Geometry


 * TEKS:**

3.6 Patterns, relationships, and algebraic thinking. //The student uses patterns to solve problems.// 3.6A Identify and extend whole-number and __geometric patterns__ to make predictions and solve problems. //*(Focus on geometric patterns in this Nine Weeks as whole-number patterns were covered in 1st Nine Weeks.)// 3.8 Geometry and spatial reasoning. //The student uses formal geometric vocabulary.// 3.8 Identify, classify, and describe two- and three-dimensional figures by their attributes. The student compares two-dimensional figures, three-dimensional figures, or both by their attributes using formal geometry vocabulary. 3.9 Geometry and spatial reasoning. //The student recognizes congruence and symmetry.// 3.9A Identify congruent two-dimensional figures. 3.9B Create two-dimensional figures with lines of symmetry using concrete models and technology. 3.9C Identify lines of symmetry in two-dimensional geometric figures.


 * Core Components:**


 * Recognizes that real world objects can represent 3-dimensional shapes. (Ex. balls resemble spheres, cans are cylinders)
 * Recognizes and lists attributes of these shapes: circle, polygon, triangle, square, rectangle, quadrilateral, trapezoid, parallelogram, rhombus, pentagon, hexagon, octagon, sphere, cone, cylinder, cube, rectangular prism, triangular prism, square pyramid, triangular pyramid.
 * Describes two-dimensional figures using sides and angles.
 * Describes three-dimensional figures using faces, edges, and vertices
 * Identifies shapes that are the same size and same shape
 * Recognizes shapes that are congruent but may have a different orientation (turned a different direction).
 * Uses geoboards or patty paper (tracing paper) to model congruent shapes in various orientations
 * Uses KidPix software, Microsoft Word and/or other drawing tools to create figures with an axis of symmetry.
 * Models symmetry using mirrors, pattern blocks, geoboards, paper folding, and/or patty paper
 * Recognizes that lines of symmetry can be vertical, horizontal or diagonal. Identifies multiple lines of symmetry in objects and symbols using shapes and pictures.


 * The Envision Resources for the Geometery unit are excellent. I have tried to put them under the correct topic for each day. If you see something out of place, please move it for us. This was a crazy task! (I have not finished adding them all if someone wants to HELP!)

Also, the TEKS tell us we are to use "formal geometric vocabulary". I think this is where the vocabulary (perpendicular, parallel, obstuse, angles, acutes, etc) comes in to play. There are plenty of Envision resources for these as well so I have plugged those into the days we have. I am worried we are going to cover this unit way too fast. There is a TON of information. Let me know if you think we should add some extra days. **


 * Day One and Two: Geometric Patterns**

Found some cool stuff after all!

Introduce elementary students to the concept of functions by investigating growing patterns. Visual patterns formed with manipulatives are especially effective for elementary students and allow them to concretely build understanding as they first reproduce, then extend the pattern to the next couple of stages.

Following this concrete modeling, the teacher introduces the use of an input-output table to organize data about the number of blocks used for each stage of the pattern. The table helps quantify the pattern so that students see both the growing pictures and the growing numbers in the table. They can note the change from stage to stage and work to explain how the change in the table matches the change in the picture of the growing pattern.

Finally, students can learn to write a general rule that will work for any stage of the pattern without having to build it or know how many blocks were used in the stage before it. This is an important abstraction of the pattern and the rule must make sense to students and be in their own words or in their own mathematical notation that reflects the level of their current understanding.



Fir Tree uses pattern block triangles to create growing fir trees. Students must extend the pattern, complete the table of values and describe the 10th tree.



Hexagon Dragons requires students to extend the pattern, create an input/output table to describe the growing pattern, then draw and/or describe the 10th dragon in words. An extra challenge asks students to generate a rule for this pattern so that Miguel can figure out how many blocks he will need to build a dragon of any size.



Tables and Chairs challenges students to find a rule to describe the relationship between the number of small square restaurant tables placed together in a line and the number of diners that can be seated at the larger table if only one person sits on each side.

These would make a great center or to do in small groups. They are task cards for working with growing geometric patterns.




 * How Does A Pattern Grow?**

Students extend a given pattern using tiles or pattern blocks.


 * Overview of Math Concept:**

Generalize a rule for how a pattern grows. Extend a pattern using manipulatives.


 * Materials:**
 * Blackline master of Growing Patterns Task Cards
 * Cardstock or construction paper
 * Set of approximately 30 square tiles or triangles per student


 * Teacher Preparation:**
 * Copy the task cards from the blackline master on cardstock or construction paper and laminate.
 * Cut the cards apart.
 * Make copies of directions as needed for students, assistants, or teachers to use in a center or small group setting.
 * Arrange for a large table or rug space for students to build the patterns. This activity can be done in a center (either individually or with a partner) or as a whole class.
 * Review growing patterns before doing this activity.


 * Directions:**
 * 1) Choose a task card.
 * 2) Take a pile of square tiles or triangles.
 * 3) Look at the pattern. Decide how it is growing.
 * 4) Use the tiles to make the next two shapes in the pattern. Be prepared to explian how the pattern is growing.
 * 5) Follow our teacher's directions for checking your work.
 * 6) If there is time, choose another task card.

Link to Task Cards @http://teams.lacoe.edu/documentation/classrooms/linda/algebra/activities/patterns/patterns.html


 * Growing Patterns:**

Students create a growing pattern using tiles.


 * Overview of Math Concept:**

Generalize a rule for how a pattern grows. Create and extend a pattern, using manipulatives. >
 * **Materials:**
 * Blackline master of Growing Pattern Cards @http://teams.lacoe.edu/documentation/classrooms/linda/algebra/activities/patterns/starters.html
 * Cardstock or construction paper
 * Set of approximately 30 square tiles per student group
 * Set of approximately 30-40 1" paper squares per student group
 * 1 large sheet of paper per student group
 * Glue


 * Teacher Preparation:**
 * 1) Copy the Growing Patterns Starters from the blackline master on cardstock or construction paper and laminate.
 * 2) Cut the cards apart.
 * 3) Make copies of directions as needed for students, assistants, or teachers to use in a center or small group setting.
 * 4) Cut paper squares.
 * 5) Assemble other needed materials.
 * 6) Arrange for a large table or rug space for students to build the patterns. This activity can be done in a center or as a whole class. Decide whether students will work individually or in partners.
 * 7) Review growing patterns before doing this activity.


 * Directions:**
 * 1) Choose a Pattern Starter card.
 * 2) Take a pile of square tiles.
 * 3) Copy the starter pattern.
 * 4) Try some different ways to make it grow.
 * 5) Choose your favorite way to make it grow.
 * 6) Make your pattern grow until you have at least four shapes in your pattern. Make more if you can!
 * 7) Be prepared to explain how the pattern is growing.
 * 8) Follow your teacher's directions for checking your work.
 * 9) After your work has been checked, copy your pattern onto the large paper using the paper squares.
 * 10) Glue the squares onto the paper.
 * 11) Write on the paper, telling how your pattern grows. Be sure to use words and numbers.

@http://pbskids.org/cyberchase/webisode_1/web_1game.html

@http://nlvm.usu.edu/en/nav/frames_asid_184_g_1_t_2.html




 * Day Three and Four: 2D Shapes, Lines and Angles**

Cute book the kids can make that covers EVERYTHING Geometry.


 * Good Review of Geometry:**

http://www.quia.com/cb/29134.html




 * Day Five and Six: 3D Shapes

[|Cube, Cylinder, Cone, Sphere Song]



Day Seven: Congruency**



@http://www.harcourtschool.com/activity/similar_congruent/




 * Day Eight and Nine: Symmetry**

@http://www.innovationslearning.co.uk/subjects/maths/activities/year3/symmetry/shape_game.asp


 * [[file:Symmetrical Faces.pdf]][[file:Symmetry Sketching.pdf]][[file:Symmetry Houses.pdf]][[file:Symmetry Color Design.pdf]][[file:Symmetry.pdf]][[file:Lines of Symmetry.pdf]][[file:Drawing Lines of Symmetry.pdf]][[file:Dividing Shapes.pdf]][[file:Cut and Fold Symmetry.pdf]][[file:reflectivepatterns.doc]]

Day Ten: Review and Test**




 * Common Assessments:



Literature Connections:** //A Cloak for Dreamers// //Grandfather Tang’s Story// //Jim and the Beanstalk// //Spaghetti and Meatballs for All// //How Big Is a Foot?// //Changes, Changes// //Draw Me a Star// //Eight Hands Round,// //If You Look Around You// //I Read Signs// //Look at Annette// //Shadows and Reflections// //The Greedy Triangle,// //The Silly Story of Goldie Locks and the Three Squares, // MacCarone