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Course: 7th grade Mathematics
Unit: Unit 4: Exploring Our World Through Geometry
Unit Length: 56 days (45 minute periods) / 28 days (80 minute periods)
Unit Overview: The study of Geometry was born in Ancient Greece, where mathematics was thought to be in
everything from music to art to the governing of the universe. Plato, an ancient philosopher and teacher, had the
statement, “Let no man ignorant of geometry enter here,” placed at the entrance of his school. This illustrates the
importance of the study of shapes and logic during that era. While working through this unit, students will build
from prior knowledge to connect to real world applications using geometric shapes and solids.
Next Generation Content Standards and Objectives:
M.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. (NxG
M.7.G.1 and CCSS M.7.G.1)
M.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. (NxG
M.7.G.2 and CCSS M.7.G.2)
M.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. (NxG M.7.G.3 and
CCSS M.7.G.3)
M.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. (NxG M.7.G.4 and CCSS M.7.G.4)
M.7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. (NxG M.7.G.5
and CCSS M.7.G.5)
M.7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of
two-and-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right
prisms. (NxG M.7.G.6 and CCSS M.7.G.6)
Standards for Mathematical Practices:
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning.
Driving question: How does geometry play an important part in the world around us?
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The students will know:
 The students will be able to differentiate between the terms: scale and scale factor.
 The students will be able to describe what happens to the area of figures when they are
enlarged or reduced.
 The students will know the sum of the angles of any triangle equals 180 degrees.
 The students will know the sum of two side lengths of any triangle will be greater than the
third side.
 The students will know that every three-dimensional solid can be cut to create a twodimensional cross section.
 The students will have an understanding of the derivation of pi in relation to the
circumference and diameter of circles.
 The students will have an understanding of the derivation of the circle area formula and use
the formula to find different missing elements of circles.
 The students will be able to name the various angles formed and their relationships when
two parallel lines are cut by a transversal.
 The students will understand the derivation of the surface area formula.
 The students will have an understanding of the derivation of the volume formula.
The students will do:
 Compute the actual length of a figure from a scale drawing.
 Compute the actual area of a figure from a scale drawing.
 Apply a scale from one drawing to create a second scale for that drawing.
 Solve problems involving scale drawings of geometric figures.
 Construct a triangle (freehand, with ruler and protractor, and technology) given three angle
measures.
 Construct a triangle (freehand, with ruler and protractor, and technology) given three side
measures.
 Construct a geometric shape given side lengths /angle measures.
 Describe when angle measures determine a triangle (given angles equal 180°) or no triangle
(given angles are greater or less than 180°).
 Describe when side measures determine a unique triangle (a+b>c) or no triangle (a+b ≤ c).
 Define a two-dimensional cross section that results from slicing a right rectangular prism
vertically and horizontally.
 Define a two-dimensional cross section that results from slicing a right rectangular pyramid
vertically and horizontally.
 Derive the relationship between the circumference and area of a circle.
 Solve problems utilizing the circumference formula.
 Solve problems utilizing the area of a circle formula.
 Define supplementary, complementary, vertical, and adjacent angles.
 Solve for an unknown angle in a figure utilizing definitions of supplementary,
WVU K12 Partnerships Unit Overview Construction Tool

complementary, vertical, and adjacent angles.
Solve problems using two- and three-dimensional objects from real world situations
o Calculating the area
o Calculating the surface area
o Calculating the volume
Course: Math 7
Unit: 4
Lesson: Exploring Our World Through Geometry
Video Title: Math 7, Unit 4: Exploring Our World Through Geometry
Video Script:
Video Display:
WVU K12 Partnerships Unit Overview Construction Tool
Unit Four is based upon the following
driving questions:
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How does geometry play an
important part in the world
around us?
Why are scale drawings
necessary?
How can you construct a
triangle with given
conditions?
What happens when we cut
vertically and horizontally
through sections of
geometric solids?
Can you use the area of a
circle to find the
circumference?
Can you use the
circumference of a circle to
find the area?
What relationships can be
determined by the angles
formed when parallel lines
are cut by a transversal?
What is the difference
between area and surface
area?
What is the relationship
between surface area and
volume?
The study of Geometry was born in
Ancient Greece, where mathematics
was thought to be embedded in
everything from music to art to the
governing of the universe. Plato, an
ancient philosopher and teacher, had
the statement, “Let no man ignorant of
geometry enter here,” placed at the
entrance of his school. This illustrates
the importance of the study of shapes
and logic during that era. While
WVU K12 Partnerships Unit Overview Construction Tool
working through this unit, students will
build from prior knowledge to connect
to real world applications using
geometric shapes and solids.
WVU K12 Partnerships Unit Overview Construction Tool
Geometry is used daily by almost
everyone. It requires us to explore
spacial sense and geometric reasoning. In
this unit, you will see how the concepts of
geometry are used in everyday life.
WVU K12 Partnerships Unit Overview Construction Tool
In this unit, you will focus on two- and
three – dimensional shapes, use logic,
abstract thinking, and problem solving
skills as you play the role of an architect.
Why do I have to learn this? When am I
ever going to use this in real life?
Geometry is linked to many other topics,
such as measurement, volume, and area.
Geometry can be found everywhere:
architecture, astronomy, art, cars,
engineering, land surveys, nature, sports,
and machines.
WVU K12 Partnerships Unit Overview Construction Tool
The key performance tasks for this unit
include:
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Creating scale drawings
(enlarging and shrinking)
Creating triangles based on
given measurements
Identifying cross sections of
right rectangular prisms and
right rectangular pyramids
Calculating the area of a
circle using the
circumference
Calculating the
circumference of a circle
using the area
Calculating the measures of
complementary and
supplementary angles
Calculating the area, surface
area, and volume of two- and
three- dimensional objects