Beacon Lesson Plan Library

10 by 10 Tessellations

Susanna Vondeck

Description

The students will work cooperatively to create tessellation patterns by playing 10" by 10" Tessellations. They need to use critical thinking skills to decide if pattern block plane figures will tessellate and how each block will best fit into the pattern.

Objectives

The student explores tessellations.

Materials

-Cardboard or oaktag, enough to make 10" by 10" squares for each pair of students in the class
-6 section spinners, enough for each pair of students
-Buckets of pattern blocks, enough for each 4-6 students to share a bucket of 250 blocks
-Overhead projector with a workspace of 10" by 10" for modeling game
-Overhead pattern blocks for modeling game
-One 10" by 10" paper for each student to recreate their tessellation
-Markers and crayons for labeling and coloring the tessellation patterns or have enough color coded cardboard pieces and glue for each student's pattern, instead of coloring

Preparations

1. Cut cardboard or oaktag into 10" by 10" squares for each pair of students. This is their game board.
2. Draw or trace a pattern block plane figure on to each section of 6 section spinners (One section yellow hexagon, 1 section red trapezoid, 1 section blue rhombus, 1 section tan rhombus, 1 section orange square, and 1 section green triangle). Create one spinner for each game board.
3. Acquire several buckets of pattern blocks. Each pair of students will need about one-third to one-half of a bucket of 250. If you cannot find this many pattern blocks, you have 3 options.
a. Make the game boards smaller.
b. Trace and cut out extra pattern blocks onto colored paper or oaktag.
c. Have students work on this in a center.
4. If you choose to not have the students color their tessellation patterns, you need to trace and cut out pattern blocks onto to colored paper or oaktag. You will need to have double the amount of pattern blocks from preparation step #3, so there will be enough pieces for each student to recreate a tessellation.

Procedures

1. Discuss with students that a tessellation is a pattern of one or more shapes that covers a plane surface without any gaps or overlaps. Show examples of tessellations to the students. At the fifth grade level, this should be a review.

2. Explain to students that they will be playing a game that requires them to create tessellations with a partner.

3. Explain that they will take turns spinning the spinner. Talk about what polygons are on the spinner and how each one of them is a pattern block piece.

4. Model spinning the spinner and landing on a pattern block. Pick up one overhead pattern block manipulative and model the critical thinking process of deciding where to place it on the overhead game board.

5. Explain to students that the only place they can have blank space is at the edges. They may not have space between pattern blocks (gaps) nor may they be placed on top of each other (overlaps).

6. Model placing a few more pieces so they can see how the game is played with a partner (taking turns) and the critical thinking involved in placing blocks to create a pattern.

7. Tell them that at the end of the game it will get harder to place pieces. Discuss why this is (it will be harder to spin the piece you need to fit in the pattern). If they cannot put down a piece, they skip their turn.

8. Remind them that they must work cooperatively to make decisions about the placement of pieces in the tessellation.

9. Have students move to groups of two.

10. Give each pair one game board, one spinner, and approximately 100 pattern blocks.

11. Observe students as they play the game. Circulate among groups to guide game playing and question the students about their decision-making.

12. When pairs complete their tessellations, they will work by themselves to recreate the pattern on 10" by 10" paper. They will either trace the blocks and color them in or glue down the pre-cut pieces. Then, they should pick one of each of the 6 possible polygons and label it with its correct geometric name.

Assessments

Observe the students as they play the game. Are they able to easily decide where the pattern blocks can be placed on the board with no gaps between or overlapping blocks? Did they create a pattern with their pattern blocks? During the extension, are they able to recreate their tessellation on paper, correctly namimg each shape? Can they identify how the original figure was transformed (slid, turned, or flipped) throughout the tessellation as it repeats? After the lesson, are they able to identify tessellations that occur in everyday life (quilts, tiles, bricks, patterned sweaters, rugs, carpets, etc.)?

Extensions

The tessellation patterns can also be used to review transformations (verifies which figures could result from a flip, turn, or slide of a given figure). Discuss the terms transformations, slide/translation, flip/reflection, and turn/rotation and their definitions. Place an overhead triangle pattern block on the overhead. Invite one student to come up to the overhead and model sliding the triangle in several directions. Have another come up and flip the triangle over imaginary horizontal and vertical lines. Have a third student come up and rotate the triangle around until they complete a 360 degree turn. Make corrections as necessary. Tell the students they will be searching for transformations in their tessellations. Students should pick a polygon that repeats in their pattern and label one "original". As the figure repeats throughout the pattern, it should be labeled as a "flip/reflection, turn/rotation, or slide/translation" of the original. After the lesson, the students should write and draw in their journal about tessellations they see in everyday life.
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