By Thomas E. Hodges, Malisa Johnson, and Kyrsten Fandrich, Posted December 8, 2014 –   

With increased attention on STEM-focused curricula at the elementary school level, we are often interested in activities that afford opportunities for students to engage in design processes connected to the Common Core State Standards for Mathematics (CCSSM). Geometry standards provide a particularly fertile area for exploration. For example, K.G.5 calls on students to “model shapes in the world by building shapes from components” (CCSSI 2010, p. 12); 4.G.3 asks students to recognize lines of symmetry; and by the middle grades, students are expected to use nets, make cross sections, and measure three-dimensional shapes. Students’ opportunities to engage in visual spatial reasoning at the elementary school level provide a critical backdrop for not only CCSSM but also related STEM activities.

One problem-solving task that you could engage students in is an extension of the Cut-a-Card activity (Stenmark and Thompson 1986). In this task, students have opportunities to visualize the effects of flips and rotations, giving them the ability to see the structure of objects in multiple ways—a critical component of design.

First, we provide a 3 x 5 note card that has been adapted in the following way:

1.   Make three cuts:
2.   Fold the bottom flap up:
3.   Rotate the right side 180°:
4.   The finished product should look like this:

We tape the 3 x 5 card to a piece of paper and then ask students to re-create the design. Students often believe that sections have been removed from the card. As a way of scaffolding, we have at times told students that the entire card is still present and that we have made just two types of adaptations: straight cuts and rotations.

After students have opportunities to explore this variation, instruct them to work with a partner to create their own designs using the same parameters (only straight cuts and rotations) for adaptations. After each student creates his or her own design, have students trade with a partner and attempt to re-create the partner’s design.

What designs did your students generate? In part 2 of the post, we’ll share some of our students’ designs and discuss how we’ve used those designs to discuss important mathematical ideas.

Your Turn

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	Thomas E. Hodges is an assistant professor of mathematics education at the University of South Carolina. He teaches field-based mathematics methods courses, capitalizing on opportunities for preservice teachers, teacher educators, classroom teachers, and elementary students to learn with and from one another. He published on the field-based design in NCTM’s 2014 Annual Perspectives in Mathematics Education and regularly contributes manuscripts to Teaching Children Mathematics, Mathematics Teaching in the Middle School, and Mathematics Teacher.
	Malisa Johnson teaches a self-contained fourth-grade class at Oak Pointe Elementary School in Irmo, South Carolina. In her thirteenth year of teaching, Johnson often hosts mathematics methods courses in her classroom and collaborates with university faculty and other classroom teachers on mathematics education publications. She is interested in productive discourse and students’ use of representations in mathematics classrooms.
	Kyrsten Fandrich is a Master of Arts in Teaching candidate at the University of South Carolina, completing her internship experience in Johnson’s classroom. She is interested in learning alongside her fourth  graders through careful attention to students’ mathematical thinking.

Archived Comments

I love the idea of students copying the design that they see. For k-1 students the idea of having them do this with two dimensional or 3 dimensional shapes and having them make a replica of composite shapes is a grest activity!
Posted by: DrewP_77482 at 12/12/2014 9:44 AM