Classroom Activities
Activity One: Measuring With Square Tiles
Materials: Multiple color square tiles, classroom objects
Students will measure different classroom objects using the edges of square tiles. They will make sure there are no overlaps, no gaps, and the tiles are edge to edge. After showing mastery in measuring different classroom objects with the tiles, they will get time for exploratory play.
Working in groups, the students will create “paths” using the square tiles. They will use as many tiles as possible to see who can create the “pathway” that takes up the most space. The pathway that takes up the most space has the greatest area. Pathways are created by having tiles touch edge to edge. This activity is an introduction to polyominoes since students are creating them when they connect the tiles by edges.
Activity Two: Using a Ruler
Materials: Rulers, classroom objects, poster paper, markers
In this lesson students will be introduced to using rulers. The teacher will gather the students on the carpet and model how to use a ruler. Certain misconceptions must be addressed. The first misconception would be where to start measuring. Some rulers have zero listed at the very edge or the ruler. Others, have the zero further in. It is important to reiterate to students that they start measuring at the zero. This will be justified later on in the activities, by having the students line up one inch square tiles along the ruler, so that they can see that the number at the end of the row of tiles tells the number of tiles, which is the length of the row. Secondly, students must be taught that in order to measure the ruler must lie flat. The reason for this being that you are counting the linear distance between zero and the end of the object. After these misconceptions are addressed, the students may help the teacher to make a poster which explains how to use a ruler. They can reference this poster throughout the unit.
After making the poster, students will be allowed to measure with the rulers. They can use the same objects they used when using the square tiles to measure length. The students will line up the tiles against the ruler. Students will be able to observe that the length of the line of tiles is the same as how many tiles are being used. This will allow them to explore if the length changes based on which measurement tool is used. Since the square tiles are one inch in length, the objects will have the same length in inches as tiles used. This can lead to a hearty discussion where students discover that the tiles are one inch long on each side.
Activity Three: Intro to Pentominoes and Enclosing Rectangles
Materials: two different color square tiles, poster paper, markers
In this lesson I will first tell my students we will be creating figures called pentominoes. I will explain that pentominoes use five tiles and that there are twelve pentominoes in all. I will challenge my students to create pentominoes using the square tiles. The overall goal of this lesson is that the students find all twelve. They will be informed that the pentominoes must have edges touching, and two adjacent tiles must match along a whole edge of each.
Students will work in groups to find the different pentominoes. After a certain period (I will probably use 15 to 20 minutes) we will come together as a group for students to share their different figures. We will add their figures to the poster as they share. At this point, students will be made aware that two shapes that can be rotated or flipped into each other count as only one pentomino. If the students are missing any of the twelve we will work as a class to find the missing pentominoes.
Once we have found all twelve pentominoes, and they have been listed on the poster, I will introduce the concept of enclosing rectangles. Using a different color square tile I will fill in the gaps in the pentomino. When all the gaps have been closed, I will have a rectangle composed of two different color square tiles. I will ask my students to create enclosing rectangles as well. Once my students have created enclosing rectangles, I will ask them what they notice about the new shape. This new question will lead to a discussion. The goal of this discussion is for students to come to the conclusion that rectangles can be composed with squares.
Activity Four: Pentomino Walkways
Materials: graph paper, colored pencils
In this lesson students will use graph paper and colored pencils to design the pentomino walkways for our garden. The enclosing rectangles will be filled in with plants which is why the colored pencils are necessary.
Working in groups students will design different walkways for our garden. They must use pentominoes as the “shape” for their walkways. They will be told that the edges must touch. Instead of using tiles, students will use the squares on the graph paper as their basic shape. They must use five and edges must touch. These walkway designs will be used when we create the walkways in our real garden.
Activity Five: Tetris Garden
Materials, a 6 ft X 10 ft plot of land, twelve different types of plants to represent each pentomino, plastic pentominoes for planning use, square tiles, graph paper, colored pencils
Students will first plan out their “tetris plot”. They can either use plastic pentominoes, square tiles, or draw the designs using the graph paper and colored pencils. Students will work in groups to determine how all twelve pentominoes fit together in this plot. There is only one way for all twelve of these pentominoes to fit together in this rectangular shape, therefore, all groups will eventually come up with the same design. The groups will share their designs with the whole class using math terminology. If students are struggling to figure out how the pentominoes all fit together, I will provide them with certain hints. One hint would be giving them the outline of the enclosing rectangle which all the plastic pentominoes fit inside. Another would be giving them a piece of graph paper with some of the pentominoes already drawn. I will have several versions of this paper available. They be scaffolded to different levels. Depending on how much help the group needs they can get a paper with either 1, 2, or 3 pentominoes drawn on already. These hints would allow the students to explore the way the pentominoes fit together with extra support. If they continue to struggle we can work together as a whole group.
After the designs have been drawn up, the plot will be divided into the pentomino shapes. Each shape will have a designated plant and color that represents it. When the garden in finished, you will be able to clearly see each shape due to this.
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