

Unit 5 Geometry
and Measurement Grade
7 Math 

Unit
Length and Description: 32
days Unit
5 is designed to engage students in Geometry.
This unit has students drawing, constructing, and describing
geometrical figures and describing the relationships between them. The
constructions the students do in this unit will focus on triangles and
provide students the opportunity to formalize their understanding of what
conditions define a unique triangle, more than one triangle, or no triangle. Students also solve a variety of reallife
and mathematical problems involving angle measure, area, surface area, and
volume of two and threedimensional objects. They revisit unknown angles and
continue to use proportional reasoning as they revisit and analyze scale
drawings. This unit is the first time
the students have engaged in circles since 4th grade where they gained a
conceptual understanding of circles and their properties with an emphasis on
angle measures. Students will apply
their conceptual understanding of area and perimeter to circles, and will be
introduced to pi for the first time.
Students use the formulas for the area and circumference of a circle
to solve problems involving circles. Additionally, the focus of this unit is
on irregular figures which distinguish this unit from similar units on area,
volume, and surface area in previous courses. All two and threedimensional
objects used in this unit should be a composition of triangles,
quadrilaterals, polygons, cubes, and right prisms. This will require students
to be able to recognize and decompose the objects into pieces they can work
with. To support their work with irregular two and threedimensional
objects, students will slice three dimensional figures to describe the
resulting twodimensional figure. 

Standards: 7.G.A.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.A.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.A.3
Describe the
twodimensional figures that result from slicing threedimensional figures,
as in plane sections of right rectangular prisms and right rectangular
pyramids. 7.G.B.4 Know the formulas for the area and circumference of a circle
and solve problems; give an informal derivation of the relationship between
the circumference and area of a circle.
o
Standards
Clarification: Irrational numbers are
not introduced until the 8^{th} grade. An approximate value of pi can
be discovered by allowing the students to derive experimentally the formulas
for area and circumference. The approximations that are discovered should be
used for pi and the actual value of pi as an irrational number will be
discussed in the 8^{th} grade. 7.G.B.5 Use facts about supplementary, complementary, vertical, and
adjacent angles in a multistep problem to write and use them to solve simple
equations for an unknown angle in a figure. o
Standards
Clarification: Students will be
expected to write and solve equations for an unknown angle in a figure. This
provides an opportunity to reinforce students’ fluency in solving equations;
also, this unit provides an opportunity to model realworld situations
involving angles with equations and inequalities. The standards do not
explicitly address at any grade level the measure of a straight angle. It may
need to be discovered by applying the students’ understanding of right angles
and angle addition. 7.G.B.6 Solve realworld and
mathematical problems involving area, volume and surface area of two and
threedimensional objects composed of triangles, quadrilaterals, polygons,
cubes, and right prisms.
Focus Standards of
Mathematical Practice: MP.1 Make
sense of problems and persevere in solving them. MP.2 Reason
abstractly and quantitatively. MP.3
Construct viable arguments and critique the reasoning of others. MP.4 Model
with mathematics. MP.5 Use
appropriate tools strategically. MP.6 Attend
to precision. MP.7 Look for
and make use of structure. MP.8 Look for
and express regularity in repeated reasoning. Instructional
Outcomes: Full Development of the Major Clusters,
Supporting Clusters, Additional Clusters and Mathematical Practices for this
unit could include the following instructional outcomes: 7.G.A.1
7.G.A.2
7.G.A.3
7.G.B.4
7.G.B.5
7.G.B.6


Enduring Understandings: ·
Scale
drawings and scale models are used to represent objects that are too large or
too small to be drawn or built at actual size. ·
The scale
gives the ratio that compares the measurements of the drawing or model to the
measurements of the real object. ·
The
measurements on a drawing or model are proportional to the measurements on
the actual objects. ·
Scale drawings can be applied to problem solving situations
involving geometric figures. ·
Geometrical figures can be used to reproduce a drawing at a
different scale. ·
Writing and solving
reallife and mathematical problems involving simple equations for an unknown
angle in a figure helps students as they engage in higher geometry concepts. ·
Reason about relationships among twodimensional
figures, which leads to gaining familiarity with the relationships between
angles formed by intersecting lines. ·
Solve problems involving the area and circumference of a
circle and surface area of threedimensional objects. ·
Solve realworld and mathematical problems involving
area, surface area, and volume of two and threedimensional objects composed
of triangles, quadrilaterals, polygons, cubes and right prisms. ·
Geometry
and spatial sense offer ways to interpret and reflect on our physical environment. ·
Analyzing
geometric relationships develops reasoning and justification skills. 
Essential
Questions: ·
How
does geometry help us describe realworld objects? ·
How can I use geometric figures to reproduce a drawing at a
different scale? ·
How can I use and
relate facts about special pairs of angles to write and solve simple
equations involving unknown angles? ·
What is the total number of degrees in supplementary and
complementary angles? ·
What is the relationship between vertical and adjacent
angles? ·
How can geometry be
used to solve problems about realworld situations, spatial relationships,
and logical reasoning? ·
How
do geometric models describe spatial relationships? ·
How
are geometric shapes and object classified? ·
Where
do you see shapes in the world around you? ·
How
are angles related to the sides that create them? ·
What
characteristics are necessary for shapes to be defined? ·
How
do you describe triangles? ·
What
twodimensional figures result from slicing prisms, pyramids, cubes,
cylinders, and cones? 
