Austin ISD Instructional Planning Guide – Mathematics
5th Six Weeks IPG- February 23rd– April 17th (34 days; 2 days for 6 weeks review/test, 1 day for TAKS)
©2008 Austin ISD
Geometry
Major Concept #1: Area
Overarching Idea



How can you derive the formula to find the area for any polygon if you know how to find the area of a rectangle?
How are the perimeter and area of polygons related?
How are the areas of individual polygons related to the area of composite figures formed by those polygons?
Matrix
Strand
TEKS
Knowledge & Skill
Congruence and the Geometry of
Size
Matrix
#
Conjectures that include polygon properties support varied strategies to find regular and irregular areas of polygons.
The student uses
tools to determine
measurements of
geometric figures
and extends
measurement
concepts to find
perimeter, area,
and volume in
problem situations.
(G.8)
Geometric
Patterns
Teacher
Guiding Questions
The student uses a
variety of
representations to
describe geometric
relationships and
solve problems.
(G.5)
410
417
210
Geometry
Geometric Structure
Student Expectation
The student
applies logical
reasoning to justify
and prove
mathematical
statements. (G.3)
TAKS
OBJ
8
Derive, extend, and use the
Pythagorean Theorem.
(G.8C) B11; T11
Use numeric and geometric
patterns to develop
algebraic expressions
representing geometric
properties. (G.5A)
Resource
By Lesson Flow
Teacher Tools
Guiding Questions for Students:
 How do you use formulas to find perimeter and area?
 How is finding the area of composite figures similar to or different
from finding the area of common polygons?
 Why do you half the product of the base and height to find the area of
a triangle?
Core Lessons: Holt 9-1
Developing Formulas for
Triangles and
Quadrilaterals OR ETQ
Investigating Area
Formulas (30 min.)
Vocabulary: base, height, nonoverlapping, bases b1 and b2, tangram,
Practice: Holt 9-1 Texas
Practice B or Guided
Practice Exercises
(15 min.)
TAKS Information: July 2006 Exit Level #10, 18, 46; Dec. 2005 Exit Level
#43; Apr. 2004 Exit Level #46
Centers: (30 min.)
1. Patty Paper Inv. 11.1,
11.2, 11.3
2.Tangram station
3.Holt On Track for
TAKS – Literal
Equations (p. 588)
Extension: Students
could create a Tangram
figure and then enlarge
or reduce it and find the
area
Use deductive reasoning to
prove a statement. (G.3E)
Time/
Pace
Foundation Activities:
Holt Exploration 9-1 OR
ETQ What is Area?
(15 min.)
Find the areas of regular
polygons, circles, and
composite figures. (G.8A)
B11; T11
Use logical reasoning to
prove statements are true
and find counter examples
to disprove statements that
are false. (G.3C)
351
353
15 days
Homework: Holt 9-1
Texas Practice B or
selected Practice and
Problem Solving
exercises
Materials: Scissors, rulers, patty paper, graphing calculators (for each
student)
 Holt textbook and Practice sheets
 Patty Paper Geometry – Inv. Set 11
2 days
or 90
min.
Teacher Notes: Although the students are able to use the formula chart
on TAKS, it is important that students understand the origins of the
formulas to aid in the proper application of the formulas available.
Questioning:
 How are the areas of a parallelogram and a triangle related?
 Can students explain why you can find the area of a kite by
multiplying the diagonals and dividing by 2?
 Why do you need to know the height of a parallelogram and not just
the length of the sides to find the area?
 What tool do you use to find the height of a parallelogram if you know
the length of the sides?
 What tool do you use to find the height of a triangle if you know the
length of the sides?
 What is the relationship between the height of a triangle or
parallelogram and the Pythagorean Theorem (right angles)?
Differentiation strategies: Use grid paper or dot paper for students that
need a more visual representation of area. Stations can be extended over
several days with 15-20 min. allowed for each station.
Technology incorporation ideas: Tangram applets are available on the
following websites: http://pbskids.org/sagwa/games/tangrams/index.html;
http://www.enchantedmind.com/puzzles/tangram/tangram.html
http://standards.nctm.org/document/eexamples/chap4/4.4/
Page 1 of 9
Holt = Geometry text DG = Discovering Geometry DC = Dana Center GSP = Geometer’s Sketchpad MCM = Region IV Making Connections w/Measurement ETQ = Ensuring Teacher Quality Modules
MTC = Geometry Math TEKS Connections
Austin ISD Instructional Planning Guide – Mathematics
5th Six Weeks IPG- February 23rd– April 17th (34 days; 2 days for 6 weeks review/test, 1 day for TAKS)
©2008 Austin ISD
Geometry
15 days (Cont’d.)
Major Concept #1: Area (Continued)
Overarching Idea
Teacher
Guiding Questions
Matrix
Strand
410
Congruence and the Geometry of Size
Matrix
#
Conjectures that include polygon properties support varied strategies to find regular and irregular areas of polygons.



How can you derive the formula to find the area for any polygon if you know how to find the area of a rectangle?
How are the perimeter and area of polygons related?
How are the areas of individual polygons related to the area of composite figures formed by those polygons?
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
By Lesson Flow
(G.8)
(G.8A) B11; T11
Geometric Patterns

Why do you notate the area of a circle using ?
Develop  OR MTC
Geometry – Going in
Circles (20 min.)
Vocabulary: circle, center of a circle, center of a regular polygon,
apothem, central angle of a regular polygon
Core Lessons: Holt 9-2
Developing Formulas for
Circles and Regular
Polygons (30 min.)
Materials: compass, straightedge, patty paper, cm grid paper
 Going in Circles cooperative activity sheets
 Holt textbook and Practice sheets
 Patty Paper Geometry – Inv. Set 11
8
TAKS Information: July 2006 Exit Level #6; Apr. 2006 Exit Level #35;
Oct. 2005 Exit Level #48
Practice: Holt 9-2
Problem Solving
(10 min.)
Extension: DC
Geometry Assessments
– Nesting Hexagons (p.
267-273)
(G.5)
Teacher Tools
Guiding Questions for Students:
 How can you use the perimeter and apothem of a regular polygon to
calculate the area?
 What is ? How was  discovered?
Foundation Activities:
Holt 9-2 Geometry Lab –
Centers: (30 min.)
1. Patty Paper Inv. 11.4
2. Discovering 
3. Holt Exploration 9-2
(p. 600)
210
Time/
Pace
(G.5A)
Homework: Complete
Holt 9-2 Problem Solving
and/or selected items
from Texas Practice B
2 days
or 90
min.
Teacher Notes: The July 2006 Exit TAKS #6 problem is an earlier version
of using the apothem to find the area of a regular polygon. Subsequent
problems do not provide as much information as this problem. Students
need to have a good understanding of how to find area using the apothem.
Be aware: Chapter 8 was skipped and introduced trig ratios. Choose your
problems and examples carefully. Trig ratios will be introduced during the
6th 6 weeks.
Questioning:
 How can you find the area of a circle when given the circumference?
 How can you find the circumference of a circle when given its area?
 What is the apothem?
 How can you use the apothem to find the area of a regular polygon?
Differentiation strategies: Pre-AP Geometry students could be
challenged with the Dana Center Assessment indicated in the resource
column. Stations can be extended over several days with 15-20 min.
allowed for each station. Some stations may be changed to match the
geometry content.
Technology incorporation ideas: Holt 9-2 online resources provide a
technology lab 9-2 to use with the graphing calculator. The lab specifies
using GeoMaster but the same activity can be completed using Cabri, Jr.
on the TI-84 graphing calculator.
Geometry
Page 2 of 9
Holt = Geometry text DG = Discovering Geometry DC = Dana Center GSP = Geometer’s Sketchpad MCM = Region IV Making Connections w/Measurement ETQ = Ensuring Teacher Quality Modules
MTC = Geometry Math TEKS Connections
Austin ISD Instructional Planning Guide – Mathematics
5th Six Weeks IPG- February 23rd– April 17th (34 days; 2 days for 6 weeks review/test, 1 day for TAKS)
©2008 Austin ISD
Geometry
15 days (Cont’d.)
Major Concept #1: Area (Continued)
Overarching Idea
Teacher
Guiding Questions
410
348
Congruence and
the Geometry of
Size
Matrix
Strand
Geometric Structure
Matrix
#
Conjectures that include polygon properties support varied strategies to find regular and irregular areas of polygons.



How can you derive the formula to find the area for any polygon if you know how to find the area of a rectangle?
How are the perimeter and area of polygons related?
How are the areas of individual polygons related to the area of composite figures formed by those polygons?
TEKS
Knowledge & Skill
(G.8)
Student Expectation
(G.8A) B11; T11
TAKS
OBJ
8
Resource
By Lesson Flow
Foundation Activities:
Holt Exploration 9-3
Composite Figures
(10 min.)
The student
analyzes geometric
relationships in
order to make and
verify conjectures.
(G.2)
Make conjectures about
angles, lines, polygons,
circles, and threedimensional figures and
determine the validity of the
conjectures, choosing from
a variety of approaches
such as coordinate,
transformational, or
axiomatic. (G.2B)
Practice: Holt 9-3 Texas
Practice B or Guided
Practice (20 min.)
Centers: (45 min.)
1. HoltGeometry Lab 9-3
2. Tangram area
3. House plans
Homework: Holt 9-3
Texas Practice B or
Problem Solving
Teacher Tools
Guiding Questions for Students:
 When is it helpful to subdivide a given shape into smaller shapes to
find the area? Why?
 How is “finding the area of composite figures by adding” similar to or
different from “finding the area of composite figures by subtracting”?
 How can you estimate the area of an irregular figure?
Core Lessons: Holt 9-3
Composite Figures
(20 min.)
Perplexing Puzzle Part 2
(30 min.)
Assessments: Google
Sketchup file:
ThreeD_Construct_Disc
GeomPg233 (10 min.)
Geometry
Time/
Pace
Vocabulary: composite figure, Area Addition Postulate
Materials: compass, straightedge, patty paper, cm grid paper, chart paper
 Teacher created activity – Perplexing Puzzle Part 2
 Holt textbook and Practice sheets
3 days
or 135
min.
TAKS Information: Apr. 2004 Exit Level #43; Oct. 2005 Exit Level #44;
Feb. 2006 Exit Level #47; Apr. 2006 Exit Level #33
Teacher Notes: Some suggestions for the design of a new lesson from
the Perplexing Puzzles lesson can be used to introduce area. This lesson
could be used in conjunction with the Holt 9-3 lesson materials.
Differentiation strategies: The Perplexing Puzzle Part 2 lesson
addresses the needs of diverse learners and allows students to work
cooperatively to find the area of composite figures.
Technology incorporation ideas: The Google Sketchup files provided to
teachers that attended Day 6 of the Geometry PLC includes sketches with
labeled dimensions that can be used as practice.
Page 3 of 9
Holt = Geometry text DG = Discovering Geometry DC = Dana Center GSP = Geometer’s Sketchpad MCM = Region IV Making Connections w/Measurement ETQ = Ensuring Teacher Quality Modules
MTC = Geometry Math TEKS Connections
Austin ISD Instructional Planning Guide – Mathematics
5th Six Weeks IPG- February 23rd– April 17th (34 days; 2 days for 6 weeks review/test, 1 day for TAKS)
©2008 Austin ISD
Geometry
15 days (Cont’d.)
Major Concept #1: Area (Continued)
Overarching Idea
Teacher
Guiding Questions
Congruence
and the
Geometry of
Size
332
333
422
Geometry
Similarity and the Geometry of Shape
410
Matrix
Strand
Dimensionality and the Geometry of
Location
Matrix
#
Conjectures that include polygon properties support varied strategies to find regular and irregular areas of polygons.



How can you derive the formula to find the area for any polygon if you know how to find the area of a rectangle?
How are the perimeter and area of polygons related?
How are the areas of individual polygons related to the area of composite figures formed by those polygons?
TEKS
Knowledge & Skill
(G.8)
The student
understands that
coordinate systems
provide convenient
and efficient ways
of representing
geometric figures
and uses them
accordingly. (G.7)
The student
applies the
concepts of
similarity to justify
properties of
figures and solve
problems. (G.11)
Student Expectation
(G.8A) B11; T11
TAKS
OBJ
8
Use one- and twodimensional coordinate
systems to represent points,
lines, line segments, rays,
and figures. (G.7A) B11;
T11
Derive and use formulas
involving length, slope, and
midpoint. (G.7C) B11; T11
8
Time/
Pace
Teacher Tools
Foundation Activities:
Geometry Lab 8.4
Geoboard Area or Patty
Paper Activity
(20 min.)
Guiding Questions for Students:
 How is finding the area of irregular shapes similar to or different from
finding the area of composite figures?
 How is finding area on the coordinate plane different from using
formulas to find area? How are these strategies similar?
Core Lessons: Holt 9-4
Perimeter and Area in the
Coordinate Plane
(20 min.)
Vocabulary: irregular shapes, approximate
Practice: Holt 9-4
Guided Practice (20 min.)
7
Describe the effect on
perimeter, area, and volume
when one or more
dimensions of a figure are
changed and apply this idea
in solving problems.
(G.11D) B11; T11
Resource
By Lesson Flow
2 days
or 90
min.
Centers: (30 min.)
1. Lab 8.4 Geoboard
Area #7 – Puzzle
2. Holt Exploration 9-4
Perimeter and Area on
the Coordinate Plane
Materials: patty paper, cm grid paper, geoboards or geoboard dot paper
 Geometry Labs (included in Resources file)
 Holt textbook and Practice sheets
TAKS Information: Oct. 2005 Exit Level #50; July 2006 Exit Level #24
Teacher Notes: The Geoboard Area lab included as a foundation activity
is directly correlated to the Exit Level TAKS 10/05 #50 item. Puzzle
problem #7 from this lab could be used in a station.
Differentiation strategies: Setting up time for stations allows the teacher
flexibility in grouping and working with struggling students.
Homework: Holt 9-4
Texas Practice B or
Problem Solving
Technology incorporation ideas: Exploring Geometry with Geometer’s
Sketchpad includes a Pick’s Theorem investigation in Chapter 7, p. 148149.
Foundation Activities:
Holt Exploration 9-5
(15 min.)
Guiding Questions for Students:
 How does changing one or more dimensions affect the perimeter and
area of a figure? (TEKS 8.10A)
Core Lessons: Holt 9-5
Effects of Changing
Dimensions
Proportionally (30 min.)
Geometry Lab 10.3
Polyomino Blowups (30
min.)
Practice: Holt 9-5
Guided Practice or Texas
Practice B (15 min.)
Homework: Holt 9-5
Texas Practice B or
Problem Solving
Vocabulary: doubled, tripled, proportional, dimensions, radius,
circumference, perimeter, area
3 days
or 135
min.
Materials: cm grid paper, interlocking cubes (opt.)
 Geometry Labs (included in Resources file)
 Holt textbook and Practice sheets
TAKS Information: SE 8.10A; Apr. 2004 Grade 9 #29, 37; Apr. 2006
Grade 9 #26; Apr. 2004 Grade 10 #21; Apr. 2006 Grade 10 #23
Teacher Notes: This lesson focuses on changes in only one and/or two
dimensions. This concept will be revisited later in the six weeks as it
pertains to three-dimensions and the affect on the volume of a solid.
Additional 45 min. included for Quiz or Test.
Page 4 of 9
Holt = Geometry text DG = Discovering Geometry DC = Dana Center GSP = Geometer’s Sketchpad MCM = Region IV Making Connections w/Measurement ETQ = Ensuring Teacher Quality Modules
MTC = Geometry Math TEKS Connections
Austin ISD Instructional Planning Guide – Mathematics
5th Six Weeks IPG- February 23rd– April 17th (34 days; 2 days for 6 weeks review/test, 1 day for TAKS)
©2008 Austin ISD
Overarching Idea
Teacher
Guiding Questions
Matrix
Strand
410
Congruence and the Geometry of Size
Matrix
#
Major Concept #1: Area (Continued)
Conjectures that include polygon properties support varied strategies to find regular and irregular areas of polygons.



15 days (Cont’d.)
How can you derive the formula to find the area for any polygon if you know how to find the area of a rectangle?
How are the perimeter and area of polygons related?
How are the areas of individual polygons related to the area of composite figures formed by those polygons?
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
By Lesson Flow
Time/
Pace
Vocabulary: event, outcome, sample space, geometric probability
Materials: compass, straightedge, patty paper, cm grid paper
 Holt textbook and Practice sheets
Core Lessons: Holt 9-6
Geometric Probability
(15 min.)
(G.8A) B11; T11
8
Practice: Holt 9-6
Guided Practice (15 min.)
Homework: Holt 9-6
Texas Practice B or
Problem Solving
Assessments: Examine
TAKS Information in
Teacher Tools for
possible connections to
Geometric Probability
Teacher Tools
Guiding Questions for Students:
 How is geometric probability useful in life?
 What are the important components of the ratio used to determine
geometric probability?
 What is the difference between experimental and theoretical
probability?
Foundation Activities:
Holt Exploration 9-6
(15 min.)
(G.8)
Geometry
TAKS Information: Apr. 2004 Exit Level #2; Jul. 2004 Exit Level #28, 31
3 days
or 135
min.*
Teacher Notes: Geometric probability is tested on TAKS under the
8.11B,C 8th grade standards. Assess student understanding of probability
and spend time reviewing how probability is tested on TAKS.
One to two additional days are included for testing perimeter and area
before Spring Break.
Differentiation strategies: Provide opportunities for students to actually
experiment with geometric probability. The Holt Exploration Alternate
Opener is a good example for tactile learners.
Technology incorporation ideas: The NCTM Illuminations website has a
Java applet for a geometric probability simulation involving a forest fire.
The simulation does not require a software download or install. Here is the
link to the activity - http://illuminations.nctm.org/ActivityDetail.aspx?ID=143
There is also an adjustable spinner that can be used to explore
experimental vs. theoretical probability on the NCTM Illuminations website
at http://illuminations.nctm.org/ActivityDetail.aspx?ID=79
*Includes 1-2 days (45-90 min.) for review and unit or major test
Geometry
Page 5 of 9
Holt = Geometry text DG = Discovering Geometry DC = Dana Center GSP = Geometer’s Sketchpad MCM = Region IV Making Connections w/Measurement ETQ = Ensuring Teacher Quality Modules
MTC = Geometry Math TEKS Connections
Austin ISD Instructional Planning Guide – Mathematics
5th Six Weeks IPG- February 23rd– April 17th (34 days; 2 days for 6 weeks review/test, 1 day for TAKS)
©2008 Austin ISD
Overarching Idea
Geometry
Major Concept #2: Three dimensional solids
16 days
Make and verify conjectures about Polyhedrons, Prisms, Pyramids, Cylinders, Cones, Spheres and the surface area and volume of each solid.
 Which two-dimensional figures make up the net of a given solid?
Teacher
Guiding Questions
 How do you determine the surface area of a given solid?
 How do you determine the volume of a given solid?
 If the dimensions of a solid are changed (i.e. height doubled), what happens to the surface area and volume of the solid?
Matrix
Strand
Dimensionality and the
Geometry of Location
341
340
Congruence
and the
Geometry of
Size
337
339
340
Geometry
Congruence and the Geometry of Size
Matrix
#
TEKS
Knowledge & Skill
The student
analyzes the
relationship
between threedimensional
geometric figures
and related twodimensional
representations
and uses these
representations to
solve problems.
(G.6)
The student
analyzes properties
and describes
relationships in
geometric figures.
(G.9)
(G.6)
Student Expectation
TAKS
OBJ
Describe and draw the
intersection of a given
plane with various threedimensional geometric
figures. (G.6A)
Resource
By Lesson Flow
Core Lessons: Holt 10-1
Solid Geometry (20 min.)
Practice: Holt 10-1 Texas
Practice B (15 min.)
Use nets to represent and
construct three-dimensional
geometric figures (such as
drawing at least two
different nets for a cereal
box). (G.6B) B11; T11
7
Analyze the characteristics
of polyhedra and other
three-dimensional figures
and their component parts
based on explorations and
concrete models. (G.9D)
B11; T11
Use orthographic and
isometric views of threedimensional geometric
figures to represent and
construct three-dimensional
geometric figures and solve
problems. (G.6C) B11; T11
Centers: (45 min.)
1. Polydron frameworks
or PolyConstructo
pieces for exploration
2. Lateral Area Sets or
small boxes that can
be cut apart and
flattened
Practice: Holt 10-2
Guided Practice (20 min.)
(G.9D) B11; T11
Materials:
 Holt textbook and Practice sheets
2 days
or 90
min.
Homework: Holt 10-2
Texas Practice B
Assessments: DC
Geometry Assessments
Different Views (Ch. 5)
(40 min.)
TAKS Information: Apr. 2004 Exit Level #38; Oct. 2005 Exit Level #10,
26; Dec. 2005 Exit Level #30; Feb. 2006 Exit Level #8; Apr. 2006 Exit
Level #10, 31; July 2006 Exit Level #4
Teacher Notes: Students are expected to make a net (two-dimensional
model) of the surface area of a three-dimensional figure (7.8B) beginning
in Grade 7. By Grade 8 students find lateral and total surface area of
prisms, pyramids, and cylinders using concrete models and nets.
Differentiation strategies: Display vocabulary words using the Frayer
model to help students internalize the names and characteristics of
different solid figures. Use tactile three-dimensional modeling pieces in a
center.
Homework: Provide
students with nets to
construct 3-D solids
Foundation Activities:
TAKS Mathematics
Preparation Grades 9-11
What’s Your View on
This? Lesson (30 min.)
OR
Core Lessons: Holt 10-2
Representations of ThreeDimensional Figures (30
min.)
Teacher Tools
Guiding Questions for Students:
 What are the common names of the parts of a solid figure?
 How can you identify a solid figure from a net?
Vocabulary: face, edge, vertex, prism, cylinder, pyramid, cone, cube, net,
cross section
Foundation Activities:
Holt Exploration 10-1
(10 min.)
7
(G.9)
Time/
Pace
Guiding Questions for Students:
 How can three-dimensional figures be represented in twodimensions?
 How are the different views (top, front, right or left) of threedimensional figures similar or different?
Vocabulary: orthographic drawing, isometric drawing, perspective,
drawing, vanishing point, horizon
2 days
or 90
min.
Materials: isometric dot paper, cubes,
 TAKS Mathematics Preparation Grades 9-11 (Region IV) resource
 Holt textbook and Practice sheets
TAKS Information: Apr. 2004 Exit Level #15; July 2004 Exit Level #39;
Oct. 2005 Exit Level #57; Dec. 2005 Exit Level #49; Apr. 2006 Exit Level
#14, 60; July 2006 Exit Level #60
Teacher Notes: Students are expected to sketch three-dimensional
figures from different views beginning in Grade 7. The Foundation Activity
from Region IV appears in the high school TAKS Mathematics Preparation
book (this is also a review of 8.7A).
Additional resources for different views and changing dimensions
are included at the end of the teacher resource document.
Page 6 of 9
Holt = Geometry text DG = Discovering Geometry DC = Dana Center GSP = Geometer’s Sketchpad MCM = Region IV Making Connections w/Measurement ETQ = Ensuring Teacher Quality Modules
MTC = Geometry Math TEKS Connections
Austin ISD Instructional Planning Guide – Mathematics
5th Six Weeks IPG- February 23rd– April 17th (34 days; 2 days for 6 weeks review/test, 1 day for TAKS)
©2008 Austin ISD
Geometry
16 days (Cont’d.)
Major Concept #2: Three dimensional solids (Continued)
Overarching Idea
Make and verify conjectures about Polyhedrons, Prisms, Pyramids, Cylinders, Cones, Spheres and the surface area and volume of each solid.
 Which two-dimensional figures make up the net of a given solid?
Teacher
Guiding Questions
 How do you determine the surface area of a given solid?
 How do you determine the volume of a given solid?
 If the dimensions of a solid are changed (i.e. height doubled), what happens to the surface area and volume of the solid?
Matrix
Strand
Dimensionality and
the Geometry of
Location
Matrix
#
Congruence and the
Geometry of Size
333
417
Congruence and the
Geometry of Size
340
422
Similarity
and the
Geometry of
Shape
337
Dimensiona
lity & the
Geometry
of Location
415
Geometry
TEKS
Knowledge & Skill
(G.7)
(G.8)
(G.9)
The student uses
tools to determine
measurements of
geometric figures
and extends
measurement
concepts to find
perimeter, area,
and volume in
problem situations.
(G.8)
(G.6)
Student Expectation
(G.7C) B11; T11
(G.8C) B11; T11
(G.9D) B11; T11
Find surface areas and
volumes of prisms,
pyramids, spheres, cones,
cylinders, and composites
of these figures in problem
situation. (G.8D) B11; T11
(G.6B) B11; T11
TAKS
OBJ
7
8
7
7
Resource
By Lesson Flow
Foundation Activities:
Holt Exploration 10-3
Formulas in ThreeDimensions
(10 min.)
Core Lessons: Holt 10-3
Formulas in ThreeDimensions (20 min.)
Practice: 10-3 Reteach or
10-3 Problem Solving (15
min.)
(G.11D) B11; T11
7
Guiding Questions for Students:
 What three-dimensional applications of distance formula or
Pythagorean theorem are used in designing real-world objects?
 How do you use formulas to solve problems involving distance in
three-dimensions?
Vocabulary: polyhedron, space, vertices, faces, edges, ordered triple
1 day
or 45
min.
Materials:
 Geometry Assessments
 Holt textbook and Practice sheets
TAKS Information: Oct. 2005 Exit Level #40; Apr. 2006 Exit Level #19
Teacher Notes: Students are not tested on formulas in three-dimensions
and three-dimensional coordinate system is not part of the state
standards. Make connections between extending the Pythagorean
Theorem to solve TAKS problems similar to the exploration.
Homework: Carefully
chosen items from 10-3
Exercises
Differentiation strategies: The Geometry Assessments could be used in
place of the textbook lesson to challenge Pre-AP students.
Technology incorporation ideas: http://sketchup.google.com/download/
Foundation Activities:
Closing the Distance
Grade 10 Lesson 12
Surface Area and Volume
OR ETQ What is Surface
Area?
(40 min.)
Guiding Questions for Students:
 How do you know when to find total surface area or lateral surface
area?
 How is a capital “B” different from a lower case “b” and what do these
letters represent in formulas?
Practice: TAKS
Mathematics Preparation
Grade 10 Surface Area
and Volume Lesson (30”)
Homework: Holt 10-4
Texas Practice B (20”)
(G.11)
Teacher Tools
Extension: Geometry
Assessments – The Most
Juice
Core Lessons: Holt 10-4
Surface Area of Prisms
and Cylinders (30 min.)
8
Time/
Pace
Assessments: Closing
the Distance Grade 10
Lesson 12 Evaluate (15”)
3 days
or 135
min.
Vocabulary: lateral face, lateral edge, right prism, oblique prism, altitude,
surface area, lateral surface, axis of a cylinder, right cylinder, oblique
cylinder, approximate, base
Materials:
 Closing the Distance Grade 10
 Holt textbook and Practice sheets
 TAKS Mathematics Preparation Grade 10
TAKS Information: July 2004 Exit Level #30; Oct. 2005 Exit Level #54;
Dec. 2005 Exit Level #47; Feb. 2006 Exit Level #7,24, 60; Apr. 2006 Exit
Level #27
Teacher Notes: Students struggle with the concept of how changing
dimensions effects the surface area and/or volume of solid figures. The
additional resources listed will assess current student understanding and
assist in developing conceptual understanding of these difficult ideas.
Page 7 of 9
Holt = Geometry text DG = Discovering Geometry DC = Dana Center GSP = Geometer’s Sketchpad MCM = Region IV Making Connections w/Measurement ETQ = Ensuring Teacher Quality Modules
MTC = Geometry Math TEKS Connections
Austin ISD Instructional Planning Guide – Mathematics
5th Six Weeks IPG- February 23rd– April 17th (34 days; 2 days for 6 weeks review/test, 1 day for TAKS)
©2008 Austin ISD
Geometry
16 days (Cont’d.)
Major Concept #2: Three dimensional solids (Continued)
Overarching Idea
Make and verify conjectures about Polyhedrons, Prisms, Pyramids, Cylinders, Cones, Spheres and the surface area and volume of each solid.
 Which two-dimensional figures make up the net of a given solid?
Teacher
Guiding Questions
 How do you determine the surface area of a given solid?
 How do you determine the volume of a given solid?
 If the dimensions of a solid are changed (i.e. height doubled), what happens to the surface area and volume of the solid?
Matrix
Strand
Congruence and
the Geometry of
Size
Matrix
#
(G.8)
422
(G.6)
Congruence and
the Geometry of
Size
(G.11)
337
Dimension
ality & the
Geometry
of Location
415
Student Expectation
(G.8D) B11; T11
TAKS
OBJ
Resource
By Lesson Flow
7
Foundation Activities:
Making Connections with
Measurement Grade 10
Lateral and Total Surface
Area of Pyramids
(30 min.)
Core Lessons: Holt 10-5
Surface Area of Pyramids
and Cones (20 min.)
Simil
arity
and
the
Geo
metry
of
Shap
e
337
Dimension
ality & the
Geometry
of Location
415
TEKS
Knowledge & Skill
(G.8)
(G.6B) B11; T11
(G.11D) B11; T11
(G.8D) B11; T11
8
7
7
(G.6B) B11; T11
8
Geometry
Similarity and the
Geometry of Shape
Homework:
422
(G.11)
(G.11D) B11; T11
7
2 days
or 90
min.
Assessment: Students
use an individual cereal
box to design a cylindrical
box with the same volume
(25 min.)
Vocabulary: vertex of a pyramid, regular pyramid, slant height, altitude,
vertex of a cone, axis of a cone, right cone, oblique cone
Materials:
 Making Connections with Measurement Grade 10 TAKS
 Holt textbook and Practice sheets
TAKS Information: No direct correlations to TAKS released items found.
Teacher Notes: TAKS released problems related to changing dimensions
have involved only prisms, cylinders, and spheres to date. Prism and
pyramid nets with similar dimensions http://www.fcpsteach.org/docs/prisms.pdf
Guiding Questions for Students:
 How do you know which dimensions to measure to calculate the area
of the base (B) and the volume of the solid?
 How does finding the volume of a prism differ from finding the volume
of a cylinder? How are the procedures the same?
Vocabulary: volume, length, width, height, base (B), cubic
Foundation Activities:
Making Connections with
Measurement Grade 10
Volume OR ETQWhat is
Volume?
(15 min.)
Practice: Holt 10-6
Guided Practice or Texas
Practice B (20 min.)
Teacher Tools
Guiding Questions for Students:
 How is finding the surface area of pyramids and cones similar to or
different from finding the surface area of prisms and cylinders?
 How are slant height and altitude used to find the surface area of
pyramids and cones?
Practice/Centers: (40
min.) Find surface area
1 Provide nets for
pyramids
2 Provide nets for cones
Core Lessons: Holt 10-6
Volume of Prisms and
Cylinders (30 min.)
(G.6)
Time/
Pace
Materials:
 Making Connections with Measurement Grade 10 TAKS
 Holt textbook and Practice sheets
2 days
or 90
min.
TAKS Information: Apr. 2004 Exit Level #9; Oct. 2005 Exit Level #54;
Dec. 2005 Exit Level #26, 46; Feb. 2006 Exit Level #32; Apr. 2006 Exit
Level #3, 20
Teacher Notes: Grade 8 TEKS involving solids require students to find
lateral and total surface area of prisms, pyramids, and cylinders and to
connect models of these solids including spheres and cones to formulas.
In grade 7 students are required to connect models for the volume of
prisms (rectangular and triangular) and cylinders to the formulas of these
solids. The focus of geometry should be to synthesize these concepts to
find the volume of composite figures.
Assessment: Individual cereal boxes are available in the school cafeteria
for breakfast. Ask students to save their cereal box for this activity.
Page 8 of 9
Holt = Geometry text DG = Discovering Geometry DC = Dana Center GSP = Geometer’s Sketchpad MCM = Region IV Making Connections w/Measurement ETQ = Ensuring Teacher Quality Modules
MTC = Geometry Math TEKS Connections
Austin ISD Instructional Planning Guide – Mathematics
5th Six Weeks IPG- February 23rd– April 17th (34 days; 2 days for 6 weeks review/test, 1 day for TAKS)
©2008 Austin ISD
Geometry
16 days (Cont’d.)
Major Concept #2: Three dimensional solids (Continued)
Overarching Idea
Make and verify conjectures about Polyhedrons, Prisms, Pyramids, Cylinders, Cones, Spheres and the surface area and volume of each solid.
 Which two-dimensional figures make up the net of a given solid?
Teacher
Guiding Questions
 How do you determine the surface area of a given solid?
 How do you determine the volume of a given solid?
 If the dimensions of a solid are changed (i.e. height doubled), what happens to the surface area and volume of the solid?
Matrix
Strand
Congruence and
the Geometry of
Size
Matrix
#
415
422
Geometry
Similarity and the
Geometry of Shape
422
Similarity and the
Geometry of Shape
(G.6)
Congruence
and the
Geometry of
Size
337
(G.8)
Dimensio
nality &
the
Geometry
of
Location
415
TEKS
Knowledge & Skill
Student Expectation
(G.8D) B11; T11
(G.6B) B11; T11
TAKS
OBJ
7
8
Resource
By Lesson Flow
Foundation Activities:
MTC Geometry Activity 42
Modeling the Volume of
Pyramids
(30 min.)
Core Lessons: Holt 10-7
Volume of Pyramids and
Cones (20 min.)
Practice: Texas Lab
Manual 10-7 Volume of
Composite Figures (20
min.)
Time/
Pace
Guiding Questions for Students:
 What dimensions of pyramids and cones are used to calculate the
volume? How are these dimensions used to find volume?
 How do the volumes of rectangular prisms and rectangular pyramids
with similar dimensions compare?
 How do the volumes of cylinders and cones with similar dimensions
compare?
Vocabulary: vertex of a pyramid, regular pyramid, slant height, altitude,
vertex of a cone, axis of a cone, right cone, oblique cone
2 days
or 90
min.
Homework: Holt 10-7
Texas Practice B or
Problem Solving
(G.11)
(G.8)
(G.11D) B11; T11
7
Teacher Notes: Teachers that worked the MTC Geometry at the Day 6
Geometry PLC suggested just giving the nets to students and having them
puzzle out how to put it together. There is a detailed set of directions that
some teachers found could be confusing for students.
Technology incorporation ideas: Java applets for pyramids and cones
are available – email kanders@austinisd.org for these files.
Assessment: MTC
Geometry Activity 37 Ice
Cream Cone Excursion
(20 min.)
Core Lessons: Holt 10-8
Spheres (30 min.)
7
(G.11)
(G.11D) B11; T11
Practice: Holt 10-8
Guided Practice or Texas
Practice B (20 min.)
Homework: Holt 10-8
Texas Practice B or
Problem Solving (20 min.)
Assessments: DC
Geometry Assessments –
Boxing Basketballs
Materials:
 MTC Geometry Activity 42
 Holt textbook and Practice sheets
 Holt Texas Lab Manual 10-7
TAKS Information: No direct correlations to TAKS released items found.
Foundation Activities:
The Orange Problem
(20 min.)
(G.8D) B11; T11
Teacher Tools
2 days
or 90
min.
Guiding Questions for Students:
 How is the surface area of a sphere related to radius of the sphere?
 How can you find the volume of a sphere if you know its surface
area?
 How does changing the radius of a sphere affect the surface area
and volume?
Vocabulary: sphere, center of a sphere, radius of a sphere, hemisphere,
great circle
Materials:
 Holt textbook and Practice sheets
TAKS Information: July 2004 Exit Level #12, 24; Oct. 2005 Exit Level
#18, 41; Feb. 2006 Exit Level #32; July 2006 Exit #47; Apr. 2006 Exit #44
Teacher Notes: Whenever teachers have shared The Orange Problem
with their students, both the teacher and student responses have been
extremely positive. Try this before you use it with students.
Page 9 of 9
Holt = Geometry text DG = Discovering Geometry DC = Dana Center GSP = Geometer’s Sketchpad MCM = Region IV Making Connections w/Measurement ETQ = Ensuring Teacher Quality Modules
MTC = Geometry Math TEKS Connections