Download TCI_MathUnitPlan_Unit 7_Geometry

Gary School Community Corporation
Mathematics Department Unit Document
Unit Number: 7
Grade: 7
Unit Name: Geometry
Duration of Unit: 20 - 25 Days
UNIT FOCUS
Standards for Mathematical Content
Standard Emphasis
Critical
Important
Additional
7.GM.5: Understand the formulas for area and circumference of a circle ********
and use them to solve real-world and other mathematical problems;
give an informal derivation of the relationship between circumference
and area of a circle
7.GM.6: Solve real-world and other mathematical problems involving ********
volume of cylinders and three-dimensional objects composed of right
rectangular prisms.
7. GM.2: Identify and describe similarity relationships of polygons
including the angle-angle criterion for similar triangles, and solve
problems involving similarity.
********
7.GM.4: Solve real-world and other mathematical problems that
involve vertical, adjacent, complementary, and supplementary angles.
********
7.GM.7: Construct nets for right rectangular prisms and cylinders and
use the nets to compute the surface area; apply this technique to solve
real-world and other mathematical problems.
********
7.GM.1: Draw triangles (freehand, with ruler and protractor, and using
technology) with given conditions from three measures of angles or
sides, and notice when the conditions determine a unique triangle,
more than one triangle, or no triangle
Mathematical Process Standards:
PS.1: Make sense of problems and persevere in solving them.
********
PS.2: Reason abstractly and quantitatively
PS.3: Construct viable arguments and critique the reasoning of others
PS.4: Model with mathematics
PS.5: Use appropriate tools strategically
PS.6: Attend to Precision
PS.7: Look for and make use of structure
PS.8: Look for and express regularity in repeated reasoning
Vertical Articulation documents for K – 2, 3 – 5, and 6 – 8 can be found at:
http://www.doe.in.gov/standards/mathematics (scroll to bottom)
********
Big Ideas/Goals
Essential Questions/
Learning Targets
“I Can” Statements
Students will solve real-life and How can the formulas for area
mathematical problems involving and circumference of a circle be
angle measure, area, surface area, derived and used to solve
and volume.
problems?
I can derive the formula for the
circumference of a circle.
I can derive the formula for the area of
a circle.
I can describe the relationship
between the circumference and area
of a circle.
I can use the formula for the
circumference of a circle to solve
problems.
I can use the formula for the area of a
circle to solve problems.
I can determine the radius or diameter
of a circle when the area or
circumference is known.
Students will solve real-life and How can area, surface area, and
mathematical problems involving volume be used to solve
angle measure, area, surface area, problems?
and volume.
I can solve mathematical and realworld problems involving area.
I can solve mathematical and realworld problems involving volume.
I can solve mathematical and realworld problems involving surface area.
Students will understand
congruence and similarity using
physical models, transparencies,
or geometry software.
I can use exploration and deductive
reasoning to determine relationships
that exists between interior and
exterior sums of triangles.
I can use exploration and deductive
reasoning to determine relationships
that exists between angles created
when parallel lines are cut by a
transversal.
I can use exploration and deductive
reasoning to determine relationships
that exists between the angle-angle
criterions for similarity of triangles.
How can exploration be used to
determine the relationships that
exist between interior and
exterior sums of triangles? How
can exploration be used to
determine the relationships that
exist between angles created
when parallel lines are cut by a
transversal? How can
explorations be used to
determine the relationships that
exist between the angle-angle
criterion for similarity of
triangles?
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Students will understand
concepts of angle and measure
angles (decomposing and
composing).
How can the properties of angles I can state relationships between
supplementary, complementary,
be used to solve multi-step
vertical, and adjacent angles.
problems?
Distinguish between 2D and 3D
shapes and how does a 3D shape
appear in 2D form (nets) and
surface area.
How can I identify a 3D shape by I can use nets of rectangles and
seeing its net?
triangles to find the surface area
How can I calculate the surface of three-dimensional figures.
area of a 3D shape from viewing
its net?
I can use facts about angles in a multistep problem to write simple
equations for an unknown angle in a
figure.
I can solve simple equations for an
unknown angle in a figure.
I can recognize than angle can be
divided into smaller angles.
I can solve addition and subtraction
equations to find unknown angle
measurements on a diagram.
I can find an angle measure by adding
the measurements of the smaller
angles that make up the larger angle.
I can find an angle measure by
subtracting the measurements of the
smaller angle from the larger angle.
Students will draw, construct, and How do the given conditions
describe geometrical figures and affect the drawing of a geometric
describe the relationships
shape?
between them.
Students will solve real-life and
mathematical problems involving
angle measure, area, surface area,
and volume.
I can draw geometric shapes from
given conditions using multiple
methods.
I can construct triangles from three
measures of angles.
I can construct triangles from three
measures of sides.
I can determine if the given measures
of angles or sides produce a unique
triangle, more than one triangle, or no
triangle.
UNIT ASSESSMENT TIME LINE
Beginning of Unit – Pre-Assessment
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Assessment Name: Grade 7 Pre-assessment Geometry
Assessment Type: Pre-assessment Geometry
Assessment Standards: 7.GM.1, 7.GM.2, 7.GM.4, 7.GM.5, 7.GM.6 & 7.GM.7
Assessment Description: Understand the difference between 2D and 3D shapes and calculate the
perimeter, area and volume of each of the shapes. Also, understand Congruence and Similarity with
angles, triangles and other polygons.
Throughout the Unit – Formative Assessment
Assessment Name: Congruence & Similarity
Assessment Type: Performance Assessment
Assessing Standards: 7.GM.1 & 7.GM.2
Assessment Description: Students will draw, construct, and describe geometrical figures and
describe the relationships between them. Students will understand congruence and similarity using
physical models, transparencies, or geometry software.
Assessment Name: Angles, Parallel lines, Circumference and Area of Circles
Assessment Type: Performance Assessment - Tasks
Assessing Standards: 7.GM.4 & 7.GM.5
Assessment Description: Students will understand concepts of angle and measure angles
(decomposing and composing). Derive and the formulas for area and circumference of a circle in real
world problems.
Assessment Name: 2D and 3D shapes with Area and Volume Real world Problems
Assessment Type: Performance Assessment - Tasks
Assessing Standards: 7.GM.6 & 7.GM.7
Assessment Description: Students will solve real-life and mathematical problems involving angle
measure, area, surface area, and volume.
End of Unit – Summative Assessments
Assessment Name: Grade 7 Summative Assessment Geometry
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Assessment Type: Benchmark Tests or Sample Standardized Assessment
Assessing Standards: 7.GM.1, 7.GM.2, 7.GM.4, 7.GM.5, 7.GM.6 & 7.GM.7
Assessment Description: Understand the difference between 2D and 3D shapes and calculate the
perimeter, area and volume of each of the shapes. Also, understand Congruence and Similarity with
angles, triangles and other polygons.
PLAN FOR INSTRUCTION
Unit Vocabulary
Key terms are those that are newly introduced and explicitly taught with expectation of student
mastery by end of unit. Prerequisite terms are those with which students have previous
experience and are foundational terms to use for differentiation.
Key Terms for Unit
scale
scale factor
scale drawings
area
polygon
triangle
quadrilateral
angle sum
exterior angle
transversal
alternate interior angles
alternate exterior angles
corresponding angles
angle-angle criterion
interior angle
angle
supplementary angles
complementary angles
vertical angles
adjacent angles
equation
Circumference
Area (circle)
surface area
Prerequisite Math Terms
Points
Lines
Planes
Shapes
Angle
Degrees
Parallel
Perpendicular
2-Dimensional
3-Dimensional
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volume
area
area (regular polygon)
area (quadrilateral)
area (triangle)
surface area
Surface area (right prism)
Cube
Prisms
Volume (cube)
Right prism volume (right prism)
nets
cylinders
right rectangular prisms
Unit Resources/Notes
Include district and supplemental resources for use in weekly planning
Pre-Assessment – Geometry iSTEP or Acuity Strands for Geometry
Formative Assessment 1 - http://www.map.mathshell.org/tasks.php?collection=9&unit=HA04,
http://www.map.mathshell.org/tasks.php?collection=9&unit=HE05,
http://www.map.mathshell.org/tasks.php?collection=9&unit=HE09,
Formative Assessment 2 – Performance Task from any of the areas for 7.G.4 or 7.G.5
(http://www.insidemathematics.org/common-core-resources/mathematical-contentstandards/standards-by-grade/7th-grade)
Assessment Items:
Illustrative Mathematics: Designs
Illustrative Mathematics: Eight Circles
Illustrative Mathematics: Stained Glass
Illustrative Mathematics: The Circumference of a Circle and the Area of the Region it
Encloses
Illustrative Mathematics: Measuring the area of a circle
Formative Assessment 3 – Use 7.G.6 for Performance Tasks
(http://www.insidemathematics.org/common-core-resources/mathematical-contentstandards/standards-by-grade/7th-grade),
Illustrative Mathematics: Sand under the swing set
Summative Assessment – Geometry iSTEP or Acuity Strands for Geometry.
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More resources - https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_7_7thGrade_Unit5.pdf,
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry
https://www.engageny.org/resource/grade-7-mathematics-module-1-topic-lesson-1
https://www.engageny.org/resource/grade-7-mathematics
Targeted Process Standards for this Unit
PS.1: Make sense of problems and persevere in solving them
Mathematically proficient students start by explaining to themselves the meaning of a problem and
looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They
make conjectures about the form and meaning of the solution and plan a solution pathway, rather than
simply jumping into a solution attempt. They consider analogous problems and try special cases and
simpler forms of the original problem in order to gain insight into its solution. They monitor and
evaluate their progress and change course if necessary. Mathematically proficient students check their
answers to problems using a different method, and they continually ask themselves, “Does this make
sense?” and "Is my answer reasonable?" They understand the approaches of others to solving complex
problems and identify correspondences between different approaches. Mathematically proficient
students understand how mathematical ideas interconnect and build on one another to produce a
coherent whole.
PS.2: Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem
situations. They bring two complementary abilities to bear on problems involving quantitative
relationships: the ability to decontextualize—to abstract a given situation and represent it
symbolically and manipulate the representing symbols as if they have a life of their own, without
necessarily attending to their referents—and the ability to contextualize, to pause as needed during
the manipulation process in order to probe into the referents for the symbols involved. Quantitative
reasoning entails habits of creating a coherent representation of the problem at hand; considering the
units involved; attending to the meaning of quantities, not just how to compute them; and knowing
and flexibly using different properties of operations and objects.
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PS.3: Construct viable arguments and critique the reasoning of others
Mathematically proficient students understand and use stated assumptions, definitions, and
previously established results in constructing arguments. They make conjectures and build a logical
progression of statements to explore the truth of their conjectures. They analyze situations by
breaking them into cases and recognize and use counterexamples. They organize their mathematical
thinking, justify their conclusions and communicate them to others, and respond to the arguments of
others. They reason inductively about data, making plausible arguments that take into account the
context from which the data arose. Mathematically proficient students are also able to compare the
effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is
flawed, and—if there is a flaw in an argument—explain what it is. They justify whether a given
statement is true always, sometimes, or never. Mathematically proficient students participate and
collaborate in a mathematics community. They listen to or read the arguments of others, decide
whether they make sense, and ask useful questions to clarify or improve the arguments.
PS.4: Model with mathematics
Mathematically proficient students apply the mathematics they know to solve problems arising in
everyday life, society, and the workplace using a variety of appropriate strategies. They create and use
a variety of representations to solve problems and to organize and communicate mathematical ideas.
Mathematically proficient students apply what they know and are comfortable making assumptions
and approximations to simplify a complicated situation, realizing that these may need revision later.
They are able to identify important quantities in a practical situation and map their relationships using
such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They analyze those
relationships mathematically to draw conclusions. They routinely interpret their mathematical results
in the context of the situation and reflect on whether the results make sense, possibly improving the
model if it has not served its purpose.
PS.5: Use appropriate Tools Strategically
Mathematically proficient students consider the available tools when solving a mathematical problem.
These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a
spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.
Proficient students are sufficiently familiar with tools appropriate for their grade or course to make
sound decisions about when each of these tools might be helpful, recognizing both the insight to be
gained and their limitations. For example, mathematically proficient high school students analyze
graphs of functions and solutions generated using a graphing calculator. They detect possible errors
by strategically using estimation and other mathematical knowledge. When making mathematical
models, they know that technology can enable them to visualize the results of varying assumptions,
explore consequences, and compare predictions with data. Mathematically proficient students at
various grade levels are able to identify relevant external mathematical resources, such as digital
content located on a website, and use them to pose or solve problems. They are able to use
technological tools to explore and deepen their understanding of concepts.
PS.6: Attend to precision
Mathematically proficient students communicate precisely to others. They use clear definitions,
including correct mathematical language, in discussion with others and in their own reasoning. They
state the meaning of the symbols they choose, including using the equal sign consistently and
appropriately. They express solutions clearly and logically by using the appropriate mathematical
terms and notation. They specify units of measure and label axes to clarify the correspondence with
quantities in a problem. They calculate accurately and efficiently and check the validity of their results
in the context of the problem. They express numerical answers with a degree of precision appropriate
for the problem context.
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PS.7: Look for and make use of structure
Mathematically proficient students look closely to discern a pattern or structure. They step back for an
overview and shift perspective. They recognize and use properties of operations and equality. They
organize and classify geometric shapes based on their attributes. They see expressions, equations, and
geometric figures as single objects or as being composed of several objects.
PS.8: Look for and express regularity in repeated reasoning
Mathematically proficient students notice if calculations are repeated and look for general methods
and shortcuts. They notice regularity in mathematical problems and their work to create a rule or
formula. Mathematically proficient students maintain oversight of the process, while attending to the
details as they solve a problem. They continually evaluate the reasonableness of their intermediate
results.
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