s e s s i o n 3 . 1 A What’s the Area? · Session 3.1A Unit 5 26D Finding the Area (page 3 of 4) 5. Use tiles to build a rectangle that has one side that is 8 tiles long and another

Vocabularysquare units square inchesdimensionsby (as in 5 by 7)

s e s s i o n 3 . 1 A

Ten-Minute MathWhat Time Is It? Ask students to set their clocks to 4:16. Then write 4:16 on the board and set the large demonstration clock to 4:16.• How did you know where to put the small hand? How about the big hand? How

many minutes is it past 4:00? What two five-minute interval times is it in between? (4:15 and 4:20)

Ask additional similar questions using these times: 11:46, 1:04, 5:32.

Today’s Plan MaterialsAcTiViTy

Introducing Finding the Area 15 Min clAss

• Paper Draw or cut out a 5-inch by 7-inch rectangle.

• Color tiles

AcTiViTy

Finding the Area30 Min indiViduAls

• Student Activity Book, pp. 26B–26E orc22–c25, Finding the Area Make copies. (as needed)• Color tiles

discussion

Finding the Area15 Min clAss

• Students’ completed copies of Student Activity Book, pp. 26B–26E or C22–C25 (from Activity 2)• chart paper Replicate the chart on Student

Activity Book page 26E or C25. Add a column titled “Equation.”

session Follow-uP

Daily Practice • Student Activity Book, p. 26F orc26, what’s the Area? Make copies. (as needed)

What’s the Area?Math Focus Points

Using tiles to find the area of a rectangle

Developing an understanding that area can be found by multiplying the dimensions of a rectangle

cc32 inVesTigATion 3 Arrays

INV12_TE03_U05_S3.1A.indd 32 6/10/11 8:48 AM

1 Activity 2 Activity 3 Discussion 4 Session Follow-Up

Teaching Note 1 Terminology Use this discussion as an

opportunity to review the words row and column and introduce the word dimensions.

A c T i v i T y

Introducing Finding the AreaclASS15 MiN

A few weeks ago, we spent time finding the area of different shapes. Who can remind us what it means to find the area of a shape? What were some ways we did that?

Review what finding the area of a shape involves. Be sure that students recall that they used square units such as cubes, paper squares, and color tiles, as well as triangles, to find the area of shapes.

Today you’re going to find the area of several different rectangles. We’re going to see if there’s any connection to the multiplication ideas we’ve been talking about.

Show students the 5-inch by 7-inch rectangle. Ask them how you could use tiles to find the area of the rectangle, and use their ideas to do so.

Discuss a few strategies for figuring out the total number of tiles. Once there is agreement about the area, remind students that the edges of the color tiles are each 1 inch long as you discuss how to name the final measurement.

We used tiles to completely fill this rectangle. We found out that the area of the rectangle was 35 square units, or 35 square inches. How would you describe this rectangle? What if you were trying to tell someone who couldn’t see it how to build it? 1

Students might say:

“They need 35 tiles.”

“The rectangle has 5 rows.”

“Each row should be 7 tiles long.”

One way to describe a rectangle is by the length of its sides. How long is this side? [Trace the side that is 5 tiles long.] How about this side? [Trace the side that is 7 tiles long.] The dimensions of this rectangle are 5 and 7. It is 5 tiles [trace the side] by 7 tiles [trace the side]. You can also call this a 5 by 7 rectangle.

Session 3.1A What’s the Area? cc33

INV12_TE03_U05_S3.1A.indd 33 6/10/11 8:48 AM

C

inches

inches

D

inches

inches

© P

ears

on E

duca

tion

3

DateNameEqual Groups

26C Unit 5 Session 3.1A

Finding the Area (page 2 of 4)

Use color tiles to completely fill each rectangle. Label each rectangle with the dimensions. Then find the area of the rectangle.

3.

What is the area of the rectangle? square inches

4.


INV12_SE03_U5.indd 3 5/19/11 9:54 AM

B

inches

inches

A

inches

inches

© P

ears

on E

duca

tion

3


26B


Use color tiles to completely fill each rectangle. Label each rectangle with the dimensions. Then find the area of the rectangle.

1.


2.


Session 3.1A Unit 5

INV12_SE03_U5.indd 2 5/19/11 9:51 AM


Sketch the rectangle on the board and label the dimensions.

Connect this sketch back to the array of color tiles. Ask students what the 5 and the 7 in the sketch represent in the tile arrangement.

Explain that students will be solving similar problems, and recording what they find in a table. Sketch one row of the table from Student Activity Book page 26E or C25, and discuss how you would record the information about the rectangle you’ve just explored together.

Dimensions(in inches)

Area(in square inches)

Example: 5 by 7 35

A c t i v i t y

Finding the AreainDiviDUAlS30 Min

Students complete Student Activity Book pages 26B–26E or C22–C25.

Introduce the activity to students.

• On the first two pages, students use tiles to find the area of each rectangle. They record the dimensions and the area of each rectangle.

• On the third page, students build a rectangle described in words, and then answer the same questions.

• On the final page, students compile the dimensions and area for each rectangle in a table.

Each student needs to complete the activity individually, but encourage students to check their work with each other.

OngOing ASSeSSMent: Obser ving Student s at Work

Studentsusetilestofindtheareaofrectangles.Theyalsorecordthedimensionsofeachrectangle.

• Canstudentsfindtheareaofagivenrectangle? Cantheyrecordboththeareaandthedimensions?

▲ Student Activity Book, Unit 5, p. 26B;Resource Masters, c22

▲ Student Activity Book, Unit 5, p. 26c;Resource Masters, c23

cc34 inveStigAtiOn 3 Arrays

INV12_TE03_U05_S3.1A.indd 34 6/10/11 12:02 PM

© P

ears

on E

duca

tion

3


26E Unit 5 Session 3.1A


Complete the table by recording the dimensions and the area of each rectangle.



Example: 5 by 7 35

Rectangle A

Rectangle B

Rectangle C

Rectangle D

Rectangle E

Rectangle F

Rectangle G

Rectangle H

INV12_SE03_U5.indd 5 6/8/11 1:15 PM

© P

ears

on E

duca

tion

3


26DSession 3.1A Unit 5


5. Use tiles to build a rectangle that has one side that is 8 tiles long and another side that is 3 tiles long. Think of this as Rectangle E. Record the dimensions and area of the rectangle below.

Dimensions: by Area: square inches

6. Use tiles to build a rectangle that is 7 tiles by 4 tiles. Think of this as Rectangle F. Record the dimensions and area of the rectangle below.


7. Use tiles to build a rectangle that is 5 tiles by 5 tiles. Think of this as Rectangle G. Record the dimensions and area of the rectangle below.


8. Use tiles to build a rectangle with the dimensions 6 tiles by 5 tiles. Think of this as Rectangle H. Record the dimensions and area of the rectangle below.


INV12_SE03_U5.indd 4 6/8/11 4:45 PM


▲ Student Activity Book, Unit 5, p. 26E;Resource Masters, C25

▲ Student Activity Book, Unit 5, p. 26D;Resource Masters, C24

• How do students find the total number of tiles? Do they count by 1s? Add the number in each row or column? Count by the number in each row or column? Do any students multiply the dimensions?

• Can students build a rectangle based on a description?

• Do students complete the table with the correct dimensions and areas?

Talk with students as they work to fill in the table on the fourth page.

Are you noticing anything interesting as you fill in this table? Have you noticed any patterns in your table?

Keep track of students who have thoughts about these questions that would contribute to the discussion.

DiFFEREntiAtion: Suppor ting the Range of Lear ner s

Some students may not have an efficient strategy for finding the total number of tiles. Work with these students to help them begin to see and use groups in their work. For example, as they are covering the rectangle, have them use different colors for alternating rows. Ask: How many tiles did you use in the first row? So how many tiles do you think you’ll need for the second row? What about the third row? Now we have a rectangle that’s 5 [trace the first row] and 5 [trace the 2nd row] and 5 [trace the 3rd row]. What’s an equation for that? How would you solve that problem?

Ask students who accurately finish the activity to look closely at the completed table on the last page. Challenge them to look for and describe any patterns they notice.

D i S C U S S i o n

Finding the AreaCLASS15 Min

Math Focus Points for Discussion Developing an understanding that area can be found by

multiplying the dimensions of a rectangle

Gather students to discuss their work on Student Activity Book pages 26B–26E or C22–C25. Use the chart paper table you prepared. Build any of the rectangles in the activity as necessary.

Session 3.1A What’s the Area? CC35

INV12_TE03_U05_S3.1A.indd 35 6/10/11 8:48 AM

© P

ears

on E

duca

tion

3

DateNameEqual Groups Daily Practice

26FSession 3.1A Unit 5

What’s the Area?Record the dimensions and the area of each rectangle.

1.

Dimensions: by

Area: square units

2.

Dimensions: by

Area: square units

note Students find the dimensions and the area of rectangles.

114

INV12_SE03_U5.indd 6 6/8/11 1:22 PM




Equation

Example:

Rectangle A

Rectangle B

Rectangle C

Rectangle D

Rectangle E

Rectangle F

Rectangle G

Rectangle H

5 by 7 35

Ask students to study the finished table.

We’ve been thinking a lot about multiplication the last couple of weeks. Why do you think we went back to thinking about area today? Do you see any connections? Turn and talk to a partner. What do you notice about this table?

Discuss students’ ideas. Many students will see that, in addition to representing the area in square inches, each row can form a multiplication equation. If you multiply the dimensions, you get the area.

So we found that Rectangle A, which is 2 by 4, has an area of 8 square inches. [Build or have a student build the rectangle with tiles.] The product of 2 and 4 is 8. [Point to each number in the table and in the model.]

Do you agree that 2 times 4 is 8? I’m going to write that equation in this column. Do you think that will be true for every row in our table?

Look at another example or two as time permits.

We’ve been using groups of things or skip counting as ways to think about multiplication. We can also think of the area of rectangles, or of arrays of squares, as multiplication.

S e S S i o n F o l l o w - U p

Daily Practice Daily Practice: For reinforcement of this unit’s content,

have students complete Student Activity Book page 26F or C26.

▲ Student Activity Book, Unit 5, p. 26F;Resource Masters, C26

CC36 inveStigAtion 3 Arrays

INV12_TE03_U05_S3.1A.indd 36 6/10/11 8:49 AM

B

inches

inches

A

inches

inches

C22 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3


Unit 5 Session 3.1A

Finding the Area (page 1 of 4)Use color tiles to completely fill each rectangle. Label each rectangle with the dimensions. Then find the area of the rectangle.

1.


2.


INV12_BLM03_U5.indd 22 6/23/11 2:08 PM

C

inches

inches

D

inches

inches



Unit 5 Session 3.1A

Finding the Area (page 2 of 4)Use color tiles to completely fill each rectangle. Label each rectangle with the dimensions. Then find the area of the rectangle.

3.


4.


INV12_BLM03_U5.indd 23 6/23/11 2:10 PM



Unit 5 Session 3.1A


5. Use tiles to build a rectangle that has one side that is 8 tiles long and another side that is 3 tiles long. Think of this as Rectangle E. Record the dimensions and area of the rectangle below.


6. Use tiles to build a rectangle that is 7 tiles by 4 tiles. Think of this as Rectangle F. Record the dimensions and area of the rectangle below.


7. Use tiles to build a rectangle that is 5 tiles by 5 tiles. Think of this as Rectangle G. Record the dimensions and area of the rectangle below.


8. Use tiles to build a rectangle with the dimensions 6 tiles by 5 tiles. Think of this as Rectangle H. Record the dimensions and area of the rectangle below.


INV12_BLM03_U5.indd 24 6/20/11 11:56 AM



Unit 5 Session 3.1A

Finding the Area (page 4 of 4)Complete the table by recording the dimensions and the area of each rectangle.



Example: 5 by 7 35

Rectangle A

Rectangle B

Rectangle C

Rectangle D

Rectangle E

Rectangle F

Rectangle G

Rectangle H

INV12_BLM03_U5.indd 25 6/20/11 11:56 AM


DateNameEqual Groups Daily Practice

Unit 5 Session 3.1A

notE Students find the dimensions and the area of rectangles.

114

What’s the Area?Record the dimensions and the area of each rectangle.

1.

Dimensions: by

Area: square units

2.

Dimensions: by

Area: square units

INV12_BLM03_U5.indd 26 6/20/11 11:56 AM

C27 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3Unit 5 Session 3.2


Array Cards (page 9 of 11)

6 ∙ 9

9 ∙ 6

9 ∙ 9

INV12_BLM03_U5.indd 27 5/19/11 10:35 AM



7 ∙ 9

9 ∙ 7


8 ∙ 8

INV12_BLM03_U5.indd 28 5/19/11 10:35 AM




7 ∙ 88 ∙ 7

8 ∙ 99 ∙ 8

INV12_BLM03_U5.indd 29 5/19/11 10:36 AM


FechaNombreGrupos iguales

Unidad 5 Sesión 3.5B

Tarjetas de multiplicar (página 7 de 7)

6 × 99 × 6

Comienza con

7 × 88 × 7

Comienza con

7 × 99 × 7

Comienza con

8 × 8

Comienza con

8 × 99 × 8

Comienza con

9 × 9

Comienza con

INV12_SP_BLM03_U5.indd 34 6/27/11 3:20 PM



Unidad 5 Sesión 3.7A

Problemas sobre contar en la clase (página 1 de 2)

Escribe una ecuación para representar cada problema. Luego resuelve el problema y muestra tu trabajo.

1. La clase de Denzel estaba contando en la clase de 10 en 10. ¿Qué número dijo la 6a. persona?

Ecuación:

2.La clase de Gina estaba contando en la clase de 20 en 20. ¿Qué número dijo la 4a. persona?

Ecuación:

3.La clase de Kenji estaba contando en la clase de 30 en 30. ¿Qué número dijo la 5a. persona?

Ecuación:




Unidad 5 Sesión 3.7A

Problemas sobre contar en la clase (página 2 de 2)

Escribe una ecuación para representar cada problema. Luego resuelve el problema y muestra tu trabajo.

4.La clase de Nancy estaba contando en la clase de 60 en 60. ¿Qué número dijo la 3era. persona?

Ecuación:

5.La clase de Adam estaba contando en la clase de 90 en 90. ¿Qué número dijo la 5a. persona?

Ecuación:

6.La clase de Keisha estaba contando en la clase de 20 en 20. ¿Qué número dijo la 9 a. persona?

Ecuación:



Práctica diaria


Más problemas sobre contar en la claseEscribe una ecuación para representar cada problema. Luego resuelve el problema y muestra tu trabajo.

1. La clase de Edwin estaba contando en la clase de 50 en 50. ¿Qué número dijo la 8a. persona?

Ecuación:

2.La clase de Pilar estaba contando en la clase de 40 en 40. ¿Qué número dijo la 7 a. persona?

Ecuación:

3.La clase de Zhang estaba contando en la clase de 70 en 70. ¿Qué número dijo la 3era. persona?

Ecuación:

Unit 5 Session 3.7A

notA Los estudiantes resuelven problemas que incluyen multiplicar por múltiplos de 10.

43


Documents

s e s s i o n 3 . 1 A What’s the Area? · Session 3.1A Unit 5 26D Finding the Area (page 3 of 4) 5. Use tiles to build a rectangle that has one side that is 8 tiles long and another