Document Sample

Fourth Grade – 3rd 9 Weeks Unit 2: Probability, Measurement, and Geometry Focus of Unit: The study of translations, rotations, and reflections. Investigation 1: Geometry Part 1: Introduction to Translations, Rotations, and Reflections Part 2: Reflection and Symmetry Note: Use SBISD lessons as good first Part 3: Translations – A Tessellation lesson instruction and textbook lessons as Part 4: Rotation – A Tessellation lesson supplemental resources. Part 5: How to use translations, rotations, and reflections as a tool Workstations HSP Math Lesson Correlation Unit 4 Geometry Chapter 11 Transformations, Symmetry, & Congruence 11.1 Congruent Figures Note: 11.7 11.2 Translations Tessellations 11.3 Rotations may be used as 11.4 Reflections enrichment 11.5 Symmetry 11.6 Problem Solving Strategy: Act it Out Hands-On Standards – Book 3-4 Geometry Lesson 8 Congruent & Similar Figures Lesson 9 Symmetrical Figures Lesson 10 Tangram Puzzles Lesson 11 Tiling Patterns Lesson 12 Tessellations Lesson 14 Flips(Reflections) Lesson 15 Rotational Symmetry Lesson 16 Vertical & Horizontal Line Symmetry Grade 4 – 3rd 9 Weeks 1 SBISD 2006-2007 Unit 2: Probability, Measurement, and Geometry Notes Problem Solving Investigation 1: Geometry “In a differentiated Part 1: Introduction of Translation, Rotation, and Reflection classroom, the teacher (Physical Lesson) proactively plans and carries out varied TEKS: approaches to content, 4.9A Demonstrate translations, reflections, and rotations using concrete process, and product models (TAKS 3) in anticipation of and 4.9B Use translations, reflections, and rotations to verify that two shapes response to student are congruent (TAKS 3) differences in 4.9C Use reflections to verify that a shape has symmetry (TAKS 3) readiness, interest, and learning needs.” 4.14A Identify the mathematics in everyday situations (TAKS 6) Carol Ann Tomlinson, 4.14B Use problem solving model (TAKS 6) How to Differentiate 4.14C Independently use the problem solving model and apply strategies Instruction in Mixed (TAKS 6) Ability Classrooms 4.14D Use tools to solve problems (TAKS 6) 4.15A Explain/ record observations (TAKS 6) Review your 4.15B Relate informal language to math language and symbols (TAKS 6) Mathematics 4.16A Make generalizations (TAKS 6) Standards to 4.16B Justify why an answer is reasonable and explain the solution process understand how this (TAKS 6) concept is assessed on TAKS and to guide you in your evaluation Vocabulary: of students’ progress. Translation Traslación Rotation Rotación Display Vocabulary Reflection Reflexión on a Math Work Wall Horizontal Horizontal for future reference Vertical Vertical and activities Parallel Paralelo Perpendicular Perpendicular Attribute Atributo Materials: Pentominoes Using the SBISD Fact Strategy Packet Literature: strengthens and The Greedy Triangle by Marilyn Burns reinforces facts at The Amazing Book of Shapes by Lydia Sharman (includes projects) individual student’s Reflections by Ann Jonas level of ability. TEKS 4.4C, 4.6A Recall facts: addition Student Handouts: & subtraction to 18; Paper letters (ex. Die Cut letters) – 1st initial letter of each student’s name multiplication and related division fact Procedures: families: x1, doubles Practice Facts Daily (x2), doubles and double again (x4), x5, x10, x11, squares, double & one more set (x3), x9, x12, half then double (x6, x8), x7 Grade 4 – 3rd 9 Weeks 2 SBISD 2006-2007 Opening Activity: Parallel and perpendicular lines review: Have students find 3 examples of parallel lines and three examples of Notes perpendicular lines in the classroom. Give them a 2 minute time limit and then share findings. Mini Lesson: 1. Remind students that shapes have attributes. Ask for examples of attributes such as angles and sides. 2. Ask students “Will the attributes of a shape change if we changed the position of the shape?” (No) 3. Tell students that there are three ways that a shape can move and that they’re going to use some body movements to help them remember. 4. The first is translation, which is a sliding action. Link “SL” in translation to a slide. Have students move their hands or their body to demonstrate a slide. 5. The second is rotation, which is turning in a clockwise or counter clockwise direction. Link “T” in rotation to turning. Have students again demonstrate the turning motion with their hands or their bodies. 6. The third motion is reflection, which is a flipping action (like a mirror image). Link the “FL” in reflection to flipping. Have student demonstrate with their hand or their bodies the flipping action. 7. Say, “Knowing these movements can tell us whether a shape has changed or not.” 8. Provide students with examples. Display a pentominoe on the overhead. Trace it on a transparency. Draw a vertical line next to the *Any object can be pentominoe vertically. Flip the pentominoe and trace it again. Ask used if pentominoes students how the pentominoe moved. How do the two tracings look in are not available. relation to each other? Remind students that this is an example of a reflection. 9. Repeat the process of flipping shapes over a line in various directions. Before flipping have students predict what the shape will look like after it is flipped. They can describe it verbally or illustrate it. 10. Provide students with a die-cut of the first initial of their name. 11. Tell students to place the letter on paper and trace it. Then flip the letter over a vertical line and trace it again. You should continue this process in order to make a pattern. 12. Discuss the patterns: - How many times did you flip your initial before it looked as it did originally? - How would the pattern change if you flipped it over a horizontal line? - What do you think the pattern will look if you flipped your initial horizontally then vertically? 13. Use their initial to show a translation and a rotation. Record by tracing and labeling. Reflection: What body parts may be considered as reflected images of each other? Grade 4 – 3rd 9 Weeks 3 SBISD 2006-2007 Part 2: Reflection and Symmetry Notes TEKS: 4.9A Demonstrate translations, reflections, and rotations using concrete models (TAKS 3) 4.9B Use translations, reflections, and rotations to verify that two shapes are congruent (TAKS 3) 4.9C Use reflections to verify that a shape has symmetry (TAKS 3) 4.14A Identify the mathematics in everyday situations (TAKS 6) 4.14B Use problem solving model (TAKS 6) 4.14C Independently use the problem solving model and apply strategies (TAKS 6) 4.14D Use tools to solve problems (TAKS 6) 4.15A Explain/ record observations (TAKS 6) 4.15B Relate informal language to math language and symbols (TAKS 6) 4.16A Make generalizations (TAKS 6) 4.16B Justify why an answer is reasonable and explain the solution process (TAKS 6) Vocabulary: Congruent Congruente Symmetry Simetría Line of symmetry Línea de simetría Horizontal Horizontal Vertical Vertical Materials: Geoboards Overhead Geoboard Rubber bands Dot Paper Transparency Student Handouts: Dot Paper Procedures: Practice Facts Daily Opening Activity: Write several words on a transparency (without students seeing). Flip the transparency over and display the words. Students will try to figure out what the words are. Ask students what this activity was a model of (reflection). Mini Lesson: 1. Draw a rectangle on the dot paper transparency. Give students a geoboard and one rubber band. Tell students to make a square that is congruent to your square. Students hold their board to their chest until you ask them all to reveal their square. 2. Ask a volunteer to verify that his or her square is congruent. “What Grade 4 – 3rd 9 Weeks 4 SBISD 2006-2007 Notes does congruent mean?” (The figure has the same size and shape.) 3. Draw your triangle on dot paper transparency. Ask students to make a triangle that is congruent to yours. Again ask students to cover their sample until everyone is done. When all students are done, have all students reveal their model. Ask a volunteer to verify and explain how s/he knows that his or her creation is correct. 4. Use the rubber band to make the letter “O” on your dot paper transparency. Ask students if they could draw a line through the letter “O” where one side would be the mirror image or reflection of the other half. Let a volunteer go to the overhead and draw a line between the two parts. Confirm with the class that the volunteer completed the task correctly. 5. Say, “Does anyone know what this line is called?” (Line of symmetry) Define for students that an object with one line of symmetry can be cut in half and each half would be the mirror image of the other; one half would be symmetrical to the other half. 6. To demonstrate symmetry further, show students a piece of rectangular 8 x 11 paper. Fold the paper along the vertical midline and ask whether or not both sides are symmetrical. Next, fold the paper along the horizontal midline and ask whether or not both sides are symmetrical. Does the rectangle have a diagonal line of symmetry? Ask students to estimate. Then fold the paper along the diagonal to show that one side would not disappear behind the other, therefore, the rectangle only has two lines of symmetry, a horizontal and vertical. 7. For an independent activity, ask students to create each letter of their first name on the geoboard. Record the letters and identify the lines of symmetry of each letter on dot paper. Find the total number of lines of symmetry that are in their name. Reflection: Find a word whose letters have at least 6 lines of symmetry. Explain how you found the word. Grade 4 – 3rd 9 Weeks 5 SBISD 2006-2007 Part 3: Translation* - A Tessellation Lesson TEKS: Notes 4.9A Demonstrate translation, reflections, and rotations using concrete models (TAKS 3) A tessellation is a 4.9B Use translations, reflections, and rotations to verify that two shapes repeated pattern of are congruent (TAKS 3) polygons covering an entire area. Ceiling Vocabulary: tiles, floor tiles, a Tessellation honeycomb are all Translation Traslación examples of Reflection Reflexión tessellations. The Rotation Rotación artist Escher used tessellations to create elaborate art from a Materials: single shape. Search Pattern blocks for Escher prints on 3 x3 squares (cut index cards or manila folders) the internet to show White construction paper students examples of Scissors his work. Crayons or map pencil Tape Teaching Tessellation Procedures: Art By Jill Britton and Practice Facts Daily Walter Britton. Published by Dale Opening Activity: Seymour Publications Give students 2 pattern blocks to create a design. The students are to is a good resource if use their design to show a translation, rotation and reflection, tracing it you’re interested in all three ways. Check with a partner. delving further. Mini Lesson: 1. Define what a tessellation is to students and give an example of Escher’s art, which used tessellations to create dramatic designs. 2. Give students each a 3 x 3 card stock (index card) square. Demonstrate to students on transparency before students begin. Students will cut a small design off the right hand edge of the square. Slide and tape it to the left hand edge of the square. (Step 1 & 2 – see below) 3. Apply the same procedure to the bottom edge. Cut, slide, and tape it to the top edge of the square. This is the students’ template for their translation. (Step 3 & 4) 4. Have students rotate their shape to see if they can visualize a design. Students have to give meaning to their shape. For example, when a person looks at a cloud formation, s/he may see an ice cream cone where someone else sees a clown. Ask students what their shape suggests. 5. Afterwards, have students trace their template on paper, translate it so there is not a gap and continue translating until s/he runs out of room. Begin a second and third row translating the template. Once the tracing is done, have students draw in the details and color their tessellation. Students will then give their artwork a title and write a brief (3 to 4 sentences) description of how it was created. Be certain Grade 4 – 3rd 9 Weeks 6 SBISD 2006-2007 that students include that they used translation to create the effect. Notes (Step 5) Step 1 Step 2 The shaded portion is the portion that has been cut out, translated and taped. *Assessment – You may evaluate the students description of his/her artwork as one form of evaluation. You may also use Step 3 Step 4 worksheet No. 1 on pp 106-107 (English) and pp 108- 109 (Spanish) to evaluate students’ understanding of symmetry. *After students create Step 5 tessellation art, they can try their hand at Tessellmania, a software program. (Check with your technology SIS to see if your school has the software.) http://www.coolmath.c om/tesspag1.htm also provides some information on tessellations and its use with regular Reflection: polygons. Describe what a tessellation is and give examples of tessellation designs in real life. Grade 4 – 3rd 9 Weeks 7 SBISD 2006-2007 Part 4: Rotation - A Tessellation Lesson Notes TEKS: 4.9A Demonstrate translations, reflections, and rotations using concrete Be sure to study the models (TAKS 3) model and practice 4.9B Use translations, reflections, and rotations to verify that two shapes creating designs are congruent (TAKS 3) yourself until you feel 4.9C Use reflections to verify that a shape has symmetry (TAKS 3) comfortable. 4.14A Identify the mathematics in everyday situations (TAKS 6) Experiment with the 4.14B Use problem solving model (TAKS 6) shape. It will take 4.14C Independently use the problem solving model and apply strategies more than one try (TAKS 6) before you feel at ease with manipulating the 4.14D Use tools to solve problems (TAKS 6) shape. 4.15A Explain/ record observations (TAKS 6) 4.15B Relate informal language to math language and symbols (TAKS 6) 4.16A Make generalizations (TAKS 6) Suggestion: Begin 4.16B Justify why an answer is reasonable and explain the solution process cutting the design from (TAKS 6) the corner of the shape and paste the Vocabulary: cut-out on the other Rotation Rotación corner. Reflection Reflexión Translation Traslación Vertical Vertical Horizontal Horizontal Congruent Congruente Tessellation Materials: 3 x 3 square (made from index card or manila folder) White construction paper Over-head Geoboard Student Geoboards Shapes Procedures: Practice Facts Daily Opening Activity: Use an overhead geoboard to create a shape. Ask students to create a shape that is congruent to yours. Once students have created the shape, have the students make a reflection of your shape, and then rotate it clockwise. Ask students to show their designs by holding it up when teacher says, “go.” Grade 4 – 3rd 9 Weeks 8 SBISD 2006-2007 Notes Mini Lesson: 1. Show students basic shapes such as 2. Using these shapes, if students rotate the shape at one vertex, how many turns would the shape take to arrive back at its original shape? (4, 6, and 4) 3. Tell students that in today’s activity, they are going to using translations, reflections, and rotations to create their tessellations. Share with students that they will be experimenting with squares again. Give students each a 3 x 3 card stock (index card) square. Demonstrate to students on transparency before they begin. Students will cut a small design off half of the top left hand edge of the square and reflect twice. The first reflection is a reflection horizontally. The second reflection is vertical. Slide and tape it to the other half of the same edge. (Step 1) 4. Apply the same procedure to the right edge. Cut, reflect horizontally and vertically, slide, and tape it to the other half of the same edge. (Step 2) 5. Repeat again to the bottom and left edge of square. This is the students’ template. (Step 3 and 4) 6. Have students rotate their shape to see if they can visualize a design as they did in Part 3. Ask students what their shape suggests. 7. Afterwards, have students trace their template on paper, rotate it so there is not a gap and continue rotating until s/he runs out of room. Students will have to try different rotation configurations until they find edges that fit like a jigsaw puzzle. (Step 5 and Step 6) 8. Once the tracing is done, have students draw in the details and color their tessellation. Students will then give their artwork a title and write a brief (3 to 4 sentence) description of how it was created. Be certain that students include that they used translation to create the effect. Step 1 Step 2 The shaded portion is the cut-out that is reflected twice, translated and taped. Grade 4 – 3rd 9 Weeks 9 SBISD 2006-2007 Notes Step 3 Step 4 Step 5 Rotate until an edge fits another edge like a jigsaw puzzle. Grade 4 – 3rd 9 Weeks 10 SBISD 2006-2007 Notes Step 6 Reflections: What kind of everyday objects rotate? What objects translate? Grade 4 – 3rd 9 Weeks 11 SBISD 2006-2007 Part 5: Using Translation, Reflection and Rotation as a Tool How Many Different Rectangles Can You Find? Notes TEKS: 4.8C Use essential attributes to define two-and three-dimensional geometric figures (TAKS 3) 4.9B Use translations, reflections, and rotations to verify that two shapes are congruent (TAKS 3) 4.9C Use reflections to verify that a shape has symmetry (TAKS 3) 4.14A Identify the mathematics in everyday situations (TAKS 6) 4.14B Use problem solving model (TAKS 6) 4.14C Independently use the problem solving model and apply strategies (TAKS 6) Objective 6 – 4.14D Use tools to solve problems (TAKS 6) Mathematical 4.15A Explain/ record observations (TAKS 6) Reasoning also 4.15B Relate informal language to math language and symbols (TAKS includes problems in 6) which students have to 4.16A Make generalizations (TAKS 6) distinguish between 4.16B Justify why an answer is reasonable and explain the solution examples and non- examples. See your process (TAKS 6) Mathematics Standards Document Vocabulary: for clarification. Example Ejemplo Nonexample No ejemplo Rectangle Rectángulo Square Cuadrado Rhombus Rombo Trapezoid Trapezoide, trapecio Quadrilateral Cuadrilátero Materials: Geoboards Geoboard transparency Rubber bands Student Handouts: Dot Paper Procedures: Practice Facts Daily Opening Activity: Review division with this word problem: Maria has 76 geometric designs she wants to display on 3 poster boards. How many designs will she put on each poster, if she puts an equal amount on each? Mini Lesson: Grade 4 – 3rd 9 Weeks 12 SBISD 2006-2007 1. Display a rectangle and a square and tell students that these are examples of a rectangle. Have students record on paper that the Notes rectangle and square are rectangles. Ask students to define what are the attributes of a rectangle. *Creative Publications 2. Be sure students understand that a rectangle is any quadrilateral with - Geoboards four right angles. 3. Next, hold up a trapezoid or a rhombus and ask with a show of thumbs whether these are examples or non-examples of a rectangle. Ask students to explain why. 4. After introducing the idea of examples and non-examples, explain to students that their task today is to fine as many different examples of *If students are given rectangles as they can make on a geoboard. * one rubber band , they 5. Show students on dot paper transparency an example of a square. will be able to focus on Then show the same square, only rotate it this time and ask students one shape at a time, whether or not you can count it as a second rectangle. Ask, “How can recording it before reflection, translation, or rotation help us to decide whether or not the they construct the next shape that you create is a repeat example of a shape that has already shape. been counted?” 6. Let students work in pairs. Some students may find all 16 rectangles and some may not. The important focus is for students to practicing using rotation, translation, or reflection as a tool to help them decide whether or not they’ve created a new rectangle. 7. When all groups are finished, have students post their findings. Ask students to reflect on their strategies for finding the different rectangles. Reflection: How would you describe a rectangle and a square to someone who doesn’t know what they are? Grade 4 – 3rd 9 Weeks 13 SBISD 2006-2007 Workstations: 1. Multiplication Transformation - A Problem Solving Station Notes Students solve a multiplication word problem and create a division problem using the same numbers, including the product, and subject matter. 2. Wrangler Materials: 0-5 cube, paper, pencil, plastic animals (optional) Players: 2-4 The object of this game is to capture as many remainders/ horses (any animal) as possible. The person with the highest total of remainders at the end of a 15 minute round is the winner. Students must use the long division algorithm in this game. To play, the students have a herd of 50 horses. The players want to capture as many remainders/horses as possible. The first player rolls a low die and divides the 50 horses by the number rolled. For instance, if the player rolls a 2, then 50 divided by 2 is 25. The horses split off into two groups with 25 in each group. There are no leftovers. Player does not score. The next player rolls a 3. The herd is divided into 3 groups and flees. 50 divided by 3 is 16 with 2 left over. So 2 horses are captured reducing the herd to 48. Player one now plays with 48 horses and rolls his die. This time he rolls a 5 and divides 48 by 5. The horses split off into 5 groups with 9 in each group. There are 3 horses left out of the group and the first player scores 3. At this point, player one has a score of 3 and player 2 has a score of 2. Play continues until 15 minutes are over or all the animals have been captured. 3. Triangle Area Search Materials: Geoboards, geoboard dot paper (end of investigation) Have students find triangles on their geoboard that have an area of 5 and 8 square units Record findings on geoboard dot paper. Students will display their finding on butcher paper for the class to see. 4. Partner Design Construction: Materials: Geoboards, geoboard dot paper (end of investigation) Students will work in pairs. One student will make a design on his/her geoboard. The partner will then make a congruent design on his/her geoboard. Together they will find the area of the design and its lines of symmetry. Record design and lines of symmetry on geoboard dot paper. Label what the area of the design is on the paper. Grade 4 – 3rd 9 Weeks 14 SBISD 2006-2007 Worksheet 1 1. What is true about a figure if it has one line of symmetry? 2-5 Draw the lines of symmetry found in each of the pictures below. Be sure to draw more than one line if a figure has more than one line of symmetry. Look at the figures below. Circle the congruent shapes. 6. 7. Write whether each pair of figures shows a translation, rotation, or reflection. 8. 9. 10. Grade 4 – 3rd 9 Weeks 15 SBISD 2006-2007 Worksheet 2 Examples and Non-Examples 1. These are swigwams. Which of these is a swigwam? 2. These are rectangles. Which of these is a rectangle? 3. These are Reflectors. Which of these is NOT a Reflector? Grade 4 – 3rd 9 Weeks 16 SBISD 2006-2007 Hoja 1 1. ¿Qué es verdadero sobre una figura que tiene solo una línea de simetría? 2-6 Dibuja las líneas de simetría en cada uno de los siguientes dibujos. Asegúrate de dibujar más de una línea si la figura tiene más de una línea de simetría. Mira las figuras de abajo. Circula las figuras congruentes. 6. 7. Escribe si cada par de figuras es una traslación, rotación, o reflexión. 8. 9. 10. Grade 4 – 3rd 9 Weeks 17 SBISD 2006-2007 Hoja 2 Ejemplos y no ejemplos 1. Estas son swigwames. ¿Cuál de estas figuras es una swigwam? 3. Estas figuras son rectángulos. ¿Cuál de estas figuras es un rectángulo? 3. Estas figuras son reflectores. ¿Cuál de estas figuras NO es un reflector? Grade 4 – 3rd 9 Weeks 18 SBISD 2006-2007 Answer Key Worksheet 1 1. What is true about a figure if it has one line of symmetry? A figure that has one line of symmetry has two sides that are mirror images of one another. If you fold one side behind the other one part will disappear behind the other. Each side is in exact agreement with the other in size and shape. 2-5 Draw the lines of symmetry found in each of the pictures below. Be sure to draw more than one line if a figure has more than one line of symmetry. Look at the figures below. Circle the congruent shapes. 6. X 7. X Write whether the examples below are examples of translation, rotation, or reflection. 8. 9. 10. translation rotation reflection Grade 4 – 3rd 9 Weeks 19 SBISD 2006-2007 Worksheet 2 Examples and Non-Examples 1. These are swigwams. Which of these is a swigwam? X 4. These are rectangles. Which of these is a rectangle? X 3. These are Reflectors. Which of these is NOT a Reflector? X Grade 4 – 3rd 9 Weeks 20 SBISD 2006-2007 Grade 4 – 3rd 9 Weeks 21 SBISD 2006-2007

DOCUMENT INFO

Shared By:

Categories:

Tags:
back together, jigsaw puzzle pieces, Jigsaw Puzzles, Piece Jigsaw Puzzle, full colour, full bleed, jigsaw puzzle, Promotional Products, Promotional Merchandise, Family Games

Stats:

views: | 468 |

posted: | 11/30/2010 |

language: | English |

pages: | 21 |

Description:
4 Piece Jigsaw Puzzle Template document sample

OTHER DOCS BY jik21010

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.