Professional Development Learning Plan

“Geometry Tools for Instruction”

Kelly ManzanoHill Elementary

According to Dictionary.com, geometry is the branch of mathematics that deals with the understanding of the properties, measurement, and relationships of points, lines, angles, and figures in space. Students can best understand geometry by directly interacting with shapes, lines, angles in their environment. In Elementary and Middle School Mathematics, Van de Walle lists several big ideas for geometric thinking. The big ideas include what makes shapes alike and different can be determined by an array of geometric properties, shapes can be described in terms of their location in a plane or space, shapes can be moved in a plane or in space, and shapes can be seen from different perspectives. All of these big ideas require hands on learning with manipulatives.

Each year at the end of school, the custodians put up a table and teachers can place any unwanted materials on the table. Anyone can come and shop at the “freebie” table. Unfortunately, in past years I’ve seen base ten blocks and geometric shape sets. This year, there was a class set of geoboards and a box of inch cubes. I think these materials ended up on the table because teachers don’t know how to use them to benefit students’ learning of geometry.

This professional development learning plan would address how to use manipulatives and materials to teach about geometrical thinking and spatial sense. Then the materials will not just take up prime closet space, the materials will be valued and used.

TEKS Addressed in Professional Development Plan:

K K.6(A) identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectanglesK.6(D) identify attributes of two-dimensional shapes using informal and formal geometric language interchangeableK.6(E)* classify and sort a variety of regular and irregular two- and three dimensional figures regardless of orientation or size

1 1.6(A)* classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language1.6(C) create two-dimensional figures, including circles, triangles, rectangles, and squares as special rectangles, rhombuses, and hexagons1.6(D) identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles, rhombuses, and hexagons, and describe their attributes using formal

geometric language2 2.8(B)* classify and sort three-dimensional solids, including spheres, cones, cylinders,

rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language2.8(C)* classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices2.8(D) compose two-dimensional shapes and three-dimensional solids with given properties or attributes

3 3.6(A) classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language3.6(B) use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories

4 4.6(A) identify points, lines, line segments, rays, angles, and perpendicular and parallel lines4.6(B) identify and draw one or more lines of symmetry, if they exist, for a two-dimensional4.6(D) classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified sizefigure

5 5.5(A) classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties5.6(A) recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible5.8(C) graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table

Learning Objectives: Teachers will investigate the vertical alignment of the TEKS: Numerical Representations

and Relationships for Grades K-6. Teachers will actively participate in student learning activities and games. Teachers will implement activities in their own classrooms. Teachers will reflect and report on results.

SMART Goals: By the end of the training, 80% of teachers will participate in the 5 sessions. By May, 90% of the students in Grades 3, 4, and 5 will pass the Geometry Unit Math test

with a score of 80% mastery.

Timeline:January Launch: This professional development will help you with your New Year’s

Resolution.

Explain purpose of professional development series. “We will be exploring manipulatives in order to understand how to use them in our classrooms. Each session we will explore two types of materials and activities that we can use to help students’ understanding.”

Explore: The first manipulative we are going to use today is attribute blocks. These activities are mainly geared for K-2. These activities can also be used for 3-5 intervention and vocabulary review and development for ELL learners.

Attribute Blocks:Lead teachers through following activities:

1. Sorting attribute blocks based on one characteristic. Possible sorts – color, size and thickness

2. Sorting attribute blocks based on two characteristics. Examples – small and red, thin and large, more than 3 sides and 3 vertices. Then students can learn to use a Venn diagram.

3. What’s My Attribute Rule? I used this activity when I taught second grade. It’s also included in the 5th grade curriculum. http://everydaymath.uchicago.edu/about/understanding-em/EM2007_G5_samples.pdf

red thin

red and thin

Pattern Blocks1. The first activity can easily be modified for different grade levels depending

on the design and the vocabulary used.

http://www.k-5mathteachingresources.com/support-files/pattern-block-barrier-game.pdf

Kinder students can be given a sheet with three boxes and have sentence starters to help. Or the activity can be extended by putting two shapes in one box or by not letting the students name the shape or color.

Older students can make more complicated designs:

Or they could use vocabulary terms such as parallel and perpendicular lines and angles of a specified size like 90 °.

2. The next activity is great for linking math vocabulary and writing. http://www.k-5mathteachingresources.com/support-files/my-shape-riddle.pdf

3. This last activity is an example of how to develop spatial reasoning. This example is from fourth grade.https://grade4commoncoremath.wikispaces.hcpss.org/file/view/4.G.1_BetweentheLines.pdf/446463344/4.G.1_BetweentheLines.pdf

Both of these materials can and should be used to teach fraction concepts as well. They can be used to teach and model parts of a whole. We can explore this in a later staff development if anyone is interested.

Closing: Just a reminder: Before students are expected to complete activities with manipulatives, they should have time for free exploration with the manipulative. Younger children will need more exploration time.Assignment: Use one of these materials in your classroom. Try two new activities. Reflect on the Google Doc shared with you. You may add a picture or other artifact.

Action Steps:Order Wooden cubes http://www.craftparts.com/blocks-squares-wooden-blocks-cubes-wooden-c-209_212.html ¾ in. wooden blocks, 50 for $4, 100 for $6.75, 500 for $28.75Copy tangram sets for teachers.

Copy nets for teachers.Bring scissors and tape for next meeting.

February Launch: Isn’t this what your students might say?

Read Grandfather Tang’s Story by Ann Tompert.https://www.youtube.com/watch?v=PTEpoKSNuq4

Explore: This session we will work with tangrams and nets.

TangramsLike building blocks, tangrams can teach students about spatial relationships. They help students learn geometric terms and develop stronger problem solving skills. They can be used to compose and decompose shapes.

A tangram is a Chinese puzzle consisting of 7 shapes (or “tans"):

Two large right triangles

One medium sized right triangle Two small right triangles One small square One parallelogram

- See more at: http://www.parentingscience.com/tangrams-for-kids.html#sthash.P6zbAzzD.dpuf

Interesting information about tangrams:A mathematician has calculated that there are at least 1600 designs that can be made with the seven tangram pieces/tans.

Keep these simple rules in mind:All seven tans are used in each picture (except where noted).All tans remain flat, none standing.Each tan may touch another, but none may overlap

Make a tangram set with teachers. Here are directions:http://www.auntannie.com/Geometric/Tangrams/

Here are the tangram animals from the story:http://www.auntannie.com/Geometric/Tangrams/PuzzleSheets/TangAnimalsClr.pdf

Have teachers make these animals from the tangram set. Tangram activities are easily differentiated. Younger students can simply match the shapes in the solutions or make their own shapes. Older students can make the shapes with only the outline.

Interesting information about tangrams:A mathematician has calculated that there are at least 1600 designs that can be made with the seven tangram pieces/tans.Keep these simple rules in mind:All seven tans are used in each picture (except where noted).All tans remain flat, none standing.Each tan may touch another, but none may overlap

Nets

http://www.onlinemathlearning.com/geometry-nets.htmlA geometry net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. Or a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. A solid may have different nets.

There are altogether 11 possible nets for a cube as shown in the following figures.

Here is a website where you can print 15 different nets.http://www.senteacher.org/worksheet/12/NetsPolyhedra.html

Have teachers choose a net, cut it out and fold into the 3D solid. Fill out a blank chart like this picture.

Second graders and up can do this activity with guidance. Younger students could watch the teacher make a net.

There is also a video on the online math learning link that shows how to make a net for a shape. Teachers can make a net for an existing solid and then show how the net folds up to form the solid. Students can examine the plane shapes that comprise the solid.

Here is a great way for students to add vocabulary to their math notebooks.

Closing: Assignment: Use one of these materials in your classroom. Try two new activities. Reflect on the Google Doc shared with you. You may add a picture or other artifact.

Action Steps: Collect geoboards and geobands for next session.Make copies of geoboard paper.

March Launch: Hopefully, you don’t feel like this. Today we will explore another geometry material that will make it easier to teach geometry.

Explore: Today we are just going to work with geoboards. There are so many different concepts that can be taught with geoboards.

GeoboardsSet up stations for each activity. Teachers will rotate through stations and try the various activities.Here is a great activity that can be differentiated depending on the vocabulary the students use. (Kinder activity)

Another activity involves squares. http://www.k-5mathteachingresources.com/support-files/geoboard-squares.pdf (Second grade activity)

This activity involves

quadrilaterals. http://www.k-5mathteachingresources.com/support-files/geoboard-quadrilaterals.pdf

http://www.k-5mathteachingresources.com/support-files/quadrilateral-criteria.pdf

Finally, geoboards can be great hands on tools to teach angles. http://www.k-5mathteachingresources.com/support-files/angles-on-the-geoboard.pdf(Grade 5 activities on the website but they cover the 4th grade TEKS)

“Angles on the Geoboard” may prevent:

http://www.k-5mathteachingresources.com/support-files/right-triangles-on-the-geoboard.pdf

http://www.k-5mathteachingresources.com/support-files/coordinate-grid-geoboards.pdf

Here is an example of geoboard recording paper:

Closing: Reminder: Students should have time for free exploration with geoboards before beginning activities. Students will also need a safety lesson on how to handle geobands. Geobands are not rubber bands. They are special math materials for use with geoboards. Demonstrate that when students take off the geobands, they should put a finger on top of the nail. Then the geobands can’t fly off and hurt anyone or get lost.Assignment: Use one of these materials in your classroom. Try two new activities. Reflect on the Google Doc shared with you. You may add a picture or other artifact.

Action Steps: Organize cubes for next week. Bring glue.

April Launch: More math humor!

Explore:SOMA cube history http://www.fam-bundgaard.dk/SOMA/HISTORY.HTM

The Soma cube is a solid dissection puzzle invented by Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pieces can also be used to make a variety of other 3D shapes. Explain that a Danish Author Piet Hein took only the irregular shapes that could be formed by no more than four cubes and made them into a puzzle. Decide as a class which pieces Mr. Hein might have considered to be “irregular” (no figures with all the cubes in just a straight line to form a rectangular prism). From the class drawings, determine the 7 pieces Mr. Hein used.

Make and take – Lead teachers through steps to make their own set of Soma cubes.

Some ideas to explore include:

How many blocks will you need to construct all 7 pieces?

When you finally put all seven pieces together to form a cube, what size will the cube be? (record the length, width, and height—good time to note that a cube has the same length, width and height)

How many small square faces will be showing on the outside faces of the giant cube?

Here are more shapes to make with Soma cubes. Can your students come up with others?

Closing: Next month is our final geometry session. Assignment: Use one of these materials in your classroom. Try two new activities. Reflect on the Google Doc

shared with you. You may add a picture or other artifact.

Action Steps: Send out reminder email for last session. Teachers need to bring an artifact.

May Launch: One more for our last session!

Explore:Share Session – Teachers share artifacts. These can include videos, student samples, games, etc.Reflection on activities used in classroom – Did you “give it a go”? What did you implement? How did you implement it? What worked and what didn’t work? On what topic would you like more training?

Closing:Final Reflection: What was your biggest “aha” moment?Now that you’ve heard your colleagues’ experiences, where will you go now?What would you like to try now?

Resources:

Gavin, M. K., & Cuevas, G.J. (2001). Navigating through Geometry in Grades 3-5. Reston, VA: National Council of Teachers of Mathematics.

Van de Walle, J. A. (2004). Elementary and Middle School Mathematics: Teaching developmentally. Boston: Allyn and Bacon.