Common Core State Standard(s): 5.G.3, 5.G.4

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1 Common Core State Standard(s): 5.G.3, 5.G.4 Materials Needed: Internet access Plain paper Blackline Master: o Error Analysis o Investigating Quadrilaterals Unit IV: Geometry Unit (2 D Figures) Instructional Days Enrichment Investigation #1 Standard(s) for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure. Instructions: 1. Have the students complete the Quadrilateral Quest and Quiz at 8/activities/quad_quest/quad_quest.html 2. After completing the Quadrilateral Quest and Quiz, have the students draw a Venn diagram that represents the relationship(s) among polygons, including quadrilaterals, parallelograms, rectangles, and squares. This should be drawn on plain paper. 3. To explain their work, students should write a justification of shape placements within the Venn diagram. 4. To further explore the relationships of quadrilaterals, students should complete the Error Analysis handout. They will examine various venn diagrams and determine where each is correct or incorrect. Emphasis should be placed on the explanations provided. Students could also discuss their findings with a partner. 5. Instruction in identifying specific classes of quadrilaterals and in understanding the hierarchy of quadrilaterals does help students move to a higher level of reasoning about two dimensional figures (NRC, 2001). Have the students complete the comparison matrix, Investigating Quadrilaterals, to summarize the relationships of various quadrilaterals. When finished, students should answer the reflection questions. Sources: Baroody, A. (1998). Fostering Children s Mathematical Power: An Investigative Approach to K 8 Mathematics Instruction National Research Council. Adding It Up: Helping Children Learn Mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, D.C.: National Academy Press, Wake County Public Schools, Grade 5 Page 1

2 ERROR ANALYSIS Mrs. Brill asked her class to draw a Venn diagram illustrating the relationships among parallelograms (P), rectangles (Rec), rhombi (Rh), and squares (S). Evaluate the following diagrams by identifying if a student s drawing is correct or incorrect. Be sure to explain your thinking. Roger: Explanation: S Rh Rec P Ramon: Explanation: Rec S Rh P Explanation: Rita: Rec S Rh P Wake County Public Schools, Grade 5 Page 2

3 Investigating Quadrilaterals Attributes of Shapes Number of sides Quadrilateral Square Rectangle Rhombus Trapezoid Parallelogram Number of angles Congruent sides Congruent angles Right angles Parallel sides Symmetry (Line) Wake County Public Schools, Grade 5 Page 3

4 Investigating Quadrilaterals 1. What knowledge did you need to complete this task? 2. What insights did you gain about the process of identifying similarities and differences while using the comparison matrix? Wake County Public Schools, Grade 5 Page 4

5 ANSWER KEY: Attributes of Quadrilateral Square Rectangle Rhombus Trapezoid Parallelogram Shapes Number of sides Number of angles Congruent sides have congruent sides have congruent angles Opposite sides are congruent All sides are congruent have congruent sides Opposite sides are congruent Congruent angles Does not have congruent sides All angles are congruent All angles are congruent Opposite angles are congruent have congruent angles Opposite angles are congruent Right angles have a right angle All angles are right angles All angles are right angles have right angles have right angles have right angles Parallel sides have parallel sides Opposite sides are parallel Opposite sides are parallel Opposite sides are parallel One set of opposite sides are parallel Opposite sides are parallel Symmetry (Line) have symmetry Has four lines of symmetry Has at least two lines of symmetry Has at least two lines of symmetry have symmetry have symmetry Wake County Public Schools, Grade 5 Page 5

6 Common Core State Standard(s): 5.G.3 5.G.4 Unit IV: Geometry Unit (2 D Figures) Instructional Days Enrichment Investigation #2 Standard(s) for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 7. Look for and make use of structure. Materials Needed: Internet access Lesson: Blackline Master: o Polygon Capture Game Rules o Polygon Capture Game Cards (photocopied onto cardstock) o Polygon Capture Game Polygons (photocopied onto cardstock) o Triangle Grid Paper Instructions: 1. Have students complete the activity on the website: Students will need a copy of the Triangle Grid Paper. If students have limited prior knowledge of the various polygons, it may be helpful for the students to read A Greedy Triangle by Marilyn Burns prior to completing the activity. 2. Have students play Polygon Capture. The purpose of this game is to motivate students to examine relationships among geometric properties. From the perspective of the Van Hiele model of geometry, the students move from recognition or description to analysis (Fuys 1988). Often, when asked to describe geometric figures, middle school students mention the sides ("The opposite sides are equal") or the angles ("It has four right angles"), but they rarely use more than one property or describe how two properties are related. For example, is it possible to have a four sided figure with opposite sides not equal and four right angles? Or a triangle with three right angles? What geometric relationships make such figures possible or impossible? By having to choose figures according to a pair of properties, players go beyond simple recognition to an analysis of the properties and how they interrelate (NCTM 2008). Sources: 2008 National Council of Teachers of Mathematics 8/polygon/PolygonCapture AS GameCards.pdf 8/polygon/PolygonCapture AS GamePolygons.pdf Wake County Public Schools, Grade 5 Page 6

7 Triangle Grid Paper Wake County Public Schools, Grade 5 Page 7

8 Polygon Capture RULES OF THE GAME Preparation Before playing the game, cut out the cards on the Polygon Capture Game Cards sheet. Mark the back of the top eight cards with "A" for angle. Mark the back of the bottom eight cards with "S" for side. Cut out the polygons on the Polygon Capture Game Polygons sheet. Place the twenty polygons in the center of the playing area. Put the cards in two decks: angle cards and side cards. Basic Play 1. Player 1 turns over one card from the angle deck and then one card from the side deck. All polygons that match both these properties may be captured. Captured polygons are removed from play. 2. If player 1 has missed any figures, player 2 may now capture them. 3. Player 2 chooses a card from each deck and tries to capture polygons. If no polygons can be captured with the cards chosen, the player may choose one more card from either deck. If no polygons can then be captured, that turn is over. A player may challenge the opponent's capture. If the piece was incorrectly chosen, it is put back in play in the center. Play until two or fewer polygons remain. If you run out of cards, reshuffle the deck. The player with the most polygons wins. Wild Card If the Wild Card comes up, you may choose any side property. For example, if you have chosen All angles are right angles and the Wild Card, you may say, "All opposite sides are the same length" and capture all rectangles. Steal Card If you select the Steal Card, do not turn over a second card. This card allows you to steal polygons from your opponent. Without selecting another card, pick two properties, one for sides and one for angles, that will allow you to steal as many polygons from your opponent as possible. Make up these properties on your own. If your opponent has no cards to steal, put the Steal Card back in the angle deck and choose two new cards. Example Player 1 turns over the cards All angles have the same measure and It is a quadrilateral. Player 1 captures shapes D, E, and G. Player 2 may now capture shape T, since it was missed by player 1. Player 2 now turns over two cards National Council of Teachers of Mathematics Wake County Public Schools, Grade 5 Page 8

9 Polygon Capture GAME CARDS On the back of each of the top eight cards (first sheet), write an A for angle. On the back of each of the bottom eight cards (second sheet), write S for side. Cut out the cards. All angles are right angles. At least one angle is obtuse. No angle is a right angle. At least one angle is less than 90o. At least one angle is a right angle. At least two angles are acute. All angles have the same measure. STEAL CARD: Select a pair of properties. Steal all those polygons Wake County Public Schools, Grade 5 Page National Council of Teachers of Mathematics

10 No pairs of sides are parallel. All sides are of equal length. Only one pair of sides is parallel. At least one pair of sides is perpendicular. All pairs of opposite sides are It is a quadrilateral. All pairs of opposite sides have WILD CARD: Pick your own side Wake County Public Schools, Grade 5 Page National Council of Teachers of Mathematics

11 Polygon Capture GAME POLYGONS Wake County Public Schools, Grade 5 Page National Council of Teachers of Mathematics

12 Common Core State Standard(s): 5.G.3 5.G.4 Unit IV: Geometry Unit (2 D Figures) Instructional Days Enrichment Investigation #3 Standard(s) for Mathematical Practice: 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. Materials Needed: Internet access Digital cameras Blackline Masters: o Real World Geometry o Geometry Journey Guidelines o Planning Guide Real World Geometry slideshow: Instructions: 1. Show the Real World Geometry slideshow to the students. As each slide is shown, have students locate as many geometrical features as they see. Observations should be recorded on the Real World Geometry handout. Be sure students explain their thinking. (For example: If a student sees parallel lines, ask the student to explain why the lines are parallel.) The slideshow can be paused for discussion of features at any time. Students should be encouraged to discuss their explanations with a partner. 2. Give each group a digital camera and the guidelines for the journey. Explain to the students they will travel throughout the school (this can be limited to areas such as the playground or cafeteria if need be) to photograph real world examples of geometry. Be sure students understand the guidelines for working with groups and traveling throughout the school. An alternative to this activity could be that, students search the Internet for examples instead of taking pictures. 3. When they have completed their Geometry Journey, students will meet together to plan their video (PhotoStory, Animoto etc.) using the planning guide. The script should explain why they chose a specific picture and the math behind the picture. Example: The corner of this bulletin board is a right angle because if measured we would find it measures 90 degrees. The video needs to contain a minimum of 10 slides/images. 4. Students should be given time to present their finished projects. This would be a good project to post to the class website. This project could be extended by having students take pictures at home and around the community (with the help from a parent). Sources: ALEX (Alabama Learning Exchange) Wake County Public Schools, Grade 5 Page 12

13 Real World Geometry Geometric Features (from slides) Explain your thinking Wake County Public Schools, Grade 5 Page 13

14 Geometry Journey Guidelines 1. Travel throughout our school to take pictures of items that represent realworld examples of geometry. 2. Adhere to hallway rules and work quietly as you travel. 3. Your video must contain at least 10 slides/images. You may take a picture of your group to use as the first slide in your story, but this doesn t count towards the requirement of 10 slides/images. 4. When recording your script, be sure that every member reads the script for at least two photos. Be descriptive and thoroughly explain why each photo was included specifically detailing the real world examples of geometry evident in the photo. Geometry Journey Guidelines 1. Travel throughout our school to take pictures of items that represent realworld examples of geometry. 2. Adhere to hallway rules and work quietly as you travel. 3. Your video must contain at least 10 slides/images. You may take a picture of your group to use as the first slide in your story, but this doesn t count towards the requirement of 10 slides/images. 4. When recording your script, be sure that every member reads the script for at least two photos. Be descriptive and thoroughly explain why each photo was included specifically detailing the real world examples of geometry evident in the photo. Wake County Public Schools, Grade 5 Page 14

15 Planning Guide Write the script and identify the photo and reader for each slide. Example: This is a picture of a ladder. The steps on the ladder are an example of parallel lines because if they kept going they would never intersect. Reader: Shelly Wake County Public Schools, Grade 5 Page 15

16 Common Core State Standard(s): 5.G.3 5.G.4 Unit IV: Geometry Unit (2 D Figures) Instructional Days Enrichment Investigation #4 Standard(s) for Mathematical Practice: 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 6. Attend to precision. Materials Needed: Blackline Masters: o Geometry RAFT Activity o Reflection Possible rubric: Instructions: 1. Have the students complete one of the self selected RAFT activities based on interest and learning style. RAFT is an acronym for Role, Audience, Format, and Topic. In a RAFT, students take on a particular role, develop a product for a specified audience in a particular format and on a topic that gets right at the heart of what matters most in a particular segment of study. 2. The students should choose one Role with its accompanying Audience, Format, and Topic. The format should incorporate various forms of technology if possible. The students may work individually or in pairs. 3. Have the students complete the reflection after the completion of the RAFT activity. 4. Students should share their final products with an audience. Encourage the students to ask one another questions about each other s work. Sources: Tomlinson, C.A. and Eidson, C.C. (2003). Differentiation in Practice: A Resource Guide for Differentiating Curriculum in Grades K 5 Wake County Public Schools, Grade 5 Page 16

17 Geometry RAFT Activity Options Role Audience Format Topic Writer/Illustrator Kindergarteners Illustrated children s book Shapes in My House Acute Triangle Obtuse Triangle Dr. John Letter Our Differences Trapezoid Kite Song (write and sing) Why We Don t Belong in the Parallelogram Family Regular Polygons Irregular Polygons News Report Lines of Symmetry Quadrilateral Square Love Letter Why You re So Perfect! Teacher Students Crossword puzzle Geometric Terms Square Rectangle and Rhombus Club Membership Form How to Join my Club Wake County Public Schools, Grade 5 Page 17

18 RAFT Reflection 1. How does your product reflect what you have learned in regards to geometry? 2. What do you like best about your final product? 3. What might you do differently next time? 4. What was most challenging about completing this task? Wake County Public Schools, Grade 5 Page 18

19 Common Core State Standard(s): 5.G.3 5.G.4 Materials Needed: Blackline Masters: o Geometry Product Menu o Product Rubric Unit IV: Geometry Unit (2 D Figures) Instructional Days Enrichment Investigation #5 Standard(s) for Mathematical Practice: 3. Construct viable arguments and critique the reasoning of others. 6. Attend to precision. Instructions: 1. The product menu allows students to self select products based on student interest and learning style. The students should have ample time to complete the tasks to ensure quality products. Depending on time, the students could complete one of the products or one per column for a total of two. The first column allows students to demonstrate mastery of geometric concepts while integrating writing/literacy. The product choices in the second column include more creative options that assess application and synthesis of geometric concepts. Students may complete the tasks individually or in pairs. 2. Have the students complete the Product Rubric. Explain that they will be turning in self evaluations when their product is complete. The self evaluations should be used as the rubric for scoring the final product. 3. Students should share their final product(s) with an audience. Encourage the students to ask one another questions about each other s work. Sources: Tomlinson, C.A. and Eidson, C.C. (2003). Differentiation in Practice: A Resource Guide for Differentiating Curriculum in Grades K 5 Coil, C. (2004). Standards Based Activities and Assessments for the Differentiated Classroom Wake County Public Schools, Grade 5 Page 19

20 Geometry Product Menu Task #1: Construct a picture book using polygons as characters. (Example: Ralph Rectangle, Suzy Square) The problem/solution should revolve around classifying two dimensional figures based on their properties/attributes: how triangles are classified, characteristics of parallelograms etc. Questions to consider: What is the situation at the beginning of your story? What is your character s problem? How s the problem resolved? What will be the theme of the story? Task #3: Create a character named specifically after a polygon. Write a monologue based on this character. Through monologues we learn the most about whom a character is, what their thought process is and what they plan to do to change their current circumstances. Dress like this character and perform a 2 minute monologue as this character, telling about yourself and what you like to do. You may also decide to include what you would like to change and why. Task #5: Make a book titled The ABCs of Geometry. Try to include a geometric term or concept for each letter of the alphabet. For example, A is for Angle or D is for Diameter. Illustrate your book with specific examples of each geometric term as well as a brief description. Where you can, include as many terms as possible for the letters. Be creative some letters will pose a challenge! Task #2: Create a Polygon game board. The game cards should include questions that require identifying polygons, comparing/contrasting various polygons, defining attributes of polygons etc. Such questions may be: How is a square similar to a rectangle? How is a rhombus like a parallelogram? Why does a trapezoid not fit in with the parallelogram, rectangle, rhombus, and square? Write a manual for parents and teachers that explain the rules and procedures of the game and discuss the benefits of playing the game (answer key should also be included). What things will students who play your game learn about polygons? Task #4: Imagine that your state has decided to split into two states: East Carolina and West Carolina. You have been commissioned to design flags for the two new states. Draw and color the two flags that include geometric features. Write two or three paragraphs discussing your designs. Include in your discussion the geometric features of your designs, the symbolism shown by the geometric features, and how the two flags are alike and different. Task #6: Design a robot that is made of many different geometric lines, angles, polygons, and circles. Write three or four paragraphs describing your robot. Include drawings or blueprints of your plans, and tell why you chose to use the shapes you did. Is your robot symmetrical or asymmetrical? Explain why your robot is special and what kinds of things it can do. Create a short advertisement for your robot to put in the Sharper Image catalog. Wake County Public Schools, Grade 5 Page 20

21 Product Rubric Name: Date: Task Number/Product: Level of Achievement 4: Exemplary Achievement Scoring Criteria I have gone above and beyond what was required in the following ways: These things are extra special about my product: 3: Proficient (Expected Achievement) I have completed my product on time. I have done my best work. My product shows that I understand geometric concepts and can apply them. Some examples are: 2: Limited Achievement I have tried to show what I know, but I know this is not my best effort. My product could have been better in the following ways: 1: Minimal Achievement This product did not get much attention or effort from me. There are many ways I could improve this product. Some of them are listed below: Tomlinson, C.A. and Eidson, C.C. (2003). Differentiation in Practice: A Resource Guide for Differentiating Curriculum in Grades K 5 Wake County Public Schools, Grade 5 Page 21

MCC5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that categories.

MCC5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that categories. Fifth Grade Mathematics Unit 6 CONSTRUCTING TASK: Property Lists of Quadrilaterals Adapted from Van De Walle, Teaching Student-Centered Math pg. 207 The purpose of this task is for students to become familiar