Geometry: Finding Pentominoes
|Grade span:||3 to 5|
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Description:This sample lesson is one example of how you can implement Math Centers. In this activity, students explore and build pentominoes, figures that are made up of five squares and can be arranged to form different geometrical shapes.
- Understand basic features of shapes, such as sides and angles
- Explore geometric relationships by arranging objects
- Understand what a pentomino is and how it is formed
- Work together to find different pentominoes and problem solve
- Reflect on and communicate mathematical reasoning
- Graph paper and/or unlined paper
- Pentomino blocks (optional)
- Domino (optional)
- Small blocks or tiles work well for this activity, but if you don't have them, students can draw pentominoes on graph paper.
- Use the materials you have to create inviting areas (centers) where students have access to all the materials they may need.
- Print out the Finding Pentominoes (PDF) and review the possible shapes students can make with up to five squares. The bottom row will show you the 12 possible shapes students can make with pentominoes.
What to Do:
- Create groups of four to five students for each center. You may want to assign students to groups based on their needs and abilities, or ask students to count off for random groups.
- Draw or configure a pentomino using the sample image at the top of this page. Introduce the word to students, and ask guiding questions about how many squares there are in this new shape and what they notice about it to come up with a group definition. (A pentomino is a shape made up of five squares, connected on at least one side.)
- Using the pentomino you created, turn it so that it is still the same arrangement of squares, but facing in a different direction. Explain that this is not a different pentomino because the combination of squares is the same.
- Explain that there are 12 possible pentominoes, or 12 possible shapes that can be created by combining five squares. You have already created one pentomino. Working in groups, students' task is to find the other eleven.
- Now, ask students to work together in groups, taking turns, to find as many different pentominoes as they can. As they create a pentomino, they should draw it on graph paper.
- Circulate among the centers to make sure all students are participating. Ask questions, and provide positive feedback to encourage learning.
- As each group finishes, check in to see if they found the other 11 pentominoes.
- Discuss the activity with the whole group. Which pentominoes were the easiest to find? Which were the hardest? What did you learn?
- Begin with something students already know. Show them a domino and ask them how many squares are in a domino. Next, add a square to the domino to make a triomino, a three-square shape.
- Ask students what the domino and triomino have in common. They should be able to see that in each shape, the squares are connected on at least one side.
- Ask students to use their squares to see how many different shapes they can make with the triomino. Remember that at least one side of a square must line up with the side of another square.
- As students are working in centers to find all 12 pentominoes, use the guiding questions below to assess students' progress and encourage them to think for themselves.
- Can you tell me how you know that this shape is a pentomino?
- How do you know that each pentomino you have created is different?
- How can you figure out if one of your pentominoes is the same as another?
Evaluate (Outcomes to look for):
- Student participation and interest in the activity
- Students working and talking together to problem solve and find pentominoes
- Answers that reflect an understanding of geometric relationships
- Answers and configurations that reflect an understanding of what a pentomino is
- Students using different strategies to find other pentominoes
- Students' ability to explain different shapes and how they found their answers
Click this link to see additional learning goals, grade-level benchmarks, and standards covered in this lesson.