Web viewThe vocabulary word concave and hexagon might cause students hesitation on the problem even though a picture is provided and in this problem it is not

Lesson Plan Template (Stages adapted from the UBD model by McTighe and Wiggins)

Teacher: Date(s): 9/8-9/15

Grade Level or Course: Geometry Content or Unit: Coordinate Formulas

STAGE 1: Desired Results ~ What will students be learning?

SOL/Learning Objective

G.3 The students will use pictorial representations, including computer software, constructions, and coordinate methods to solve problems involving symmetry and transformations. This will include:a. investigating and using formulas for finding distance, midpoint, and slope;b. applying slope to verify and determine whether lines are parallel or perpendicular;c. investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; andd. determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.

Daily Lesson Objectives:9/8-9/9 9/10-9/11 9/12-9/15

Given the coordinates of the endpoints, students will find the coordinates of the midpoint and apply the distance formula to find the length of a line segment with at least 70% accuracy on the mastery check.

1. Given a graph or coordinates, students will use a formula to find the slope of a line. 2. Students will compare the slopes to determine whether two lines are parallel, perpendicular or neither. 3. Students will plot points that are either parallel or perpendicular to a given line. Once students have completed objectives 1-3, they will complete a mastery check with at least 70% accuracy.

Students will determine whether a figure has point symmetry, line symmetry, both, or neither. Students, given an image, will identify the transformation that has taken place as a reflection, rotation, dilation, or translation with at least 70% accuracy.

NOTE: Students with scores 69% or below will complete corrections and are required to retake the mastery check during tutoring or Falcon 45. Students who score between 70 and 99% are required to complete corrections. Students who receive 100% join the Wall of Champions board.

Richmond Public Schools 2014-15 1


Essential Questions &

Understandings/Big Ideas

Transformations and combinations of transformations can be used to describe movement of objects in a plane. The distance formula is an application of the Pythagorean Theorem. Geometric figures can be represented in the coordinate plane.Techniques for investigating symmetry may include paper folding, coordinate methods, and dynamic geometry software. Slope is a rate of change. Parallel lines have the same slope. The product of the slopes of perpendicular lines is -1.The image of an object or function graph after an isomorphic transformation is congruent to the preimage of the object.

How would you derive the distance formula? How would you find the distance between 2 points? What is the relationship between the distance formula and the Pythagorean Theorem? How do I find the midpoint? If a midpoint and endpoint of a segment are given, what does it mean to find the other endpoint? How do you find the slope between 2 points? How do you know if lines are parallel? How do you know if lines are perpendicular? What is line symmetry? When is a figure symmetric about a point? What types of symmetrical problems are found in real-life? How is a figure translated, reflected, rotated, or dilated? How does the concept of midpoint and slope relate to symmetry and transformation?

NOTE: Always ask the questions: How do you know you’re right? How do you know you’re done?

Key Vocabulary Dilation, distance, distance formula, image, isometry, midpoint, midpoint formula, parallel, perpendicular lines, preimage, Pythagorean Theorem, reflection, rotation, slope, slope formula, symmetry, transformation, translation

STAGE 2: Assessment Evidence ~ What is evidence of mastery?

Assessment Part 1

1. On a map, two cities are located at (2,4 ) and (–2,2 ). What is the distance between the cities on the map? Round your answer to the nearest hundredth.2. What is the midpoint of KL ?

6. Line a passes through points (– 4,7 ) and (1 ,−3 ). What is the slope of a line that is perpendicular to line a?4. Line t contains the points (-3,0) and (3,2). Plot a point other than point P with integral coordinates that lies on a line that is parallel to t and passes through point P.

1. Concave hexagon ABCDEF is reflected over x=0 and then translated 4 units up and 3 units to the left. Plot the new coordinates of B' after these transformations.



Possible misconceptions or learning gaps

In #1, students may use the formula or the Pythagorean theorem on the graph. Students could make arithmetic mistakes, calculator error mistakes. They could fail to answer the question by not rounding correctly.In #2, students must be able to find the coordinates of L and K first. Then be able to apply the midpoint formula, which they confuse with the distance formula.

In #6, when using the slope formula, students may get confused as to which goes in the numerator, x’s or y’s. They might just answer the slope and not realize that they must flip and change the sign to get the perpendicular slope.In #4, students may be confused over the word integral. There is a lot of wording in the problem that may also confuse students. If they do not know how to plot points or find slope students will be confused.

The vocabulary word concave and hexagon might cause students hesitation on the problem even though a picture is provided and in this problem it is not necessary information they need to solve. This is a two step problem which if students are not familiar with equations of lines the first step will not be right and then even know students might understand the second part, the answer will be incorrect.

STAGE 3: Learning Plan ~ What are the strategies and activities you plan to use?Snapshot/Warm-up

Name:Date:

SS 2 Period:

1. Give another name for line r.

2. Name the intersection of lines r and s.

3. Name three collinear points.

4. Give another name for plane N.

Name:Date:

SS 3Period:

1. Staunton is approximately halfway between Winchester and Martinsville. On a coordinate grid, Winchester is located at (2,9) and Martinsville at (-2,-1). What is Staunton’s location on the coordinate grid?

2. Let A(-2,5) and B(5,0) be the endpoints of AB. What is the length of the segment?

A √34 C 8

Name:Date:

SS 4 Period:

1. What is the slope of the line shown in the graph?

2. On a coordinate grid of Colonial Williamsburg, Duke of Gloucester Street passes through points (-3,7) and (1,-2). Nicholson Street passes through points (0,9) and (4,0). Which of the following best describes the two streets?



5. Name a point coplanar to point K .

6. Name the intersection of plane R and JL.

7. Name two non-collinear points.

8. Give another name for line JK.

B √74 D 12

3. Point R is located halfway between points C and W on a coordinate grid. W is located at (5,-2) and R is located at (1,2). Where is point C located?

4. A map of a town is drawn on a coordinate grid. The high school is found at point (3,1) and town hall is found at(-5,7).

a. If the high school is at the midpoint between the town hall and the town library, at which ordered pair should you find the library?

b. If one unit on the grid is equivalent to 50 meters, how far is the high school from town hall?

A parallel Cperpendicular

B coinciding Dintersecting, but not

perpendicular

3. Given AB and point C, plot another point D, so that CD⊥ AB.

Instructional Strategies

I am using a combination of the Model-lead-test strategy and Systematic strategy in my direct instruction described below.Direct instruction will include pacing the lesson, allowing adequate processing and feedback time, encouraging frequent student responses, and listening and monitoring throughout the lesson.Model-lead-test strategy instruction (MLT): 3 stage process for teaching students to independently use learning

Model-Lead-TestSystematic instructionThink-Pair-ShareVisual Representations

Model-Lead-TestSystematic instructionVisual RepresentationsCooperative LearningMath StationsKinesthetic Learning


Lesson Plan Template (Stages adapted from the UBD model by McTighe and Wiggins)strategies: 1) teacher models correct use of strategy; 2)teacher leads students to practice correct use; 3) teacher tests’ students’ independent use of it. Once students attain a score of 70% correct on two consecutive assessments, instruction on the strategy stops.Systematic instruction(This method focuses on teaching students how to learn. The teacher models strategy use for students using memory devices, strategy steps in everyday language, strategy steps in order, and strategy steps that prompt students to use cognitive abilities)Cooperative LearningMath StationsKinesthetic LearningReciprocal Peer Tutoring

Teaching and Learning Activities

“I do…”I will provide background and notes on distance, midpoint, and endpoint formulas. I will model the first problems for each formula.

I will provide background information and connect slope with what students learned from last year in Algebra class. I will model the first problems in their notes.

I will provide vocabulary and notes on transformations and symmetry.


Lesson Plan Template (Stages adapted from the UBD model by McTighe and Wiggins)“We do…”

We will work out the 2nd and 3rd example problems out. I will freeze the document camera and work out the problems as students work them out at their seats. Some students will be called upon to explain their answers to the class.

We will work out the 2nd and 3rd example problems out. I will freeze the document camera and work out the problems as students work them out at their seats. Some students will be called upon to explain their answers to the class.

I will distribute scissors and copies of Transformation cards on VDOE lesson and students will cut out cards. Students will work in small groups to match each graph with the description of the transformation. We will then discuss findings as a whole group.

“Students do…”Students will practice using the distance and midpoint formulas between two points by completing a stations math lib activity. The teacher will print and post the ten stations around the room. Each student will be given a worksheet to record their work as they travel to the stations. The teacher will group students of 2 and assign a starting problem. The timer will be set for 2-3 minutes (more if needed). Students will write down and solve the problem using the distance formula and midpoint formula. They will look for their answer and record the piece to the story. When the timer goes off, they move to the next station.

Students will be given a set of graphs that contain student

answers to problems such as: Plot the point with integral

coordinates that would be on a line perpendicular to the one

shown that goes through point Q. Students must analyze these

problems to determine if the answers are justified. Questions I will ask students: How do you know you’re right? How do you

know you’re done?What is the mistake in this

problem?Why is it a mistake?

Students will practice graphing transformations including reflections, translations, rotations, and dilations by going on a transformation scavenger hunt. Reflections include the x-axis, y=x, and y=-x. Rotations include 90 degrees, 180 degrees, and 270 degrees about the origin. The teacher will print the 15 stations and scatter them around the room and in the hallway. The teacher will distribute the recording sheet to each student, then place students in groups of 2 and assign each group a starting problem. The students graph according to the directions, then identify the coordinates of a point after a


Lesson Plan Template (Stages adapted from the UBD model by McTighe and Wiggins)As student are moving about the teacher will be listening and prompting students with questions.

transformation. This answer will lead them to the next station. They will continue until they have looped through all 15 stations.

Differentiation Higher Level Thinking Technology Use Connections to other subject areas and/or authentic

applications

9/8-9/9

Think-Pair-Share

Flexible Grouping

Tiered Instruction

Use of graph paper

SAD vs. DMSE

9/8-9/9

Students will solve the following problem in their interactive notebooks. You are a land developer looking to start a new subdivision. Your subdivision is rectangular and you must have security lights at all four corners. The subdivision is 12,000 feet in length and 5,000 feet in width. You desire no electrical wires to be seen; therefore, electrical wiring will be underground. As the land developer, you must keep cost down as much as possible. The electrical company’s representative requires you to make a grid using a coordinate system to layout where you would like the lights. Using the distance formula, explain why you know that it will require 13,000 feet to reach diagonally from the northwest corner to the southeast corner. Also, tell the cost of running that diagonal line. Verify your calculations using the Pythagorean Theorem.

Students will enter the answers to their snapshots

using Socrative Student either on their phone, tablet,

or computer.TI-84 calculators will be

utilized.

9/8-

9/9

Students will solve the following problem in their interactive notebooks. You are a land developer looking to start a new subdivision. Your subdivision is rectangular and you must have security lights at all four corners. The subdivision is 12,000 feet in length and 5,000 feet in width. You desire no electrical wires to be seen; therefore, electrical wiring will be underground. As the land developer, you must keep cost down as much as possible. The electrical company’s representative requires you to make a grid using a coordinate system to layout where you would like the lights. Using the distance formula, explain why you know that it will require 13,000 feet to reach diagonally from the northwest corner to the southeast corner. Also, tell the cost of running that diagonal line. Verify your calculations using the Pythagorean Theorem.

9/10-

Think-Pair-Share

9/10-

Students will be asked to compare the slope of a

9/10-

Students will be given a Think-Pair-Share question: A store



9/11

Use of graph paper.

To get the rise,

subtract the y’s.

To get the run,

subtract the other

one.

9/11

parallel line to the slope of a perpendicular line.

9/11

needs to install a ramp for people in wheelchairs. The slope of this ramp must be no more than 1/12. If the ramp must reach a height of 28 inches, how long must the ramp be?

9/12-

9/15

Think-Pair-Share

Flexible Grouping

Tiered Instruction

9/12-

9/15

Students will work in teams to solve the following problem in their interactive notebooks. Use the three segments provided to design a polygon that has:a. one line of symmetryb. two lines of symmetryc. rotational symmetry about a point

9/12-9/15

Students must complete a project, you and your team members are to find examples of each type of transformation that happens in nature. Each group member must find an example of each transformation. You are to print out a picture of that transformation, and write a paragraph (3-5 sentences) about why that picture represents that particular transformation. You will put the title, picture, and paragraph (with YOUR name) on a piece of construction paper that I will provide to you. Your group will put all examples together to form a big book. The book must be ordered so that all transformations of the same type are together. The book must be bound in some way. These will be worth 10 points per transformation set, for a total of 40 points. (ie. 10 points for having all reflections, 10 points for having all rotations, and so on.)

Checking for Students will reflect on what they have learned, what worked during their lessons, and their Richmond Public Schools 2014-15 8


Understanding understanding level of the lesson. Teacher will ask students “How do you know you are right?” and “How do you know you are done?” when students ask “Is this right?” or “Can you check this?” or in response to “Here is the answer…”STAGE 4: Closure ~ What did the students master & what are they missing?

Lesson Closure & Student

Summarizing of their Learning

TEAMS- Students will summarize in their ISNs what is important from today’s lesson to add to the class brain dump. Then they will discuss their answers with their teams. The team leader will combine all their answers on a sticky note and add it to the brain dump wall.INDIVIDUALLY – Students will take a sticky note and place it on the wall under one of the following categories. Comments to the teacher about the lesson may be written on the sticky note.

The teacher will use this information to adjust plans for the next lesson.Assessment

Part 2Name: Date:Distance Quiz A

Period:

1. On a map, two cities are located at (2,4 ) and (–2,2 ). What is the distance between the cities on the map? Round your answer to the nearest hundredth.

2. The positions of two airplanes approaching an airport are plotted on a graph grid with the airport located at (0,0 ). The locations of the planes are given by the coordinates (−8,5 ) and (–2,2 ). Each grid square is 1 mile wide. How far apart are the approaching airplanes? Round your answer to the nearest tenth of a mile.3. Find the length of segment AB. Round your answer to the nearest tenth.

Name: Date:Slope Quiz A Period:

1. What is the slope between the points (0,-5) and (6,4)? Write your answer as a fraction in simplest form.

2. Which lines are parallel?

Name: Date:Symmetry & Transformations Quiz A1. Concave hexagon ABCDEF is reflected over x=0 and then translated 4 units up and 3 units to the left. Plot the new coordinates of B' after these transformations.

2. Place the letters into the correct regions of the Venn diagram.



4. Select the ordered pair that would form a segment with the endpoint (−1, 8) that has a length 5.

5. Given the endpoints (3,-6) and (-9,7), determine the length of the segment.

6. Find the coordinates of the other endpoint of a segment with endpoint X (−2,3 ) and midpoint M (1 ,−2 ).( , )7. What is the midpoint of KL ?( , )

8. Segment AB is the diameter of circle M. The coordinates of A are (-4,3). The coordinates of M are (1,5). What are the coordinates of B?

A (6,7) B (5,8)C (-3,8) D (-5,2)

9. A rectangle has coordinates A(-10,5), B(-2,18), C(21,5), and D(13,-8). Find the intersection of diagonal AC.( , )

3. Grant wrote an equation of a line through the point Q(4,1) that is perpendicular to the one shown. Plot another point with integral coordinates that would be on this line.

4. Line t contains the points (-3,0) and (3,2). Plot a point other than point P with integral coordinates that lies on a line that is parallel to t and passes through point P.

5. What is the slope of the line segment AB in the grid below? Write your answer as a fraction in simplest form.

3. Which of the following best describes the line of reflection symmetry in the figure?

A vertical line through the point (-2,3)B horizontal line through the point (-2,3)C diagonal line through point BD diagonal line through points A and C

4. Directions: Circle all lines of symmetry. You must choose all correct answers.

Circle all equations that could be a line of symmetry.


Lesson Plan Template (Stages adapted from the UBD model by McTighe and Wiggins)10. The intersection of diagonals, AC and BD is (2,2 ) of parallelogram ABCD. The coordinates of A are (1,5 ). What are the coordinates of C?

Teacher Reflection / Effectiveness of Learning

Teachers will reflect on the student learning and use assessment data to determine if students have mastered the material.


Documents

Web viewThe vocabulary word concave and hexagon might cause students hesitation on the problem even though a picture is provided and in this problem it is not