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DURHAM PUBLIC SCHOOLS 2013-2014
UNIT 4 PLAN FOR 7TH GRADE MATHEMATICS
Unit Overview:
Instructional Time: 7 weeks
Quarter
One
Two
Three
Four
Grade Level: 7th Grade
Unit Theme:
Depth of Knowledge: Level 1, Level 2, Level 3
Geometry
Unit Summary: The unit expands students’ understanding of two-dimensional figures by incorporating ideas of angle congruence as well as
complementary and supplementary angles. Students will draw and construct two- and three-dimensional figures with given conditions. They will
also explore the criteria needed to construct a triangle. Students will find area of two-dimensional figures composed of triangles, quadrilaterals,
and polygons. This unit will guide students through the exploration of pi as they uncover the formulas for area of a circle and circumference of a
circle. This unit will also enhance students’ understanding of the connections between two-and three-dimensional figures by exploring the crosssections of three-dimensional solids. Students will apply their understanding of three-dimensional figures to solve real-life problems involving
surface area and volume of right prisms and cubes.
Critical Area of Concentration: Critical Area #3: Solving problems involving scale drawings and informal geometric constructions, and working
with two- and three-dimensional shapes to solve problems involving area, surface area, and volume.
North Carolina Informational Technology Essential Standards:
7.TT.1.1 Use appropriate technology tools and other resources to access information.
7.SE.1.2 Apply the safety precautions necessary when using online resources (personal information, passwords, etc.)
Common Core State Standards
Geometry:
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.
Learning Targets:
 I can create scale models based on the ratios of dimensions
Draw, construct, and describe geometrical figures and describe
the relationships between them.
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.
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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.
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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 the area of a circle.
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I can determine which conditions create unique triangles, more
than one triangles, or no triangle
I can analyze given conditions based on the three measures of
angles or sides of a triangle to determine when there is a unique
triangle, more than one triangle or no triangle
I can construct triangles from three given angle measures to
determine when there is a unique triangle, more than one
triangle or no triangle using appropriate tools (freehand, rulers,
protractors, and technology)
I can construct triangles from three given side measures to
determine when there is a unique triangle, more than one
triangle or no triangle using appropriate tools (freehand, rulers,
protractors, and technology)
I can define slicing as the cross-section of a 3D figure
I can describe the two-dimensional figures that result from
slicing a three-dimensional figure such as a right rectangular
prism or pyramid
I can analyze three-dimensional shapes by examining two
dimensional cross-sections
I can determine the parts of a circle including radius, diameter,
area, circumference, center and chord
I can identify π
I can recognize the formulas for area and circumference of a
circle
I can determine the formulas for area and circumference of a
circle, find its area
I can find its circumference, given the area of a circle
I can justify that π can be derived from the circumference and
diameter of a circle
I can apply the circumference or area formulas to solve
mathematical and real-world problems
I can justify the formulas for area and circumference of a circle
and how they relate to π
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I can informally derive the relationship between 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.
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I can identify and recognize types of angles: supplementary,
complementary, vertical, adjacent
I can determine complements and supplements of a given angle
I can determine unknown angle measures by writing and solving
algebraic equations based on relationships between angles
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.
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I can determine the formulas for area and volume and then
procedure for finding surface area and when to use them in realworld and math problems for two- and three- dimensional
objects composed of triangles, quadrilaterals, polygons, cubes
and right prisms
I can solve real-world and math problems involving area,
surface area and volume of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons, cubes, and
right prisms
Essential Questions:
 How does geometry help us to interact with the physical world around us?
 Is more space (i.e. more land, more soda in a cup, more trash storage, more square footage etc.) always better?
 How can we be more efficient with our usage of space?
Enduring Understanding(s):
 Geometry can help us to view the physical world around us from a variety of perspectives.
 Geometry enables us to make wise decisions about the creation and usage of physical structures.
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Vocabulary:
Complementary Angles
Perimeter
Supplementary Angles
Circumference
Vertical Angles
Volume
Adjacent Angles
Surface Area
Congruent
Net
Area
Cross section
Interdisciplinary Connections (Standards would be listed):
RI.7.4: English Language Arts (Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and
technical meanings; analyze the impact of a specific word choice on meaning and tone.)
W.7.2: English Language Arts (Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the
selection, organization, and analysis of relevant content.)
W.7.10: English Language Arts (Write routinely over extended time frames (time for research, reflection, and revision and shorter time frames (a
single sitting or a day or two) for a range of discipline specific tasks, purposes, and audiences.)
SL.7.3: English Language Arts (Delineate a speaker’s argument and specific claims, evaluating the soundness of reasoning and relevance and
sufficiency of the evidence.)
Evidence of Learning (Formative Assessment):
Summative Assessment:
 Weekly journal entries that detail their reasoning
 Teacher-made test
 Teacher observation during classroom activities
 Exit slips
 Homework
 Small quizzes
 Durham Public Schools’ Small Goal Assessment
Unit Implementation:
Scale 7.G.1
To review graphing proportional ratios, using maps, have students find the scale for the map. Students will plan a trip from a Durham, NC to another city in NC or VA. Using the map (or the
projected/displayed map using Google Maps) have students measure the distance from starting point to destination. If using a hardcopy, using string to place over the highways/roads will help in
getting an accurate measurement. Then, have students measure the length of the string to set up the proportion. To extend this activity: Have students calculate the length of time the trip will take. For
example, traveling at 60 mph, how long will it take the student to travel to a particular city? Have them use conversions to calculate the hours, days, and weeks. Have students estimate the cost of
money for food, gas, and lodging to get to the destination. Students may display this data using a spreadsheet. Use the spreadsheet to predict traveling times for different speeds and to track costs for
different destinations.
To introduce proportionality using shapes Using coordinate grid paper, have one student draw shapes using coordinate pairs (square, rectangle, or triangle). Have partners make shapes similar to the
one drawn on their paper. Have each student measure the length of the sides. Set up a proportion to see if the shapes are truly similar. Have students do this again, leaving out a measurement this
time. Have students set up proportions to solve for missing length. To extend this activity, have students experiment with dilation. Have one student draw a shape (pentagon, trapezoid, rhombus), and
have to partner draw a shape on the same graph that is proportional larger or smaller, outside or inside the original drawing. Have students use the coordinate pairs to set up proportions, and
determine whether or not the shape is actually 2x/4x the size or (½ the size).
Real World Application Activity: Have students redesign your classroom into their dream recreational room. Students will have to measure the dimensions of the room. Using Floorplanner, have
students design a new room by determining what they scale factor should be to create a comparable blueprint of the space to give to the interior decorators. Once they have designed the room and
placed objects in the room, have students convert the information into what the real-world size of each object would be using the scale-factor. Have students record their creative process and
frustrations in their math journal/reflective blog.
Connected Mathematics Lessons:
CMP2 Unit - Comparing and Scaling, Investigations 4
CMP2 Unit - Stretching and Shrinking, Investigations 1-5
Angle Relationships and Constructions of Polygons (CCSS 7.G.5, 7.G.2)
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Introduce students to concepts of supplementary angles, complementary angles, vertical angles and adjacent angles.
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CMP: Shapes and Designs: 2.5 Angles and Parallel Lines
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CMP: Shapes and Designs: 4.1 Building Triangles
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NCTM’s Navigating Through Geometry in Grades 6-8: Exploring Triangles
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CMP: Shapes and Designs: 4.2 Building Quadrilaterals
Area of Two-Dimensional Figures including Circles (CCSS 7.G.6)
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Glencoe – Course 2: 11-7 Area of Complex Figures
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CMP: Covering and Surrounding: 7.1 Pricing Pizza
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CMP: Covering and Surrounding: 7.2 Surrounding a Circle
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NCTM Illuminations Applet: Circle Tool http://illuminations.nctm.org/ActivityDetail.aspx?ID=116
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NCTM Illuminations Applet: Computing Pi http://illuminations.nctm.org/ActivityDetail.aspx?ID=161
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CMP: Covering and Surrounding: 7.3 Covering a Circle
Area and Circumference of Circles and Cross-sections of Three Dimensional Solids (CCSS 7.G.4, 7.G.3)
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CMP: Covering and Surrounding: 7.4 “Squaring” a Circle
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CMP: Covering and Surrounding: 7.5 Replacing Trees
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NCTM’s Navigating Through Geometry in Grades 6-8: Cross Sections of Three Dimensional Shapes
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National Library of Virtual Manipulatives: Slicing Solids http://nlvm.usu.edu/en/nav/frames_asid_126_g_3_t_3.html?open=instructions
Shodor: Interactivate – Cross Sections http://www.shodor.org/interactivate/lessons/CrossSections/
Cross-sections of Three Dimensional Solids and Volume and Surface Area of Three-Dimensional Solids (CCSS 7.G.3, 7.G.2, 7.G.6)
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MathScape: Shapes and Space: “Any Way You Slice It”
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NCTM Navigating Through Geometry in Grades 6-8: Constructing Three-Dimensional Figures
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MathScape: Shapes and Space: “Nets that Catch Cubes”
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MathScape: Shapes and Space: “Take One for Good Measure”
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MathScape: Shapes and Space: “Move the Cube”
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CMP: Filling and Wrapping: Problem 3.2 Burying Garbage
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CMP: Filling and Wrapping: Problem 3.3 Filling Fancy Boxes
Volume and Surface Area of Three-Dimensional Solids (CCSS 7.G.6)
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MathScape: Shapes and Space: “All Boxed Up”
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MathScape: Shapes and Space: “Wrapping Up Prisms”
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Shodor Interactivate – Surface Area of Prisms http://www.shodor.org/interactivate/lessons/SurfaceAreaPrisms/
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Shodor Interactivate – Volume of Prisms http://www.shodor.org/interactivate/lessons/VolumePrisms/
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MathScape: Shapes and Space: “Does the Unit Fit?”
Review, Enrichment, Remediation, Summative Assessment (CCSS 7.G.2-6)
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Review Content from previous weeks
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Summative Assessment – Teacher Made
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Enrichment: Students can expand upon the “Burying Garbage” Lesson via a mini-project. Students can research the amount of packaging that is needed when various solids are used to
encase a particular item. Students can perform meaningful calculations regarding the amount of garbage produced due to inefficient packaging. Students can demonstrate their knowledge
of how the idea of limited space in our environment is impacted by inefficient packaging that eventually becomes trash.
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Remediation: If students require remediation for the concepts and skills in this unit they will participate in remediation activities and be reassessed.
Supportive Unit Resources: (Please note that these are resources that can be used to supplement instruction before or during a lesson.)
Instructional
Activities:
Scaffolding Option 1:
Intervention
(CCSS 7.G.2, 7.G.4, 7.G.5, 7.G.6)
Manipulatives – Usage of Polydrons to help students
better envision three dimensional solids.
Khan Academy – www.khanacademy.org Watch relevant
videos to help students better understand key concepts.
Scaffolding Option 2:
Maintenance
(CCSS 7.G.2, 7.G.3, 7.G.4, 7.G.5, 7.G.6)
Test Prep: Students will complete sample Common Core
Assessment Question or questions similar in structure and
content.
Scaffolding Option 3:
Extension
(CCSS 7.G.6)
Expansion on Burying Garbage Lesson – Students
will complete a mini-project analyzing the amount of
garbage created due to inefficient packaging and how
that fills up our landfills over time. Students will make
recommendations for more efficient packaging.
Technology Integration: (Please note that these are resources that can be used to supplement instruction before or during a lesson.)
Multimedia
Activities:
(CCSS 7.G.5)
Interactive Supplementary Angles
http://www.mathwarehouse.com/geometry/angle/interactivesupplementary-angles.php
(CCSS 7.G.2)
Virtual Polystrips
http://connectedmath.msu.edu/CD/Grade6/linkages/index.html
Geometer’s Sketchpad
http://www.keypress.com/x24070.xml
(CCSS 7.G.4)
Computing Pi
http://illuminations.nctm.org/ActivityDetail.aspx?ID=161