## Perfectly Puzzling Pentominoes

### Mary Bohannon

#### Description

Students utilize manipulatives (pentominoes) to demonstrate knowledge of: lines of symmetry, slides, reflections(flips), rotations(turns), area, and perimeter.

#### Objectives

The student determines which units of measurement, such as seconds, square inches, dollars per tankful, to use with answers to real-world problems.

The student given a verbal description, draws and/or models two- and three-dimensional shapes and uses appropriate geometric vocabulary to write a description of a figure or a picture composed of geometric figures.

The student understands the concepts of spatial relationships, symmetry, reflections, congruency, and similarity.

The student predicts, illustrates, and verifies which figures could result from a flip, slide, or turn of a given figure.

#### Materials

-Teacher set of overhead pentominoes™ labeled 1-12 (see activity sheets #1 and 2)
-Class set of overhead pentominoes labeled 1-12 (see activity sheets #1 and 2)
-Activity sheet #3 for Lesson 2
-Activity sheet #4 for Lesson 3
-One-inch grid paper on transparency
-One-inch grid paper (4-5 per student)
-Plain 8 ˝ x 11 paper {2-3 per student)
-Color crayons
-Class set of dish towels (optional)
-Scissors
-Activity sheets in the Associated File

#### Preparations

1. Complete a unit in geometry which will provide students with the necessary knowledge and skills for this lesson.
2. Gather needed materials for these activities.
3. Print one copy of activity sheets #1 and #2. Label each Pentomino piece as seen on the activity sheets with a black permanent marker.
4. Print one copy of activity sheet #3.
5. Copy a class set of activity sheet #4.
6. Obtain a class set of one-inch grid paper.

#### Procedures

Objectives:
* Students will be able to demonstrate correct usage of the vocabulary terms: symmetry, slide, reflection (flip), rotation (turn), area, and perimeter.
* Students will be able to demonstrate knowledge and understanding of the terms: symmetry, slide, reflection, rotation, area, and perimeter through the use of manipulatives and hands-on activities.
* Students will be able to calculate the area and perimeter of geometric shapes.

Lesson 1
You will need the following items: overhead and class set of pentominoes, plain paper, scissors, and activity sheets 1 and 2. (See Associated File.)

Part I
1. Introduce the lesson by activating prior knowledge of the vocabulary terms: symmetry, slide, flip(reflection), and turn (rotation).

2. Explain to the students that they are going to do hands-on activities that will help them visualize and understand these concepts by using the pentominoes.

3. Distribute materials to class. Give the students a few minutes to explore with their manipulatives. (You may want to have dish towels on the student desks to muffle the noise of the pentominoes.)

Part II
4. On the overhead projector, draw a four-inch vertical line.

5. Ask the students to study their pentominoes and set aside the pieces that they think are symmetrical. Choose student volunteers to come to the overhead to demonstrate which pentomino pieces are symmetrical. (Students will be using overhead pentominoes.) Piece #’s 1-6 are symmetrical; piece #’s 1 and 3 have 2 lines of symmetry. Students should be able to tell why each shape is symmetrical. Have the students trace around and cut out piece #1. Demonstrate the line of symmetry by folding the piece of paper in half lengthwise. Have students do this. Check for understanding. Ask the students if there is another line of symmetry. Ask a student to demonstrate. Have the other students fold the other line of symmetry.

7. Have students demonstrate which pieces are not symmetrical and explain why they are not. Choose students to come to the overhead. (Pieces 7-12 are not symmetrical.)
8. Have the students trace around and cut out piece #7. Have the students demonstrate that their are no lines of symmetry with this piece. Check for understanding.

Part III
1. Demonstrate a slide by tracing piece #6 (see activity sheet) on the overhead, then moving it over and tracing it again. Have the students explain why this is a slide.

2. Have students take piece #8 and trace around it on plain paper. Have students slide this piece and trace around it. Check students' papers for understanding.

Part IV
1. Demonstrate a reflection (flip) by tracing piece #9 (see activity sheet) on the overhead, then flipping it over and tracing it again. Have the students explain why this is a reflection.

2. Have students take piece #5 and trace around it. Have students flip this piece and trace around it. Check students' papers for understanding. You may want to extend this activity by combining two or more pieces and have the students demonstrate a reflection.

Part V
1. Draw a midpoint on the overhead. Demonstrate a rotation (turn) by tracing piece #10 on the overhead. Start in one position on the midpoint, trace around the piece, rotate the piece, and trace around it again. Do this several times. Have the students explain why this is a rotation.

2. Have students take piece #2 and do the same procedure on plain paper. Check students' papers for understanding.

3. Have students draw geometric shapes with the pentominoes that demonstrate all of the concepts they have learned about on plain paper. Have the students label their shapes with the correct vocabulary terms. Collect their papers and distribute them to the other students. Have the students check each other's papers for understanding.

Lesson 2
You will need the following items: pentominoes, one-inch grid paper (teacher and students), crayons, and scissors.
Part I
1. Introduce the lesson by activating prior knowledge of the vocabulary term: area.

2. Explain to the students that they are going to do hands-on activities that will help them to visualize and to understand these concepts through the use of the pentominoes.

3. Distribute materials.

Part II
1. Distribute one-inch grid paper, a set of pentominoes, and a pair of scissors per student or small group. On the overhead, demonstrate the area of piece #1 on the grid. You should tell the students that the scale of the grid is measured in inches, and the area is always expressed in square units. In this instance, it is expressed in square inches. Ask the students if they can tell you how many square units are covered with piece #1. Have them explain how they know. Display their answer in square inches on the overhead. The area of piece #1 is 5 square inches.

Part III
1. Have the students place piece #4 on their grid paper, trace around it, and color it in with a crayon, and express the area on their paper. Students should have written 5 square inches. Check for understanding. Engage the students in a discussion about why the shape of the area of something is not always the same. You could give them examples, such as a garden or a room and so on.

2. Have the students do the same procedures for piece #’s 6, 9, and 12. Check for understanding.

Part IV
1. Demonstrate a larger area by combining piece #’s 7 and 8 on the overhead (see activity sheet #3). Have the students tell how much area the two pieces cover. Ask them to explain how they know. They should tell you 10 square inches. Display the answer on the overhead. Using the same two pieces, change the way you put them together and ask the students if the area is the same. Engage them in a discussion about how the area is the same even
though the shape has changed.

2. Have the students put piece #’s 8 and 12 together on their grid paper, trace around them, color it in with a crayon, and express the area on their paper. Note that the students will not put their pieces together in the same way. Check for understanding. Have several students, who have different designs, come to the overhead to demonstrate their findings.

3. Have the students combine their own pieces to demonstrate area and put their answers inside of the shapes along with their names. Check for understanding. Have the students cut them out and post them on the chalkboard.

Lesson 3
You will need the following items: pentominoes, one-inch grid paper (teacher and students), scissors, activity sheet #4.

Part I
1. Review what the students learned about area in the previous lesson. Introduce the lesson by activating prior knowledge of the vocabulary term: perimeter.

2. Explain to the students that they are going to do hands-on activities that will help them visualize and understand these concepts through the use of the pentominoes.

3. Distribute materials.

Part II
1. Place piece #1 on the overhead on one-inch grid paper and trace around it. Demonstrate the perimeter of piece #1 to the students. Engage the students in a discussion about the differences between area and perimeter. The perimeter is 12 inches. Be sure to point out the difference in the ways area and perimeter are expressed.

Part III
1. Distribute one-inch grid paper and pentominoes.
2. Have the students trace around piece #10 on the grid paper and express the perimeter on their paper. Check for understanding. Have a student come to the overhead to demonstrate and explain his/her findings. The perimeter is 10 inches.

3. Repeat the same procedure with piece #’s 6 and 11. The perimeter of piece #6 is 12 inches. The perimeter of piece #11 is 12 inches.

Part IV
1. The students are going to combine piece #’s 3 and 8 (P= 20 inches), and 2 and 6 (P= 20 inches) to make larger perimeters. Distribute activity sheet #4. Have the students combine the pieces shown on the activity sheet to calculate the perimeter of the combined pieces. Have the students express their answers on their activity sheet. Check for understanding. Ask for students to come to the overhead to demonstrate and to explain their findings.

Part V
1. Have students combine their own pieces to make two to three different shapes. Ask the students to predict whether or not the perimeter will change based on how the pieces are combined. Have students calculate the perimeter and write down their answers underneath the shape with their name. Check for understanding. Have students cut those shapes out and put them on the chalkboard.

2. Assess the activity.

#### Assessments

The assessment is embedded into the activities through the use of observation and anecdotal records. Teachers could make a list of the students, and check off each skill as it is observed being done correctly by the student throughout the activities. This would be a formative assessment to let teachers know which students need extra help.

#### Attached Files

Four drawings and may take a while to open.     File Extension: pdf