MIDDLE SCHOOL
Geometry
Lesson Plans
A Practical Guide For Educators
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Introduction
This is a set of lesson plans that complement the app ‘Shapes - 3D Geometry Learning’
on the iPad, Android tablet or desktop computer. These are suggested devices to use
in the classroom, but teachers may use also other Android or iOS mobile devices. An experienced
educator who has taught every single grade ranging from kindergarten to twelfth grade wrote
the lesson plans. Too often teachers find an app they like but are unable to find the time to align
it with the curriculum that they are required to teach. Our intent with these plans is to allow
the teachers using them to be able to access the lesson plans and seamlessly integrate the plans
into their teaching.
The ‘Shapes’ lesson plans are divided into two groups, one set of lesson plans for younger
students and one set of plans for older students. This is the older students set of plans which can
be used with middle school and high school students and they are lessons seven through ten.
For the teachers of older children there are lessons for grade six, grade seven, grade eight,
and grade ten. Geometry is not taught in ninth grade in the United States so that is why there
is no grade nine lesson plan.
The lesson plans are ready to use in the classroom. The purpose of these lessons is to encourage
the acquisition of various math skills through creative play. These lessons cater to students who have
a variety of learning styles and emphasize visual learning as well as hands-on kinesthetic activities.
Each lesson plan has the same organizational structure. There is a lesson title. The next element
in the lesson objective which is in the SWBAT format, students will be able to followed by an action
verb related to learning. Most lessons in the set have more than one lesson objective with action verbs
from Bloom’s Taxonomy. The third element of each lesson is the Common Core State Standards
to which they are aligned. Next there is an activity title followed by a list of materials needed to teach
the lesson and suggested amount of time/number of classes that the teachers should use to teach
the lesson. After that there is an activity description which explains how to execute the lesson. Finally,
each lesson ends with the supporting worksheet.
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The benefit of using these lessons is not only that you will be teaching your students math lessons
and skills that are aligned to the Common Core State Standards, but you will also see high levels
of engagement in your classroom. This current generation of students who sit in our classrooms are
digital natives and they respond well to instruction that infuses technology into the lesson plans.
If your classroom is equipped with iPADs using ARKit you may use Augmented
Reality features with which students can place solids on their desks and
examine them in 3D.
“Shapes - 3D Geometry Learning” app is integrated with Schoolwork app
available on iPads. Schoolwork helps you easily distribute and collect
assignments, keep an eye on student progress in educational apps, and
collaborate one on one with students from anywhere, in real time.
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LESSON SEVEN
Using Shapes in the 6th Grade
Multi-Disciplinary Project on the History of the Platonic Solids
Teachers using Shapes at the sixth grade level could use the following lesson objectives in their
lesson plans:
• SWBAT identify the number of faces, vertices, and edges there are in diferent platonic
solids
• SWBAT calculate the surface area of the five platonic solids
• SWBAT synthesize information about the history of polyhedra and the platonic solids with
hands-on application knowledge in an iMovie, WeVideo, Power Point or similar software for
presentation purposes, or oral report
This lesson relates to the following Common Core State Standards:
Solve real-world and mathematical problems involving area, surface
area, and volume.
CCSS.Math.Content.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by
composing into rectangles or decomposing into triangles and other shapes; apply these
techniques in the context of solving real-world and mathematical problems.
CCSS.Math.Content.6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates
to find the length of a side joining points with the same first coordinate or the same second
coordinate. Apply these techniques in the context of solving real-world and mathematical
problems.
CCSS.Math.Content.6.G.A.4
Represent three-dimensional figures using nets made up of rectangles and triangles, and
use the nets to find the surface area of these figures. Apply these techniques in the context
of solving real-world and mathematical problems.
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Activity Seven Part One – Using the Worksheets Below
Students Practice the Concepts of Counting Edges, Faces,
Vertices, and Calculate Surface Area of Each Object
Activity Seven Part Two - Using the Nets Section of the Shapes
App, students create a net for each of the 5 platonic solids and
print out the nets and use these 2d print out to build 3D Platonic
Solids
Activity Seven Part Three - Students Use the Knowledge You
Have Gained in Parts and Two Apply that Knowledge to Create
an Multimedia or Oral Presentation
Materials Needed:
• Part One: Class Set of the Worksheets Below, Writing Utensil for each student, if you are
in a 1 to 1 environment the worksheets can be filled out digitally and submitted digitally
depending upon the infrastructure
• This activity may be easily managed with Schoolwork, so that students can add their
Worksheet to the assignment handed out by teacher with a link to the Shapes app screen
• If students have iPads with ARKit they can examine 3D shapes in Augmented Reality when
completing the activity. They only need to click AR button when a displaying a single solid
in Shapes app
• Part Two: An iPad, Android tablet or desktop computer for each student in the class. If you
are not in a 1 to 1 setting students can work in pairs; also need a set of class scissors, set
of glue sticks, and you will also need the capacity to print out the nets of platonic solids
once you create them in the class.
• Part Three: iPad, Android tablet or desktop computer if the students are completing the
slide deck or video presentation. If the school has more bare bones technology the
students can complete the oral presentation choice for the project.
Suggested Time Frame for the Activity:
• Part One: 45 to 60 minutes of class time
• Part Two: 60 minutes of class time
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• Part Three: This summative activity will take one to two weeks: add on an additional one
to two class periods to allow the students to present their work
Activity description:
This is Our Sixth Grade Lesson, But Since It Is Very Open-Ended You Could Adapt the
Project to Another Grade Level Based Upon the Needs of Your Students.
Teachers provide the following background information for the students.
The platonic solids are regular polyhedra. This is a Greek word meaning “many faces”.
There are five platonic solids that are defined by the fact that each one of their faces
is a regular polygon, a polygon with equal angles and equal sides.
• Before you open your Shapes App, please complete the following exercise
• There are images of the five platonic solids on the worksheet below
• Please identify each of the following platonic solids
• Once you have identified each of the platonic solids, please identify how many faces
the solid has, how many vertices, and how many edges.
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Activity Seven Worksheet
Name:
How many faces?
How many vertices?
How many edges?
What is the surface area of the figure?
Name:
How many faces?
How many vertices?
How many edges?
What is the surface area of the figure?
Name:
How many faces?
How many vertices?
How many edges?
What is the surface area of the figure?
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Name:
How many faces?
How many vertices?
How many edges?
What is the surface area of the figure?
Name:
How many faces?
How many vertices?
How many edges?
What is the surface area of the figure?
Once you have completed the first step in this exercise, please go into the platonic solids section
of the app and complete the nets exercise for each one of the five platonic shapes. Below
is a series of screen shots showing how to do this.
This activity may be easily managed with Schoolwork, so that a teacher may redirect students
to the Step 3 and monitor their progres on-line.
In order to do that a teacher:
1) creates a handout in Schoolwork
2) adds an activity and chooses Shapes app
3) chooses „Platonic solids: Tetrahedron” from building nets actvities.
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STEP 1
STEP 2
STEP 3
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STEP 4
STEP 5
STEP 6
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STEP 7
Once you have successfully created the shape within the nets section of
the app, choose the print option for each shape and print out the five
platonic solids:
STEP 8
So you will print out the nets as displayed below.
This activity may be easily managed with Schoolwork so that students can add PDF with a net if
a teacher requests this as an item in a handout.
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• Partner Activity, After You Print Out the Five Platonic Solids Please Build the Five Shapes
in the Classroom
• Once you have completed this create an iMovie, WeVideo, PowerPoint slide presentation,
or dramatic skit with your partner about the history of the platonic solids and the modern
day application of the surface area formulas
• Your presentation should include the following people as they relate to the history of the
platonic solids
• Plato
• Kepler
• MC Escher
• Paul Carter
• Your presentation should also talk about how you use the formulas for surface area to
calculate the surface area of each of the Platonic Solids.
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LESSON EIGHT
Using Shapes in the 7th Grade
Teachers using Shapes at the seventh grade level could use the following lesson objectives
in their lesson plans:
• SWBAT determine the area of triangles, pentagons, squares
• SWBAT determine the surface area of the five platonic solids
This lesson relates to the following Common Core State Standards:
Solve real-life and mathematical problems involving angle measure,
area, surface area, and volume.
CCSS.Math.Content.7.G.B.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.
Activity Three - Screencasting Shape Lesson
Materials Needed: (this depends upon how many choices are available to your
students):
• Class set of the 5 nets worksheets that can be found in lesson six
• Rulers, pencils
• Formula cheat sheet (depending upon the level of scaolding you would like to
provide - see below)
Formula Cheat Sheet
Area of a triangle = ½ base * height
Area of a square = side * side
Area of a pentagon = perimeter * apothem/2
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If your classroom is 1:1 environment equipped with iPADs using ARKit you may use Augmented
Reality features with which students can place solids on their desks, unfold their nets and examine
them without the need to print them
Suggested Time Frame for the Activity:
• Depending upon the level of the students this lesson could take 30-60
minutes
Activity description:
• This lesson is connected to elements in lesson six and the nets
feature of the Shapes App
• The classroom teacher will print out the five nets worksheets that were
displayed in lesson six and distribute them to the students
• As an alternative, if a classroom is a 1:1 using iPADs with ARKit, a teacher
may ask students to click AR button when one of the five solids from lesson
six is displayed in Shapes app, then instruct students to place a solid in front
of them and unfold a net in AR mode.
• The students will measure the base and height of the triangle faces in the
Tetrahedron
• Based upon this base and the height measurement the students will calculate
the area of each face of the tetrahedron and the surface area of the platonic
solid
• The students will measure the base and height of the triangle faces in the
Octahedron
• Based upon this base and height measurement the students will calculate the
area of each face of the octahedron and the overall surface area of the platonic
solid
• The students will measure the side and apothem of the pentagon
faces in the Dodecahedron
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• Based upon this apothem and side measurement the students will calculate
the area of each face of the dodecahedron and the overall surface area of
the platonic solid
• The students will measure the base and height of the triangle faces in the
Icosohedron
• Based upon this base and height measurement the students will calculate the
area of each face of the icosahedron and the overall surface area of the platonic
solid
This activity may be easily managed with Schoolwork, so that students can add their worksheets
to the assignments handed out by teacher with a link to the Shapes app.
Activity Eight Worksheet
Height (in case
Overall
of the Dodeca- Area of One
Surface Area
Base hedron this Face on the
Shape of the Platonic
column will be Platonic Solid
Solid
the apothem)
Dodecahedron
Tetrahedron
Cube
Octahedron
Icosahedron
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LESSON NINE
Using Shapes in 8th grade
Teachers using Shapes at the eighth grade level could use the following lesson objectives in their
lesson plans:
• SWBAT create real world problems involving the formulas for cylinders,
cones, and spheres
This lesson relates to the following Common Core State Standards:
Solve real-world and mathematical problems involving volume
of cylinders, cones, and spheres.
CCSS.Math.Content.8.G.C.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve
real-world and mathematical problems.
Activity Nine - The students will create word problems related to the Solids
of Revolution Figures in the Shapes App
Materials Needed: (this depends upon how many choices are available to your students):
Shapes app on iPads, Android tablets or desktop computers pencil and paper class
set of worksheets (see below) signs for stations (Station One, Station Two, Station
Three, Station Four)
Formula Cheat Sheet
Volume of a Cylinder = V=πr2h
Volume of a Sphere = V=4/3πr3
Volume of a Cone = V=π r2 h/3
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Suggested Time Frame for the Activity:
This lesson should be taught in separate pieces; one lesson should be the creation of the word
problems (45 minutes), and the other lesson should be the Station Activity where the groups solve
each other’s problems (45 minutes)
Activity description:
• This lesson is connected to the Solids of Revolution Section of the Shapes App. The
teacher will bring up the solids of revolution section in the shapes App and show the
cylinder, cone, and sphere
• The teacher will use this as an opportunity to review the volume formulas for cones,
cylinders, and spheres
• The teacher and the students will then brainstorm examples of where you see examples
of cones, spheres, and cylinders in everyday life (i.e. ice cream cones, soda cans,
baseballs, etc.)
• After the brainstorming activity, the students will then break up into groups of three of
four
• Each group will be required to create three word problems 1) related to finding the
volume of a cylinder 2) related to finding the volume of a cone 3) related to finding the
volume of a sphere – the word problems must involve the occurrence of the shape in
the everyday world based upon brainstorming done as a class The word problems can
be generated on paper or they can take on a digital output like a screencast on the iPad,
Android tablet or desktop computer;
• Once the class has completed the word problems, the teacher should set the class up
in stations
• Groups will circulate through stations and complete word problems created by their
peers
• Teacher will collect data while this is going on (How long did it take for the students to
solve a problem? How accurate was the answer?)
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This activity may be easily managed with Schoolwork, so that students can add their worksheets
to the assignments handed out by teacher with a link to the Shapes app.
Solid of Revolution Real life examples of shapes Create Your Own Word
Problems for Each Solid
Cone
Cylinder
Sphere
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LESSON TEN
Using Shapes in the 10th
Grade
Teachers using Shapes at the tenth grade level could use the following lesson objectives in their
lesson plans:
• SWBAT create real world problems involving the concepts of density, area, and volume
• SWBAT calculate the density of the prism when given the mass and volume of that object.
This lesson relates to the following Common Core State Standards:
Apply geometric concepts in modeling situations:
CCSS.Math.Content.3.G.A.1
Apply concepts of density based on area and volume in modeling situations (e.g., persons
per square mile, BTUs per cubic foot).
Activity Ten - The students will create word problems
related to the Prisms section on the Shapes App
The students will create screencasts solving theses word problems
The students will create QR Codes that link to their word problems
The students will solve the word problems created by their peers
Materials Needed:
• Shapes app on iPads, Android tablets or desktop computers
• QR Code Reader app on the chosen device
• Computers to Create QR Codes on the Following Website: http://www.qrstu .com/
• Writing Utensils
• Class Set of Worksheets
• Measurement Tool
• Scissors, tape, and glue
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• Volume Formula Website Cheat Sheet for the Prisms (see links below)
http://www.math.com/tables/geometry/volumes.htm
http://www.softschools.com/math/geometry/volume_of_a_isotrianprism/
http://funwaytolearnmath.jimdo.com/geometry/volume-of-trapezoidal-prism/Weighing
device like a triple beam balance
Suggested Time Frame for the Activity:
The students should create the word problems related to their specific prism in one class and this
should take 45 minutes. It will take an additional 45 minutes for them to create the QR Codes and
the permanent product aspect of their project in Nets feature of the Shapes App The QR Code
Gallery walk in which the students will scan the QR Codes on the Prisms of their classmates will
take 90 minutes, and can be done in one or two classes depending upon whether or not you have
block scheduling
This activity may be managed with Schoolwork, so that teachers can easily:
• Redirect students to a specific 3D shape in the net creator mode
• Monitor students’ progress when creating nets of 3D shapes
• Collect worksheets with calculations made by students
• Collect students’ screencasts/videos and/or QR Codes.
Activity description:
• The teacher will divide the students into groups so that there are 2-3 students in
11 different groups, but each group is assigned to a Shape in the Prism section
of the Shapes App
• In their groups, the students use the nets creator mode to print out their prisms
Once they print out their assigned prisms on paper they take the
appropriate measurements to calculate the volume of that object Next the students
build the shape in 3d
• Then they find the mass of their shape by weighing it on the triple beam balance Then
based upon the mass and the volume of the 3d Prisms the students will use this
information to create a screencast in which they calculate the density of the prisms
• The students create a QR Code that they link to their screencast/video
• The students glue the QR Code onto their 3d figure
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The students take turns going around to the 11 stations, taking measurement of the prisms, filling
out the worksheet below, weighing the prisms, and then they use that information to calculate the
density of each object
Then the students scan the QR Codes and use the screencasts created by their peers to check
the work.
Activity Ten Worksheet
Did Our
Density
Formula for
Name of the Volume of Mass of the Density of the Calculations
Volume of the
Prism the Prism 3d Prism Prism Match Our
Prism
Peers? Why
or Why Not?
Cube
Hexagonal
Prism
Pentagonal
Prism
Right
Trapezoidal
Prism
Triangular
Prism
Trapezoidal
Prism
Parallelpiped
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Rhombic
Prism
Isosceles
triangular
prism
Right
triangular
prism
Quadrilateral
Prism
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