6th grade unit 1 lesson 02.notebook...6th grade unit 1 lesson 02.notebook 3. objective. objectives:...

6th Grade Unit 1 Lesson 02.notebook

1MATERIALS

Lesson 2Finding Area by Decomposing

and Rearranging

Materials

needed

for this

lesson

• preassembled (blackline master) or commercially produced tangrams

• geometry toolkits

UNIT 1

Prepare 1 set of tangrams that contains 4 small, 1 medium, and 2 large right triangles for every 2 students. Print and cut out the blackline master (printing on card stock is recommended), or use commerciallyavailable tangrams. Note that the tangram pieces used here differs from a standard set in that two additional small triangles are used instead of a rhombus.

crudiselText Boxteacher page


2LESSON TITLE


and Rearranging

UNIT 1


3OBJECTIVE

Objectives: • I know what it means for two figures to

have the same area.• I can explain how to find the area of a

figure that is composed of other shapes.• I know how to find the area of a figure by

decomposing it and rearranging the parts.

Let’s create shapes and find their areas.


and Rearranging

UNIT 1


4WARMUP

Warmup

link to worksheet Cont...


5WARMUP

Warmup2.1 What Is Area?

2 students

1 min quiet time

34 min partner talk

Cont...

You may recall that the term area tells us something about the number of squares inside a twodimensional shape.

1. Here are four drawings that each show squares inside a shape. Select all drawings whose squares could be used to find the area of the shape. Be prepared to explain your reasoning.

2. Write a definition of area that includes all the information that you think is important.

link to worksheet

crudiselText Boxthe next 4 pages just show different ways to present the same warm up


6WARMUP


2 students

1 min quiet time

34 min partner talk

Cont...

What is it about C that might make it unhelpful for finding area?

What is it about A and D that can help us find the area?

link to worksheet


7WARMUP


2 students

1 min quiet time

34 min partner talk

Cont...

If you think B cannot be used to find area, why not?

If you think you can use B to find area, how?

link to worksheet


8WARMUP


2 students

1 min quiet time

34 min partner talk

Cont...

How are A and D different?Will they give us different areas?

Class Definition of AREA

link to worksheet


92.2 ACTIVITY

Activity 2.2

Cont...link to worksheetlink to blackline master


102.2 ACTIVITY

2.2 Activity partner

Cont...link to applet

2 students

23 min quiet time

34 min partner talk

What shape do you consider to be1 "square unit"?

Manipulative: Students can model by dragging these on the SB

2.2 Composing Shapes

What is the area of the square

composed of two small triangles? Be prepared to explain your reasoning.

Use your shapes to create a new shape with an area of 1 square unit

that is not a square.

http://m.openup.org/1/6-1-2-2


112.2 ACTIVITY



2 students

23 min quiet time

34 min partner talk



Use your shapes to

create a new shape with an area of 2

square units.

Use your shapes to create a different

shape with an area of 2 square units.

Manipulative



122.2 ACTIVITY



2 students

23 min quiet time

34 min partner talk


Manipulative


Use your shapes to

create a new shape with an area of 4

square units.



13ACTIVITY SYNTHESIS

Activity Synthesis

Cont...

Two blue triangles __________ one square. drag correct word

What does it mean for two shapes to be "IDENTICAL"?

composedecompose

rearrange

We say that if a region can be placed on top of another region so that they match up exactly, then they have the same area.


CLICK



Activity Synthesis

Cont...

If a figure is __________ and ___________ as a new figure, the area of the new figure is the same as the area of the original figure.

composed decomposedrearranged




Activity Synthesis

Cont...

A large triangle is _________ of 4 smaller triangles.

A large triangle can be _________ into 4 smaller triangles.

4 small triangles can be _______ into 2 unit squares.


composed decomposedrearranged


16ARE YOU READY FOR MORE

Activity 2.2Are You Ready For More


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172.3 ACTIVITY

Activity 2.3 OPTIONAL

Cont...link to worksheetlink to blackline master


182.3 ACTIVITY

Activity 2.3OPTIONAL

partner


1. The area of the small triangle is _________ square units. I know this because . . .

2. The area of the medium triangle is _________ square units. I know this because . . .

3. The area of the large triangle is _________ square units. I know this because . . .

Recall that the area of the square you saw earlier is 1 square unit. Complete each statement and explain your reasoning.

2 students

34 min quiet time

34 min partner talk

Manipulative




Activity 2.3 Synthesis

link to applet

“Did you and your

partner use the sam

e

strategy to find the

area of each triangle

?”

“How were your

explanations similar?"

"How were they different?”

Cont...

Manipulative



20LESSON SYNTHESIS

Lesson Synthesis

If two figures can be placed one on top of the other so that they match up exactly,

then they have the same area.

What's your guess?

CLICK

Manipulative


21LESSON SYNTHESIS

Lesson Synthesis

The area of a figure can be found by adding the areas of its parts.

If we compose (put together) a new figure from smaller pieces without overlapping them, then the sum of the areas of the pieces is the area of

the new figure.

Which has a greater area?

CLICK

CLICK

+

+

+

The sum of the areas

OR


22LESSON SYNTHESIS

Lesson SynthesisLikewise, if we decompose (cut or break apart) a given figure into pieces, then the area of the given figure is the sum of the areas of the

pieces.

Even if we rearrange the pieces, the overall area does not change.

+

+

+

CLICK

CLICK


23LESSON SUMMARY

Lesson Summary

link to worksheet

Read through your Lesson Summary...


24COOL DOWN

Cool Downcomplete your "cool down"

link to worksheet


25PRACTICE PROBLEMS

PRACTICE PROBLEMS


Page 1


26PRACTICE PROBLEMS

PRACTICE PROBLEMS

Cont...

Page 2

link to worksheet


27PRACTICE PROBLEMS

PRACTICE PROBLEMS

Cont...

Page 3

link to worksheet


28PRACTICE PROBLEMS

PRACTICE PROBLEMS

Cont...

Page 4

link to worksheet


29PRACTICE SOLUTIONS

PRACTICE PROBLEMS

Cont...

SOLUTIONS

link to worksheet

Problem 1

Problem 2

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PRACTICE PROBLEMS

Cont...

SOLUTIONS

link to worksheet

Problem 3

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PRACTICE PROBLEMSSOLUTIONS

link to worksheet

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32Jun 411:27 AM

Attachments

6122blackline_master.pdf

612a student_task_statements.pdf

612b student_cool_down.pdf

612c practice_problems.pdf

Blackline Master for Classroom Activity 6.1.2.2: Composing Shapes

Blank Page

SMART Notebook

Unit 1, Lesson 2: Finding Area by Decomposing andRearrangingLet’s create shapes and find their areas.

2.1: What is Area?

You may recall that the term area tells us something about the number of squares inside a two-dimensional shape.

1. Here are four drawings that each show squares inside a shape. Select all drawings whosesquares could be used to find the area of the shape. Be prepared to explain your reasoning.

2. Write a definition of area that includes all the information that you think is important.

GRADE 6 MATHEMATICS BY

NAME DATE PERIOD

Student Task Statement

m.openup.org/1/6-1-2-22.2: Composing Shapes

Your teacher will give you one square and some small, medium, and large righttriangles. The area of the square is 1 square unit.

1. Notice that you can put together two small triangles to make a square. What is the area of the squarecomposed of two small triangles? Be prepared to explain your reasoning.

2. Use your shapes to create a new shape with an area of 1 square unit that is not a square. Trace yourshape.

3. Use your shapes to create a new shape with an area of 2 square units. Trace your shape.


NAME DATE PERIOD

4. Use your shapes to create a different shape with an area of 2 square units. Trace your shape.

5. Use your shapes to create a new shape with an area of 4 square units. Trace your shape.

Are you ready for more?

Find a way to use all of your pieces to compose a single large square. What is the area of this large square?


NAME DATE PERIOD

m.openup.org/1/6-1-2-32.3: Tangram Triangles

Recall that the area of the square you saw earlier is 1 square unit. Complete eachstatement and explain your reasoning.

1. The area of the small triangle is _________ square units. I know this because . . .

2. The area of the medium triangle is _________ square units. I know this because . . .

3. The area of the large triangle is _________ square units. I know this because . . .


NAME DATE PERIOD

Lesson 2 Summary

Here are two important principles for finding area:

1. If two figures can be placed one on top of the other so that they match up exactly, then they have thesame area.

2. We can decompose a figure (break a figure into pieces) and rearrange the pieces (move the piecesaround) to find its area.

Here are illustrations of the two principles.

Each square on the left can be decomposed into 2 triangles. These triangles can be rearranged into alarge triangle. So the large triangle has the same area as the 2 squares.

Similarly, the large triangle on the right can be decomposed into 4 equal triangles. The triangles canbe rearranged to form 2 squares. If each square has an area of 1 square unit, then the area of thelarge triangle is 2 square units. We also can say that each small triangle has an area of square unit.

Lesson 2 Glossary Terms

area

•

•

•


NAME DATE PERIOD

rearrange

compose/decompose

•

•


NAME DATE PERIOD

Unit 1: Area and Surface Area Lesson 2: Finding Area by Decomposing andRearranging

6

Unit 1, Lesson 2: Finding Area by Decomposing and Rearranging

2.1: What is Area?

2.2: Composing Shapes

Are you ready for more?

2.3: Tangram Triangles

Lesson 2 Summary

Lesson 2 Glossary Terms

SMART Notebook


The square in the middle has an area of 1 square unit. What is the area of the entire rectangle in squareunits? Explain your reasoning.


NAME DATE PERIOD

Unit 1: Area and Surface Area Lesson 2: Finding Area by Decomposing andRearranging

1

COOL DOWN


Blank Page

SMART Notebook

NAME DATE PERIOD

OpenUpResources(openupresources.org) 1

Unit 1, Lesson 2: Finding Area by Decomposing and Rearranging 1. Thediagonalofarectangleisshown.

a. Decomposetherectanglealongthediagonal,andrecomposethetwopiecestomakeadifferentshape.

b. Howdoestheareaofthisnewshapecomparetotheareaoftheoriginalrectangle?Explainhowyouknow.

Practice Problems

NAME DATE PERIOD


2. Theareaofthesquareis1squareunit.Twosmalltrianglescanbeputtogethertomakeasquareortomakeamediumtriangle.

Whichfigurealsohasanareaof1 squareunits?Selectallthatapply.

NAME DATE PERIOD


3. Priyadecomposedasquareinto16smaller,equal‐sizesquaresandthencutout4ofthesmallsquaresandattachedthemaroundtheoutsideoforiginalsquaretomakeanewfigure.Howdoestheareaofhernewfigurecomparewiththatoftheoriginalsquare?

A. Theareaofthenewfigureisgreater.B. Thetwofigureshavethesamearea.C. Theareaoftheoriginalsquareisgreater.D. Wedon’tknowbecauseneitherthesidelengthnortheareaoftheoriginal

squareisknown.4. Theareaofarectangularplaygroundis78squaremeters.Ifthelengthofthe

playgroundis13meters,whatisitswidth?(fromUnit1,Lesson1)

NAME DATE PERIOD


5. Astudentsaid,“Wecan’tfindtheareaoftheshadedregionbecausetheshapehasmanydifferentmeasurements,insteadofjustalengthandawidththatwecouldmultiply.”

Explainwhythestudent’sstatementaboutareaisincorrect.(fromUnit1,Lesson1)

SMART Notebook

Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8Page 9Page 10Page 11Page 12Page 13Page 14Page 15Page 16Page 17Page 18Page 19Page 20Page 21Page 22Page 23Page 24Page 25Page 26Page 27Page 28Page 29Page 30Page 31Page 32Attachments Page 1

6th grade unit 1 lesson 02.notebook...6th grade unit 1 lesson 02.notebook 3. objective. objectives:...

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