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6th Grade Unit 1 Lesson 03.notebook

1MATERIALS

Lesson 3Reasoning to Find Area

Materials

needed

for this

lesson

• copies of blackline master

• geometry toolkits

UNIT 1

link to Blankline Master

For the warmup activity, prepare several copies of the pair of figures on the blackline master, in case students propose cutting them out to compare the areas.

crudiselText Boxteacher page


2LESSON TITLE

UNIT 1 Lesson 3Reasoning to Find Area


3OBJECTIVE

UNIT 1 Lesson 3

Objective: • I can use different reasoning strategies

to find the area of shapes.

Let’s decompose and rearrange shapes to find their areas.

Reasoning to Find Area

crudiselText BoxThis lesson does not include any applets


4WARMUP

Warmup

link to worksheet Cont...link to Blackline Master


5WARMUP

Warmup3.1 Comparing Regions

2 min quiet time

2 min partner talk

Cont...link to worksheet

Is the area of Figure A greater than, less than, or equal to the area of the shaded region in Figure B? Be prepared to explain your reasoning.

link to Blackline Master


6WARMUP

Warmup3.1 Comparing Regions

2 min quiet time

2 min partner talk


Will all of the shaded areas of Figure B overlap and match exactly with the area of Figure A?

What strategy can you use to prove if it does or if it doesn't?

decomposerearrangecompose

When two figures that are overlaid one on top of another match up exactly, we can say that their

areas are equal.

Is the area of Figure A greater than, less than, or equal to the area of the shaded region in Figure B? Be prepared to explain your reasoning.

link to Blackline Master


73.2 ACTIVITY

Activity 3.2

link to worksheetCont...


83.2 ACTIVITY

3.2 Activity 2 students45 min quiet time

45 min partner talk

partner

Cont...

You should notice similarities and differences in the strategies shared and be ready to explain them.

decompose

enclose

rearrange subtract

compose

3.2: On the GridEach grid square is 1 square unit. Find the area, in square units, of each shaded region without counting every square. Be prepared to explain your reasoning.

link to worksheet

Manipulative Manipulative


9ACTIVITY SYNTHESIS

Activity Synthesis

Cont...

"The strategies used to find the areas of figures ____ and ____ are alike in that. . .""The strategies used to find the areas of figures ____ and ____ are different in that. . ." STRATEGY WORD BANK

• Decomposing• Decomposing and Rearranging

• Subtracting• Enclosing and Subtracting

3.2: On the Grid


10ARE YOU READY FOR MORE

Activity 3.2Are You Ready For More

link to worksheet Cont...

C D

Manipulative


113.3 ACTIVITY

Activity 3.3



123.3 ACTIVITY

3.3 Activity 4 students67 min quiet time67 min partner talk

partner


Compare your answers and strategies for finding the area of each figure.

ManipulativeManipulative

Manipulative

What units did you use for each area?

How are your strategies the same? How are they different?

Which strategies are similar to the ones you used in the previous activity?

3.3 Off the Grid


13ACTIVITY SYNTHESIS


ManipulativeManipulative Manipulative

Which strategies are similar to the ones you used in the previous activity?

Activity Synthesis

Can the same strategies for finding area be used whether we use the measurements indicated by a grid, or whether the measurements are given directly (without a grid)?

3.3 Off the Grid


14LESSON SYNTHESIS

Lesson Synthesis

decomposing it

into

familiar shapes

What strategies were iden

tified for finding

area in this lesson?

decomposing it and rearranging the pieces into familiar shapes

considering it as a shape with missing pieces, then subtracting the areas of the missing pieces from the area of

the shape.

Go back through the activities and find problems in which each of these strategies

were used. Share.


15LESSON SUMMARY

Lesson Summary

link to worksheet

Read through your Lesson Summary...


16COOL DOWN

Cool Downcomplete your "cool down"

link to worksheet


17PRACTICE PROBLEMS

PRACTICE PROBLEMS


Page 1


18PRACTICE PROBLEMS

PRACTICE PROBLEMS


Page 2


19PRACTICE SOLUTIONS

PRACTICE SOLUTIONS


Problem 1

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PRACTICE SOLUTIONS


Problem 2

crudiselText Boxnope



PRACTICE SOLUTIONS


crudiselText Boxno peeking



PRACTICE SOLUTIONS

link to worksheet

Problem 4

crudiselText Boxnice try


23Jun 412:45 PM

Attachments

6131blackline_master.pdf

613a student_task_statements.pdf

613b student_cool_down.pdf

613c practice_problems.pdf

Blackline Master for Classroom Activity 6.1.3.1: Comparing Regions

Blank Page

SMART Notebook

Unit 1, Lesson 3: Reasoning to Find AreaLet’s decompose and rearrange shapes to find their areas.

3.1: Comparing Regions

Is the area of Figure A greater than, less than, or equal to the area of the shaded region in Figure B? Beprepared to explain your reasoning.

3.2: On the Grid

Each grid square is 1 square unit. Find the area, in square units, of each shaded region without countingevery square. Be prepared to explain your reasoning.

GRADE 6 MATHEMATICS BY

NAME DATE PERIOD

Student Task Statement

Are you ready for more?

Rearrange the triangles from Figure C so they fit inside Figure D. Draw and color a diagram of your workon the grid.

3.3: Off the Grid

Find the area of the shaded region(s) of each figure. Explain or show your reasoning.


NAME DATE PERIOD

Lesson 3 Summary

There are different strategies we can use to find the area of a region. We can:

Decompose it into shapes whose areas you know how to calculate; find the area of each of thoseshapes, and then add the areas.

Decompose it and rearrange the pieces into shapes whose areas you know how to calculate; find thearea of each of those shapes, and then add the areas.

Consider it as a shape with a missing piece; calculate the area of the shape and the missing piece, andthen subtract the area of the piece from the area of the shape.

The area of a figure is always measured in square units. When both side lengths of a rectangle are givenin centimeters, then the area is given in square centimeters.

•

•

•


NAME DATE PERIOD

The area of this rectangle is 32 square centimeters.


NAME DATE PERIOD

Unit 1: Area and Surface Area Lesson 3: Reasoning to Find Area 4

Unit 1, Lesson 3: Reasoning to Find Area

3.1: Comparing Regions

3.2: On the Grid

Are you ready for more?

3.3: Off the Grid

Lesson 3 Summary

SMART Notebook


A maritime flag is shown. What is the area of the shaded part of the flag? Explain or show your reasoning.


NAME DATE PERIOD


COOL DOWN


Blank Page

SMART Notebook

Unit 1, Lesson 3: Reasoning to Find Area1. Find the area of each shaded region. Show your reasoning.

2. Find the area of each shaded region. Show or explain your reasoning.


NAME DATE PERIOD


Practice Problems

3. Two plots of land have very different shapes. Noah said that both plots of land have the same area.

4. A homeowner is deciding on the size of tiles to use to fully tile a rectangular wall in her bathroom thatis 80 inches by 40 inches. The tiles are squares and come in three side lengths: 8 inches, 4 inches, and2 inches. State if you agree with each statement about the tiles. Explain your reasoning.

a. Regardless of the size she chooses, she will need the same number of tiles.

b. Regardless of the size she chooses, the area of the wall that is being tiled is the same.

c. She will need two 2-inch tiles to cover the same area as one 4-inch tile.

d. She will need four 4-inch tiles to cover the same area as one 8-inch tile.

e. If she chooses the 8-inch tiles, she will need a quarter as many tiles as she would with 2-inch tiles.

(from Unit 1, Lesson 2)

Do you agree with Noah? Explain your reasoning.


NAME DATE PERIOD



SMART Notebook

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6th grade unit 1 lesson 03.notebook › cms › lib › az01901092 › centricity...6th grade unit 1...

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