fourth sheet of paper, repeat Instruction number 2 again. This time folding the set of triangle 4 times. This time there ought to be 19 folds / 16 triangles. Write on each triangle 1/16, 2/16, 3/16, 4/16, 5/16, 6/16, …etc….up to 16/16, denoting the 16 fractions.
7. Explain that when added each group together, the total equals to the whole number 1.

Question – What is the Lowest Common Denominator?

Check out some of our other Math Games:

http://www.math-lessons.ca/fraction-games-activities/.

3/4 Shortening
1 cup brown sugar
1/4 Molasses
1 egg
Cream shortening, sugar and molasses until fluffy

2 1/4 cups all-purpose sifted flour
2 tsps baking soda
1/2 tsp salt
1 tsp ground ginger
1 tsp ground cinnamon
1/2 tsp ground cloves
Still together flour, soda, salt and spices together, and then stir into molasses mixture.

Flatten out the mixture. Cut out the gingerbread men.
Bake at 375 for 12 minutes.

Cut out 3 – 8 1/2 x 11 paper into 6 parts
Write on each piece fractions that add up to a whole number.
1/4, 2/4, 3/4, 4/4, 1/6, 2/6, 3/6, 4/6, 5/6, 6/6, 1/8, 2/8,3/8, 4/8, 5/8, 6/8, 7/8, 8/8
That is enough for 18 students
Shuffle the fractions and hand them out face down to each student.
Instruct the students to find the other matching pair to their fraction that will add up to a whole number fraction.

Once the student finds the matching pair that adds to a whole number, they win their Christmas Cookie!

For our Math Learning Games, you can visit: www.math-lessons.ca; or
www.butterflybooks.ca

## Fractions in The Kitchen

Choose a recipe from home; notice the fractions used in the recipe.  Formulate fraction questions; and calculate the questions.  Then go ahead and have an baking extravaganza in your school’s kitchen, or at home.  Here is a sample:

Potato Tea Buns

This classroom kitchen recipe was a combination of Tea Buns from the Telephone Pioneers oF AmerIca, Ch. 49; Nova ScoTIa; WhaT Am I Gonna Cook? RecIpe of PaT Brooks; HunT’s PoInT, NS; with some of our personal add-ons such as Brown sugar

1 Pckg Dry YeasT

1/4 cup waTer Mixed wITh 1 Tsp Sugar sIc. We prefer Brown; HealThIer)

1/2 Cup Mashed PoTaToes

1/4 Cup BuTTer (sIc. PaT says ShorTenIng or MargarIne; We prefer Real BuTTer)

1/4 cup Sugar (sIc. We prefer Brown; or a bIT of Molasses, Though The rolls would be a dIfferenT Color.

1 & 1/2 Tsp SaLT

1 Cup Milk (sIc. Almond Milk)

1 Egg (We prefer a dollap of Flax Gel, made by parboIlIng 1 Tbls Flax Seeds In 1 Cup of waTer for 10-12 mInuTes)

4 Cups WhITe Flour

CombIne WaTer and 1 Tsp Sugar and YeasT

LeT sTand For 10 mInuTes

In a saucepan, combIne Milk, PoZTaToes, BuTTer, SaLT and Sugar;

heaT unTIl BuTTer has MelTed

Add yeasT mIxTure To Flax Gel In a Large BowL

STIr In boTh Cups of WaTer and BeaT well

Place In a Warm spoT for 1 Hour unTIl double

Cover wITh Damp CloTh; Leave For 1 Hr To RIse

Bake aT 400 degrees For 10-12 MInuTes

Lovely wITh a bIT of buTTer and chowder

The MaTh

Altogether, How many cups of Ingredients are does this recipe make?

Cups:

1/4 cup waTer                                 1/4

1/2 Cup Mashed PoTaToes            1/2

1/4 Cup BuTTer (sIc. PaT               1/4

1/4 cup Brown Sugar                      1/4

1 Cup Milk (sIc. Almond Milk)          1

4 Cups WhITe Flour                         4

Plus

1 & 1/2 Tsp SaLT

Answer:  6 and 1/4 cups of Ingredients; and 1 and 1/2 Tsp

Question:  How many Teaspoons of Ingredients are in a cup?  If we really want  to add the small still, we would have to calculate that from a chart, or physically fill up a cup of salt, one tsp at a time.

Have a quick gander at some our Learning Math Games:

Teaching Fractions with Chocolate

## Developing Number Theory and Fraction Concepts

Many students can begin to feel challenged in math in middle school. Students who have been good at, and have even enjoyed, math suddenly look to their teachers, friends or parents for assistance. Why does this happen? If you look at the concepts that are significant in middle school grades (fractions, decimals and integers), you find that these concepts appear to break all the rules their teachers have told them up to this point.

Typically, students are taught that when you multiply two numbers, the product is always larger. When you divide two numbers, the quotient is always smaller. However, these rules apply to whole numbers, not fractions. When you multiply two fractions, the resulting product may be smaller! When you divide two fractions, the quotient may be larger!  Many students become frustrated, confused and give up on math. As teachers, we need to make sure our students understand concepts, not just memorize rules about them. Students need time to explore and discuss real life examples of the concepts we are teaching. Below are some high-level tasks that allow students to explore number theory and fraction concepts. As with all tasks, students should represent their work in numbers, pictures and/or words. They should have time to communicate their thoughts and findings with others.

Topic: Factors and Multiples

Task: Max is making table favors for a party. The candles come in boxes of 15 and the candleholders come in boxes of 9. Max does not want any leftover candles or holders. What is the fewest number of candles and candleholders he needs without any leftover? How many boxes of each should he buy? Task: At a day camp, there are 12 girls and 18 boys. The camp counselors would like to split the campers into teams. However, they must follow these rules: 1) All campers must be on a team; nobody can be left out, 2) all teams must have the same number of campers, and 3) each team can only have all boys or all girls; no boys and girls can be on the same team. What is the greatest number of camperseach team could have?

Topic: Understanding Fractions

Task: In Penny’s Pet Shop,  of the pets were dogs,  of the pets were cats,  of the pets were birds and the rest were gerbils. There were 48 pets in all. How many of each type of pet were there? Task: Ms. Kinny has  tank of gas in her Volkswagen Beetle. Miss Jamison has  tank of gas in her Ford Mustang. Dr. Beck has  tank of gas in her Honda Accord. Mrs. Hughey has  tank of gas in her Toyota Prius. Without finding common denominators, list the women in order from the person who has the least amount of gas in her car to the person who has the greatest amount of gas in her car.

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/Geometry.html

## Ordering and Comparing Fractions

When students are asked to order and compare fractions, they almost always start by finding common denominators. This strategy is based on rote memorization and leads to little or no true understanding of fractions (and can be utterly frustrating!). Students cannot visualize the fractions. This article explains how to help your students compare and order fractions using reasoning skills, not math formulas.

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

## 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