Roselle School District
Roselle School District
Mathematics Curriculum
Grade 8 Unit 9: Foundations of Geometry: Transformations, Angle Relations, Parallel lines with Transversals
Essential Question(s) / Enduring Understanding(s)What is the effect of dilations, translations, rotations, and reflections on two-dimensional figures in the coordinate plane?
How can you determine if a figure is similar to a second figure on the coordinate plane?
How can you determine if a figure is congruent to another figure on the coordinate plane? / A two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.
A two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.
Summative Assessment Task
See attached word document
Common Core Standards, 2010
Understand congruence and similarity using physical models, transparencies, or geometry software.
- 8. G.1. Verify experimentally the properties of rotations, reflections, and translations:
- a. Lines are taken to lines, and line segments to line segments of the same length.
- b. Angles are taken to angles of the same measure.
- c. Parallel lines are taken to parallel lines.
- 8. G.2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
- 8. G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
- 8. G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
- 8. G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
- W8.2 Write informative/explanatory texts to examine a topic and convey ideas, concepts and information through the selection, organization, and analysis of relevant content.
- 8. G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Learning Expectations
TLWBAT… / Activities/Resources / Student Strategies/Modifications/Differentiation / Formative Assessments / Technology Integration
Classify angles and find their measurements when parallel lines are cut by a transversal(Parallel, perpendicular, and intersecting planes/ Complementary and supplementary angles) / Introduction:
Students will be given various pictures of angles (acute, right, obtuse, and straight line). There task is to hold up a card (with the names of the cards of the angles), and identify each angle.
Guided practice:
Students will classify angles and find their measures. Three new angle measures will be introduced using Smart board activities (straight angle, complementary angle, and supplementary angle). Students will use various diagrams to find the measure of each angle.
Students will then be introduced to adjacent, congruent, and vertical angles. They will see these special relationships have similarities because of their positions to other angles.
Independent Practice:
Students will complete math stations based on naming each angle in the given diagrams and use the diagram to find the measure of each angle.
Students will also complete a true/false portion of open ended questions by identifying if the statement is true based on definitions or false based on wrong measurements.
Students will identify parallel and perpendicular lines and the angles formed by the transversal.
SECOND LESSON
Introduction:
Students will be shown a window picture on the Smart board. They will identify the transversal and parallel lines located on window. These lines will be shown as the panes in the window.
Students will also draw tic tac toe boards and will describe the lines in the given board.
Guided practice:
Students will identify alternate interior angles, alternate exterior angles, and corresponding angles.
After indentifying congruent angles formed by a transversal, students will then find the missing angle measurements formed by the transversal. Smart board examples will be shown for guided practice.
Independent practice:
Students will work on a practice math handout identifying congruent angles and their measurements. Challenging questions will be given in order to make conjectures and solve extended responses.
Mini Review:
2-5-8 menu
Students will complete any activity from the 2-5-8 menu. Rubrics will be shown. All work must be shown for review / Small group instruction
Review of printed notes from smart board. Activities completed in small group for more of an understanding
Individualized instruction
Peer tutoring
Team up stronger math skills with lower math skills
Use of manipulatives
Reference sheets
Classroom posters
Computer activities for remediation
Choice activities/Chunking information
Reference sheets for each transformation
Rephrasing of questions
Red robin questionnaire
Review discussion
Working with partner
Video tutorials from textbook / Exit ticket
7-2 transparency (page 339 in teacher edition)
Name all congruent angles
Name all supplementary angles
Find the measure of angle 3 and 6.
Journal entry
Think of two real world scenarios of parallel lines. Write about how these examples are different from the mathematical concept of parallel lines.
Do now
LOTI POD
Problem of the Day form textbook
Quiz
Parallel lines with Transversals
Congruent measurements
Angle Relationships A, B, C (quiz, advanced, and modified)
Test
Summative Assessment
Oral questioning
IEP recommendation
Minute paper
Name all alternate interior angles
Alternate exterior
Corresponding
Supplementary
Complementary angles
Transfer and apply
Knowledge of math stations from previous day
Homework
Holt McDougal worksheet
Stations work
2-5-8 Menu / Jeopardy game:
Angle relations:
Geometry questions:
Quizlet:
Rags to riches angle relationships:
who wants to be a millionaire:
angle relations jeopardy game:
Google Sites:
Determine the unknown angle sum of interior and exterior angles and possible length of any triangle / Introduction: Students will be given a geo board in order to create triangles with rubber bands. They will create three different triangles (small, medium, and large).
Students will shown and determine if one of the angles gets larger, another angle gets smaller. This fact, once discussed, will support the Triangle Sum Theorem (all angles add up to 180 degrees for all triangles)
Guided practice: In this lesson, students learn to find the unknown angles in triangles. The Triangle Sum Theorem is one of the most important theorems in geometry. Illustrate the theorem by tearing off tow corners of a paper triangle and placing them next to the third corner to form a straight line, which measures 180 degrees. Explain triangles can have at most one right triangle or one obtuse angle because of the theorem.
Examples will be shown on the Smart board for student interaction and modeling.
Independent practice: Triangles will be displayed on the white board (blown up). Students must find the missing angle measurement for each triangle and display their answer in the answer key. Packets will be given out to others if they choose not to move up to board.
Students will also complete a check list for each problem using the Triangle Sum Theorem. / Small group instruction
Review of printed notes from smart board. Activities completed in small group for more of an understanding
Individualized instruction
Peer tutoring
Team up stronger math skills with lower math skills
Use of manipulatives
Reference sheets
Classroom posters
Geo boards
Rubber bands
Ripped triangle papers
Computer activities for remediation
Choice activities/Chunking information
Reference sheets for each transformation
Rephrasing of questions
Red robin questionnaire
Review discussion
Working with partner
Video tutorials from textbook / Exit ticket
Solve each equation to determine the missing value:
62 + x + 37 = 180
X + 90 + 11 = 180
180 = 3 x + 72
Transparency Display:
Find c in the right triangle
Find m in the obtuse triangle
Find the angle measures in the isosceles triangle
Find the angle measures in the scalene triangle.
Journal entry
Explain whether a right triangle can be equilateral. Can it be isosceles? Scalene?
Explain whether a triangle can have 2 right angles. Can it have 2 obtuse angles?
Do now
LOTI POD
Problem of the Day form textbook (look in each section of the chapter)
Quiz
Triangle Sum Theorem Quiz
Test
Summative Assessment
Oral questioning
IEP recommendation
Minute paper
Given as many equations as possible, find the value of x
Transfer and apply
Knowledge of math stations from previous day
Homework
Holt McDougal worksheet
Stations work / ESL learners
Drag definitions
More advance
Videos
Google Sites:
Identify polygons and midpoints of segments in a coordinate plane / Introduction:
Students will identify polygons and midpoints of segments in the coordinate plane. Students will be given graph paper and coordinates displayed on the smart board. They will identify the quadrilateral with the proper names for it (i.e. parallelogram, square, rectangle, rhombus, trapezoid, and quadrilateral). Although the figure seems to be some form of a quadrilateral, we need to prove it mathematically.
Students will determine the proper name by plotting the points and finding the distance from one coordinate to another. (alternate opener from Holt/McDougal 7-5)
Guided Instruction:
In this lesson, students will learn to identify polygons on a coordinate plane. They will show different ways for a quadrilateral via Smart board. They will then work in pairs to create various quadrilaterals given the different vertices. They then will exchange papers and write the length of each line segment along with calculating the midpoint to each line segment.
Independent practice:
Students will create a mystery image on a coordinate plane for the fall (you can choose any picture).
The will then plot the points and find the midpoint of each line. All work will be shown on a separate sheet of paper. Students will then cut out different leaves and place it on construction paper. Rubric will be given for grading scale. / Small group instruction
Review of printed notes from smart board. Activities completed in small group for more of an understanding
Individualized instruction
Peer tutoring
Team up stronger math skills with lower math skills
Use of manipulatives
Reference sheets for midpoint formula
Classroom posters
Geo boards
Rubber bands
Graph paper with coordinate graph already displayed
Computer activities for remediation
Choice activities/Chunking information
Rephrasing of questions
Red robin questionnaire
Review discussion
Working with partner
Video tutorials from textbook (Holt/McDougal website)
Google Site with remediation / Exit ticket
Find the coordinates of the midpoint of AB (page 355 from teacher textbook)
Journal entry
Explain how you can determine whether a triangle on the coordinate plane is isosceles.
Write step by step instructions for finding the midpoint of a line segment on the coordinate plane.
Do now
LOTI POD
Problem of the Day form textbook
Quiz
Midpoint formula
Coordinate graphing (A, B, and C for modifications)
Test
Summative Assessment
Oral questioning
IEP recommendation
Minute paper
Plot as many points as possible on a coordinate graph
Transfer and apply
Knowledge of math stations from previous day
Homework
Holt McDougal worksheet
Google Site / Google Site created b teacher:
Midpoint formula project
Midpoint formula:
Videos for help:
4.2.8A
Understand and apply concepts involving lines, angles, and planes.
Bisectors and perpendicular bisectors
Using proportions to find missing measures
Scale drawings / Introduction:
Students will be introduce to the concept of parallel and perpendicular lines by asking them to describe the liens that separate the panes in a window or the lines between tiles on a tic-tac-toe game on the board. Students will then have an open discussion in describing the lines.
Guided Practice:
Real world scenario: A carpenter cuts boards at different angles. The board below is cut at a 45 degree angle.
(Diagram given on page 336)
- Label the angles formed by the cut
- Which angles are congruent, or have the same measure?
- Which angles are supplementary, or have measures that add to 180 degrees?
- Label the angles formed by the cut
- Which angles are congruent, or have the same measure?
- Which angles are supplementary, or have measures that add to 180 degrees?
- Describe the top and bottom edges of the board above. What kinds of lines do they form
- Describe the angles formed after cutting the board at a 90 degree angle.
Math tutoring session at small round table
Individualized instruction
Students work independently
Peer tutoring
Use of manipulatives
Windows in classroom
Smart board
White erase boards
Computer activities for remediation
See technology
Choice activities
Various examples given for reference and exemplars
Chunking information
Calculate all vertical angles
Calculate all supplementary angles
Calculate all complementary angles
Identify corresponding, alternate interior/exterior angles
Video tutorials from textbook / Exit ticket
What are corresponding angles?
What are alternate interior angles?
What are alternate exterior angles?
What is the definition of complementary angles?
What is the definition of supplementary angles?
Do now
POD from LOTI
Quiz
Angle Identification
Angles with Lines quiz
Test
Summative Assessment
Oral questioning
IEP recommendation
Minute paper
Name all angles for corresponding, alternate interior, exterior, supplementary, complementary
Transfer and apply
Knowledge from grade 6 and 7 on angles
Cubing Activities
Separate various angles for remediation
Homework
Holt McDougal book
Stations work / Complementary quiz:
Supplementary angles
Find pairs:
Quiz game:
Practice Problems for transversals:
Crossword puzzle:
Angle quiz show:
Google Sites:
Describe a sequence that exhibits the congruence between two congruent figures / Introduction:
Students will examine a transparency on the Smart board of various figures. A statement will be shown: “Congruent figures have the same size and shape.”
They will determine whether the figures in each pair are congruent by writing congruent or not congruent on white boards.
Think and Discuss questions:
- How do you decide whether figures in problems 1-4 were congruent?
- Find two examples of objects that are congruent. What makes the two objects congruent?
Students learn to use properties of congruent figures to solve problems. Lesson will begin by showing students how to write a congruence statement for a pair of congruent polygons. Make sure students understand the concepts of corresponding sides and corresponding angles.
Guided practice problems with vocabulary words on smart board created by teacher
Independent practice:
Power point on Congruent statements and finding the missing unknown measurement on a Google Site for guided practice on labeling congruent statements and determining the missing measurement or angle measure. .
What’s the error? Word problem
Write about it: how can knowing two polygons are congruent help you find angle measures of the polygons?
Challenge: Triangle ABC is congruent to triangle LMN and line segment AE is parallel BD. Find the measure of ACD (page 363).
Problem solving activity:
7-6 handout / Small group instruction
Review of printed notes from smart board. Activities completed in small group for more of an understanding
Individualized instruction
Peer tutoring
Team up stronger math skills with lower math skills
Use of manipulatives
Reference sheets
Classroom posters
Computer activities for remediation
Choice activities
Power point: start at any point
Working with partner
Video tutorials from textbook / Exit ticket
Write the congruence statement for each pair of congruent polygons
In the figure, quadrilateral VWXY is congruent to quadrilateral JKLM
Find a, b, and c
(page 361 teacher edition)
Journal entry
Explain the difference between congruent and similar polygons
Tell how to write a congruence statement for two polygons
Do now
LOTI PODs
Problem of the Day form textbook
Quiz
Congruence quiz
Finding the missing unknown (10 open ended problems)
Test
Summative Assessment
Oral questioning
IEP recommendation
Accommodation
Minute paper
Name all corresponding sides and angles
Transfer and apply
Degrees of polygons activity
Homework
Handout from Holt McDougal
Stations work / Congruent shapes:
Relations and size
Congruent shapes
Similar or Congruent
Google Site:
Verify experimentally the properties of rotations, reflections, and translations.
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Understand that a two-dimensional figure is congruent/ similar to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.
4.2.8B
Understand and apply transformations.
Finding the image, given the pre-image, and vice-versa
Use iterative procedures to generate geometric patterns.
Self-similarity
Construction of initial stages / Introduction:
Video on an amusement park for a Problem based learning introduction:
Scariest roller coasters
Students will answer the following questions when viewing videos: