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Sample Units Designs

Designing Units Around Math and Science Topics

University of Illinois at Chicago College of Education

ED312, Spring 1995; Professor Maria Varelas



* Lesson by Jackie Cohen, Migdalia Paniagua, and Tara Schultz
* Teaching geometry in grades k-4
* Lesson for:
K-4
*Project description

Why teach geometry? Because geometry can be found virtually everywhere! It is in the structure of our solar system, in geological formations, in plants and animals, in art and architecture,and in cars and machines. It is important for our students to engage in hands-on experience while learning geometry. Manipulating concrete mataerials they encounter in their everyday lives will spark their interest much more than simply using a pencil and paper to complete a worksheet.

According to the National Council of Teachers of Mathematics (NCTM), in grades K-4, the mathematics curriculum should include two and three-dimensional geometry so that students can:

I. Describe, model, draw, and classify shapes

  1. Literature: The Greedy Triangle by Marilyn Burns
  2. Activity: "Growing Up" Levels 1 or 2
    Students are asked to color the shapes in different colors according to sizes from largest to smallest. You can also ask students to name each shape and tell how many sides each shape has.
  3. Assessment:
    Students must be able to successfully draw and name shapes.
  4. Difficulties:
    • Students might have a difficult time remembering the names of shapes and their properties, such as a hexagon having six sides and a pentagon having five sides.
    • Being able to successfully draw shapes with more than five sides can be very challenging for students of all levels.
    • Since some students' spatial sense is not yet fully developed, you should have them experiment with combining shapes with manipulatives.

II. Investigate and predict the results of combining, subdividing, and changing shapes

  1. Literature: Mario Cumo's New York City by Mario Cumo
  2. Activity: "Cut and Paste Shapes" Levels 2, 3, or 4
    Students are asked to predict what shapes put together will cover the shaded region. To check their answers they can cut and paste their predictions on top of the black region.
  3. Assessment:
    Informal assessment can be done while students are engaged in the actual activity.
  4. Difficulties:
    Predicting which combination of shapes would create the black region can be diffficult for students in level 2.

III. Develop spatial sense which is an intuitive feeling for one's surroundings and the objects in them. Students need to learn the interrelationships between shapes and the effects of changes to the shapes. They also need to learn directions, such as below, above, etc.

  1. Literature: Becca Backward, Becca Forward Book of Concept of Pairs by Bruce Macmillan.
  2. Activity:
    • "Simon Says" will help Level K students develop a sense of direction and space. One student is Simon. He tells the class what to do, "Simon says." He gives a direction such as, "take one step forward," but for students to follow, Simon has to say "Simon says."
    • "Cut-out Shape Box"- Level K or 1. The teacher can give each student a shoe box with various cut out shapes on the top of the box. Then students can cut out these shapes from construction paper and have them laminated. The objective is for each student to be able to drop the shape into the proper opening in the shoe box.
    • "Perfection" (a battery operated game)-Level 4 Students attempt to place plastic shapes into the gameboard in sixty seconds before all the pieces "pop up".
  3. Assessment:
    The teacher can observe students while they are participating in the activities.
  4. Difficulties:
    Students may have difficulty distinguishing the various directions.

IV. Recognize and appreciate geometry in the world

  1. Literature: Round Building, Square Buildings and Building that Wiggle like a Fish by Phillip Isaacson.
  2. Activity: Level K-4
    • Field Trips: Identify familiar shapes in a particular surrounding such as a square and a triangle making up a house.
    • Students can create their ideal house by incorporating combinations of different shapes discussed in the lesson.
  3. Difficulties:
    • Students may find it hard to distinguish shapes that are not distinct.
    • Recognizing a trapezoid as a base at a building, thus most teach background.
  4. Assessment:
    They can properly classify or identify a given shape.

V. Relate geometric ideas to number and measurement ideas

  1. Activities:
    • "Price Tags"-Levels 3 and 4
      Students are given a aheet that contains line segments and each has different prices. They must be able to figure out the price by adding the cost of each side.
    • "Communication Skills"-Levels K-4
      Materials needed are pencil, paper, and drawings of combined shapes. An example of instructions can be found at the end of this paper.
    • Circumference of a circle
      Students are given round objects, such as jelly jars, mugs. Then have them measure the circumference and diameter. Next, have them create a draft to see relationship between the circumference and diameter, which is Pi 3.14, which is what Pi is.
  2. Difficulties:
    • Telling the shape of the object to the partner can be a challenge.
    • Measurement and estimating can be difficult.

Students can keep a portfolio of special projects that they have done to see their improvements and the knowledge that they have gained throughtout the school year.





Attachment


Instructions


  1. Do not let your partner see your drawing.

  2. You are to give your partner instructions on how to draw the drawing in front of you.

  3. Those who are on the right side of the classroom cannot look over to coach your partner. You have to make sure that your instructions are accurate enough for your partner to be able to draw from them.

  4. Those in the left side of the classroom are going to be allowed to look over and coach your partner to do the drawing.

  5. Guidance can only be given through words; you are not allowed to touch your partner to prompt them.

  6. Remember the main goal is to learn and have fun.




Bibliography


Burns, Marilyn. The Greedy Triangle. New York: Scholastic Inc., 1994.
This is a great book to introduce classification of shapes and their names. Students become familiar with the ideas of how shapes are created, what a side means, and what happens when another side is added to a shape.

Isaacson, Philip M. Round Buildings, Square Buildings, and Buildings that Wiggle like a Fish. New York: Knof, 1988.
This book looks at different architectural structures around the world that stand out because of their beauty and practicality. Can lead into a discussion of why certain buildings look the way they do, which shapes are appropriate for certain structures. Can be also a great lead into a lesson on geography.

Immerzeel, George; Thomas, Melvin. Ideas from the Arithmetic Teacher: Grades 1-4. Virginia: National Council of Teachers of Mathematics, Inc., 1990.
This book presents activities for students in grades 1-4 for units on numeration, computation, geometry, measurement, and problem solving.

Macmillan, Bruce. Becca Backward, Becca Forward Book of Concept of Pairs. New York: Lathrop, Lathrop, Lee and Shepard, 1986.
A book that explores spatial relationships and introduces new vocabulary terms, i.e., above and below.

Muro, Roxie. The In-Side-Outside Book of New York City. New York: Dodd, Mead, 1985.
This book is mainly picture book of places that are in New York. Students can see how shapes are put together to create buildings and statues and why certain shapes are used for different structures.

Whitin, David J.; Wilde, Sandra. Read Any Good Math Lately? Children's Books for Mathematical Learning K-6. Portsmouth, NH: Heinmann, 1992.
Integrates children's literature books with mathematical lessons. Provides a bibliography of which books are good for what lessons.


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