## 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
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## Measuring Noah’s Rainbow Arc

Have your class make a homemade Noah’s arc.  You will need creative materials:

a ruler

a tetra pack or other recycled container that floats

sticky pine pitch or an eco-friendly sealant

other thoughtful decorative creative materials

In the bible, Noah is instructed to make an arc large enough and strong enough to fit a lot of animals and to last in the flood that is to come.  The name Noah is noted as “comforter”:  Make thee an ark of gopher wood; rooms shalt thou make in the ark, and shalt pitch it within and without with pitch.  (Blue Letter Bible; Genesis 6:14)…And this is the fashion which thou shalt make it of: The length of the ark shall be three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits.  (Blue Letter Bible Genesis 6:15.  A window shalt thou make to the ark, and in a cubit shalt thou finish it above; and the door of the ark shalt thou set in the side thereof; with lower, second, and third stories shalt thou make it.  (Genesis 6:16) (This passage could either be 4 stories in Height in its description, or 3, depending how it is interpreted – is the lower basement floor considered to be counted as a floor.  The passage in Genesis (Genesis 6:15) says that God instructed Noah to build the Arc in these dimensions using Cubits.  The cubit is an ancient unit based on the forearm length from the tip of the middle finger to the bottom of the elbow.  The estimate varies depending on which version of a biblical text one reads.  Approximately 17.5-20.6 inches (https://answersingenesis.org/noahs-ark/how-long-was-the-original-cubit/)  What in Today’s world can be compared with The Length of Noah’s Arc about 450 Feet Long?  a Baseball Field; a 7 story Building.  There would be 3-4 stories of height (including the lower) and a giraffe would have to fit (approximately and up to 15-18 feet)!  How tall is a giraffe?

300 Cubits = 450’ L

50 Cubits = 75 ‘ W

30 Cubits = 45 ‘ H

where L = Length

W = Width

H = Height

Metric Conversion (where 1 inch – 2.5 cm):

L   300mm = 30cm

W 50 mm = 5cm

H 30 mm = 3 cm

Have your class find homemade materials from the recycle bucket or pieces of materials that your folks have no need for, and make a miniature version of the arc as it is described.  Fashion a window 18 inches from the roof, and make a door.

Rainbow Covenant (Genesis 9:11-16… And I will establish my covenant with you; neither shall all flesh be cut off any more by the waters of a flood; neither shall there any more be a flood to destroy the earth….And God said, This is the token of the covenant which I make between me and you and every living creature that is with you, for perpetual generations:…And I shall set my bow in the cloud, and it shall be for a token of a covenant between me and the earth….

9:11-17

(Photo Here)

Our homemade prototype turned out to be 12 inches x 1 inch x 1.5inches, with a window just under the top, and it floats!  Have fun decorating your Arc as you would be living it for 150 days before the waters receded.  Pine Tar is a term for what is called “Pitch”.   It can act as a sealer for the bottom of your arc, but be careful as it is sticky stuff!  Have fun!

For more fun activities, please feel free to visit:

HexaRace

## 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

# Roll to Win Investigation – Graphing Classroom Activity

Graphing is an excellent way to display data visually. Students will come in contact with a variety of data and ways to display this data over time. It is important that students understand that there are three main types of graphs used to display information. The three types of graphs are line graphs, pie charts, and bar graphs.

## Finding Area – Classroom Exercises

Area is All Around Us!  Simple Geometry Classroom Activities

One challenge that students often face is realizing that math DOES actually relate to the real world and that they will actually use the information they are learning at some point in their life. Area happens to be one of those topics that students struggle to understand the reasoning behind.  Before introducing the topic of area, you may want to ask your students some engaging questions such as: “If you wanted to put new tile down on the floor, how would you know how much to buy?” or “If you wanted to put wallpaper on the walls of the classroom, how much wallpaper would you buy?”. These questions will be sure to get them thinking about how to calculate these answers.

## Multiplication Can Be Simple! – with a handout game!

Multiplication is an operation that requires you to add another number to itself a certain number of times as indicated in the multiplication equation.

When students first start learning the concept of multiplication, it is more simple as time goes on for kids to learn. Memorizing multiplication facts works for some students but not for all! Some students need to learn by using different models and representations. When students have a conceptual understanding of multiplication and realize that it is connected to the real world, they tend to perform better on assessments. If a child is only ever taught isolated facts or memorized facts, they risk the chance of not understanding the meaning behind the objects they are multiplying. Knowing a variety of ways to solve multiplication problems will allow a student to figure out which strategy works best for them.

## Identifying Polygons

Polygons can be defined as two-dimensional, closed figures that are described by the number of sides, length of sides, and the kinds of angles. Many polygons have a respective name depending on their description. Some common polygons you will work with include: triangles, squares, rectangles, trapezoids, quadrilaterals, rhombus, pentagons, hexagons, parallelogram, and octagons.

When learning the names of polygons, students can easily be confused by terms that are used interchangeably at times. For example, a quadrilateral is considered to be a four-sided figure. So one might easily confuse this by calling all quadrilaterals squares or rectangles. However, by definition a rectangle is a special quadrilateral because it has opposite sides that are congruent or the same length and each angle is a right angle that measures 90 degrees. Another special quadrilateral is a square. A square has four sides that are all congruent or the same length as well as four angles that are all right angles measuring 90 degrees. This becomes easily confusing for a student when they are trying to identify polygons by name and descriptors.

Ever launched a Rocket and wanted to determine how High it goes? Polynomials can come in handy when trying to model the flight path of a Rocket.  Did You Know that  when shooting a rocket straight up in the air, the rocket’s path can be modeled using the polynomial equation: y = -16t2 + vt + ho? Yes, it is True. Using this Equation you can easily Determine when the Rocket will hit the ground and even how far the Rocket will shoot into the sky. The Height the Rocket will reach is dependent on the initial velocity of the rocket and the initial height.  (Rocket Photo:  http://upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Apollo_15_launch.jpg/640px-Apollo_15_launch.jpg)

Notice that the Rocket Equation does not involve the weight of the Rocket. As a Rocket is launched the initial Velocity allows it to overcome Gravity. However, eventually, that initial force from the launch dissipates and Gravity takes hold. A Rocket reaches its Maximum Height shortly before Gravity forces it back toward the ground.

Learn More!  Let’s try an example, using the Polynomial Equation: d = -16t2 + vt + ho. If a Rocket is launched with an initial Velocity of 50 meters per second off of the ground, how high will the Rocket be after 3 seconds?  Solution:  So, the Rocket will be 6 Meters off the ground. The Rocket is likely on its way back down toward the ground.

To Peruse another One of our Great Learning Math Articles, you can visit Here:

http://www.math-lessons.ca/patterning-algebra.html/

## Math and The Chromatic Scale: Loving Music, Loving Math

Harmony
occurs in music when two pitches vibrate at frequencies in small integer ratios.  Long ago, Greek people realized the concept of harmony occurred when sounds and frequencies are in rational proportion. i.e., One Octave is equal to when the frequency is doubled, and a tripling of frequency brings the key One Octave higher, and is called a perfect fifth. Though not knowing this in relation to “frequency”, ancient Greeks knew this in relation to lengths of vibrating strings; http://www.math.uwaterloo.ca/~mrubinst/tuning/12.html  (Why 12 Notes to The Octave?)

1/1  unison              C

2/1  octave              C

3/2  perfect fifth       G

4/3  fourth              F

5/4  major third         E

8/5  minor 6th           Ab

6/5  minor 3rd           Eb

5/3  major 6th           A

9/8  major 2nd           D

16/9 minor 7th           Bb

15/8  major 7th          B

16/15 minor 2nd          C#

The most common conception of the chromatic scale before the 13th century was the Pythagorean chromatic scale. Due to a different tuning technique, the twelve semitones in this scale have two slightly different sizes. (En. Wikipedia. org/wiki/Chromatic_scale)  Thus, the scale is not perfectly symmetric.  http://strathmaths.wordpress.com/2012/02/22/tipping-the-scales-some-of-the-mathematics-behind-music/.  Pythagoras, 13thC Greek mathematician, was famous in geometry for the Pythagorean theorem (en.  Wikipedia. org / wiki/Pythagoras).  The theorem states that in a right-angled triangle, the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides—that is, a^2 + b^2 = c^2.  Pythagoras experimented with a monochord, noticing that subdividing a vibrating string into rational proportions produced resonant sounds. When the frequency of the string is inversely proportional to its length, its other frequencies are simply whole number multiples of the fundamental.  (En. Wikipedia. org/wiki/Chromatic_scale)

The term chromatic derives from the Greek word chroma, meaning color, where the total chromatic / aggregate is the set of all twelve pitch classes; an array being a succession of aggregates.  Shí-èr-lǜ (Chinese: 十二律 (twelve-pitch scale) is a standardized gamut of twelve notes. The Chinese scale uses the same intervals as the Pythagorean scale, based on 2/3 ratios (2:3, 8:9, 16:27, 64:81, etc.). The gamut or its subsets were used for tuning and are preserved in bells and pipes.  In China, the first reference to “the standardization of bells and pitch,” dates back to around 600 BCE.  According to ancient scroll/script literature, Pythagoras taught that music was not intended for entertainment, though for calming the mind and bringing about order from chaos of life and the universe using spiritual instruments.  Music of the Spheres is one of the phrases used to describe Ancient Greek Pythagorean Music.  Here is a sample of what this music sounds like: http://www.youtube.com/watch?v=Bm2Pn_8Oxww  This clip is a short educational video on a Pythagorean Tone Generator: Pythagorean Tone Generator: http://www.youtube.com/watch?v=BhqgOH0gDIc

James Hopkins, a student and practitioner of Pythagorean Monochords visually shows us his handmade Monochord Stringed instruments: http://www.youtube.com/watch?v=tbCZO6rPcY8

For more cool Learning Math Games, feel free to visit us here:

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

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