7th GRADE MATH UNIT 4: Geometry
Unit Description/ Topic Length: This 7-week unit concentrates on the concept of geometry and
measurement. It includes solving problems involving scale drawings and constructing triangles from
three measures of angles or sides. In this unit, students are also expected to discover relationships
between angles and use them to solve multi-step problems. In addition, it involves knowing how
formulas are derived and applied in solving real-world math problems, which deal with area, volume
and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals,
polygons, cubes and right prisms.
Essential Question: How are geometric shapes and formulas used in the real world?
Big Ideas/Enduring Understandings
1. Similarity and Proportionality between
Shapes.
2. Relationships between 2-dimensional
and 3-dimensional figures
3. Derivation of Formulas and their
application in solving real-world and
mathematical problems
Guiding Questions:
1. What is proportion?
2. How are similar figures used in real life
situations?
3. What is a 2-dimensional and 3-dimensional
figures?
4. How are formulas derived?
5. How are formulas used in the real world.
6. What are angle pairs?
7. How are equations used in finding the
unknown angle in an angle pair?
4. Equations can be used to solve the
missing angle in an angle pair.
NYS Common Core Standards for Mathematics Assessed:
8.EE
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.
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.
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Content
Skills
1. Proportions and similarity
1. Set up proportions
2. Finding area, volume and surface area
2. Use proportions and scale drawings to
of 2-dimensional and 3-dimensional
find missing measurements
figures
3. Estimate the height of objects using
3. Identifying angle pairs
measurement device
4. Drawing geometric shapes using given
4. Use of models to identify the
conditions
dimensions of a figure.
5.
Identifying 2d and 3d figures
5. Finding the unknown angle using
6. Use formulas to compute for area,
equations
volume and surface area
7. Writing and solving equations
Vocabulary/ Key Terms
proportion, scale drawing, similar figures, 2-dimensional, 3-dimensional, area, volume
surface area, complementary angles, supplementary angles, vertical angles, adjacent angles,
circle, polygons, cube, right prisms
ASSESSMENT EVIDENCE
Diagnostic and Pre/Post Assessments:
Students will respond to the essential question at the start of the unit and at the end of the
unit.(pre/post)
Formative Assessment Tasks:
1.
2.
3.
4.
Discussions
Exit slips
Homework
Conferencing
Summative Assessments:
1.
2.
3.
4.
Quizzes (graded)
Performance Tasks
interim assessments
unit test
TEACHING PLAN
Teaching and Learning Activities:
1. 1. Students use scale factor to enlarge a picture/photograph of themselves or someone else.
(7.G.1)
2. Students find the surface area of an orange by changing a 3-d shape into a 2-d shape. (7.G.3,
7.G.4)
3. Students investigate the relationship between the surface area of a leaf and its volume and
summarize their findings in a report. (7.G.6)
4. Students draw a triangle where one angle is twice as large as another and measure the third
angle. What is the relationship between the three angles? (7.G.2)
5. Students find all the possible angle combinations that will form a triangle given the
following angles: 0°, 10°, 15°, 30°, 35°, 65°, 70°, 75°, 80°, and 100°. (7.G.2)
6. Students precisely draw all possible triangles using a protractor and ruler. (7.G.2)
7. Students use patty paper or a reflecting device to explore relationships among the measures
of angles formed by intersecting lines. (7.G.2)
8. Students draw two intersecting lines and measure one angle and find the measures of the
others without measuring. (7.G.2)
9. Students provide explicit examples of supplementary, complementary, vertical and adjacent
angles and demonstrate their relationships. (7.G.2)
10. Students write and solve an equation to find the measure of angle x. (7.G.2)
Teaching:
7.G.1: Introduce the concepts of ratios, proportions, and scale factoring by posing questions on
perimeter and area.
7.G.2: Introduce the concept of polygons and review triangles and quadrilaterals.
7.G.3: Introduce the concepts of 2 dimensional and 3 dimensional shapes and pose the following
question to students: What is the difference between 2-d and 3-d when calculating area and volume?
7.G.4: Introduce the concepts of circle and the parts of a circle and pose the following questions:
What is the relationship between the radius and diameter of a circle? Does size change the
relationship between the diameter and circumference of a circle?
7.G.5: Introduce the concepts of right, acute, obtuse and straight angles and discuss the different
types of triangle. Ask the following questions. What is the total measure of supplementary angles?
What is the total measure of complementary angles?
7.G.6: Review the concepts of polygons in 2-d and 3-d figures and show students examples of 2-d
and 3-d shapes and how to apply formulas to find area, volume and surface area.
Materials Needed: Impact book, Skills Intervention Workbook, Quick Review book, ruler,
Protractor, 3-dimensional shapes models
Web Resources:
NYC Common Core Library
http://schools.nyc.gov/Academics/CommonCoreLibrary/About/NY+State+and+CCLS.htm
*Unpacking the Math CCLS: Network Resource
http://www.projectpaced.com/index.html
Pedagogical Shifts demanded by the Common Core State Standards
http://engageny.org/wp-content/uploads/2012/08/common-core-shifts.pdf
Emphases in Common Core Standards for Mathematical Content
http://engageny.org/wp-content/uploads/2012/03/nys-math-emphases-k-8.pdf
New York State P-12 Common Core Learning Standards for Mathematics
http://www.p12.nysed.gov/ciai/common_core_standards/pdfdocs/nysp12cclsmath.pdf
CALENDAR
Time
Spent on
Standard
6 days
CCLS
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.
Topics To Assess
Materials/References
SIW: Skill 32, pp. 63-64



Definition of scale
drawing, scale
factor
Areas of
geometric figures
Reproduction of a
scale drawing at a
different scale
6 days
6 days
5 days
6 days
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 twodimensional figures that
result from slicing three
dimensional figures, as in
plane sections of right
rectangular prisms and right
rectangular pyramids.





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.





Construction of
triangles given 3
sides
Construction of
triangles given 3
angles
Construction of
triangles given 2
sides and an angle
Construction of
triangles given 2
angles and a side
Difference
between a 2d and
a 3d shapes.
Identify 2d shapes
that result from
slicing a 3d
figures
Definition of a
circle, its radius,
diameter, area
and
circumference.
Derive formulas
Solve word
problems using
formulas
Definition of
complementary,
supplementary,
vertical and adjacent
angles
Write and solve
simple equations for
an unknown angle in a
figure
Lesson 1.1 (Course 1)
Patterns in Geometry
P. 16
Lesson 2.3 (Course 3)
Constructions
Pp. 100-105
www.nymathstandards.pbworks.com
NYRS: pp. 187-192
Lesson 1.3 (Course 1)
Measure Around, pp. 44-47
Lesson 5.1
Surface Area and Volume, pp.
216-226
Lesson 5.2
Nets and Solids,pp. 228-239
Lesson 7.2 (Course 1)
Calculate Areas, pp. 419-421
Lesson 1.2 (Course 1)
Angles pp. 25-39
Lesson 2.2 (Course 3)
Angle Relationships, pp. 419-421
http://www.uen.org/Lessonplan/preview
.cgi?LPid=23373
[Angle Relationships]
http://www.uen.org/Lessonplan/preview
.cgi?LPid=20372
[Are you a Geometer? Examining
Angles]

6 days
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

Area of regular and
irregular figures
Surface area and
volume of 3d objects
composed of
polygons, cubes and
right prisms
Lesson 5.1
Surface Area and Volume, pp.
212-239
CRM: Leveled Lesson Resources, pp.
8-12
SIW: Skill 63: pp. 125–126.
QR: 6.6: Surface Area, pp. 324-326
NYRS: pp. 187-192
IYOW: p. 238, #20
QQ: p. 239 TG
IN&RJ: pp. 45-47