Big Ideas for Small Mathematicians

Kids Discovering the Beauty of Math with 22 Ready-to-Go Activities

Ann Kajander

• Publisher: Zephyr Press
• Year: 2007
• Print ISBN: 9781569761557
• eBook ISBN: 9781613741368
• Edition: 1
• Topic: Education
• Subtopic: Teaching Mathematics

Introducing sophisticated mathematical ideas like fractals and infinity, these hands-on activity books present concepts to children using interactive and comprehensible methods. With intriguing projects that cover a wide range of math content and skills, these are ideal resources for elementary school mathematics enrichment programs, regular classroom instruction, and home-school programs. Reproducible activity sheets lead students through a process of engaged inquiry with plenty of helpful tips along the way. A list of useful terms specific to each activity encourages teachers and parents to introduce students to the vocabulary of math.  Projects in this first of the two Big Ideas books include "Straw Structures," where children get hands-on experience with measurement and 3-D visualization; "Kaleidoscopes," in which students use geometry to build a mathematical toy; and "Crawling Around the Möbius Strip," where kids build a physical example of infinity.

Activity 1

PATTERN SHAPES

The BIG Idea

Geometric patterns are the very essence of discovering new mathematical relationships.

Content Areas in This Activity

• Geometric patterning
• Pattern rules

Process Skills Used in This Activity

• Communication (optional)
• Creativity
• Aesthetics of mathematics

Prerequisite Knowledge and Skills

None

Age Appropriateness

This simple activity is appropriate for all ages.

The Mathematical Idea

Patterns are a central idea in mathematics. Almost anything that has a pattern contains some mathematics, and most mathematical ideas contain some rule or pattern. Recognizing increasingly subtle patterns is an important mathematical skill. This activity will introduce children to the concept of patterns, with an emphasis on enjoying their visual appeal. Showing examples of aesthetically pleasing patterns will enhance the activity and encourage children to be creative. Many quilts, for example, show remarkable patterns.

The central notion of a pattern is that it is predictable, once we see what is repeated. The pattern may change as we progress, but in a predictable way. Children should be able to identify what is repeated in their patterns, and what would come next. Patterns can be linear, nonlinear, or rotational. (See the box on page 2 for definitions of these terms.)

Wherever there is a pattern, there will be some math. Even if they can’t yet name the patterns mathematically, children can still enjoy inventing them. Have fun creating!

HELPFUL TERMS

Patterns: Mathematical objects, such as numbers or shapes, that are continued in a predictable way are called patterns.

Geometric patterns: Patterns created using shapes are called geometric patterns.

Linear patterns: Linear patterns change by the same amount each time: for example, 2, 4, 6, 8, . . . (changing by 2) or red, blue, red, blue.

Nonlinear patterns: Nonlinear patterns change by a different amount each time: for example, 2, 4, 7, 11, 16, . . . (changing by 2, then 3, then 4, then 5, and so on) or red, blue, red, blue, blue, red, blue, blue, blue, . . .

Rotational patterns: Rotational patterns are patterns created by rotating a shape or image. For example, a minute hand traces a rotational pattern around a clock face.

An important aspect of a pattern is that we can predict what would come next.

Pattern Shapes: Making It Work

Objectives

• Children will create geometric patterns.
• Children will connect the skills of pattern recognition, pattern creation, and spatial reasoning.
• The activity will encourage creativity and an aesthetic sense of mathematics.

Materials

• a few 8 ½”x 11” pieces of light cardboard or construction paper in several colors for each child
• scissors for each child
• glue stick for each child
• 11” x 17” piece of background paper for each child
• photographs of quilts and other geometric designs
• colored pens or pastels (unless using multicolored cardboard or paper)
• photocopy of the Pattern Shapes Activity Sheet (on page 5) for each child

Try cutting the shapes out of heavy wrapping paper or textured paper as well as cardboard. Alternatively, you could purchase pattern blocks, as shown in the photo on page 4.

Preparation

• You could speed up the process by creating shapes ahead of time. Copy and cut out the shapes on the activity sheet (on page 5). You can enlarge the shapes as desired. Trace them onto light cardboard or construction paper, cut them out, and color them (or use different colors of construction paper).
  Precut shapes in a variety of colors may help inspire children to be creative. You could even put together a few patterns as examples for the children.

Most children enjoy creating their own patterns from precut shapes.

• If you don’t cut out the shapes ahead of time, make enough copies of the activity sheet for each child to have one.
• Enhance child creativity and comprehension by gathering photographs of quilts and other geometric designs.

The book Mathematical Quilts: No Sewing Required, by Diana Venters and Elaine Krajenke Ellison (Emeryville, Calif: Curriculum Press, 1999), is a source of many wonderful ideas. The mathematics in each design allows for application at the secondary and even post-secondary levels. The Long Island Children’s Museum website (www.licm.com) also has a hands-on quiltmaking feature. After entering the site, click on their hands-on activities and scroll down to the “QuiltMaker” link.

Procedure

1. Show children pictures of geometric patterns, such as quilts, to stimulate discussion and understanding of what a pattern is. Ask children what they think a pattern is and what it is not. Guide the discussion to include the idea that a pattern involves repetition.
2. Hand out the activity sheet (page 5), the background paper, glue sticks, cardboard or construction paper (and heavy wrapping paper or textured paper, if desired), and colored pens or pastels (unless using multicolored paper).
   If you precut the shapes, just hand out the shapes themselves. Give each child several of each shape so that everyone has plenty of shapes to choose from and can repeat shapes to form a pattern as desired.
3. Tell the children that they are to create any pattern they wish with the shapes. Encourage them to make a pattern, not just a pretty picture or set of random shapes. They do not need to use all of the shapes. For example, a young child could simply make a checkerboard pattern with two colors of squares.
   
   The pattern on the left contains both linear and rotational elements.
4. Choo...

Table of contents

• Cover
• Title
• Copyright
• Acknowledgments
• Contents
• Introduction
• 1. Pattern Shapes
• 2. Squares and Odd Numbers
• 3. Cubes in a Room
• 4. Straw Structures
• 5. Soma Cubes
• 6. Divisibility Circle30
• 7. Discovering Pi
• 8. Tessellations
• 9. Geometric Memory Game
• 10. The Three Bears
• 11. Party Fractions
• 12. Suncatcher Reflections
• 13. Kaleidoscope
• 14. Crawling around the Moebius Strip
• 15. What Color?
• 16. Balloons and Dice Game
• 17. Balances and Equations
• 18. Proof with Pythagoras and Fermat
• 19. Streamers Problem
• 20. 3-D Tic Tac Toe
• 21. Fractals and Infinity
• 22. Tetrahedral Fractal
• Glossary
• Index
• About the Author