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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.
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6th Grade Unit 1 Lesson 03.notebook
2LESSON TITLE
UNIT 1 Lesson 3Reasoning to Find Area
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6th Grade Unit 1 Lesson 03.notebook
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
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6th Grade Unit 1 Lesson 03.notebook
4WARMUP
Warmup
link to worksheet Cont...link to Blackline Master
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6th Grade Unit 1 Lesson 03.notebook
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
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6th Grade Unit 1 Lesson 03.notebook
6WARMUP
Warmup3.1 Comparing Regions
2 min quiet time
2 min partner talk
Cont...link to worksheet
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
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6th Grade Unit 1 Lesson 03.notebook
73.2 ACTIVITY
Activity 3.2
link to worksheetCont...
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6th Grade Unit 1 Lesson 03.notebook
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
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6th Grade Unit 1 Lesson 03.notebook
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
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6th Grade Unit 1 Lesson 03.notebook
10ARE YOU READY FOR MORE
Activity 3.2Are You Ready For More
link to worksheet Cont...
C D
Manipulative
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6th Grade Unit 1 Lesson 03.notebook
113.3 ACTIVITY
Activity 3.3
link to worksheet Cont...
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6th Grade Unit 1 Lesson 03.notebook
123.3 ACTIVITY
3.3 Activity 4 students67 min quiet time67 min partner talk
partner
Cont...link to worksheet
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
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6th Grade Unit 1 Lesson 03.notebook
13ACTIVITY SYNTHESIS
Cont...link to worksheet
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
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6th Grade Unit 1 Lesson 03.notebook
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.
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6th Grade Unit 1 Lesson 03.notebook
15LESSON SUMMARY
Lesson Summary
link to worksheet
Read through your Lesson Summary...
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6th Grade Unit 1 Lesson 03.notebook
16COOL DOWN
Cool Downcomplete your "cool down"
link to worksheet
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6th Grade Unit 1 Lesson 03.notebook
17PRACTICE PROBLEMS
PRACTICE PROBLEMS
link to worksheet Cont...
Page 1
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6th Grade Unit 1 Lesson 03.notebook
18PRACTICE PROBLEMS
PRACTICE PROBLEMS
link to worksheet Cont...
Page 2
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6th Grade Unit 1 Lesson 03.notebook
19PRACTICE SOLUTIONS
PRACTICE SOLUTIONS
link to worksheet Cont...
Problem 1
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6th Grade Unit 1 Lesson 03.notebook
20PRACTICE SOLUTIONS
PRACTICE SOLUTIONS
link to worksheet Cont...
Problem 2
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6th Grade Unit 1 Lesson 03.notebook
21PRACTICE SOLUTIONS
PRACTICE SOLUTIONS
link to worksheet Cont...
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6th Grade Unit 1 Lesson 03.notebook
22PRACTICE SOLUTIONS
PRACTICE SOLUTIONS
link to worksheet
Problem 4
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6th Grade Unit 1 Lesson 03.notebook
23Jun 412:45 PM
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Attachments
6131blackline_master.pdf
613a student_task_statements.pdf
613b student_cool_down.pdf
613c practice_problems.pdf
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Blackline Master for Classroom Activity 6.1.3.1: Comparing Regions
Blank Page
SMART Notebook
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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
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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.
GRADE 6 MATHEMATICS BY
NAME DATE PERIOD
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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.
•
•
•
GRADE 6 MATHEMATICS BY
NAME DATE PERIOD
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The area of this rectangle is 32 square centimeters.
GRADE 6 MATHEMATICS BY
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
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Unit 1, Lesson 3: Reasoning to Find Area
A maritime flag is shown. What is the area of the shaded part of the flag? Explain or show your reasoning.
GRADE 6 MATHEMATICS BY
NAME DATE PERIOD
Unit 1: Area and Surface Area Lesson 3: Reasoning to Find Area 1
COOL DOWN
Unit 1, Lesson 3: Reasoning to Find Area
Blank Page
SMART Notebook
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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.
GRADE 6 MATHEMATICS BY
NAME DATE PERIOD
Unit 1: Area and Surface Area Lesson 3: Reasoning to Find Area 1
Practice Problems
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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.
GRADE 6 MATHEMATICS BY
NAME DATE PERIOD
Unit 1: Area and Surface Area Lesson 3: Reasoning to Find Area 2
Unit 1, Lesson 3: Reasoning to Find Area
SMART Notebook
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