Required Materials

$\frac12$-inch cubes

1-inch strips cut from card stock with evenly-spaced holes

Copy the two sizes of strips on different colors of card stock, so that students can see at a glance whether the two strips being used are congruent or not.

After the strips are cut, punch holes as indicated in each segment. A standard hole punch makes holes that are a little larger than needed for the metal paper fasteners, causing the cardboard strips to wiggle around. If possible, find a way to punch holes that are slightly smaller than the size of a standard hole punch.

A commercial version of these materials is available, sometimes called geo strips.

Blank paper



any fair two-sided coin

Colored pencils

Copies of blackline master

Cylindrical food items

Approximately cylindrical food items that can be easily sliced. Examples include carrots or cheese sticks.

Data collected from the previous activity

Dental floss

Dried linguine pasta

We specified linguine since it is flatter and less likely to roll around than spaghetti.

Dynamic geometry software

Four-function calculators

Geometry toolkits (HS)

Index cards to use as straightedges, compasses, tracing paper, blank paper, colored pencils, and scissors.

Note: "Tracing paper" is easiest to use when it's a smaller size. Commercially-available "patty paper" is 5 inches by 5 inches and ideal for this. If using larger sheets of tracing paper, consider cutting them down for student use. 

Graphing technology

Examples of graphing technology are: a handheld graphing calculator, a computer with a graphing calculator application installed, and an internet-enabled device with access to a site like or For students using the digital materials, a separate graphing calculator tool isn't necessary; interactive applets are embedded throughout, and a graphing calculator tool is accessible on the student digital toolkit page. 

Graph paper


Index cards

Internet-enabled device

Isometric dot paper

Masking tape

Measuring tapes

Measuring tools

Metal paper fasteners

brass brads


Flat mirrors. A mirror should be small enough to be portable, but large enough that it can be placed on the ground a few feet away from an observer, and the observer can site the top of a tall object in the mirror.

Number cubes

cubes with sides numbered from 1 to 6

Origami paper

Paper bags

Pre-cut figures

Figures cut from cardboard or card stock with at least one straight side that can be taped to a pencil. Shapes might include various polygons, half-discs, and composites of these.

Pre-printed cards, cut from copies of the blackline master

Pre-printed slips, cut from copies of the blackline master


Clear protractors with no holes and with radial lines printed on them are recommended.


Rulers marked with centimeters

Scientific calculators


Spreadsheet technology

Sticky notes




Tools for creating a visual display

Any way for students to create work that can be easily displayed to the class. Examples: chart paper and markers, whiteboard space and markers, shared online drawing tool, access to a document camera.

Unlined index cards