Download Unit 5 Geometry Math 7 - Long Beach Unified School District

Unit 5 Geometry
Math 7
Unit Goals – Stage 1
Number of Days: 29 days
3/13/17 – 4/28/17
Unit Description: Students will begin to explore the concepts of congruency and similarity by investigating the relationships between angles formed by
intersecting lines, constructing geometrical figures with given conditions, and using scale drawings. They also solve problems involving area and
circumference of circles. Additionally, students examine cross-sections of three-dimensional figures. Their work with expressions and equations is
applied to finding unknown angles and problems involving area, surface area, and volume.
Materials: protractor*, compass, GeoSolids, modeling dough, calculators
(* Paper tool available at LBUSD Curriculum Intranet  Instructional Tools  Middle School  Mathematical Tools)
Standards for Mathematical
Transfer Goals
Practice
Students will be able to independently use their learning to…
SMP 1
Make sense of problems
• Make sense of never-before-seen problems and persevere in solving them.
and persevere in solving
• Construct viable arguments and critique the reasoning of others.
them.
Making Meaning
SMP 2
Reason abstractly and
UNDERSTANDINGS
ESSENTIAL QUESTIONS
quantitatively.
Students will understand that…
Students will keep
SMP 3
Construct viable
considering…
• Geometric awareness develops through visualizing, diagramming, and
arguments and critique
constructing.
• How can geometry be
the reasoning of others.
used to understand and
• The area of irregular and regular polygons can be found by decomposing
SMP 4
Model with mathematics.
explain the world around
the polygon into triangles and quadrilaterals.
SMP 5
Use appropriate tools
you?
• Using the formulas for finding area, surface area, and volume can help solve
strategically.
•
How do geometric
real-world problems.
SMP 6
Attend to precision.
relationships help solve
• Scale drawings and scale models involve proportional reasoning and are
SMP 7
Look for and make use of
problems?
used in real-world applications.
structure.
•
How can you draw,
• Cross-sections of three-dimensional objects can result in a variety of
SMP 8
Look for and express
construct, and describe
two-dimension figures, depending on the angle of the cut with the base of
regularity in repeated
geometrical figures?
the object.
reasoning.
Acquisition
KNOWLEDGE
SKILLS
Standards for Mathematical
Students
will
know…
Students will be skilled at and/or be able to…
Content Clusters Addressed
•
The
measures
of
complementary
angles
•
Use facts about supplementary, complementary, vertical,
[a] 7.G.A Draw, construct, and
and adjacent angles to write and solve equations for
add
up
to
90°
and
the
measures
of
describe geometrical
unknown angles in a figure.
supplementary
angles
add
up
to
180°.
figures and describe the
•
Draw (freehand, with ruler and protractor, and/or with
•
Vertical
angles
are
congruent.
relationships between
technology) geometric shapes with given conditions.
•
The
ratio
of
the
circumference
to
the
them.
•
Construct triangles from three measures of angles or sides
[a] 7.G.B
Solve real-life and
diameter is “pi” (π).
and notice when the conditions determine a unique
mathematical problems
• The formula for circumference of a circle is
triangle, more than one triangle, or no triangle.
involving angle
C = πd.
•
Solve problems involving scale drawings of geometric
2
measure, area, surface
• The formula for area of a circle is A = πr .
figures.
area, and volume.
LONG BEACH UNIFIED SCHOOL DISTRICT
1
Posted 2/1/17
2016-2017
Unit 5 Geometry
Math 7
Unit Goals – Stage 1
• The formula for volume of right prism is
V = Bh and for pyramids is V = 1 Bh where
3
B is the area of the base.
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
2
• Reproduce a scale drawing at a different scale.
• Find the circumference and area of a circle.
• Informally derive the relationship between circumference
and area of a circle.
• Use the formulas for area of triangles, quadrilaterals, and
circles to solve real-world and mathematical problems
involving composite figures.
• Use the formulas for volumes of right prisms and pyramids
to solve real-world and mathematical problems including
composite solids.
• Describe the two-dimensional figures that result from
slicing three-dimensional figures.
Posted 2/1/17
Unit 5 Geometry
Math 7
Assessed Grade Level Standards
Standards for Mathematical Practice
SMP 1
Make sense of problems and persevere in solving them.
SMP 2
Reason abstractly and quantitatively.
SMP 3
Construct viable arguments and critique the reasoning of others.
SMP 4
Model with mathematics.
SMP 5
Use appropriate tools strategically.
SMP 6
Attend to precision.
SMP 7
Look for and make use of structure.
SMP 8
Look for and express regularity in repeated reasoning.
Standards for Mathematical Content
[a] 7.G.A
Draw, construct, and describe geometrical figures and describe the relationships between them.
7.G.1
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and
reproducing a scale drawing at a different scale.
7.G.2
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing
triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or
no triangle.
7.G.3
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms
and right rectangular pyramids.
[a] 7.G.B
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the
relationship between the circumference and area of a circle.
7.G.5
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple
equations for an unknown angle in a figure.
7.G.6
Solve real-world and mathematical problems involving area, volume and surface area of two and three-dimensional objects composed
of triangles, quadrilaterals, polygons, cubes, and right prisms.
Key: [m] = major clusters; [s] = supporting clusters; [a] = additional clusters
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
3
Posted 2/1/17
Unit 5 Geometry
Math 7
Evidence of Learning – Stage 2
Assessment Evidence
Unit Assessment
Claim 1: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.
Concepts and skills that may be assessed in Claim1:
7.G.A
• The student creates scale drawings.
• The student solves problems involving scale drawings using proportional reasoning.
• The student draws, constructs, or describes geometric shapes given certain conditions.
• The student describes a two-dimensional figure resulting from slicing a three-dimensional figure by a plane.
7.G.B
• The student solves real-life and mathematical problems for the circumference and area of circles.
• The student solves real-life and mathematical problems involving angle measure including problems requiring writing and solving equations.
• The student solves real-life and mathematical problems for the area of two-dimensional objects composed of polygons.
• The student solves real-life and mathematical problems for the volume and surface area of three-dimensional objects composed of right prisms and
cubes.
Claim 2: Students can solve a range of wellposed problems in pure and applied
mathematics, making productive use of
knowledge and problem-solving strategies.
Standard clusters that may be assessed in
Claim 2:
•
7.G.A
•
7.G.B
Claim 3: The student can clearly and precisely
construct viable arguments to support their own
reasoning and critique the reasoning of others.
Standard clusters that may be assessed in
Claim 3:
•
NONE
Claim 4: The student can analyze complex,
real-world scenarios and can construct and use
mathematical models to interpret and solve
problems.
Standard clusters that may be assessed in
Claim 4:
•
7.G.A
•
7.G.B
Other Evidence
Formative Assessment Opportunities
•
•
•
•
•
•
•
•
•
Informal teacher observations
Checking for understanding using active participation strategies
Exit slips/summaries
Modeling Lessons (SMP 4)
Tasks
Formative Assessment Lessons (FAL)
Quizzes / Chapter Tests
Big Ideas Math Performance Tasks
SBAC Interim Assessment Blocks
Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website – “M” Mathematics – Curriculum Documents
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
4
Posted 2/1/17
Unit 5 Geometry
Math 7
Learning Plan – Stage 3
Days
Learning Target
I will explore
geometry by
participating in the
Opening Task.
1 day
I will apply facts
about angle
relationships
by…
2-3
days
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 2
Expectations
(Activities and Lessons)
OPENING TASK – Candle Box
Pass out the activity, Candle Box, for students to work
independently. Then have students work as a group to
compare and improve their drawings. After working as
a team, facilitate a large group discussion about their
drawings. If time permits, show student-work
examples that are included so that your students can
analyze them. Display only the drawings to have
students critique the reasoning of others. This task is a
gateway into the entire unit of geometry. (SMP 1, 3)
• Identifying adjacent, vertical, complementary, and
supplementary angles.
• Writing and solving equations to find unknown angle
measures using properties of adjacent and vertical
angles.
• Writing and solving equations to find unknown angle
measures using properties of complementary and
supplementary angles.
• Writing and solving equations to find unknown
angles in more complex figures that combine
adjacent, vertical, complementary, and
supplementary angles.
• Answering questions such as…
o Explain why two angles cannot be vertical and
adjacent at the same time.
o Ariana claims that two angles are complementary
only if they are adjacent and make a right angle.
Is Ariana correct? Justify your reasoning.
o How can you use angle pairs to solve problems?
o How do you use vertical angles to solve problems
with figures?
o Synergy Item Bank: Item ID 61644, 71305
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
5
• Section 7.1
(Activities 2 and 3;
Examples 1, 2, and 3)
• Section 7.2
(Activities 1 and 2;
Examples 1, 2, and 3)
Curriculum Intranet
Conceptual Understanding:
• Candle Box
Conceptual Understanding:
• Vertical Angles Dynamic
Tool
• Complementary Angles
Dynamic Tool
• Supplementary Angles
Dynamic Tool
Procedural Skills and
Fluency:
• Finding Unknown Angles
Video
• Solving for Unknown Angles
Using Equations
(EngageNY)
• Flipbook: Angle
Relationships
• Complementary Angles
Interactive
Application:
• Truss Bridge Performance
Task
Posted 2/1/17
Unit 5 Geometry
Math 7
Learning Plan – Stage 3
Days
Learning Target
I will draw
geometric shapes
with given
conditions by…
•
•
•
3-4
days
•
I will solve problems
involving scale
drawings by…
• Using proportional reasoning to compute actual
lengths and areas from a scale drawing involving
geometric figures. (SMP 6)
• Determining the scale of a drawing given the ratios
of lengths in the drawing and the actual dimensions.
• Reproducing a scale drawing at a different scale.
(SMP 5)
• Answering questions such as…
o How are scale drawings used in real-life?
o Explain how you can find an actual measure
when you know a measure on a scale drawing
and you know the scale. (SMP 3)
o How do proportions relate to a scale drawing?
o How do you draw in different scales?
I will check my
understanding of
geometry by
participating in the
FAL.
FORMATIVE ASSESSMENT LESSON
(choose 1)
• Drawing to Scale: A Garden
(SMP 1, 2, 3, 4, 5, 6, 8)
• Describing and Defining Triangles
(SMP 1, 2, 3, 5, 6, 7, 8)
3-4
days
2-3
days
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 2
Expectations
(Activities and Lessons)
Using freehand, ruler and protractor, or geometric
• What You Learned
software. (SMP 5, 6)
Before (p. 269)
Constructing triangles and quadrilaterals with given
• Section 7.3
side lengths and angle measures. (SMP 6)
(Activities 1 and 3;
Examples 2 and 3)
Justifying whether a triangle is unique, if you can
draw more than one triangle, or if no such triangle
• Section 7.4
exists given such conditions. (SMP 3)
(Example 3)
Answering questions such as…
o Can a triangle be formed by three segments of
any side lengths? Why or why not?
o Given three segments with side lengths that form
a triangle, do you get a unique triangle or more
than one triangle?
o How many different triangles can be drawn given
two angle measures? Explain. (SMP 3)
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
6
• Section 7.5
(Activities 1, 2, 3, and 4;
Examples 1, 2, 3, and
4)
• STEM Video: Matte
Shots in Film
Curriculum Intranet
Conceptual Understanding:
• Constructing a Triangle
Given Three Sides
• Linkage-Strip Constructions
Procedural Skills and
Fluency:
• Drawing Geometric Shapes
(EngageNY)
• Drawing Triangles
(EngageNY)
Application:
• Ladybug Walk Task
Application:
• Photographs Task
• Architecture Performance
Task
• Rescaling Washington Park
Task
• STEM Performance Task:
Matte Artist
• Modeling: How Much Bigger
Should They Make
Zoolander’s School?
(SMP 4)
Posted 2/1/17
Unit 5 Geometry
Math 7
Learning Plan – Stage 3
Days
Learning Target
I will explore circles
by …
•
•
•
•
•
3-4
days
I will find the area of
composite figures
and surface area of
composite solids
by…
4-5
days
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 2
Expectations
(Activities and Lessons)
Investigating the ratio between circumference and
• Section 8.1
(Activities 1 and 2;
diameter known as π . (SMP 8)
Examples 1, 2, and 3)
Discovering the formulas for circumference and
• Section 8.2
area.
(Example 3)
Applying the formulas for circumference and area to
• STEM Video: Track and
solve real-life and mathematical problems. (SMP 2)
Field
Finding the relationship between circumference and
• Section 8.3
area.
(Activities 1 and 2;
Answering questions such as…
Examples 1 and 3)
o Describe the relationship between the distance
around a circle and the distance across the
center of the circle.
o How does the circumference of a circle relate to
its area?
o Why would it be useful to find the circumference
of a circle? Connect it to a real-life scenario.
o Synergy Item Bank: Item ID 46763, 46764
• Decomposing into triangles, quadrilaterals, and
circles, using known area formulas and adding them
to find the total area. (SMP 7)
• Reviewing how to find surface area of prisms and
pyramids by applying these procedures to find the
surface area of composite solids.
• Finding surface area of cylinders.
• Solving real-life and mathematical problems.
• Answering questions such as…
o Why are you not able to use one simple formula
to find the area of a composite figure?
o Can you decompose a composite figure only one
way?
o Explain how to find the surface area of a
composite solid. (SMP 3)
o Describe a scenario where you would need to
find the area of a composite figure.
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
7
• Section 8.4
(Activities 1 and 3;
Examples 1, 2, and 3)
• Section 9.2
(Activities 2 and 3;
Exercises 14 -17)
• Section 9.3
(Activities 2;
Examples 1, 2, and 3)
Curriculum Intranet
Conceptual Understanding:
• myPD Course #3274:
Discovering Pi
• Circumference of a Circle
Task
Procedural Skills and
Fluency:
• Formulas for a Circle Video
Application:
• Eight Circles Task
• Historic Bicycle Task
• Hiking Performance Task
• Modeling: How Much Purple
Ribbon Will You Need?
(SMP 4)
• Modeling: Volcano (SMP 4)
• Modeling: Rolling Tires
(SMP 4)
Procedural Skills and
Fluency:
• Designs Task
• Surface Area of Composite
Figures (EngageNY)
Application:
• Stained Glass Task
• Parallelogram Task
• Winter Hat Task
Posted 2/1/17
Unit 5 Geometry
Math 7
Learning Plan – Stage 3
Days
Learning Target
I will explore volume
of composite solids
by …
•
•
2-3
days
I will describe crosssections of three
dimensional figures
by …
2 days
•
•
•
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 2
Expectations
(Activities and Lessons)
Reviewing how to find volume of right prisms.
• Section 9.4
(Activities 4;
Finding volume of pyramids.
Examples 1 and 2)
Decomposing into right prisms and pyramids, finding
• STEM Video: Paper
each individual solid’s volume, and adding them to
Measurements
find the total volume. (SMP 7)
• Section 9.5
Solving real-life and mathematical problems.
(Activities 1-use
Answering questions such as…
GeoSolids; and 4;
o Can you think of some geometric solids for which
Examples 1 and 2)
the formula V = Bh would not apply? Why?
o Compare and contrast the formulas for volume of
prisms and pyramids.
o How do you find the volume of a figure made up
of prisms and pyramids?
• Slicing models and observing the exposed face.
(SMP 5)
• Using technology to display the animation of a plane
cutting through a solid. (SMP 5)
• Visualizing the different cross-sections of the same
solid using parallel, perpendicular, and neither
parallel nor perpendicular plane intersections to the
base of the solid. (SMP 7, 8)
• Answering questions such as …
o How are cross-sections of three-dimensional
figures different from faces of three-dimensional
figures? How are they similar?
o Which cross-sections are easier to visualize than
others? Why?
o Describe a profession that might slice a threedimensional figure to use cross-sections. How
would they use it?
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
8
• Extension 9.5
(Examples 1 and 2)
Curriculum Intranet
Conceptual Understanding:
• How Many Pyramids Does It
Take To Fill a Prism?
(Task #1 and Task #2)
Procedural Skills and
Fluency:
• Volume of Composite
Three-Dimensional Objects
(EngageNY)
Application:
• A Drink Carton Task
• Boxes Task
Conceptual Understanding:
• Cross Sections of a Cube
Interactive
• Slicing with Modeling Dough
• Slicing Three Dimensional
Figures Video
Application:
• Slicing Puzzles
Performance Task
• Cube Ninjas!
Posted 2/1/17
Unit 5 Geometry
Math 7
Learning Plan – Stage 3
Days
Learning Target
I will prepare for the
unit assessment on
geometry by…
1 day
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 2
Expectations
(Activities and Lessons)
• Incorporating the Standards for Mathematical
• Ch. 7 Review
Practice (SMPs) along with the content standards to
(p. 307 – 309)
review the unit.
• Ch. 8 Review
(p.345 – 347)
• Ch. 9 Review
(p.391 – 393)
1 day
Curriculum Intranet
Application:
• Which is Bigger? Task
• Trough Performance Task
Unit Assessment
Synergy: 2016-17 Math 7 Unit 5
or
LBUSD Math Intranet/Assessment
At this point, all standards addressed in the Math 7 SBAC Interim Assessment Block – Geometry and Mathematics Performance Task have been
covered.
These blocks may now be administered.
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
9
Posted 2/1/17