module three equivalent fractions, part one · 2019-12-22 · fractions module three: equivalent...

Fractions Module Three: Equivalent Fractions, Part One

29www.mathwhisperer.com(c) Peak Achievement LLC 2012

M o d u l e t h r e eEQUIVALENT FRACTIONS, pART ONEGreat job! You have done a lot of work to really understand the concept of fractions. Now it’s time to move on to another big topic with fractions, equivalent fractions.

The first step is to get out your fraction pieces.

Note that for a fraction to be equivalent, the new fraction must fit exactly over the original fraction pieces. Close matches don’t count.

As an example, is equivalent to . Put them on top of each other, and see that they exactly cover each other.

Three looks aT equivalenT frac Tions

Look 1 at equivalent fractions: Use your fraction pieces

Equivalent fractions are a very, very important concept in fractions. Like all concepts, we be-gin with concrete objects. We will use fraction pieces for the concrete representation.

The word equivalent has the same sound as equal in it.

1__2

1__4

1__42__

41__2

I really urge you to use the fraction pieces. The fraction pieces give you the powerful

effects of physical modeling, which enhances conceptual understanding. So—please trust

me on this, and use your fraction pieces. It will take an extra five to ten minutes, not

much time for the positive effects.


30 www.mathwhisperer.com (c) Peak Achievement LLC 2012

What other names do you have?

Here is another example. Say you have a dollar bill. This is equivalent to four quarters.

Take out your pieces as well as the and pieces.

Area is the amount of surface. and have the same amount of surface. That is why they are equivalent. Two fourths has the same area as one half—there are just more pieces.

This is a picture of the situation:

One-half Two-fourths

My name is Bernice German. Some people call me the Math Whisperer, some call me Bernice, some call me Mrs. German, my children call me Mom. They are all names for the same person—me. The names are different, but I’m the same person. Math Whisperer is equivalent to Mrs German.

the Math WhispererBernice

Mrs. GermanMom

is equivalent to

1 - for reference 1__4

1__4

1__2

2__4

1__2

1__8

1__4

1__2

is equivalent to



Now it’s your turn. In the space below, use your fraction pieces to trace.

Trace a fraction piece. Then trace over it four fraction pieces.

Based on your tracing, covers the same area as . So , is equivalent to .

Remember the denominator tells us the number of pieces the one is cut into. The numerator tells us the number of pieces we have.

1__2

1__4

1__4

The one is cut into 2 pieces, so the denominator is 2. The numerator is 1.

The one is cut into 4 pieces, so the denominator is 4. The numerator is 2.

1__2

1__8

1__2

?__8

1__2

?__8



Look 2 at equivalent fractions: Pizza

Who gets more pizza, Jo or Joe?

The correct answer is that they get the same amount of pizza. Jo gets one giant slice that is half of the pizza. Joe gets two big slices, each of which is one fourth of the pizza, for a total of two fourths of the pizza. They get the same amount of yummy pizza.

If you want, you can tell your parent that the Math Whisperer says your homework is to check this out for yourself by ordering two pizzas. Cut one in half, and cut the other into fourths. Eat half of one, and two fourths of the other. Do you notice a difference?

Joe gets four fourths.

Jo gets two halves.



Look 3 at equivalent fractions: Algebra

In picture form:

There is an algebraic way to go from to .

Each of the halves was divided into four equal pieces. (The pink half and the white half were each divided into four equal pieces.)

And we used a factor of 4 to go from to .

Is this a coincidence?! The original fraction piece ( ) divided into four equal pieces, and a factor of 4?! Your mission, should you choose to accept it, is to find out!

1 * 4 = 4_______2 * 4 = 8

The one has been divided into two equal parts. Each is .

Now I divide each of the one halves into four equal parts. Each of these parts is .

1__8

1__8

1__2

1__8

1__2

1__2

4__8

1 * 4 = 4_______2 * 4 = 8

FActor oF 4

1__2

4__8



ac TiviT y 1: T wo looks aT equivalenT frac Tions

Equivalent Fractions

Picture

How many equal parts did you

make from each original part?

Algebraic form:

=

each of the one thirds is divided

into 2 equal pieces

=

=

=

=

=

=

1__3

2__6

1__3

3__9

2__3

4__6

1__4

2__8

3__4

6__8

2__5

4__10

1 * 2___3 * 2

2__6



Equivalent Fractions

Picture

How many equal parts did you

make from each original part?

Algebraic form:

=

=

=

=

=

=

2__5

6__15

1__5

2__10

1__5

3__15

1__7

2__14

3__7

6__14

4__4

8__8



Is this a coincidence?! Look at some of your examples in the activity you just did.

Here each of the two halves was divided into 3 pieces. And so on.

Try to make a general case here. Do your best!

means each of the halves is divided into ________(how many) pieces?

means each of the thirds is divided into ________(how many) pieces?

1 * 3 = 3_______2 * 3 = 6

1 * n = _______2 * n =

1 * n = _______3 * n =



ac TiviT y 2: more work wiTh equivalenT frac Tions

Picture Symbol Relationship Explanation

=

=

is equivalent to

because they cover the same area

=

=

is equivalent to

1__2

6__12

1 * 6___2 * 6

6__12

6 ÷ 6____12 ÷ 6

1__2

1__26__12

1__4

2__8

1 * ___4 *

2__8

2 ÷____8 ÷

1__

1__4



Picture Symbol Relationship Explanation

=

=

is equivalent to

because they cover the same area

1__4

6__24

1 * 8 ___3 * 8

8__24

8 ÷ 8____24 ÷ 8

1__3

3__8

9__24

2__316__24



ac TiviT y 3: using pic Tures To find equivalenT frac Tions—The area model

Original Fraction

Picture

Final

Fraction

Picture

Factor for Numerator and

Denominator

for every 1 piece of , there are 4

pieces for

1__2

4__8

1__2

3__6

1__2

5__10

1__4

3__12

1__4

2__8

1__3

2__6

2__5

4__10

1__3

3__9

1__2 4__

8



ac TiviT y 4: finding equivalenT frac Tions wiTh your frac Tion pieces

Use your fraction pieces for this activity.

1__2

1__3

1__5

2__3

2__5

1__2

2__4

3__6

5__10



Thinking about it:

a. What is the same about the list of equivalent fractions for and ?

b. What is the same about the list of equivalent fractions for and ?

c. How can you tell without fraction pieces that two fractions are equivalent? (more about this later)

5__10

3__12

1__4

1__2

5__10

3__12

1__4



ac TiviT y 5: more equivalenT frac Tion prac Tice Circle the fractions that are equivalent to the given fraction.

1__2

1__3

1__4

2__5

2__3

4__8

5__12

120__240

2__1

11__20

82__164

3__6

4__2

75__150

14__18

350__700

16__36

50__25

9__3

4__12

120__300

3__1

11__33

30__10

50__150

6__2

3__6

300__900

14__42

16__46

2__6

4__12

3__12

120__480

4__1

11__42

80__320

50__25

8__2

4__8

25__100

4__14

100__400

75__150

5__10

200__500

5__1

22__55

8__20

50__125

10__5

5__2

20__100

20__5

12__30

12__50

4__20

4__6

100__300

22__33

12__13

80__120

50__75

3__2

9__6

9__12

30__20

250__350

16__24

4__12



ac TiviT y 6: equivalenT frac Tion dominoes

Dominoes have been played for over 300 years. This version is a great equivalent fraction exercise, too.

In case you don’t know how to play, here is an explanation for playing dominoes:

This is a single domino:

If the value on the right of one domino matches the value on the left of the second domino, they can be connected. Whether they are connected horizontally or vertically depends on the second value on the second domino. (Generally up and down on the domino are irrel-evant, unless it bothers the students to read a number upside down.)

You can work in pairs on this, taking turns to add one domino each and check your partner’s work. Or you can play by yourself. Either way, you practice and learn!

So print pages 44 and 45 to play. You can play by yourself or with a partner.

Matches can be either numbers or pictures

5__10

1__2

2__4

1__3

2__6

1__4

2__8

1__2

module three equivalent fractions, part one · 2019-12-22 · fractions module three: equivalent...

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