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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
7D
Big Idea(s)
What enduring understandings are
essential for application to new
situations within or beyond this
content?
Unit 4: Geometry
• Draw, construct and describe geometrical figures and describe
the relationships between them.
• Solve real-life and mathematical problems involving angle measure,
area, surface area, and volume.
Essential Question(s)
What questions will provoke and
sustain student engagement while
focusing learning?
How is the circumference of a circle used to derive the area of a
circle?
How are area and volume properties related?
How can I use a model to help me solve this problem?
Enduring Standard(s)
Which standards provide
endurance beyond the course,
leverage across multiple
disciplines, and readiness for the
next level?
Enduring Understandings
• Use freehand, ruler, protractor and technology to draw geometric
shapes with give conditions.
•Construct triangles from 3 measures of angles or sides.
•Solve real-world mathematical problems involving area, volume and
surface area of two-and three-dimensional objects composed of
triangles, quadrilaterals, polygons, cubes, and right prisms.
Standards for Mathematical Practice
*1. Make sense of problems and persevere in solving them.
Students make sense of the problems involving geometric
measurements (area, volume, surface area, etc.) through their
understanding of the relationships between these measurements.
They demonstrate this by choosing appropriate strategies for
solving problems involving real-world and mathematical situations.
2. Reason abstractly and quantitatively. Students represent a wide
variety of real world contexts through the use of real numbers and
variables when working with geometric figures. Students
contextualize to understand the meaning of the number or variable
as related to a geometric shape. Students must challenge
themselves to think of three dimensional shapes with only two
dimensional representations of them on paper in some cases.
3. Construct viable arguments and critique the reasoning of others.
Students are able to construct arguments using concrete referents
such as objects, drawings, diagrams, and actions. Such arguments
can make sense and be correct, even though they are not
generalized or made formal until later grades.
Curriculum and Instruction
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
4. Model with mathematics. Students are able to apply the
geometry concepts they know to solve problems arising in
everyday life, society and the workplace. This may include
applying area and surface of 2-dimensional figures to solve interior
design problems or surface area and volume of 3-dimensional
figures to solve architectural problems.
*5. Use appropriate tools strategically. Mathematically proficient
students consider available tools that might include concrete
models, a ruler, a protractor, or dynamic geometry software such
as virtual manipulatives and simulations. 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.
*6. Attend to precision. Students continue to refine their
mathematical communication skills by using clear and precise
language in their discussions with others and in their own reasoning.
Students determine quantities of side lengths represented with
variables, specify units of measure, and label geometric figures
accurately. Students use appropriate terminology when referring to
geometric figures.
*7. Look for and make use of structure. Mathematically proficient
students look closely to discern a pattern or structure. They
recognize the significance of an existing line in a geometric figure
and can use the strategy of drawing an auxiliary line for solving
problems. They can see complicated things as single objects or as
being composed of several objects.
8. Look for and express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are
repeated, and look both for general methods and for shortcuts.
Standards for Mathematical Content
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.
Curriculum and Instruction
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
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.
Supporting Standard(s)
Which related standards will be
incorporated to support and
enhance the enduring standards?
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.
Instructional Outcomes
What must students learn by the
end of the unit?
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
I can construct a scale drawing.
I can identify corresponding sides of similar figures.
I can solve problems using scale factor.
I can solve for missing lengths in similar figures.
I can classify and construct geometric figures with given conditions.
I can use a protractor and ruler to classify and construct triangles with
specified angles or sides.
I can describe two and three dimensional figures when sliced in plane
sections.
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
I can identify and define:
•
Radius, Diameter, Area, Circumference, Center, Chord, Pi
I can find the area and the circumference of a circle.
I can describe the relationship between the area and circumference
of a circle.
I can identify and define:
•
Supplementary, Complementary, Vertical, Adjacent
I can find the complement and supplement of an angle.
I can write and solve equations for angle measures.
I can find the area of a figure composed on triangles, quadrilaterals,
and polygons.
I can find the surface area of a figure composed of cubes and prisms.
I can find the volume of a prism.
Performance Expectations
What must students be able to do
by the end of the unit to
demonstrate their mastery of the
instructional outcomes?
Students who demonstrate understanding can…
•Given conditions, determine what and how many type(s) of triangles
are possible to construct.
•Describe the two-dimensional figures that result from slicing threedimensional figures.
•Identify and describe supplementary, complementary, vertical, and
adjacent angles.
•Use understandings of supplementary, complementary, vertical and
adjacent angles to write and solve equations.
•Explain (verbally and in writing) the relationships between the angles
formed by two intersecting lines.
Essential Vocabulary
adjacent angles - Two angles that share both a side and a vertex.
What vocabulary must students
know to understand and
communicate effectively about
this content?
angle - The union of two rays with a common endpoint, called the
vertex.
area - The number of square units that covers a shape or figure.
circle - A closed curve with all of its points in one plane and the same
distance from a fixed point, the center.
circumference - Distance around a circle; its perimeter.
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
complementary - Two angles whose sum is 90 degrees.
congruence - Two plane or solid figures are congruent if they have the
same size and shape.
cross-section - The intersection of a 3-dimensional body with a plane.
cubes - A solid figure with six square faces; EX: a die.
cylinder - A 3-D figure having two parallel bases that are congruent
circles; EX: a tube.
polygons - A closed plane figure made up of line segments that are
joined together.
quadrilateral - A polygon with 4 sides.
radius - A line segment drawn from the center of a circle to any point
on a circle; half the diameter.
right prisms - A prism which has bases aligned one directly above the
other and has lateral faces that are rectangles.
right rectangular prism -A 3-D figure with two congruent parallel bases
and parallelogram sides; EX: a box.
right rectangular pyramid - A polyhedron with a rectangular base and
all the other faces triangles meeting at a common vertex at the top
known as the apex. The apex (the top) of the pyramid is directly
above the center of the rectangular base.
scale drawing - A drawing that is a reduction or enlargement of the
original.
scale factor - A number which multiples some quantity; the ratio of
any two corresponding lengths in two similar geometric figures.
supplementary - Two angles are supplementary if their sum is 180
degrees.
surface area - For a three-dimensional figure, the sum of the areas of
all the faces.
triangle - A polygon with three sides.
Curriculum and Instruction
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 7
two-dimensional - Having the dimensions of length and width
unique - the only triangle possible
vertical angles - A pair of opposite angles that is formed by
intersecting lines.
volume - A measurement of space, or capacity.
Supporting Vocabulary
geometric constructions
pi
three-dimensional
Common Core Glossary
http://www.corestandards.org/Math/Content/mathematicsglossary/glossary
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Subject and Grade Level
Unit Title
Summative Assessment of
Learning
Mathematics 7D
Unit 4: Geometry
In what way will students meet the
performance expectations to
demonstrate mastery of the
standards?
Instructional Outcomes
How will the instructional outcomes
be sequenced into a
progression of learning?
Learning Activities
What well-designed progression of
learning tasks will intellectually
engage students
in challenging content?
Formal Formative Assessments
What is the evidence to show
students have learned the lesson
objective and are progressing
toward mastery of the instructional
outcomes?
Integration Standards
What standards from other
disciplines will enrich the learning
experiences for the students?
Resources
What resources will be utilized to
enhance student learning?
Curriculum and Instruction
Resources are hyperlinked under “Topic/Resource” links on the
Long Range Plan sheet.
2014-2015
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