Geometry
Unit 4: Right Triangles and Polygon Properties
Second Grading Period – Weeks 1- 4 (18 days)
Enduring Understandings (Big Ideas)
Properties of right triangles, Pythagorean theorem and triples, special right triangles, and similarity will
be analyzed. Areas and perimeters of regular polygons will be expressed numerically and analytically.
Essential Questions
CURRICULUM OVERVIEW
Unit Rationale
Using constructions, Geometer’s Sketchpad and modeling will enhance
student learning on applications of right triangles and regular polygons.
Guiding Questions
√How do you determine if a triangle is a right triangle?
√How do you determine the sides of special right triangles?
√How do you apply special right triangles to determine the area and
Why are right triangles important?
How are right triangles useful?
perimeter of a regular polygon?
√How do you prove the Pythagorean Theorem on the coordinate plane?
√How do you visually represent the Pythagorean Theorem?
TEKS (Standards)
TEKS Specificity - Intended Outcome
(G.03.A) The student is expected to determine the validity of a conditional statement, its
converse, inverse, and contrapositive.
(G.03.B) The student is expected to construct and justify statements about geometric figures
and their properties.
(G.03.C) The student is expected to use logical reasoning to prove statements are true and find
counter examples to disprove statements that are false.
(G.5.A) use numeric and geometric patterns to develop algebraic expressions representing
geometric properties;
(G.5.B) use numeric and geometric patterns to make generalizations about geometric
properties, including properties of polygons, ratios in similar figures and solids, and angle
relationships in polygons and circles;
(G.5.D) identify and apply patterns from right triangles to solve meaningful problems, including
special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.
” I CAN” statements highlighted in yellow should be displayed
for students.
I can :
 use numeric and geometric patterns to develop algebraic
expressions representing geometric properties (G.5.A)
 use numeric patterns and apply them to regular polygons (G.5.B)
 identify right triangles and apply their properties where needed to
solve problems(G.5.D)
 determine the sides of a special right triangle using its
properties(G.5.D)
 represent geometric figures on the coordinate plane(G.7.A)
 determine the areas of regular polygons using special right
triangles(G.8.A)
 derive and model the Pythagorean theorem on the coordinate
plane(G.8.C)
 apply similarity properties to right triangles(G.11.C
(G.7.A) use one- and two-dimensional coordinate systems to represent points, lines, rays, line
segments, and figures.
(G.8.A) find areas of regular polygons, circles, and composite figures;
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
(G.8.C) derive, extend, and use the Pythagorean Theorem.
(G.09.B) The student is expected to formulate and test conjectures about the properties and
attributes of polygons and their component parts based on explorations and concrete models.
(G.11.A) The student is expected to use and extend similarity properties and transformations to
explore and justify conjectures about geometric figures.
(G.11.B) The student is expected to use ratios to solve problems involving similar figures.
(G.11.C) develop, apply, and justify triangle similarity relationships, such as right triangle
ratios, trigonometric ratios, and Pythagorean triples using a variety of methods.
ELPS






1E – Internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment.
2C – Learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions
2D – Monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed
3D – speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency
3E – Share information in cooperative learning interactions
4F – Use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop
vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language.
 5B – Write using newly acquired basic vocabulary and content-based grade-level vocabulary
College and Career Readiness Standards






III.A.3 Recognize and apply right triangle relationships including basic geometry
III.C.1 Make connections between Geometry and Algebra
III.C.3 Make connections between Geometry and Measurement
IV.C.1 Find the perimeter and area of two-dimensional figures
IV.C.3 Determine indirect measurements of figures using scale drawings, similar figures, the Pythagorean theorem, and basic trigonometry
X.B.2 Understand and use appropriate mathematical models in the natural, physical, and social sciences







Given a range of geometric properties, students will use numeric and geometric patterns to develop algebraic expressions for the properties at least 80% of the time.
Given a range of geometric properties, students will use numeric and geometric patterns to make generalizations about the properties at least 80% of the time.
Given an appropriate problem, students will identify and use patterns from right triangles to solve it at least 80% of the time.
Given geometric figures, students will use one- and two-dimensional coordinates systems to represent them at least 80% of the time.
Given a regular polygon, circle or composite figure, students will calculate the area at least 80% of the time.
Given a geometric figure, students will use the Pythagorean Theorem to calculate its properties at least 80% of the time.
Given triangle similarity relationships, students will develop, apply and justify them through a variety of methods at least 80% of the time.
Evidence of Learning (Summative Assessment)
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
Page 2 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Geometry
Unit 4: Right Triangles and Polygon Properties
CURRICULUM GUIDE
Second Grading Period – Weeks 1- 4 (18 days)
Essential Pre-requisite Skills
Grade 8
 estimate and find solutions to application problems involving percents and other proportional relationships such as similarity an rates (8.3B)
 use pictures or models to demonstrate the Pythagorean Theorem (8.7C)
 find lateral and total surface areas of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models) (8.8A)
 use the Pythagorean Theorem to solve real-life problems (8.9A)
 use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements (8.9B)
Algebra 1
 look for patterns and represent generalizations algebraically (A.3B)
The Teaching and Learning Plan
Instructional Model & Teacher Directions
The teacher will…
So students can….
Agile Mind
Instructional Hints
Make sure and read the Prepare Instruction for the given Topic. This area contains Goals and Objectives, Topic at a Glance, Prerequisite Skills, Resources and Language
support for the given Topic. Also make sure and read Delivering Instruction for the given Topic and block. This area contains Agile Mind materials, opening the lesson, framing
questions, lesson activities, and further questions for the given block. Both Prepare Instruction and Delivering Instruction can be found in the Advice for Instruction area. You
can find the Advice for Instruction area by clicking Show Professional Support under the View tab. It is also a good idea to make copies of Student Activity sheets the day
before in case the internet goes down. Also remember Agile Assessment has more TAKS formatted problems if needed.
 Days 1 -2
 Days 1 -2
 Modeling Right Triangles
 Modeling Right Triangles
 Engage
 Engage
 Provide the students with Pythagorean Models
 Draw squares with the given sides of a right triangle
 Determine the areas of the squares previously drawn (G.8.A)
 Post questions about the areas of given squares

 Explore
 Explore
 Record the areas of the squares around the given right triangles on the
activity sheet Part 1.(G.5.A)
 Explain

Divide the class in groups or individually allow the students to perform calculations
 Finish the part 1, part 2 and part 3 activity sheets.
of areas of the squares around a right triangle
 Model the use of equations to represent the Pythagorean theorem

Determine the difference between models that demonstrate the
 Explain
Pythagorean Theorem vs. others and explain them in your journal. (G.5.B)
 Elaborate

In their groups have the students finish the part 1, part 2 and part 3 activity sheets.
 Complete the Pythagorean Theorem Models – CW and HW activity sheets.
 Have students explain the Pythagorean Theorem in their journals in heir own words.
 Evaluate

 Student groups present their solutions to the rest of the class.
 Elaborate

 Have the students Complete the Pythagorean Theorem Models – CW and HW activity

sheets (Gradable Activity).
 Evaluate
 Have the student groups choose three of the problems and put the solutions on chart
paper.
 Have the student groups present their solutions to the rest of the class
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Days 3-4
Proving Pythagorean Theorem
Agile Mind Unit 13
Days 3-4
Proving Pythagorean Theorem
Agile Mind Unit 13
Day 3 Block 1 Overview, Exploring a Patty paper proof
Day 4 Block 2 Exploring Extending the Pythagorean Theorem
Day 3 Block 1 Overview, Exploring a Patty paper proof
Day 4 Block 2 Exploring Extending the Pythagorean Theorem
Days 5-6 - Section 7.1
Apply the Pythagorean Theorem
Days 5-6 - Section 7.1
Apply the Pythagorean Theorem
McDougal Littel Geometry
Section 7.1 Apply the Pythagorean Theorem
pg 435 Key Concept – Pythagorean Triples
pp436/7 Skills Practice 1-16
Explain
 Determine Pythagorean Triples
 Do the skills practice in pairs.(G.11.C)

Explain
 Use p435 to explain Pythagorean Triples

In pairs have the students do the skills practice problems. (Gradable Activity)
Evaluate
 Have each group do a class presentation of at least 2 of the problems
In your journal write at least 4 Pythagorean Triples and explain why
Pythagorean Triples they are important
Evaluate
 Do a class presentation on 2 of your problems
Days 7-8
Real World Applications
Days 7-8
Real World Applications
Similarity Pythagorean Theorem
Similarity Pythagorean Theorem HW
Elaborate
 Have the students do the activity sheets. (Gradable Activity)
 Apply Pythagorean theorem to real world applications
Elaborate
 Do the activity sheets(G.8C, G.11C)
 Place the teacher assigned on chart paper
 Do a Rotating Review
Evaluate


Assign each group 2-3 problems and have them place the solutions to these
problems on chart paper.
Evaluate
 Students should display their solutions and do a rotating review.
Day 9
Review of TAKS Geometry Questions
Evaluate
 Use TAKS samples
 Develop a Pythagorean assessment
Write the about the geometric representation of the theorem in your
journal (G.8C, G.11C)
Day 9
Review of TAKS Geometry Questions
Evaluate
 Work TAKS example problems to gain familiarity with content and format
 Present your solutions to another pair of students.

Have the students work through the problems in pairs
 Have the students discuss their problems to another pair
Days 10-11
Agile Mind Unit 16 Special Right Triangles
SAISD © 2010-11 – Second Grading Period
Days 10-11
Agile Mind Unit 16 Special Right Triangles
Mathematics- Geometry
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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Day 10 Block 1 Overview, Extending a Patty Paper Proof
Day 11 Block 2 Extending the Pythagorean Theorem
Day 10 Block 1 Overview, Extending a Patty Paper Proof
Day 11 Block 2 Extending the Pythagorean Theorem
Days 12
Section 7.4 Special Right Triangles
Days 12
Section 7.4 Special Right Triangles
McDougal Littel Geometry
Section 7.4 Practice A, B C, 49-54
Elaborate
 Provide detailed notes on how organize the measurement of
x, x, x 2
and
Elaborate
 Group the 45-45-90 and 30-60-90 exercises on MDL 7.4 practice A and B
 Regroup the exercises by the given measurement of its side i.e. those given
the hypotenuse in one group, those given the smallest side in other, and so
on (G.5.B)
x, x 3, 2 x
with its corresponding angles
 Provide detailed notes on how to determine the measure of missing sides beginning with
small side or hypotenuse or medium side
Evaluate
Evaluate
 Compare their solution with different groups
 Justify the answers verbally and algebraically

Set up class in small groups
 Observe and note mistakes made
 Have students present their solutions with justifications(Gradable Activity)
 Analyze some wrong solutions

Day 13
Problem Soving
Agile Mind Unit 16
Mars Task Hopewell Geometry
(Skip problem 2)
Days 14-17
Agile Mind Unit 17
Day 13
Problem Soving
Agile Mind Unit 16
Mars Task Hopewell Geometry
(Skip problem 2)
Days 14-17
Agile Mind Unit 17
Day 14 Block 1 Overview and the first part of the Exploring "Interior and exterior
angles of a polygon
Day 15 Block 2 Exploring " Interior and exterior angles of a polygon
Day 16 Block 3 Exploring “Special quadrilaterals”
Day 17 Block 4 Exploring “Special quadrilaterals”
Days 18
Review and Test
 Searching for student problem areas, have the students scan pages 493-497 to remind
them of what has been covered.
 In a whole class context, ask the students to list the problem areas.
 Address the problem areas first conceptually, then by working appropriate problems from
page 498.
 Consider grouping students with common challenges with peer tutors,
Evaluate
 Time allowing, assign problems to individuals to be posted during class period – one from
each section that has not yet been discussed.
 Wrap up with one last call for questions.
SAISD © 2010-11 – Second Grading Period
Cross-reference their solutions with their notes
Day 14 Block 1 Overview and the first part of the Exploring "Interior and
exterior angles of a polygon
Day 15 Block 2 Exploring " Interior and exterior angles of a polygon
Day 16 Block 3 Exploring “Special quadrilaterals”
Day 17 Block 4 Exploring “Special quadrilaterals”
Days 18
Review and Test
Engage
 review pages 493-497 to see what has been covered in this unit and to
determine where questions might still exist
 contribute challenges to the class list
Evaluate
 ensure that his/her problem area(s) is (are) addressed
 participate in peer tutor groupings
 work problems as assigned from page 498
 take assessment(Gradable Activity)
Mathematics- Geometry
Page 5 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
 Administer assessment ensuring alignment with guiding TEKS
 Ensure that assessment questions are aligned with the guiding TEKS
 Have the following materials on hand
graphing calculators
paper
pencils
Vocabulary: (Pertinent to the learning – specific)
 Pythagorean theorem
 hypotenuse
 Pythagorean triple
 Right triangle
 Special right triangle
 Angle of elevation
 Angle of depression
 Solving the right triangle
 Ratio
 Regular polygon
 Area
 Perimeter
 Pentagon
 Hexagon
 Radius
 Diagonal
 similarity
TAKS Vocabulary
 use
 develop
 represent
 generalization
 identify
 apply
 solve
 understands
 determine
 extends
 find
 derive
 applies
 justify
Resources
Resources:
Days 1-2
Activity: Pythagorean Models
Day 3-4
Agile Mind Unit 13
Proving Pythagorean Theorem
Exploring Geometry with The Geometer’s Sketchpad
• pp 163-164 The Square Root Spiral
Days 5-6
McDougal Littel Geometry
• Section 7.1 Apply the Pythagorean Theorem
• pg 435 Key Concept – Pythagorean Triples
• pp436/7 Skills Practice 1-16
Days 7-8
Activity: Similarity vs Pythagorean Theorem
Activity: Similarity vs Pythagorean Theorem HW
Day 9
TEA Website
Days 10-11
Agile Mind Unit 16 Special Right Triangles
McDougal Littel Geometry
pg 461 Skill Practice – Special Right Triangles 11,12
Days 12-13
McDougal Littel Geometry
Section 7.4 Practice A, B C, 49-54
Days 14-17
Agile Mind Unit 17
Days 18
McDougal Littel Geometry
pp 493-498 Chapter Summary, Chapter Review, Chapter Test
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
Page 6 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Evidence of Learning (Summative Assessment)
Formative Mini Assessments
TAKS
15 The drawing below shows how 3 squares
can
be joined at their vertices to form a right
triangle.
College-Readiness i.e.,
Anticipated Skills for SAT/ACT/College Board/Career/Life
42 To estimate the height of her school’s gym,
Nicole sights the top of the gym wall in a mirror
that she has placed on the ground. The mirror
is 3.6 meters from the base of the gym wall.
November 2008 FMA
Which is closest to the area in square inches
of
the largest square?
May 2009 FMA
in 2
2
B 233 in
2
C 210 in
2
D 1073 in
A 1914
Nicole is standing 0.5 meter from the mirror,
and her height is about 1.8 meters. What is
the height of the gym wall?
F1m
G 5.9 m
H 7.2 m
J 12.96 m
May 2009 FMA
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
Page 7 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Geometry
Unit 5: Coordinate Geometry
CURRICULUM OVERVIEW
Second Grading Period – Weeks 5 – 7 (11 days)
Enduring Understandings (Big Ideas)
Unit Rationale
Specify locations and describe spatial relationships using coordinate geometry and other
representational systems (NCTM Geometry standard)
Students should understand that:
The distance formula is an application of the Pythagorean theorem.
The midpoint formula is easily derived and has useful applications.
Quadrilaterals have unique and defining properties.
Essential Questions
Guiding Questions
√How can you find the midpoint of a segment?
√How can you find the distance between two points or the length of a segment?
√What properties define a square?
√What properties define a rectangle?
√What properties define a rhombus?
Why is Coordinate Geometry important?
How is Coordinate Geometry useful?
How do you find the midpoint or distance of a line?
TEKS (Standards)
TEKS Specificity - Intended Outcome
G.2(A) use constructions to explore attributes of geometric figures and to make
conjectures about geometric relationships
(G.03.A) The student is expected to determine the validity of a conditional
statement, its converse, inverse, and contrapositive.
” I CAN” statements highlighted in yellow should be displayed for students.
I can:


(G.03.B) The student is expected to construct and justify statements about
geometric figures and their properties.

(G.03.C) The student is expected to use logical reasoning to prove statements are
true and find counter examples to disprove statements that are false.


G.7(A) use one- and two-dimensional coordinate systems to represent points, lines,
rays, line segments, and figures;

use constructions to explore lengths of segments and properties of
midpoints.(G.2A)
use one and two-dimensional coordinate systems to represent points and
line segments(G.7A)
use slopes and equations of lines to investigate geometric
relationships.(G.7B)
derive and use formulas involving length, slope and midpoint.(G.7C)
use the Pythagorean theorem to find the distance between two
points.(G.8C)
formulate and test statements made about geometric figures based on
experimentation or models (G.9B)
G.7(B) use slopes and equations of lines to investigate geometric relationships,
including parallel lines, perpendicular lines, and special segments of triangles and other
polygons
G.7(C) derive and use formulas involving length, slope, and midpoint
(G.08.A) The student is expected to find areas of regular polygons, circles, and
composite figures.
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
Page 8 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
G.8(C) derive, extend, and use the Pythagorean Theorem
G.9(B) formulate and test conjectures about the properties and attributes of polygons
and their component parts based on explorations and concrete models
ELPS
1E – Internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment.
2C – Learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions
2D – Monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed
3D – speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency
3E – Share information in cooperative learning interactions
4F – Use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop
vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language.
5B – Write using newly acquired basic vocabulary and content-based grade-level vocabulary
College and Career Readiness Standards
III.A.3 Recognize and apply right triangle relationships including basic geometry
III.C.1 Make connections between Geometry and Algebra
III.C.3 Make connections between Geometry and Measurement
IV.C.1 Find the perimeter and area of two-dimensional figures
IV.C.3 Determine indirect measurements of figures using scale drawings, similar figures, the Pythagorean theorem, and basic trigonometry
X.B.2 Understand and use appropriate mathematical models in the natural, physical, and social sciences
Evidence of Learning (Summative Assessment)






Given a geometric figure, students will use constructions to explore the relationships between its properties at least 80% of the time.
Given a geometric figure, students will use either a one-or two-dimensional coordinate system to represent its parts at least 80% of the time
Given a geometric figure, students will use slopes and equations to investigate relationships at least 80% of the time.
Given a geometric figure, students will derive and use formulas for length, slope and midpoint at least 80% of the time.
Given a geometric figure, students will use the Pythagorean Theorem to determine measurements as appropriate at least 80% of the time.
Given a geometric figure, student will formulate and test conjectures regarding its properties and attributes based on investigation of concrete models at least 80% of the time.
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
Page 9 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Geometry
Unit 5: Coordinate Geometry
CURRICULUM GUIDE
Second Grading Period – Weeks 5 – 7 (11 days)
Essential Pre-requisite Skills
Grade 8



Use the Pythagorean theorem to solve real-life problems (8.9A)
Locate and name points on a coordinate plane using ordered pairs of rational numbers(8.7D)
Use geometric concepts and properties to solve problems(8.7B)
The Teaching and Learning Plan
Instructional Model & Teacher Directions
The teacher will…
So students can….
Agile Mind
Instructional Hints
Make sure and read the Prepare Instruction for the given Topic. This area contains Goals and Objectives, Topic at a Glance, Prerequisite Skills, Resources and Language
support for the given Topic. Also make sure and read Delivering Instruction for the given Topic and block. This area contains Agile Mind materials, opening the lesson, framing
questions, lesson activities, and further questions for the given block. Both Prepare Instruction and Delivering Instruction can be found in the Advice for Instruction area. You
can find the Advice for Instruction area by clicking Show Professional Support under the View tab. It is also a good idea to make copies of Student Activity sheets the day
before in case the internet goes down. Also remember Agile Assessment has more TAKS formatted problems if needed.
Day 1-3
Day 1-3
Distance and Midpoint Formula
Distance and Midpoint Formula
Agile Mind Unit 13
Agile Mind Unit 13
Day 1 Block 3 Exploring "The distance and midpoint formulas"
Day 1 Block 3 Exploring "The distance and midpoint formulas"
Day 2 Block 4 Exploring "The distance and midpoint formulas," the Summary
Day 2 Block 4 Exploring "The distance and midpoint formulas," the Summary
Day 3 Block 5 topic level assessment
Day 3 Block 5 topic level assessment
Day 4
Elaborate


Have students work on “Problem Solving with Distance and Midpoint
Formula handout” in pairs.
Have the pair present their solutions to another pair.
Day 5
Elaborate

Have students work on Problem Solving with Midpoint Formula handout
in pairs.

Have the pair present their solutions to another pair.
Evaluate

Have the students explain the use of the midpoint and distance formula in their
journals.
SAISD © 2010-11 – Second Grading Period
Day 4
Elaborate

Practice using the midpoint formula by working on assigned handout in their
groups. (Gradable Activity)

Problem Solving with Distance and Midpoint Formula.(G.7C)

In their journals have the students explain in detail how the distance
and midpoint formula are used.
Day 5
Elaborate

Work on Problem Solving with midpoint Formula (G.7C)
Evaluate
Mathematics- Geometry

Demonstrate and explain the use of the midpoint and distance formula
in your journal. (Gradable Activity)
Page 10 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Day 6-8
Agile Mind Unit 21
Day 6-8
Agile Mind Unit 21
Day 6 Block 1 Overview, the Exploring “Shear mathematical magic
Day 7 Block 2 Exploring “More area formulas”
Day 8 Block 3 Exploring “More area formulas”
Day 6 Block 1 Overview, the Exploring “Shear mathematical magic
Day 7 Block 2 Exploring “More area formulas”
Day 8 Block 3 Exploring “More area formulas”
Day 9
Investigating Quadrilaterals Teacher Notes
Day 9
Activity 1 :Squares
Activity 1: Squares
Engage:

Draw a square, either on the whiteboard or on GSP. Ask them what it is. Once
students respond, ask them how they know it is a square.
Explore:

Have students work on #1 and #2 in pairs while you walk around facilitating
if necessary.
Explain:

Have students work on # 3. Then, as a class, discuss some of the conjectures
they wrote.
Elaborate/Evaluate:

Have students work on #4 creating a square that satisfies the condition given:
(Gradable Activity)
Engage:

Respond to teacher’s questions and participate in discussion.
Explore:

Work on problems #1 and #2, asking the teacher for help if
necessary.(G.7A, G.7B, G.9B)
Explain:

Work on # 3. Then, as a class, discuss some of the conjectures
found.(G.7A, G.7B, G.9B)
Elaborate/Evaluate:

Work on #4 creating a square that satisfies the condition given:

Day 10
Activity 2 : Rectangles
Day 10
Activity 2 :Rectangles
Engage:

Draw a rectangle, either on the whiteboard or on GSP. Ask them
what it is. Once students respond, ask them how they know it is a rectangle.
Explore:

Have students work on #1 and #2 in pairs while you walk around facilitating
if necessary.
Explain:

Have students work on # 3 . Then, as a class, discuss some of the conjectures
they wrote.
Elaborate/Evaluate:

Have students work on #4 creating a rectangles that satisfies the condition given:
SAISD © 2010-11 – Second Grading Period
Explain the properties of a square in your journal.
Engage:

Respond to teacher’s questions and participate actively in discussion.
Explore:

Work on problems #1 and #2, asking the teacher for help if
necessary.(G.7A, G.7B, G.9B)
Explain:

Work on # 3 . Then, as a class, discuss some of the conjectures
found.(G.7A, G.7B, G.9B)
Elaborate/Evaluate:

Work on #4 creating a rectangle that satisfies the condition given( G.7A,
G.7B, G.9B).
Mathematics- Geometry
Page 11 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
(Gradable Activity)

Day 11
Activity 3 : Rhombi
Day 11
Activity 3 Rhombi
Engage:

Draw a rhombus, either on the whiteboard or on GSP. Ask them what it is. Some
students may answer a parallelogram, which is correct but not specific enough.
Explain that this is a rhombus.
Explore:

Have students work on #1 and #2 in pairs while you walk around facilitating
if necessary.
Explain:

Have students work on # 3. Then, as a class, discuss some of the conjectures
they wrote.
Elaborate/Evaluate:

Have students work on #4 and #5. (Gradable Activity)
Vocabulary: (Pertinent to the learning – specific)

distance

length

midpoint

Pythagorean Theorem

midpoint formula

distance formula

parallel

perpendicular

congruent

rhombus

congruence

conjecture

construction

attributes
SAISD © 2010-11 – Second Grading Period
Explain the properties of a rectangle in your journal.
Engage:

Respond to teacher’s questions and participate actively in discussion.
Explore:

Work on problems #1 and #2, asking the teacher for help if
necessary.(G.7A, G.7B, G.9B)
Explain:

Work on # 3 . Then, as a class, discuss some of the conjectures
found.(G.7A, G.7B, G.9B)
Elaborate/Evaluate:

Work on #4 and #5 ( G.7A, G.7B, G.9B).
TAKS Vocabulary

analyzes

make

verify

understands

represent

investigate

derive

use

determine

extend

find

formulate

test

Explain the properties of a square in your journal.
Resources
Day 1-3
Agile Mind Unit 13
Day 4
Problem Solving with Distance and
Midpoint Formula handout
Day 5
Problem Solving with Midpoint
Formula handout
Day 6-8
Agile Mind Unit 21
Day 9-11
Investigating Quadrilateral
Properties 2.0 Teacher Notes
Day 9
Activity 1: Squares
Day 10
Activity 2 : Rectangles
Day 11
Activity 3 : Rhombi
Mathematics- Geometry
Page 12 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Evidence of Learning (Summative Assessment)
Formative Mini Assessments
TAKS
College-Readiness i.e.,
Anticipated Skills for SAT/ACT/College Board/Career/Life
TAKS April 2006 # 25 (G.7C)
November 2008 FMA
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
Page 13 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Geometry
Unit 5: Transformations
CURRICULUM OVERVIEW
Second Grading Period – Weeks 7 – 9 (9 days)
Enduring Understandings (Big Ideas)
Unit Rationale
Students should understand:

and represent translations, reflections, rotations, and dilations of objects in the
plane by using sketches, coordinates, and vectors;

to use various representations to help understand the effects of simple
transformations and their compositions.
Apply transformations and use symmetry to analyze mathematical situations (NCTM)
Essential Questions
Guiding Questions
√How does a translation change the coordinates of a figure?
√How does a reflection affect the coordinates of a figure?
√How does a center of dilation affect where the dilated figure is located?
What are the different transformations?
How are the different transformations the same and different?
What is a tessellation?
TEKS (Standards)
TEKS Specificity - Intended Outcome
(G.02.B) The student is expected to make and verify conjectures about angles,
lines, polygons, circles, and three-dimensional figures and determine the validity of
the conjectures, choosing from a variety of approaches such as coordinate,
transformational, or axiomatic.
” I CAN” statements highlighted in yellow should be displayed for students.
I can:

(G.5C) use properties of transformations and their compositions to make
connections between mathematics and the real world, such as tessellations.

( G.7A) use one- and two-dimensional coordinate systems to represent points,
lines, rays, line segments, and figures.



(G.08.A) The student is expected to find areas of regular polygons, circles, and
composite figures.
use properties of transformations and their compositions to make connections
between mathematics and the real world. (G.5C)
use one- and two- dimensional coordinate systems to represent points, lines,
rays, line segments and figures. (G.7A)
use congruence transformations to make conjectures. (G.10A)
justify properties of geometric figures including figures represented on a
coordinate plane. (G.10A)
use and extend similarity properties and transformations to explore and justify
conjectures about geometric figures. (G.11A)
(G.10A) use congruence transformations to make conjectures and justify
properties of geometric figures including figures represented on a coordinate plane.
(G.11A) use and extend similarity properties and transformations to explore and
justify conjectures about geometric figures.
ELPS
1E – Internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment.
2C – Learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions
2D – Monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed
3D – speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency
3E – Share information in cooperative learning interactions
4F – Use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop
vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language.
5B – Write using newly acquired basic vocabulary and content-based grade-level vocabulary
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
Page 14 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
College and Career Readiness Standards
III.A.3 Recognize and apply right triangle relationships including basic geometry
III.C.1 Make connections between Geometry and Algebra
III.C.3 Make connections between Geometry and Measurement
IV.C.1 Find the perimeter and area of two-dimensional figures
IV.C.3 Determine indirect measurements of figures using scale drawings, similar figures, the Pythagorean theorem, and basic trigonometry
X.B.2 Understand and use appropriate mathematical models in the natural, physical, and social sciences
Evidence of Learning (Summative Assessment)




Given a geometric relationship, students will use the properties of transformations and their compositions to make connections to the real world at least 80% of the time.
Given a geometric figure, students will use one-and two-dimensional coordinate systems to represent its parts or properties at least 80% of the time.
Given a geometric figure, students will use congruence transformations to make conjectures about and justify its properties at least 80% of the time.
Given a geometric figure, students will use similarity properties and transformations to explore and justify conjectures at least 80% of the time.
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
Page 15 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Geometry
Unit 5: Transformations
CURRICULUM GUIDE
Second Grading Period – Weeks 7 – 9 (9 days)
Essential Pre-requisite Skills
Grade 8

generate similar figures using dilations including enlargements and reductions (8.6A)

graph dilations, reflections, and translations on a coordinate plane (8.6B)

locate and name points on a coordinate plane using ordered pairs of rational numbers (8.7D)
Algebra 1

develop the concept of a slope as a rate of change and determine slopes from graphs, tables, and algebraic representations (A.6A)
The Teaching and Learning Plan
Instructional Model & Teacher Directions
The teacher will…
So students can….
Agile Mind
Instructional Hints
Make sure and read the Prepare Instruction for the given Topic. This area contains Goals and Objectives, Topic at a Glance, Prerequisite Skills, Resources and Language
support for the given Topic. Also make sure and read Delivering Instruction for the given Topic and block. This area contains Agile Mind materials, opening the lesson, framing
questions, lesson activities, and further questions for the given block. Both Prepare Instruction and Delivering Instruction can be found in the Advice for Instruction area. You
can find the Advice for Instruction area by clicking Show Professional Support under the View tab. It is also a good idea to make copies of Student Activity sheets the day
before in case the internet goes down. Also remember Agile Assessment has more TAKS formatted problems if needed.
Day 1 – 5
Day 1 – 5
Transformations
Transformations
Agile Mind Unit 3
Agile Mind Unit 3
Day 1 Block 1 Overview, the Exploring "Translations and reflections"
Day 2 Block 2 Exploring "Translations and reflections"
Day 3 Block 3 Exploring "Reflections and rotations"
Day 4 Block 4 Exploring "Applications of rigid transformations"
Day 5 Block 5 Exploring “Applications of rigid transformations,” “Symmetry in
polygons”
Day 1 Block 1 Overview, the Exploring "Translations and reflections"
Day 2 Block 2 Exploring "Translations and reflections"
Day 3 Block 3 Exploring "Reflections and rotations"
Day 4 Block 4 Exploring "Applications of rigid transformations"
Day 5 Block 5 Exploring “Applications of rigid transformations,” “Symmetry in polygons”
Day 6 - 9
Agile Mind Unit 14
Dilations and Similarity in Polygons
Day 6 Block 1 Overview and the Exploring “Are these shapes similar?”
Day 7 Block 2 Exploring “Are these shapes similar?”
Day 8 Block 4 Exploring “Dilations”
Day 9 Block 5 Exploring “Dilations,” and the Constructed response
SAISD © 2010-11 – Second Grading Period
Day 6 -9
Agile Mind Unit 14
Dilations and Similarity in Polygons
Day 6 Block 1 Overview and the Exploring “Are these shapes similar?”
Day 7 Block 2 Exploring “Are these shapes similar?”
Day 8 Block 4 Exploring “Dilations”
Day 9 Block 5 Exploring “Dilations,” and the Constructed response
Mathematics- Geometry
Page 16 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Vocabulary: (Pertinent to the learning – specific)

Transformation

Dilation

Rotation

Reflection

Scale factor

Tessellation

Rotational symmetry

isometric

Translation
SAISD © 2010-11 – Second Grading Period
TAKS Vocabulary

Describe

Use

Understands

Represents

Apply

Justify

Solve

Make

Extend
Mathematics- Geometry
Resources
Agile Mind Unit 3
Agile Mind Unit 14
Page 17 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.
Evidence of Learning (Summative Assessment)
Formative Mini Assessments
None Available
TAKS
College-Readiness i.e.,
Anticipated Skills for SAT/ACT/College Board/Career/Life
Grade 10 2006 released test Item #4
None available
Grade 10 2006 released test Item #34
SAISD © 2010-11 – Second Grading Period
Mathematics- Geometry
Page 18 of 18
Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required
assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.