name understand fractions as numbers -...

$: Name Understand Fractions as Numbers - pearsoncmg.commediaconsole.pearsoncmg.com/curriculum/math/ma_enVCC16_g3_te_na/... · las fracciones son partes iguales de un todo, un conjunto$
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NameHome-School ConnectionTopic 12

Understand Fractions as NumbersTopic 12 Standards 3.NF.A.1, 3.NF.A.2a, 3.NF.A.2b, 3.NF.A.3c, 3.MD.B.4, 3.G.A.2

See the front of the Student’s Edition for complete standards.

Dear Family,

Your child is recognizing fractions found all around us and is learning that fractions are equal parts of a whole, of a set, or of a length. He or she is also learning to name fractions and to locate fractions on a number line. Seeing fractions on a number line will help your child enhance his or her number sense. This work with fractions on a number line will also serve as a basis for future work with fractions in measuring length.

Here is an activity that you and your child can do together.

Fractions on a Number Line

Materials paper and pencil

Write the following fractions on eight slips of paper:

18 2

8 38 4

8 58 6

8 78 8

8

Put the slips of paper in a bag or box and mix them. Have your child draw two slips of paper. He or she should write the fractions in the correct position on the number line below.

0 1

Continue with the remaining slips of paper.

Observe Your ChildFocus on Mathematical Practice 6 Attend to precision.

Help your child become proficient with Mathematical Practice 6. Have your child explain the different components of a fraction (numerator, denominator) and what they represent.


NombreDe la escuela al hogar

(en español)Tema 12

Las fracciones como númerosEstándares del Tema 12 3.NOF.A.1, 3.NOF.A.2a, 3.NOF.A.2b, 3.NOF.A.3c, 3.MD.B.4, 3.G.A.2

Los estándares completos se encuentran en las páginas preliminares del Libro del estudiante.

Estimada familia:

Su niño(a) está reconociendo fracciones en las cosas que nos rodean y aprendiendo que las fracciones son partes iguales de un todo, un conjunto o una longitud. También está aprendiendo a nombrar las fracciones y ubicarlas en una recta numérica. Ver fracciones en una recta numérica mejorará el sentido numérico de su niño(a). Este trabajo con fracciones en una recta numérica también será la base del trabajo futuro con fracciones para medir longitudes.

Pruebe esta actividad con su niño(a).

Fracciones en una recta numérica

Materiales papel y lápiz

Escriba las siguientes fracciones en ocho pedazos de papel:

18 2

8 38 4

8 58 6

8 78 8

8

Coloque los pedazos de papel en una bolsa o una caja y mézclelos. Pida a su niño(a) que saque dos pedazos de papel y que escriba las fracciones en la posición correcta en la siguiente recta numérica.

0 1

Continúe con los pedazos de papel que quedan.

Observe a su niño(a)Enfoque en la Práctica matemática 6 Prestar atención a la precisión.

Ayude a su niño(a) a adquirir competencia en la Práctica matemática 6. Pídale que explique los distintos componentes de una fracción (numerador, denominador) y lo que representa cada uno.

Vocabulary


Name Reteach to Build Understanding

12-1

1. A fraction is an equal part of a whole. The number above the bar in a fraction is the numerator. The number below the bar in a fraction is the denominator.

Label the parts of the fraction.

2. A fraction representing one part of a whole that has been divided into equal parts is a unit fraction. A unit fraction always has a numerator of 1.

This square is divided into equal parts.

The fraction for one part is .

2 equal partshalves

3 equal partsthirds

4 equal partsfourths

5 equal partsfifths

6 equal partssixths

8 equal partseighths

10 equal partstenths

12 equal partstwelfths

3. A whole can be divided into equal parts or unequal parts. Equal parts have the same area.

The shape is divided into 3 equal parts. The shape is divided into unequal parts. Each part is one third of the area of The parts do NOT have equal areas. the shape. This fraction can be written

as .

4. Draw lines to divide the shape into 5 equal parts.

Each part is fifth of the area of the shape.

The fraction for each part is .

On the Back!

5. Tell if each figure shows equal parts or unequal parts. If the parts are equal, label one of the parts using a unit fraction.

a. b. c.

14

R 12•1

Share your thinking while you work.

PartnerTalk

Toss and Talk

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3Center Game ★

Get Started or

Get 10 squares in one color and 10 in another color. Get two number cubes. Take turns with another player or team. Talk about math as you play!

At Your Turn

Toss two number cubes. Add the dots. Find your toss below.Follow the directions. Explain your thinking. Cover the answer. If the answer is taken, lose your turn. Have fun!

Play again!

If you have more time

How to Win

You win if you are the first to get four connected rectangles, like:

Toss Match the fraction that represents one equal part.

2

3

4

5

6

14

13

12

18

12

18

16

14

14

12

18

13

16

14

13

16

7

8

9

10

11

12

12•1


PartnerTalk

Toss and Talk

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3Center Game ★★

Get Started or


At Your Turn


Play again!


How to Win


Toss Say the fraction. What figure has equal parts that represent this fraction?

2 12

3 16

4 14

5 18

6 13

7 12

8 16

9 18

10 13

11 14

12 15

12•1

Vocabulary



12-2

1. A fraction can represent one or more than one of the equal parts.

Look at the first picture. How many equal pieces, or parts,

are there in the pizza?

Look at the second picture. How many parts of the pizza are

missing?

The fraction of the pizza that is missing is 14.

How many parts of the pizza remain?

The fraction of the pizza that remains is .

2. The denominator of a fraction shows the total number of equal parts in a whole. The numerator shows the number of copies of the unit fraction.

numerator denominator

The fraction above represents one part of a whole that has been divided

into equal parts.

3. Look at the figure.

What is the total number of equal parts in this figure?

This number is written in the of the fraction.

How many parts are shaded?

This number is written in the of the fraction.

The fraction of the figure that is shaded is .

The fraction of the figure that is NOT shaded is .

On the Back!

4. Draw a circle that shows 6 equal parts. Shade 2 equal parts. Write the unit fraction that represents each part of the whole. Next write the number of shaded parts. Then write the fraction of the whole that is shaded.

14

R 12•2


PartnerTalk

1 1 2 2 3 3 4 4

Teamwork


Get Started or

Get 4 red squares and 4 blue squares.Put in a bag. Work together.

Repeat for Each Round

Pick one tile. Count that number of red squares. Pick another tile. Count that number of blue squares. Use your squares to fill one of the puzzles. Say a fraction to name the red part of your puzzle. Say a fraction to name the blue part of your puzzle. Put your tiles back in the bag before beginning the next round.

If you have more time Use red squares and blue squares to make up your own fraction puzzle.

fourthseighths

sevenths halves

fifths

thirds

sixths

12•2


PartnerTalk

1 2 3 4 5 6 7 8

Teamwork



Draw a region that has equal parts. Shade in some of those parts. Ask a partner to name the shaded part of your region.

Get Started or

Put in a bag. Work together.


Pick a tile.Use that tile to replace a missing numerator or a missing denominator.Repeat until you use all of the tiles.Explain why the fraction names the shaded part of the region.

c8

b8

e2

d6

f6

g3

2h

a b c d

e f g h

a8

12•2

Vocabulary



12-3

1. Use a fraction to name part of a whole or a location on a number line.

How many equal parts are in the whole shape?

Write a fraction for one equal part.

2. Look at the fractional parts to find how many parts make a whole.

The figure shows 34 of the length of a stick. Each equal part is 14.

34 is copies of 14.

There are equal parts that make a whole.

Draw another copy of 14 to make a whole.

Four copies of make 44 or whole.

3. The denominator of the fraction tells you how many lengths you need to make the whole.

This is 45 of a diagram. 45 is lengths of 15.

15

15

15

15

Draw one more 15 to show the whole.

lengths of 15 make 55, or whole.

On the Back!

4. Draw a picture for 23. Then finish the drawing and write a fraction to represent the whole.

14

14

14

R 12•3


Name Math and Science Activity12-3

Paleontologist

Did You Know? A scientist who studies fossils and researches the history of life on Earth is a paleontologist. The research involves the study of how life forms have evolved or changed over long periods of time.

Grid mapping is a way of dividing an area of land into equal parts. Paleontologists use grid mapping to record the location of bones. Below are two grid maps used for two different fossil dig sites.

Fossil Dig Site X

A B C D

E F G H

Fossil Dig Site Y

A B C

D E F

➊ For Fossil Dig Site X, parts A, B, and C represent what fraction of the whole? Explain.

➋ For Fossil Dig Site Y, parts A, B, and C represent what fraction of the whole? Explain.

➌ Extension Samantha says that in Fossil Dig Site X, the fraction of the parts NOT shaded is 55. Do you agree? Explain.

Math and Science Activity 12•3

Vocabulary



12-4

1. A number line is a line divided into equal parts that shows numbers in order. Every number on a number line represents a distance from 0. You can use a number line to represent fractions.

Look at the number line. Label the tick marks 0 and 1.

Mark a point that is halfway between 0 and 1. This divides the distance

into equal parts. Label the point 12.

0 1

Each part of the number line is of the whole distance between 0 and 1.

2. Show 23 on the number line at the right.

Label the tick marks 0 and 1 on the number line.

The denominator of a fraction tells you the number of equal parts on the number line. The denominator of the fraction is 3.

Divide the number line into equal parts.

Each length is of the whole distance between 0 and 1.

Start at 0. The numerator is 2. Move to the right until you come to the second tick mark. This mark represents 23. Draw a point at 23. Label the point.

On the Back!

3. Draw and divide a number line into 4 equal lengths. Then mark and label 24 on the number line.

R 12•4


PartnerTalk

TossFind the fraction that fits the lettered point on your number line. Explain why you chose

that fraction.

2

3

4

5

6

7

8

9

10

11

12

A

0 1

A

0 1

A

0 1

A

0 1

A

0 1A

0 1

A

0 1

A

0 1

A

0 1

0 1

A

A

0 1

Toss and Talk


Get Started or


At Your Turn


A = 28

A = 08

A = 16

A = 14 A = 5

8

A = 13

A = 58

A = 12 A = 2

2 A = 14

A = 23 A = 1

6

A = 34 A = 4

6

A = 22 A = 1

2

Play again!


How to Win


12•4


PartnerTalk

TossFind three fractions that fit the three points on your number line. Explain why you chose

those three fractions.

2

3

4

5

6

7

8

9

10

11

12

A B C

0 1

A B C

0 1A

0 1

B C

A B C

0 1

A

0 1

B C

A

0 1

B C

A

0 1

B C

A B C

0 1

Toss and Talk


Get Started or


At Your Turn


A = 14

B = 24

C = 44

A = 16

B = 26

C = 66

A = 03

B = 13

C = 33

A = 02

B = 12

C = 22

A = 02

B = 12

C = 22

A = 18

B = 48

C = 68

A = 03

B = 13

C = 33

A = 16

B = 26

C = 66

A = 28

B = 58

C = 78

A = 16

B = 36

C = 56

A = 16

B = 46

C = 66

A = 14

B = 24

C = 44

Play again!


How to Win


A

0 1

B C

A = 14

B = 24

C = 34

A = 38

B = 48

C = 68

A = 03

B = 13

C = 23

A = 38

B = 48

C = 68

A

0 1

B C

A

0 1

B C

12•4

Vocabulary



12-5

1. A number line is a line divided into equal parts that shows fractions and numbers in order.

The number line at the right has

equal parts. Each part is of the whole.

What is the missing fraction on the number line?

0 114

34

?

2. You can represent fractions that are greater than 1 on a number line. Show 64 on the number line.

The whole is the distance between 0 and 1.

The denominator is .The whole is divided into 4 equal lengths.

Each length is of the whole.

The numerator is . There are 6 lengths of 14.

The point showing 6 lengths of 14 can be labeled as 64. Plot a point for 64.

Is 64 greater than or less than 1?

3. Any point on a number line can be named using a fraction.

0 1 ?98

118

128

18

38

48

58

? ? ?

How many equal lengths are between 0 and 1? .

Each part is of the whole.

The numerator shows the number of copies of the unit fraction.

What are the missing fractions on the number line? .

On the Back!

4. Draw and divide a number line into thirds. Label the fractions 23, 43, and 53 on the number line.

1 20

14

1 20 14

14

24

34

54

64

74

14

14

14

14

14

R 12•5

Vocabulary

Soccer Goals Scored in Games

Number of Soccer Goals Scored

••

•••

•••••

••••

•••

• •••

•••

1 2 3 4 5 76



12-6

1. Data is information you collect. A line plot shows data on a number line.

To read a line plot, count the dots above each number on the number line. In this line plot, the numbers below the number line show the number of soccer goals scored. Each dot stands for one soccer game.

Players scored 3 goals in soccer games.

Players scored goals in 1 soccer game.

2. The distance between each whole number on a ruler is 1 inch. The marks on this ruler show fourth-inch marks.

Use the ruler to measure the rectangle to the nearest fourth inch.

To the nearest fourth inch, the length of the rectangle is 114 inches.

This is whole inches and three 14 inches.

You can write this as 2□□ inches.

3. The lengths of several rectangles were measured and recorded in the line plot.

Which length did most rectangles measure?

inches

How many rectangles were measured in all?

On the Back!

4. A student has 3 stamps that are 114 inches long, 5 stamps that are

124 inches long, and 2 stamps that are 13

4 inches long. Make a line plot for the data.

Lengths of Rectangles

Length (Inches)

••••• •

••••

••

2 214 22

4 234

14

24

34

44

54

64

74

84

94

104

114

124

134

144

INCHES0 1 2 3

R 12•6


Name Math and Science Activity12-6Fossils

Did You Know? Fossils are the remains of ancient animals and plants. Over a long period of time, small pieces of animals or plants are compressed and buried under many layers of sediment. A fossilized object has the same shape as the original object, but has transformed into a rock.

When paleontologists uncover a fossil, they record the length of the fossil. The table shows the lengths of various fossils found by a paleontologist.

➊ Complete the line plot to show the data.

➋ What is the most common fossil length found by the paleontologist?

➌ What is the length of the longest fossil? What is the length of the shortest fossil?

➍ Extension The paleontologist found 2 more fossils. Both fossils are 13

4 feet long. Explain how to change the line plot to include these fossil lengths. Would your answer to Exercise 2 change? Explain.

Fossil Lengths (feet)

124 2 23

4 334 23

4

234 4 13

4 3 134

124 134 214 22

4 234 31

4 324 33

42 3 4

Math and Science Activity 12•6

Vocabulary

To the nearest half inch, the length of the string is 32 inches.

This is whole inch and one 12 inch.

You can write this as 1□□ inches.



12-7

1. You can measure to the nearest half inch. The marks on this ruler show half-inch marks. Each whole inch equals two 12 inches.

Measure the string to the nearest half inch.

INCHES0 1 2 3

12

22

32

42

52

62

2. The lengths of lines are shown below.

112 in., 21

2 in., 1 in., 212 in., 2 in., 21

2 in., 2 in., 112 in., 2 in., 21

2 in.

Record the data on the line plot.

There is data value for 1 inch.

There are data values for 112 inches.



3. Use the line plot to answer each question.

The length that occurs most often is inches.

The length that occurs least often is inch.

How many lines are measured in all? lines

On the Back!

4. The lengths of several ribbons are listed below. Use the data to make a line plot. Which length occurs most often?

212 in., 31

2 in., 3 in., 312 in., 2 in., 2 in., 21

2 in., 312 in.

Lengths of Lines

Length (Inches)

1 2112 21

2

R 12•7

Vocabulary



12-8

1. A unit fraction represents one equal part of a whole. Knowing how many equal parts are in a whole can help you solve problems.

How many equal pieces, or parts, are there in the

whole pizza?

What fraction represents one slice of pizza?

How many parts of the pizza are missing?

The fraction of the pizza that remains is .

2. Karla has art class 3 days a week. Karla draws a large circle. She divides it into 6 equal parts. She colors 2 parts black, 2 parts gray, and the rest white. What fraction did Karla color white?

You can make sense of the information by identifying the quantities that are needed to solve a problem.

Is there any missing or extra information?

Karla has art class 3 days a week is information.

Use what you know to solve the problem. A picture can help you make sense of the quantities.

The circle is divided into equal parts. Each part of the circle is 16.

parts are black and parts are gray.

There are parts left. 2 copies of 16 is .

So, of the circle is white.

On the Back!

3. Five friends go to a party that lasts 2 hours. They cut a melon into 12 equal pieces. They each eat 2 pieces of the melon. What fraction of the melon is left over? Tell how to make sense of the problem. Is there any missing or extra information? Solve the problem.

16

16

16

16

16

16

R 12•8


PartnerTalk

1 2 3 4 5

Teamwork


Get Started or

Put in a bag.


Choose a or b. Take turns reading the sentences in the problem. Take turns picking one tile. Read the fact next to your tile number. Say if that fact is extra information or information that is needed to solve the problem. Explain your decision. After you discuss all the facts, work as a team to solve the problem.


Make up your own problems that have missing information.Ask your partner to tell you what information is missing.

a. John divided a casserole into 8 equal parts. John and his 3 friends had dinner together. What fraction of the casserole is left?

1 John used pound of cheese in the casserole.

4 John served salad with the casserole.

2One friend ate 2 equal parts of the casserole. 5 John ate 2 equal parts of the casserole.

3 Each of the other friends ate 1 equal part of the casserole.

b. Janet planted a vegetable garden. She planted only onions, potatoes, and squash. What fraction of Janet’s garden contains squash?

1 Janet planted 1 part onion. 4 Janet divided her garden into 6 equal parts.

2 Janet planted 2 parts potatoes. 5 Janet wants to plant an apple tree.

3 Janet’s favorite vegetable is squash.

12

12•8


PartnerTalk

1 2 3 4

Teamwork


Get Started or

Put in a bag.


Pick one tile. Pick two tiles if your team has only two students. Read the facts listed below in order. To find your fact, find the number that matches the tile you chose. Choose a, b, c, or d. Ask a team member to read the problem. Discuss whether your fact is needed to find the answer to the problem. After you discuss all the facts, work as a team to solve the problem.

1 A mural is divided into 8 equal parts.

2 3 equal parts will be painted red.

3 2 equal parts will be painted blue.

4 1 equal part will be painted yellow.

If you have more time Try a different problem, or make up your own problem.

a. Carol painted all the red parts. What fraction of the mural did Carol paint?

b. Timothy painted all the yellow parts. What fraction of the mural did Timothy paint?

c. Isaac painted all the blue parts. What fraction of the mural did Isaac paint?

d. The rest of the mural will be painted green. What fraction of the mural will be painted green?

12•8

name understand fractions as numbers -...

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