Classroom Activity: Ten Black Dots Make an Integrated Math Activity

Rebecca M. Giles, Paige Vitulli, and Kelly Byrd

Abstract. In the standards-based climate of education today, teachers at all levels continually struggle to cover an enormous amount of content in a limited amount of time while teaching mathematics through meaningful, interactive experiences. The most effective teachers weave content from multiple disciplines into engaging lessons that allow students to make personal connections to the mathematical principles being presented. This activity, which can be adapted for children or adults, uses children’s literature to motivate mathematical thinking, specifically concepts of number, numeral, and number bonds, within a historical context.

Children’s literature, a proven avenue for integrating disciplines and provoking thought, is the ideal catalyst for enriching experiences in mathematics. It serves to motivate and engage students who suffer from math anxiety (Hunsader, 2004) while making the abstract more concrete. Further, quality children’s literature can show that math is an important part of everyday life, rather than an isolated subject (Franz and Pope, 2005), by providing avenues to explore and discuss ideas in ways that do not always arise naturally when using textbooks (Jenner, 2002). Additionally, Eisner (2002) suggests incorporating visual arts as a way of knowing, which can help students develop their sense of qualitative reasoning in any content area. Transformation is a type of productive thinking that requires changing markedly the appearance or form of a line or shape in an attempt to generate a unique product (Giles, Baggett, & Daughenbaugh, 2010). In this activity, number bonds are visually represented as students transform circles into thematic pictures modeled after the bold, simple illustrations found in a counting book.

Ten Black Dots by Donald Crews is a well-loved classic. Since its publication in 1986 children and adults alike have engaged in creative thinking as they consider “What can you do with ten black dots?” As the book progresses, one dot can make a sun or a moon; three dots become a snowman’s face, and eight dots become the wheels on a train. Counting and rhyming with everyday objects are at the core of this picture concept book, but its mathematical value lies in the opportunity it presents for developing children’s number sense.

Number sense refers to a child’s fluidity and flexibility with numbers or, more simply, their sense of what numbers mean. It also involves one’s ability to perform mental mathematics and to look at the world and make comparisons (Gersten & Chard, 1999). “Students with good number sense can move seamlessly between the real world of quantities and the mathematical world of numbers and numerical expressions” (Case, 1998, p. 1). More advanced number sense helps students make generalizations across numbers (National Mathematics Advisory Panel, 2008), laying the foundation for later mathematical achievement. Jordan, Glutting, and Ramineni (2009) found number sense to be strongly related to children’s ability to solve applied mathematics problems in various contexts.

Very young children possess an intuitive sense of number that develops into a complex and interrelated set of concepts with age and experience (Malofeeva et al., 2004). For example, older children easily recognize that a set of objects associated with a number can be broken into subsets, each of which can also be represented by a number (Fisher, 1990). This activity facilitates an understanding of how numbers can be composed and decomposed by engaging students in the process of constructing number meanings through real-world experiences using tangible materials.

Activity

Before reading, the teacher shows the students the cover of Ten Black Dots and asks students “Can someone tell me what number is shown on the cover?” “How many dots are there?” While reading, the teacher pauses periodically to ask questions such as “What can you tell me about these dots?” “In what ways are these dots arranged?” to focus students’ attention on the different ways a number can be represented by objects (i.e., a circle, straight line, scattered, etc.). Next, brainstorm possible picture topics by asking, “What are some objects related to the events of 9-11 that you can use black dots to make?” It is a good idea to record students’ ideas on chart paper or a whiteboard to use later as a word bank for their sentence writing. (See “Building Background” text box for more information.)

After reading and discussing suggested possibilities, each student is provided a 9×12 sheet of white card stock and access to self-adhesive black circle labels ¾ in diameter, markers, crayons, scrap paper, and glue. The students select a number of black dots (ranging from 1 to 10) and create their own expressive transformations portraying information and/or experiences related to the identified national event.

Photo 1

Students are instructed to label their finished products using both the numeral and a pattern sentence containing the number word to precisely identify their creations. Examples include, “8 Eight black dots make the windows on the World Trade Center” and “2 Two black dots are the eyes of the rescue dogs at 9-11” (see Photo 2). Depending upon their age and ability, students might also be challenged to generate number sentences related to their pictures (i.e., 1+1=2, 2+0=2, 2-0=2, 2×1=2, etc).

Photo 2

Following the transformation activity, mathematical understanding is further explored by discussing similarities and differences among number representations for the purpose of categorizing and graphing the illustrations. Guiding questions might include: “What can you tell the class about your number story?” “How many different number combinations did our class find?” “Did any of us use the same number groups?” “Are there any combinations you can of think of that aren’t shown? If so, what are they?”

Conclusion

Curriculum integration is a useful instructional strategy that allows teachers to cover content that might otherwise not be taught (Kinniburg & Byrd, 2008). This activity successfully engages students while covering content in four curriculum areas: mathematics, reading, social studies, and visual arts. Additionally, it can be easily adapted for ages preschool through undergraduate and used with any number of national events, including historical catastrophes such as Hurricane Katrina or the sinking of the Titanic or current happenings like the Olympic games or Presidential election. Activities such as this affirm students’ understanding that mathematics is an integral part of real life while developing students’ understanding of numbers, ways of representing numbers, and relationships among numbers.

Building Background

Building background knowledge related to the historic event depends upon the age of the participants. When this lesson was conducted with preservice elementary education teachers in September 2002, this step was not necessary, as each participant had a score of personal memories related to this most tragic day of the previous year. Recently, however, the lesson was conducted with third graders to mark the tenth anniversary of this same event and required quite a bit of preparation, as these students were not yet born when the events occurred. Preparation included viewing a short, age-appropriate video, consulting several books, and engaging in class discussion.

Elementary Resources for 9-11

  • In Memoriam: Remembering September, 11, 2001 (http://www.youtube.com/watch?v=3jlgZMZRf64)
  • September 11, 2001: Attack on New York City by Wilborn Hampton
  • America is Under Attack: September 11, 2001. The Day the Towers Fell by Don Brown
  • September 11: A Primary Source History by Alan Wachtel
  • The Attack on the Pentagon on September 11, 2011 by Carolyn Gard
  • 9.11.01: Terrorists Attack the U. S. by Patrick Lalley

References