Lesson Plan Project

4th Grade Geometry

Winona State University

Created By Jill Ziebell

Lesson Plan 1Translations of Figures

Jill Ziebell4th Grade Geometry

Unit: Translations, Reflections, & Rotations to establish congruency and understand symmetries.

Academic Content Standards Geometry & Measurement Use translations, reflections and rotations to

establish congruency and understand symmetries. o 4.3.3.1 Apply translations (slides) to figures. o 4.3.3.4 Recognize that translations preserve congruency and use them

to show that two figures are congruent.

Instructional Objectives Students will demonstrate the translation of figures by creating a new figure

in correct location and recognizing congruencies. Students will demonstrate the translation of figures on a coordinate plane by

creating a new figure in correct location. Students will describe the direction and distance of translation.

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Students will label correctly label coordinates of a translated figure on a coordinate plane.

Assessment Observation of students as they create translations of figures on Smartboard or

whiteboard and recognize congruent sides. (IO-Students will demonstrate the translation of figures by creating a new figure in correct location and recognizing congruencies.)

Students will create translations on graph paper. (IO-Students will demonstrate the translation of figures on a coordinate plane by creating a new figure in correct location.)

Students will verbally describe the direction and distance of translated figure. (IO-Students will describe the direction and distance of translation.)

Students will correctly label coordinates on graph paper. (IO-Students will label correctly label coordinates of a translated figure on a coordinate plane.)

Materials/Equipments Needed:Teacher

Smartboard or whiteboardo Load a grid on Smartboard or create a polar grid on the whiteboard

Colored markers Graph paper or coordinate plane paper “Example 1 Translations or Slides Dinosaur Walking” video from Discovery

Education web site Coordinate plane paper

Student Colored pencils or markers Pencils

Resources (and credit): http://www.mathnstuff.com/gif/9x9not.gifhttp://player.discoveryeducation.com/index.cfm?guidAssetId=3FCCD8B9-FAEE-4A25-ACD4-67AFE43147C6&blnFromSearch=1&productcode=US

Procedures: (Must include Opening, Transitions, and Closure)Opening10:00 -10:05Signal to students that it is time for math and time to put away other work by playing the song Plotting Points, from the CD Middle School Math Music or any other upbeat music relating to math.

Transition: The teacher will stop the music and students should have their books away and should have a clear desk. “Class today I want to share a short video with you about our next math unit. Please come join me in front of the Smartboard.”

10:05-10:10

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Show students Example 1 Translations or Slides Dinosaur Walking on Smartboard. http://player.discoveryeducation.com/index.cfm?guidAssetId=3FCCD8B9-FAEE-4A25-ACD4-67AFE43147C6&blnFromSearch=1&productcode=US Click on video box to watch.

Transition: When the video is over have students remain seating in front of the Smartboard. “Class we will be learning about Transformation over the next few days. The first transformation we will learn about is a translation or slide. The video demonstrated translations in animation and you will be able to create your own translations of shapes. You will be able to locate new locations on a coordinate plane or translated shapes. You will also be able to recognize congruent sides of translated shapes.”

10:10-10:25The teacher will use a grid on a Smartboard or whiteboard to demonstrate translations.

Remind students how to use a coordinate plane.o The x-axis is horizontal and the y-axis is vertical.

On the Smartboard insert a house at location (3,6) on the grid. Tell the students that the Smiths live at location (3,6) but moved 3 blocks to the

right and 5 blocks down. Using a red stylus draw a line 3 blocks right and then 5 blocks down, counting each

block aloud. Mark the location of where the Smiths moved, (6,1). Using a blue stylus draw a line from (3,6) to (6,1). The teacher now moves the house to the new location. Erase the marking created with the stylus. Tell students that the Smiths now moved 5 blocks left and 5 blocks up. Call on a student to use the red stylus and draw a line left and up the correct amount

of squares, making sure they are counting aloud. Call on a student to mark to with a blue stylus the line from original location to new

location. Tell students this is the translation line. Call on a final student to move the house to the new location. Go through other prepared examples on next slides giving additional students a turn

at the Smartboard.

Transitions: “Class you can go back to your desks and get out a pencil and your colored pencils. I will pass out coordinate plane paper for you to practice your translations on. You may work with your neighbor or on your own. Voices should be at level 1.”

10:25-10:45The teacher will draw example on Smartboard grid while students work at their desks. Students may be called on to get an opportunity to do examples on Smartboard.

Have student mark points (2,2), (4,4), (2,4) and make a triangle using these three points.

Have students label each side of the triangle (A,B,C). Tell students to translate the triangle 3 units left and 3 units up using the same

technique that was used on the house.o Using colored pencils to draw the moves and the translation line.

Have students draw another triangle at the new location.

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o Remind them that each point moves. Have students label new points of the translated triangle on the coordinate plane. Explain to students that translated shapes do not change in size, orientation, or

rotation. Have students label the new triangles sides (A,B,C) to demonstrate congruency. Have students demonstrate translation of their own on the coordinate plane paper.

o Have them describe the slide.o Have them draw lines showing slide using.o Have them label points and congruent sides.

Transitions: “Class you can spend the next 10 minutes to finish this worksheet. It is due tomorrow at Math time. It is only 3 problems but you need to show all of your steps for each problem. If you have questions, raise your hand. If you finish early get a blank piece of graph paper and create a translation of a footprint like the dinosaur in the video.”

10:45-10:55Pass out worksheet and answer any questions. Allow students the rest of the class period work.

10:55-11:00Closure: “Students, it’s time to put away your math. If you haven’t finished, put it in your homework folder. Today we learned about translations or slides. Tomorrow we will learn about another transfiguration, rotations.”

AccommodationThe teacher will give each student an opportunity to answer questions while giving more challenging questions to students who are gifted/talented.

Enrichment/ExtensionsThe teacher will give each student an opportunity to answer questions while giving more challenging questions to students who are gifted/talented.

Self-ReflectionI feel as though the lesson plan will be interesting to the students. I also feel as though the interaction with the Smartboard will ensure participation from many students. I also feel the video gives students a real-life example of how translations are used.

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Translations

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Directions: For each of the shapes above create a new shape at the new translation points. Label each of the new points.

1) Translate the pink triangle right 7 units and down 3 units.

2) Translate the yellow triangle left 8 units and up 2 units.

3) The green quadrilateral is a translation of the blue quadrilateral. Describe this translation.

Answer KeyTranslations

Name _______________________________

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Directions: For each of the shapes above create a new shape at the new translation points. Label each of the new points.

1) Translate the pink triangle right 7 units and down 3 units.

2) Translate the yellow triangle left 8 units and up 2 units.

3) The green quadrilateral is a translation of the blue quadrilateral. Describe this translation. The quadrilateral translated 9 units left and 0 units up or down.

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Lesson Plan 2Rotation of Figures

Jill Ziebell4th Grade Geometry

Unit: Translations, Reflections, & Rotations to establish congruency and understand symmetries.

Academic Content Standards Geometry & Measurement Use translations, reflections and rotations to

establish congruency and understand symmetries. o 4.3.3.1 Apply rotation to figures. o 4.3.3.4 Recognize that rotations preserve congruency and use them to

show that two figures are congruent.

Instructional Objectives Students will demonstrate the rotation of figures by creating a new figure in

correct location and recognizing congruencies. Students will demonstrate the rotation of figures on a coordinate plane by

creating a new figure in correct location. Students will describe the direction and distance of rotation. Students will label correctly label coordinates of a rotated figure on a

coordinate plane.

Assessment Observation of students as they create rotations of figures on Smartboard. (IO-

Students will demonstrate the rotation of figures by creating a new figure in correct location and recognizing congruencies.)

Students will create rotations on graph paper. (IO- Students will demonstrate the rotation of figures on a coordinate plane by creating a new figure in correct location.)

Students will verbally describe the direction of rotated figure using a pinwheel. (IO-Students will describe the direction and distance of rotation.)

Students will correctly label coordinates on graph paper. (IO-Students will label correctly label coordinates of a rotated figure on a coordinate plane.)

Materials/Equipments Needed:Teacher

Smartboard or whiteboardo Load a grid on Smartboard or create a polar grid on the whiteboard

Colored markers Graph paper or coordinate plane paper “Example 2 Translations or Slides Dinosaur Walking” video from Discovery

Education web site

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Construction paper with pinwheel pattern copied on it. One paper fastener for each student Square sheet of paper for each student Straw for each student Prepared worksheet

Student Colored pencils or markers Scissors Pencils

Resources (and credit): http://www.mathnstuff.com/gif/9x9not.gifhttp://player.discoveryeducation.com/index.cfm?guidAssetId=AA1D2D10-3831-4B7E-A11F-2C77D9BFE271&blnFromSearch=1&productcode=US

Procedures: (Must include Opening, Transitions, and Closure)Opening10:00 -10:05Signal to students that it is time for math and time to put away other work by playing the song Plotting Points, from the CD Middle School Math Music or any other upbeat music relating to math.

Transition: The teacher will stop the music and students should have their books away and should have a clear desk. “Class yesterday we learned how to translate or slide shapes. Today we will learn about another transformation. I want to share a short video with you about rotations or turns. Please come join me in front of the Smartboard.”

10:05-10:10Show students Example 2 Rotations or Turns Dragon Falling on Smartboard. http://player.discoveryeducation.com/index.cfm?guidAssetId=AA1D2D10-3831-4B7E-A11F-2C77D9BFE271&blnFromSearch=1&productcode=US

Transition: When the video is over have students remain seating in front of the Smartboard. “Class the transformation we will learn today is a rotation or turn, just like the video demonstrated. You will be able to create your own rotations of shapes. You will be able to locate new locations on a coordinate plane of rotated shapes. You will also be able to recognize congruent sides of rotated shapes. We will start learning about rotations by creating a pinwheel. Each of you need to take one pinwheel pattern, one straw, and one fastener and go back to you seats and wait for my next instruction.”

10:10-10:25The teacher will give instructions on how to create a pinwheel.

Cut out the pinwheel on the solid lines only. Cut the dotted lines from the four corners to the center circle. Try not to cut into

the center circle.

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Use the sharpened pencil to poke a hole through the four tiny dark circles. The pencil point also works well to poke a hole into the straw. Carefully push the pencil point through the straw about 1/2 inch from the top.

Make the tiny holes on the four points meet at the center circle. Push the ends of the paper fastener through the holes on the pinwheel and the

fastener through the center circle. Place the straw on the backside of your pinwheel and push the ends of the fastener

through the hole in the straw. Open-up the fastener by flattening the ends in opposite directions.

Now you are ready to try-out your pinwheel. All you will need is a little bit of wind to make your pinwheel spin round and round.

Have students watch what happens to the animals as the pinwheel spins around. Have the students turn the pinwheel slowly and watch the animals. Students will discuss what happens to the orientation of the animals as the

pinwheel turns.

Transition: “Students set you pinwheels aside and come back up to the Smartboard. We are going to try some rotations on the Smartboard.”

10:25-10:40The teacher will use a grid on a Smartboard or whiteboard to demonstrate rotations.

Remind students how to use a coordinate plane and remind them what they learned yesterday when they translated shapes.

o The x-axis is horizontal and the y-axis is vertical.o The shape slides, does not turn when translated.

On the Smartboard insert a triangle at location (3,4), (3,10), and (6,6) on the grid. Tell students we are going to rotate the triangle 90° clockwise. Have them think about how the shape on their pinwheel moved when it was rotated. Tell students that the center of the plane is like the center of the pinwheel. Call on students to draw a line to the location of the new coordinates using a red

stylus or marker. Draw a new triangle at the rotated location and label the coordinates. Ask students if they notice anything about the location of the rotated triangle. The triangles new coordinates are (4,-3),(10,-3), (6,-6) Make sure they notice that the x and y variable switch. Ask students how they can determine if the number is negative or positive. They should be able to tell positive or negative by the quadrant the new triangle is

located in. Have students rotate the new triangle 90° clockwise using another color stylus. Clear the coordinate plane and create another shape in a different quadrant of the

coordinate plane. Call on additional students to find the location of the rotated triangle. Have them draw rotated triangle and label the coordinates. Have students label congruent sides of the shape on the Smartboard. Create another polygon in a different quadrant of the coordinate plane. This time call on a student to rotate the shape counter-clockwise. Have them draw the rotated shape and label the coordinates.

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Ask students what happens to the coordinates when the shape is rotated counter-clockwise.

Have students label congruent sides of this shape. Repeat with another polygon in a different quadrant of the coordinate plane.

Transitions: “Class you can go back to your desks and get out a pencil and your colored pencils. I will pass out a worksheet that gives you more rotation practice. Think about how the coordinates change and how the shape on your pinwheel change as you work out the problems. You may work with your neighbor or on your own. If you finish early use a blank piece of graph paper and rotate unique shape, like the ones in the video we watched. Voices should be at level 1.”

10:40-10:55The teacher will leave the example on Smartboard grid for students to refer to.

Have students work alone or with a partner on worksheet. Give additional support to students. Allow students the rest of the class period to finish the worksheet.

10:55-11:00Closure: “Students, it’s time to put away your math. If you haven’t finished, put it in your homework folder. Today we learned about rotations. Tomorrow we will learn about another transfiguration, reflections.”

AccommodationThe teacher will give each student an opportunity to answer questions while giving more challenging questions to students who are gifted/talented. The teacher will also allow students to work with a partner to help students learn from each other.

Enrichment/ExtensionsThe teacher will give each student an opportunity to answer questions while giving more challenging questions to students who are gifted/talented. Allow students to try transformations on a Geometer’s Sketchpad if available. Have students play the “Transformation Game” at http://www.onlinemathlearning.com/transformation-game.html.

Self-ReflectionI feel as though the lesson plan will be interesting to the students. I also feel as though the interaction with the Smartboard will ensure participation from many students. I also feel the video gives students a real-life example of how translations are used. My greatest concern is time. I feel as though additional time may be needed for some students to completely understand rotations.

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Template for PinwheelDirections:Cut out square.

Do not cut center circle

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RotationsName__________________________

1. Rotate the blue quadrilateral 90° clockwise. Draw a new quadrilateral at the correct location and label the points.

2. Rotate the green triangle 90° clockwise. Draw a new triangle at the correct location and label the points.

3. If the quadrilateral and the triangle are rotated counter clockwise what are the coordinates of the rotated figures.

A(_____,_____) F(_____,_____)

B(_____,_____) G(_____,_____)

C(_____,_____) H(_____,_____)

D(_____,_____)

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Answer Key

1. Rotate the blue quadrilateral 90° clockwise. Draw a new quadrilateral at the correct location and label the points.

2. Rotate the green triangle 90° clockwise. Draw a new triangle at the correct location and label the points.

3. If the quadrilateral and the triangle are rotated counter clockwise what are the coordinates of the rotated figures.

A(-7,-4) F(5,3)

B(-4,-2) G(3,6)

C(-1,-5) H(7,8)

D(-5,-6)

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Lesson Plan 3Reflection of Figures

Jill Ziebell4th Grade Math

Unit: Translations, Reflections, & Rotations to establish congruency and understand symmetries.

Academic Content Standards Geometry & Measurement Use translations, reflections and rotations to

establish congruency and understand symmetries. o 4.3.3.2 Apply reflections (flips) to figures by reflecting over vertical or

horizontal lines and relate reflections to lines of symmetry. o 4.3.3.4 Recognize that reflections preserve congruency and use them

to show that two figures are congruent.

Instructional Objectives Students will demonstrate the reflection of figures by creating a new figure in

correct location and recognizing congruencies. Students will demonstrate the rotation of figures on a coordinate plane by

creating a new figure in correct location. Students will label correctly label coordinates of a rotated figure on a

coordinate plane.

Assessment Observation of students as they create reflections of figures using tracing paper

and recognize congruent sides of reflected figures. (IO-Students will demonstrate the reflection of figures by creating a new figure in correct location and recognizing congruencies.)

Students will create reflections using a Mira on graph paper and describe direction of reflection. (IO-Students will demonstrate the rotation of figures on a coordinate plane by creating a new figure in correct location.)

Students will correctly label coordinates on graph paper. (IO-Students will label correctly label coordinates of a rotated figure on a coordinate plane.)

Materials/Equipments Needed:Teacher

Smartboard or whiteboardo Load a grid on Smartboard or create a polar grid on the whiteboard

Colored markers Tracing paper for each student Mira for each student Graph paper or coordinate plane paper “Example 3 Reflections or Flips- Dinosaur and Dragon Parts” video from

Discovery Education web siteStudent

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Colored pencils or markers Pencils Rulers

Resources (and credit): http://www.mathnstuff.com/gif/9x9not.gifhttp://player.discoveryeducation.com/index.cfm?guidAssetId=AA1D2D10-3831-4B7E-A11F-2C77D9BFE271&blnFromSearch=1&productcode=US

Procedures: (Must include Opening, Transitions, and Closure)Opening10:00 -10:05Signal to students that it is time for math and time to put away other work by playing the song Plotting Points, from the CD Middle School Math Music or any other upbeat music relating to math.

Transition: The teacher will stop the music and students should have their books away and should have a clear desk. “Class yesterday we learned how to rotate shapes. Today we will learn about another transformation. I want to share a short video with you about reflections or turns. Please come join me in front of the Smartboard.”

10:05-10:10Show students Example 3 Reflections, or Flips- Dinosaur and Dragon Parts on Smartboard. http://player.discoveryeducation.com/index.cfm?guidAssetId=AA1D2D10-3831-4B7E-A11F-2C77D9BFE271&blnFromSearch=1&productcode=US

Transition: “Class you can take your seats. The transformation we will learn today is a reflection or flip, just like the video demonstrated. You will be able to create your own reflections of shapes. You will be able to locate the reflected locations on a coordinate plane. You will also be able to recognize congruent sides of reflected shapes. We will start learning about reflections using tracing paper. Each of you need to take one sheet of tracing paper and one sheet of construction paper and go back to you seats and wait for my next instructions.”10:10-10:25The teacher will give instructions on how to create a reflection using tracing paper.

Students will draw a line down the center of their construction paper using a ruler. Students will draw an object or shape on the left side of the line. Students will trace the line and shape using a pencil and the tracing paper. Students will flip their tracing paper over and match up the traced line with the

line on the paper. Students will rub the tracing paper until the tracing transfers to the construction

paper. Discuss with how reflections change.

o They flip.o They do not change size; they do not rotate, or slide.

Ask student to name some reflections in real life.

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o Looking in a mirror.o Looking in a water (stream, lake, ect.)o Looking in a shiny object (car, refrigerator, sunglasses)

Transition: “Students, you mentioned that you can see reflections in mirrors. We will be using a tool called a Mira to do reflections. Please come to the front and pick up one Mira and one sheet of coordinate plane paper.”

10:25-10:35The teacher will use the Smartboard to demonstrate reflections using Miras.

Students will flip their piece of construction paper over. Students will draw a shape no wider than their Mira. Using a ruler, students will draw a line next to their shape.

o Make sure the student leaves room on the other side of their line. Students will place the on the line and look through the Mira. Students will trace the reflected shape. Students will repeat the above steps 2 more times.

Transitions: “Class you can return the Mira and we will work on reflections on coordinate planes. Please come to the Smartboard.”

10:35-10:45The teacher will give a demonstration on the Smartboard.

Insert a coordinate grid on the Smartboard. Insert a triangle in location (4,4),(6,5),(1,9) Tell students to use the y axis as a reflection line a Mira. Ask students to determine the new location of the reflection.

o (-4,4),(-6,5),(-1,9) Call on student to come up to the Smartboard and draw the locations of the

reflections and draw the new triangle. Ask students if they notice what happens to the coordinates when they are reflected

over the y-axis.o The x value becomes negative and the y value stays the same.o Ask students what would happen if the x coordinate was already negative.

The x would become positive. Have students reflect the original triangle over they x-axis. Call on students to locate the coordinates and draw the reflected triangle. Ask students how the coordinates of this reflection change.

o The x coordinates stay the same and the y coordinates become negative.

Transition: “Students not that you get the idea of how shapes reflect you can take one sheet of coordinate plane paper and go back to your seats and create your own reflection on the coordinate plane paper. I will give instructions of this assignment when everyone is seated. Voices are at level 1.”

10:45-10:55The teacher will describe the directions for the assignment and allow the students the remainder of the class period to finish it.

Students will create 3 shapes to be reflected.

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o One will be reflected over the x-axis. Remind students to keep in mind how the coordinates change.

o One will be reflected over the y-axis. Remind students to keep in mind how the coordinates change.

o One will be reflected over a line the student draws with a ruler. Remind students that the line acts as a Mira.

o Students will be allowed to check their third reflection with a Mira if they need to.

Teacher will assist students who need it.

Closure: “Students, it’s time to put away your math. If you haven’t finished, put it in your homework folder. Don’t worry if you didn’t finish today. I will give you time at the beginning of Math tomorrow to finish. Today we learned about reflections. Tomorrow we will review all three of the transformation and begin preparing for our unit test.”

AccommodationThe teacher will give each student an opportunity to answer questions while giving more challenging questions to students who are gifted/talented. The teacher will also allow students to work with a partner to help students learn from each other.

Enrichment/ExtensionsThe teacher will give each student an opportunity to answer questions while giving more challenging questions to students who are gifted/talented. The teacher will also allow students to use Geometers Sketchpad to enhance learning, when available. Have students play the “Transformation Game” at http://www.onlinemathlearning.com/transformation-game.html

Self-ReflectionI feel as though the lesson plan will be interesting to the students. I feel the students will be very engaged using tracing paper and the Miras. I believe the manipulatives will help students better understand the reflection concepts. My greatest concern is time. I feel as though additional time may be needed for some students to understand reflections when we take away the manipulatives.

Name_________________________

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