Teaching Middle Grades Geometry and Measurement through Children’s Literature and Computer Software



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Teaching Middle Grades Geometry and Measurement through

Children’s Literature and Computer Software

Lin-Chiou Lee

April 26, 2005

Connecting Mathematics, Children’s Literature, and Technology

Learning mathematics, especially geometry and measurement, should be lively, tangible, and meaningful to all students. Mathematics is not only a tool for students to solve real-life problems, but also a means for students to look at and communicate about their world with a little more understanding and insight. Through children’s literature, students learn to work with concrete manipulatives to investigate real-life mathematical problems in meaningful contexts. Through the integration of technology, students learn to simulate, model, and represent abstract mathematical concepts in order to further reason, explain, and conjecture. Since there are so many quality children’s literature and computer software that are directly and indirectly connected to mathematics in the field, ten quality children’s literature and five quality computer programs are selected and discussed in this section for the purpose of calling more awareness upon the benefits of integrating children’s literature and technology into mathematics instruction.

Children’s Literature on Geometry and Measurement



  • What is Square? written by Rebecca Kai Dotlich and photographs by Maria Ferrari

  • What is A Triangle? written by Rebecca Kai Dotlich and photographs by Maria

Ferrari

    1. Grade Level: 4-6
    2. Summary: Geometric shapes such as squares and triangles can easily be discovered in everyday objects. A box, a checkerboard, an alphabet block, a pillow, and a cold cube of ice are all squares that can be found in everyday objects. Half of a diagonally-cut sandwich, the roof top of a church, a triangular button, and a tree are all triangles that can be found in everyday objects. Can you spot more squares and triangles in real-life objects? What other shapes can you find in objects around you?


    3. Topic/ Concept: Geometry – Shapes

    4. Rationale for Selection: These two easy picture books on squares and triangles for younger students will motivate them to identify and describe the many geometric shapes they can find in real-life objects everywhere around them. For upper elementary school students, they can be challenged and encouraged to find real-life objects that contain more complicated geometric shapes (i.e., a basketball court, a book shelf, etc) and try to represent them geometrically in the Geometer’s Sketchpad.




Weisgard

    1. Grade Level: 4-5

    2. Summary: There are many important things in The Important Book. What is important about everyday objects such as the sun, the moon, the wind, the rain, a bug, a bee, a chair, a table, a pencil, a bear, a rainbow, and a cat? Even though an object may have many things you find important, what should be the “MOST” important thing about the object that makes it distinctive from all others?

    3. Topic/ Concept: Geometry – Analyzing and describing geometric concepts of shapes
    4. Rationale for Selection: By using the poetic and recurring sentence structures in The Important Book, students are exploring and analyzing the attributes of geometric shapes and concepts such as sides, faces, angles, parallel lines, and perpendicular lines. Students can also be given the opportunity to explore and analyze the relationships among geometric shapes and geometric concepts, and even three-dimensional shapes. By stating the most important thing about a shape, a concept, or a relationship, students can start to make the distinctions between shapes, concepts, and relationships. Moreover, writing is easily incorporated into mathematics as the central way of communication.





  • A Cloak for the Dreamer written by Aileen Friedman and illustrated by Kim Howard

    1. Grade Level: 4-6

    2. Summary: A tailor and his three sons are asked to design and sew cloaks for an archduke for his soon embarkation of an important journey. Wanting to be tailors like their father, the two older sons – Ivan and Alex – show their talents by creating fine cloaks for the archduke to wear. Each cloak is made with a carefully chosen repeating geometric pattern. Ivan creates a rectangular pattern resembling the bricks on the floor. Alex combines the colors of the archduke’s carriage and his coat of arms by sewing together squares and triangles. The youngest son, Misha, who would rather travel the world than work as a tailor, makes an attractive cloak using colors to represent his love of nature. Unfortunately, the cloak is made of circles and is thus full of holes. Realizing that Misha has other dreams, the tailor and his two older sons transform the useless garment into a warm cloak as a gift for Misha to wear on his adventures around the world.

    3. Topic/ Concept: Geometry of motion and change – Tiling, tessellations, transformations (reflections, rotations, and translations), and symmetry
    4. Rationale for Selection: A Cloak for the Dreamer presents students with a question as of why the cloak made out of combinations of circles will be full of holes. Through various investigations using symmetry, tessellations, and transformations, students will explore the turning, sliding, and flipping of shapes and the fraction relationships among shapes (i.e. a trapezoid is half of a hexagon). Students are also encouraged to talk about and write about how they construct their patterns and what makes their patterns symmetrical or transformational. Furthermore, students are encouraged to uncover and represent symmetry, tessellations, and transformations in the real world.





  • Grandfather Tang’s Story – A Tale Told with Tangrams written by Ann Tompert and

illustrated by Robert Andrew Parker


    1. Grade Level: 4-7

    2. Summary: Grandfather Tang and Little Soo use tangram puzzles shifting the tangram pieces around to make shapes of different animals. As each animal is constructed, a story about the animal is told.

    3. Topic/ Concept: Geometry – Building tangram puzzles for spatial visualization

    4. Rationale for Selection: After reading Grandfather Tang’s Story, students can use various tangram pieces to make their own animal representations and write a brief story describing their animals. By working with tangram puzzles, students learn to recognize congruent pieces and the orientation of each piece. Students can also discuss how the perimeter and the area of their representations are the same or different if they all used the exact same pieces when working with their tangrams. Students are also encouraged to use tangram pieces to represent more objects. A companion online activity on the NCTM website at http://standards.nctm.org/document/eexamples/chap4/4.4/ can be used as an excellent extension activity for students to explore more about tangrams and sharpen their spatial visualization. Three Pigs, One Wolf, and Seven Magic Shapes written by Grace Maccarone, illustrated by David Neuhaus, and mathematics activities by Marilyn Burns, and The Warlord’s Puzzle written by Virginia Walton Pilegard and illustrated by Nicolas Debon are two other great books that can be used to create tangible scenarios for students to work with tangram puzzles.



  • Sir Cumference and the First Round Table: A Math Adventure written by Cindy Neuschwander and illustrated by Wayne Geehan





    1. Grade Level: 4-6

    2. Summary: Sir Cumference is one of the great knights in King Arthur’s court. With the help of his wife, Lady Di of Ameter, and their son, Radius, Sir Cumference begins his search for the perfect table that can be used when King Arthur meets with all his knights discussing a possible invasion from a neighboring kingdom. They start out by creating tables in various shapes – rectangle, square, triangle, parallelogram, and even octagon. Unfortunately, they have to discard all the tables because the knights cannot have the same amount of room when sitting around each of these tables. Finally, they decide to order the carpenter to build an egg-shaped table so that each knight is evenly spaced around, being able to see and hear each other during the meeting.

    3. Topic/ Concept: Geometry – Shapes and spatial visualization;

Measurement – Area and perimeter
    1. Rationale for Selection: Sir Cumference and the First Round Table invites students to activate their spatial visualization to re-create and study different shapes, their attributes, and how they are related. Students are encouraged to think about how one shape can be transformed into another shape by visualizing and re-creating them using paper as each shape is presented in the story. Appropriate mathematics vocabulary describing each shape are also naturally introduced and reinforced in the context of exploring shapes in the book. As an extension activity, students can be introduced to the concepts of area and perimeter. Each group of students can explore and generalize how to find the area and the perimeter of one shape of the table using the iteration and tiling methods. Students can later on compare and contrast their results to describe the similarities and differences between area and perimeter.




  • Biggest, Strongest, Fastest written and illustrated by Steve Jenkins

  1. Grade Level: 4-5

  2. Summary: Animals live all around us. Some animals are too small to see without a microscope while others, like the blue whale, are even bigger than a house. There are animals that move as fast as a car and animals that would need half an hour to cross a room. How would you describe these biggest, strongest, and fastest animals – African elephant, ant, giraffe, blue whale, Etruscan shrew, humming bird, sun jellyfish, bird spider, cheetah, electric eel, land snail, anaconda, flea, and Galapagos tortoise? In what aspect are these animals the biggest, strongest, and fastest? And what familiar objects can you compare these biggest, strongest, and fastest animals to?

  3. Topic/ Concept: Measurement – Comparing sizes of objects
  4. Rationale for Selection: Biggest, Strongest, Fastest this informational book allows students to investigate comparative lengths, heights, areas, and weights. After reading the book, students will first organize and represent each animal’s sizes – length, height, weight, and area – in a table. In order for students to make sense of many large numbers presented in the table, they are encouraged to compare the measures of the animals to measures of objects they are familiar with such as their own heights and weights and the speed of a car. For instance, a student who is four feet and eight inches tall can use his or her height to visualize just how tall an African elephant with a height of 11 feet is. A student who weighs 100 pounds can also use his or her weight to figure out just how heavy an anaconda with a weight of 400 pounds is. Most importantly, students need to be motivated to think about which factor makes these animals the biggest, strongest, and fastest? Students need to question themselves whether an animal will still be the biggest, strongest, or fastest when they change their reference point of comparison (i.e. comparing by switching from height to area).


  • Big & Little written and illustrated by Steve Jenkins

  1. Grade Level: 4-6

  2. Summary: Some animals are big and some are little. While the ruby-throated hummingbird weighs just one-half ounce, the largest bird, the ostrich, weighs almost 10,000 times more! A wide variety of sizes of animals found all over the world are presented in this book. All of the creatures in the book are illustrated at the same scale (one inch equals to eight inches). This book illustrates the concept of size by comparing different animals, from the smallest visible animals to the largest.

  3. Topic/ Concept: Measurement – Comparing sizes of objects

  4. Rationale for Selection: Big & Little this informational book will motivate students to start comparing sizes of objects using the appropriate vocabulary and language. Students, as the point of reference, will be compared to objects found in everyday life – spoons, tables, books, and walls. Through investigating and comparing everyday objects with themselves, students will measure and start to make sense of just how big and little things are. As an extension activity, students can be challenged to explore ways to express this comparative relationship.




  • The Principal’s New Clothes written by Stephanie Calmenson and illustrated by

Denise Brunkus

    1. Grade Level: 4-6
    2. Summary: Mr. Bundy, the principal of P.S. 88, is the sharpest dresser in the whole town. Students in P.S. 88 never want to miss a day of school because they all want to see what Mr. Bundy is wearing every day. Everyone in town agrees that Mr. Bundy has so many clothes that he can go a whole month without wearing the same suit. One day, two tricksters – Moe and Ivy – come to town and offer to make Mr. Bundy a new suit from the magic cloth that is only visible to people who are smart and competent for their jobs. None of the faculty and staff in the school including Mr. Bundy himself wants to admit that they cannot see the suit because they do not want to be called stupid or incompetent for their jobs. Not until when a kindergartener points out the fact that there is no such thing as an invisible suit that everyone in the school has the courage to say the same thing. In the end, everyone agrees that Mr. Bundy is smart and good at his job and still is the sharpest dresser in the whole town.


    3. Topic/ Concept: Measurement – Building two-dimensional and three-dimensional models

    4. Rationale for Selection: After reading The Principal’s New Clothes, students can invite either their school principals or other adults at school to measure them and make them three-dimensional clothes. By working with three-dimensional figures, students have to consider different attributes of the measures and to select the appropriate type of unit for measuring each attribute (customary system vs. metric system). Students can also be asked to work on flat, two-dimensional “half-size me.” By working on the two-dimensional “half-size me,” students can focus on the relationship between area and linear dimensions. Students can investigate and start to explain why the area will not be halved when linear dimensions are halved (i.e., length and width).




  • Actual Size written and illustrated by Steve Jenkins

  1. Grade Level: 5-7

  2. Summary: Have you ever wondered just how big a crocodile is? Or just how big is a Siberian tiger? Can you imagine an animal’s tongue that is two feet long? Can you imagine an animal’s eye that is bigger than your head? What are the actual sizes of an atlas moth, a giant squid, an Alaskan brown bear, an ostrich, a giant anteater, a Goliath birdeater tarantula, a saltwater crocodile, a Goliath frog, a great white shark, a gorilla, a pygmy mouse lemur, a Siberian tiger, a Goliath beetle, a giant walking stick, an African elephant, and a giant Gippsland earthworm? Is it possible for you to demonstrate their actual sizes?

  3. Topic/ Concept: Measurement relationships, ratio and proportion
  4. Rationale for Selection: After reading Actual Size, students can create their own class version of the Actual Size. They can work in pairs to further investigate more mathematical facts such as length, width, height, and weight about one animal from the story using other non-fiction books and the Internet. After gathering all necessary information, they will be required to illustrate and write a short paragraph describing their findings. In order for students to make their findings more tangible to their classmates, they will build the mathematical relationship between the animal they have researched and one object that they are familiar with. Students will have to illustrate their comparisons, clearly state the comparison in words, and write a ratio to demonstrate the mathematical relationship. Mathematics is easily integrated into science and social studies as students investigate different facts about each animal. Writing is used as a communication tool for students to convey their ideas about measurement, ratio, and proportion.





  • Jim and the Beanstalk written and illustrated by Raymond Briggs

    1. Grade Level: 5-7

    2. Summary: Early one morning as Jim looks outside the window, he finds a giant beanstalk. He decides to climb all the way up to the beanstalk to see how high it can go. As he reaches the top, he sees a castle. In the castle, he has breakfast with a far-sighted, toothless, and hairless giant who is too old to eat little boys. Jim decides to help the giant out by fetching him a new pair of glasses to read poetry and books, false teeth to chew food, and a fancy red wig to look younger again. After the giant celebrates his new appearance, he sends Jim down the beanstalk and tells him to chop it down because he can no longer resist the temptation of eating him. After the beanstalk falls, the giant rewards Jim with a gold coin and a thank you letter.

    3. Topic/ Concept: Measurement, ratio and proportion

    4. Rationale for Selection: After reading Jim and the Beanstalk, students can work in pairs, trios, or groups to measure each other in order to determine the measures if they were to ask an oculist, a dentist, and a wig-maker to make them glasses, false teeth, and wigs. When students share their results, they are encouraged to describe how they measure and why they measure that way. They should also brainstorm ways to measure effectively. As an extension activity, students can identify and describe the differences between the giant’s measures in the story and their measures of themselves. The concepts of ratio and proportion can be introduced to guide student thinking in describing the relationship of the differences between measures.

Computer Software on Geometry and Measurement

  • The Geometer’s Sketchpad by Key Curriculum Press


    1. Grade Level: 4-8

    2. Summary: The Geometer’s Sketchpad is not only a powerful instructional tool for the teachers to teach geometry and measurement, but also a wonderful learning tool for the students to learn geometry and measurement. In the Geometer’s Sketchpad, both the teachers and the students can construct objects and then explore their mathematical properties either by dragging the objects with the mouse or by clicking on the display, construct, transform, measure, and graph menus. Topics such as lines and angles, triangles, quadrilaterals, circles, similarity, transformations, three-dimensional geometry, and geometry coordinates can be easily explored by both the teachers and the students using the Geometer’s Sketchpad.

    3. Topic/ Concept: Geometry and Measurement
    4. Rationale for Selection: The Geometer’s Sketchpad is a wonderful tool for the teachers to demonstrate and for the students to explore geometry and measurement. Through the Geometer’s Sketchpad, both the teachers and the students can engage in hands-on activities modeling and representing concepts of lines and angles, triangles, quadrilaterals, polygons, circles, similarity, ratio, reflection, rotation, translation, three-dimensional geometry, and geometry coordinate. The built-in calculator allows both the teachers and the students to measure, quantify, and compare measures. Teachers can use the Geometer’s Sketchpad to do whole-class step-by-step demonstrations before letting the students trial-and-error on their own. Students can feel safe investigating in the Geometer’s Sketchpad because they can always go to the “Edit Menu” and click “Undo” when they make mistakes. The Geometer’s Sketchpad really encourages a process of discovery in which students first visualize and analyze a problem, and then make conjectures before attempting a proof.





  • Mighty Math – Cosmic Geometry by Edmark

    1. Grade Level: 7-8

    2. Summary: The Cosmic Geometry starts at the Plaza where five different learning activities are displayed – Amazing Angles, Geometry Academy, GeoMovies, Robot Studio, and Tessellation Creation Station. In Amazing Angles, students identify, classify, and compare different two-dimensional and three-dimensional geometric figures using their attributes such as points, line segments, angles, and faces. Students also experiment with the relationships between dimension, surface area, and volume. In Geometry Academy, students build a strong foundation on geometry terminologies and notations in order to describe objects and situations in the work around them. In GeoMovies, students strengthen their spatial visualization skills by constructing and measuring different geometric figures and studying geometric relationships. In Robot Studio, students explore geometric shapes in two-dimensional and three-dimensional coordinates. In Tessellation Creation Station, students create patterns to discover symmetry through reflections, rotations, and translations.

    3. Topic/ Concept: Geometry

    4. Rationale for Selection: Mighty Math – Cosmic Geometry should be used as a supplementary learning tool after the students have had basic knowledge in geometry. Cosmic Geometry can be set up either as a mathematics center or just as a mathematics computer station for students to be able to visit often every time they have extra time in the classroom. Teachers can reinforce the learning in Cosmic Geometry by bringing in some of the concepts covered in the program to motivate the students to connect what they have reviewed in the program with what they are now learning in the classroom.



  • Tessellation Exploration by Tom Snyder Productions

    1. Grade Level: 4-8

    2. Summary: Tessellation Exploration allows students to experiment tessellations with an increasing understanding of the geometric principles behind it. Through step-by-step tutorial, students can create their own tessellation designs with various complexities by applying geometric transformations – reflections (flips), rotations (turns), translations (slides) and glide reflections. Through animation of their final products, students can start to visualize and make sense of the many transformational geometry concepts.

    3. Topic/ Concept: Geometry

    4. Rationale for Selection: Tessellation Exploration can be used both in teaching and learning about geometry. Students can first create tessellation designs with the step-by-step guidance of the built-in tutorial and then animate their works. Through Tessellation Exploration, students can (1) identify, compare, and analyze attributes of shapes; (2) predict and describe the results of geometric transformations such as reflections, rotations, and translations, and glide reflections; (3) solve problems using geometric and spatial reasoning; (4) recognize and apply geometric ideas in areas outside the mathematics classroom. Teachers can enrich their instructions on tessellations by using the in-depth classroom lessons that come with the program. Interactive quizzes at the end of the program can also be used to informally assess student understanding of geometric transformations.




  • Geometry World – Middle Grades Interactive Explorer by CTC

    1. Grade Level: 6-8
    2. Summary: In Geometry World, students start off investigating basic concepts of geometry – points, lines, and angles. Students also have the chances to practice how to measure angles. Students then move on to study two-dimensional plane figures such as triangles, quadrilaterals, polygons, circles, and explore concepts of perimeter and area. Students also study symmetry and tangram puzzles. Finally, students explore three-dimensional solids and their related concepts of surface area and volume.


    3. Topic/ Concept: Geometry

    4. Rationale for Selection: Geometry World should be used as a supplementary learning tool after the students have had basic knowledge in geometry. Geometry World can be set up either as a mathematics center or just as a mathematics computer station for students to be able to visit often every time they have extra time in the classroom. Teachers can use Geometry World hand in hand with the use of real-life manipulatives such as the GeoBoards, tangrams, and Venn Diagrams to strengthen the instruction and the learning of geometry in the classroom.




  • Mathkeys – Unlocking Measurement by Houghton Mifflin

    1. Grade Level: 4-6

    2. Summary: There are five sections in the Mathkeys: (1) Length Measure, (2) Angles, (3) Angle Compare Mat, (4) Angles Measure Mat, and (5) Shape Measure. The Length Measure allows students to place an object onto the mat and to measure the object using a variety of standard or nonstandard units. The Angles allows students to measure and compare angles. The Angle Compare Mat allows students to place up to three different angles onto the mat for comparison. The Angles Measure Mat allows students to measure, resize, and rotate one angle at a time. The Shape Measure allows students to create shapes, change their configurations, and explore the relationship between area, perimeter, side lengths, and angles.

    3. Topic/ Concept: Measurement
    4. Rationale for Selection: Mathkeys can be used for both teaching and learning about measurement. Teachers can use the teacher resource material that comes with the Mathkeys for ideas of extension activities to reinforce students’ learning in the classroom. Students can use the Mathkeys as a review tool to constantly refresh their memories about what they are learning about measurement.


References

Thiessen, D. (2004). Exploring Mathematics through Literature: Articles and lessons for

Prekindergarten through Grade 8. Reston, VA: NCTM.

Welchman-Tischler, R. (1992). How to use children’s literature to teach mathematics.



Reston, VA: NCTM.






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