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©1998 University Child Development School and Bonnie Campbell Hill. No part of the Continuum may be reproduced or used without written permission of University Child Development School. Continuum adapted by University Child Development School with permission from Bonnie Campbell Hill.
Story: In this Vitamin, students are expanding on their previous work with pentomino shapes and using toothpicks to develop mathematical strategies and increase their visual thinking skills. Each student has four toothpicks to work with for this task. Following two simple rules for each shape: 1) Each toothpick has to be touching another toothpick 2) Toothpicks must be placed end to end or make a square (90 degree) corner With these rules in mind, they try and discover the 16 possible arrangements that can be made with these four toothpicks. Each student is reminded to notice flips and rotations as they could represent duplicate shapes; thus not one of the 16 designs needed. At UCDS, each student is required to build draw and record their work. They listen and share ideas with peers as well as explain their findings to their teachers. For this vitamin, students use geometric dot paper to document the shapes they have created. All Math Vitamins require students to build, draw and record their work as well as share their thoughts with peers and teachers. The strong UCDS math community within each classroom is developed through the process of peer and teacher conversations that focus on exciting mathematical tasks and engaging ideas about the various approaches to solve them.
Suggested manipulatives: Toothpicks, pick-up sticks, chopsticks, pencils, rulers. Use anything that is straight and relatively flat. Toothpicks are idea as they are small and don’t require a lot of table room and inexpensive for outfitting an entire classroom with materials.
Prep time: Adapting the vitamin wording to fit your specific story, putting manipulatives out in the room, and creating the geo-dot paper will take about 15-20 minutes. Set up is always more fun and shorter on time if you do this activity with a colleague.
Classroom time: Asking children to “do their best work” for each Math Vitamin assumes that some children will need a longer time than others. Ideally you want to offer a block of time for Math Vitamin projects and have another task available (writing, free exploration etc.) for those students who finish work prior to their peers. For this project allow 20-45 minutes for students to work through all the steps.
How to individualize/stretch: Have children start this type of work by building pentomino designs using color tiles. These are a bit larger and let them start to visualize the rotations and flips for each shape. You can also use one-inch grid paper to document and cut out each individual shape. Next would be to work on this activity with the toothpicks. Extensions include ordering your shapes by “one piece changes” in the design and then starting to explore angles.
Story: Students are exploring Pentominos as a way to solve s secret code! Their read aloud character Daniel has discovered 5 magical square stones. He knows they can be configured to resemble 12 different letters of the alphabet. If students can find all 12 configurations, they can use them to decode the missing letters in the secret message that is attached to today’s Math Vitamin sheet. When working with the magical square stones, each one needs to be touching a full side of another square stone and each unique shape they create must have an area of 5. Students are asked to build with color tiles and use one-inch grid paper to document and label each shape they create. They are advised to be carful about being deceived by shapes that are the same when flipped a different direction…part of the secret code process! All Math Vitamins require students to build, draw and record their work as well as share their thoughts with peers and teachers. The strong UCDS math community within each classroom is developed through the process of peer and teacher conversations that focus on exciting mathematical tasks and engaging ideas about the various approaches to solve them.
Suggested manipulatives: Color Tiles are ideal for this activity as they are square and flat. You could use cubes, but they add a bit too much dimensionality. Use one-inch grid paper for students to document their work. Cutting the created shapes out of paper really allows students to explore the rotations and flips to avoid duplications. Premade pentomino sets are also good to have on hand, but not needed.
Prep time: Adapting the vitamin wording to fit your specific story, putting manipulatives out in the room, creating the grid papers and copying the vitamin documentation forms will take about 15-20 minutes. Set up is always more fun and shorter on time if you do this activity with a colleague.
Classroom time: Asking children to “do their best work” for each Math Vitamin assumes that some children will need a longer time than others. Ideally you want to offer a block of time for Math Vitamin projects and have another task available (writing, free exploration etc.) for those students who finish work prior to their peers. For this project allow 45-60 minutes for students to work through all the steps.
How to individualize/stretch: Begin by using Color Tiles to create shapes with a specific area. The only requirement is that one full side of each tile must touch another full side of a tile. Then ask students to create shapes with an area of 5…can they find 12 different shapes with that area? It’s fun to link these shapes to alphabet letters as well. Move on to using the shapes to create rectangles, for example, how many ways can you make a 3x5 rectangle with your pieces? Draw and record. The premade pentomino sets have some great puzzle activities too. Strong visual spatial skills.
Story: Students are working with tangrams in an effort to discover how many different shapes they can make using a combination of tangram pieces. They are using a teacher created Tangram Shape Sheet that for documentation and direction. The sheet is a grid format noting a variety of shapes and asking students if it is possible to make them with 2,3,4,5-8 pieces of their tangram. Students document their findings on the data sheet. They are working independently as well as with peers to share ideas and solutions they have discovered. All Math Vitamins require students to build, draw and record their work as well as share their thoughts with peers and teachers. The strong UCDS math community within each classroom is developed through the process of peer and teacher conversations that focus on exciting mathematical tasks and engaging ideas about the various approaches to solve them.
Suggested manipulatives: Tangram pieces are needed for this task. You can use pre-made plastic or wooden pieces or have each student make their own with an 8x11 piece of paper. You can find the folding directions on line. Students love the folding process and the ownership of their own tangram pieces.
Prep time: Adapting the vitamin wording to fit your specific story, putting manipulatives out in the room and creating the Tangram Shape Sheet will take about 15-20 minutes. Set up is always more fun and shorter on time if you do this activity with a colleague. If you decide to have your students make their own tangram pieces, you’ll need more time to download the directions as well.
Classroom time: Asking children to “do their best work” for each Math Vitamin assumes that some children will need a longer time than others. Ideally you want to offer a block of time for Math Vitamin projects and have another task available (writing, free exploration etc.) for those students who finish work prior to their peers. For this project allow 45-60 minutes for students to work through all the steps.
How to individualize/stretch: Start by having kids make their own pieces with colored paper. Then, start putting them together and see what shapes (even animals) they can create. Next, ask them to use all the pieces to make a square. Proceed with asking them to make a variety of geometric shapes using 2 pieces, then 3 pieces etc. The Tangram Shape Sheet seen in the video is ideal for documenting their findings. Continue using this manipulative to discover the fractional values for each piece and/or all the angles for each piece.