Listings as they appear here include links to relevant Web sites and children's literature titles. All Web sites were current at the time of publication.
Note: The : symbol indicates that this activity includes a link to an online resource. The & symbol indicates that the activity includes a reference to children's literature.
Area & Perimeter (grades 4-5)
Have students construct various two-dimensional shapes with K'NEX rods and connectors (or straws and gumdrops). Using K'NEX, describe the perimeters in terms of rod colors and numbers, such as, "The perimeter of a square is four yellow rods." (Using straws, cut ones of different colors to various lengths.) Have students construct a square with a perimeter of eight yellow rods (or straws of a certain color) and then find its area.
Bubble Mania (grades 3-5) :
Have students create soap bubble prints to explore the concepts of diameter, circumference, and area of a circle. This activity is available online at the PBS site (http://www.pbs.org/teachersource/mathline/lessonplans/pdf/esmp/bubblemania.pdf), along with other outstanding measurement and geometry activities.
Build a Shape (grades 3-5)
Have students use 10 cubes to build a three-dimensional shape and draw the shape on graph paper showing how it would look from the front, back, side, top, and bottom. Have students try to match each other's drawings with the appropriate shapes.
Building Vocabulary (grades 4-5)
Have students make a word bank, looking for common roots in such words as "polygon," "polyhedron," "octagon," "octahedron," "dodecagon," "icosahedron." Have students use word roots to write definitions of words.
Calendar Locations (grades 1-3)
Have students use a calendar to locate relative positions on a plane. Ask students such questions as, "What is the date of the Wednesday in the third week of the month?"
Centimeter by Centimeter or Inch by Inch (grades 3-5)
Read the book Inch by Inch.5 Have students make a meter stick (or one-foot ruler) by cutting out and pasting 10-centimeter strips (or one-inch strips) onto a strip of cardboard, using alternating colors for each 10-centimeter strip (or one-inch strip). Use the meter stick (or one-foot ruler) to measure objects in the classroom. For fourth and fifth grade students specify an appropriate degree of accuracy. This activity is adapted from one available at http://mathforum.org/paths/measurement/inchbyinch.html.
Comparing Lengths of Arms with Links (grades K-3)
Put students in pairs and give each pair a package of commercially available links or large paper clips. Have each child use the links to make a chain as long as his or her arm. Have students in each pair compare the chains to determine whose arm-chain is longer (or shorter). Have students use the arm-chains to measure objects in the classroom. Have students compare their results to reveal that, when measuring with non-standard units, the same object can be equal to different numbers of arm-chains. Have students read the book How Big Is a Foot?6
Connect the Dots (grades 3-4)
Give a sheet of dot paper to groups of two or three students. Write the names of various polygons on slips of paper and put them in an envelope. Have each group of students select a slip of paper and take turns making one line segment on the dot paper (connecting two dots) in order to make their shape. As students complete a shape, have them put their initials in the center of the shape.
Creating Nets (grades 4-5):
Have students build shapes (rectangular prisms) with wooden cubes and then create nets (two-dimensional paper that is folded to make three-dimensional objects) to wrap the shapes. Use the nets to discuss surface area. Visit http://mathworld.wolfram.com/Cube.html to see all the possible nets for a cube.
Creating Pentominoes (grades 4-5)
Have students use square tiles to create as many different pentomino pieces as possible. Have them record their results on graph paper or square dot paper. Have students work together to find the 12 different pentomino shapes. Help students to see that, by rotating or flipping some shapes, some that they have found are not different but congruent.
Creating Tessellations (grades 1-5):
Give each student half of a 3-by-5-inch index card. Have students cut out a shape from one edge of the index card and then tape that shape onto the opposite edge of the card. This new shape will tessellate the plane. Have students experiment with this process to create various tessellations and color in their tessellations. Display the tessellations on a bulletin board. Connect this activity to the art of M. C. Escher.9 For more information, visit http://www.iproject.com/escher/teaching/teaching.html.
Creating Tilings (grades K-5)
Have students create tilings with pattern block pieces (triangle, square, rhombus, trapezoid, hexagon) and draw their tilings on triangle dot paper. Have upper-level students discuss why certain shapes will tile and why others will not.
Creative Writing Activity (grades 4-5)
Have students read books such as Sir Cumference and the First Round Table10 or Sir Cumference and the Dragon of Pi11 and write a story using as many geometry vocabulary words as possible.
Describe the Shape (grades K-2)
Help students learn to identify geometric shapes (triangle, square, rhombus, trapezoid, and hexagon) using pattern blocks, a pattern block applet, or triangle grid paper. Make connections to The Shape of Me and Other Stuff12 and The Shapes Game.13 This activity and related materials are available at http://www.mathforum.org/varnelle/kgeo.html.
Describing Attributes of Shapes (grades K-3)
Have students examine and describe attribute blocks, noting shapes (square, rectangle, triangle, hexagon, circle), size (large, small), thickness (thin, thick), and color (blue, red, yellow). Place a block where students cannot see it and have students, one by one, ask "yes" or "no" questions in a circle. If the answer to a student's question is "yes," then he or she can continue to ask questions; if the answer is "no," then it is the next student's turn to ask a question. Continue until a student can fully describe the figure.
Determining the Appropriate Unit of Measure (grades 1-3)
Give students different measuring tools, such as a 12-inch ruler, 10-centimeter strip or centimeter ruler, measuring tape, yardstick, and meter stick. Have students measure various objects around the classroom, including tables, windows, and the width of the room. Discuss with the students which tools and units are easier to use for measuring the different objects.
Draw a Shape from Memory (grades K-5)
Show students a shape for a few seconds and have them try to draw the shape from memory. Have students show each other their drawings and discuss the characteristics of the shape in their drawings. Then show the original shape again. Start with simpler shapes and then draw more complex ones.
Finding Area with a Non-Standard Unit (grades 3-5)
Using overhead pattern blocks on the overhead projector, build an equilateral triangle with four green triangles. Tell students that each green triangle has an area of one square unit and ask them to determine the area of the larger equilateral triangle. Build the same triangle with a red trapezoid and a green triangle and ask students for the area of that triangle. Build other shapes with the pattern blocks and have students find the area for each of those. Have students record their work on grid or dot paper, coloring the shapes appropriately and recording the area of each shape.
Finding Perimeter with a Non-Standard Unit (grades 3-4)
Using overhead pattern blocks on the overhead projector, demonstrate that, if each side of a triangle is one unit, the distance around the triangle is three units. Have students find the perimeter of the other pattern block pieces. Have students make drawings on grid or dot paper, coloring the shapes appropriately and recording the perimeter of each shape. To go further, have students make different shapes with the pattern blocks, draw them on the dot or grid paper, and then identify the perimeter of each shape. This activity can also be done with straws and gumdrops or K'NEX rods and connectors.
Fixed Perimeter (grades 3-5)
Cut a piece of ribbon that measures about 10.5 yards. Tie the ends of the ribbon together so the perimeter of the loop of ribbon is 10 yards. Put the ribbon on the floor. Have three students take hold of the ribbon and make an equilateral triangle. Use chalk to trace the triangle. Add another student to the group and have the group make a square. Using a different color of chalk, trace the square. Make sure that the students measure the sides of the shapes to show that the perimeter is the same. Ask whether the equilateral triangle or square appears to have the larger area. Continue making regular polygons with the same perimeter. Encourage students to draw conclusions about what happens to the area of shapes if the perimeter is constant. Additional questions could include:
Footprints in the Sand (grades K-2)
Have students use blocks of various shapes to make impressions in the sand. Have students identify the shapes and match the blocks to the impressions. Read this poem as part of the activity:
A monster made these footprints
While we were all asleep.
What funny shapes these prints are,
And they're not very deep.
I think the monster fooled us
And used our blocks instead;
And you can figure out which blocks
If you just use your head.14
Geoboard Polygons (grades 1-4)
Have students duplicate a shape on a geoboard and then break the larger shape into smaller shapes (a rectangle into two squares or triangles; a trapezoid into three triangles or two triangles and a rectangle). Give students an irregular shape and have them find as many triangles, squares, or rectangles as possible.
Geo-Dot Paper (grades 3-5)
Have students draw different quadrilaterals on dot paper and then compare their shapes with a partner. Have students note the properties that the shapes have in common; encourage students to turn (rotate) or flip their papers as they make comparisons. Have them also show congruent and similar shapes on the dot paper and show translations by indicating the direction of the translation with an arrow.
Graphing Points on a Line (grades 2-4):
Have students identify points on a number line. This activity, available at http://mathforum.org/cgraph/cplane/line.html, also includes negatives, scale, a glossary, and links.
How Many Square Feet in a Square Yard? (grades 4-5)
Put nine one-foot squares of linoleum squares together to form a square. Use a yardstick to measure the side of the larger square and to demonstrate that there are three feet in one yard. Students will see that nine square feet are equal to one square yard.
I Have, Who Has (grades 2-5)
Prepare a series of cards that each contains a statement and a question-one card for each student. The statement acknowledges that the student "has" a certain geometric shape; the question describes characteristics of another shape. The first card should have only a question, to begin the game. For example:
|[Card 1:]||Who has a figure with three sides?|
|[Card 2:]||I have a triangle.
Who has the name of two figures that have the
same size and shape?
|[Card 3:]||I have congruent figures.
Who has a figure with five sides?
(Note that the cards given to students do not identify order). The last card should answer a question and state: "This is the end of the game." Distribute one card to each student. Whoever has the card with just a question begins the game, and other students listen, process, and respond in turn.
Inching Along (grades K-2)
Read the book Inch by Inch.15 Have students measure objects using non-standard units, such as "inch worm" packing peanuts. This and other measurement activities are available online at http://eduref.org/cgi-bin/lessons.cgi/Mathematics/Measurement.
Is My Hand Bigger or Smaller Than Yours? (grades K-3)
Put students in pairs and have partners help draw around each other's hands. Have students compare the area of each partner's hand by placing one hand on top of the other to see which hand overlaps the other or has the larger area. Have students compare hands to find the hand with the smallest or largest area.
Lighting the Perimeter (grades 4-5)
Have students use their knowledge of perimeter to determine the number of lights needed to decorate the outside of a building or other structure, such as a bridge. Take a digital photo of the structure; print the photo on regular-size paper and distribute to students. Assign a scale, such as one inch on the photograph equals one foot of the actual structure. Have students measure the perimeter of the structure on the photograph and use the scale to determine the actual perimeter. Have students determine how many feet of a string of lights would be needed to trace the entire perimeter. This activity was adapted from one at http://www.educationworld.com/a_tsl/archives/01-1/lesson0031.shtml.
Line Symmetry (grades K-3)
Have students use pattern blocks, a pattern block applet, or paper folding to show lines of symmetry. Make connections to the books What Is Symmetry?16 and The Butterfly Alphabet.17 This activity is available at http://www.mathforum.org/varnelle/kgeo.html.
Measuring Desktops with Hands (grades 1-3)
Have students trace their hands and then cut out the tracings. Have each student use the cutout of his or her hand to measure the area of desktop. Emphasize that, since area is the region covered with the same hand, students might need numerous copies of the same hand to cover a desktop. Have students explore measuring parts of the desk that are not covered by a complete hand.
Mini-Metric Olympics (grade 5):
Familiarize students with metric units by having them estimate and measure in a "Metric Olympic" setting that includes six activities: paper plate discus, paper straw javelin, cotton ball shot-put, right-handed marble grab, left-handed sponge squeeze, and big foot contest. This activity18 is available at the AIMS (Activities Integrating Math and Science) Web site at http://www.aimsedu.org/Activities/middle.html.
Nature Walk (grades K-3)
Read the book If You Look Around You.19 Take students on a nature walk and have them identify various shapes in nature. Take photographs for a bulletin board display or have students draw sketches of what they find.
Number Line Message (grades 1-3)
Have students place specially chosen letters above numbers on the number line and have them read the message that appears. For example, if they place A at 2 and 12, D at 11, H at 1 and 7, I at 10, L at 9, O at 8, P at 3 and 4, and Y at 5 and 13, the message is:
Origami (grades 2-5):
Have students use origami to explore spatial relations and to investigate shapes and their properties.20 Have younger students do easier foldings, such as a cup, boat, pigeon, or swan. As students fold, introduce important mathematical terms like diagonal and midpoint and discuss the various shapes that are created, such as triangles and squares. Have upper-grade elementary students do more detailed foldings, such as a frog that jumps or a box without a top.21 Explore concepts of similarity, congruence, and classification of triangles. Different shapes appear as students fold, such as right isosceles triangles, squares, rectangles, and trapezoids. Give students printed directions for folding to help develop visualization and spatial reasoning skills; directions for simple foldings are usually included with origami paper. There are many inexpensive origami books available and numerous Web sites devoted to origami (see the Origami USA Web site at http://www.origami-usa.org/).
Paper-Penny Boxes (grades 3-5)
Have students explore the concept of volume by building a paper box that will hold 100 pennies. This activity22 is based on the Newberry Medal Award book The Hundred Penny Box.23 Have students discuss the strategies that they used to build their boxes.
Pattern Block Shapes (grades 2-3)
Introduce the pattern block shapes with students. Give students time to play with and become familiar with the shapes. Observe whether students sort the blocks by color or shape or use them to make designs or patterns. Work to develop the relationships between the different pattern block shapes by having students create one shape by using other shapes. Ask, "Can you use the triangles to make a hexagon?" and "Can you make the red trapezoid with any of the other figures?" Have students draw and color their shapes on triangle grid paper. When students have discovered how the various shapes are related, have them make a figure or picture with the shapes. Then have them draw the figure on the triangle grid paper and give a verbal explanation of the picture and the shapes they used.
See Pattern Block Program under the Web sites section.
Pentomino Boxes (grades 4-5)
Have students try to visualize which of the 12 pentomino pieces can be folded to make a box without a top. Have students make the pentomino pieces on one-inch square grid paper and fold to confirm their conjectures.
Pentomino Pieces (grades 3-5)
Have students determine which pentomino pieces have line symmetry or rotational symmetry. Have students draw the pentominoes on graph paper or square dot paper and indicate the line of symmetry. Have younger students make paper pentominoes and fold to find lines of symmetry or use a mirror or Mira.
Pi Day (grade 5)
Celebrate Pi Day, March 14 (also the birthday of Albert Einstein and Waclaw Sierpinski) with your students. Start the day with a reading of the book Sir Cumference and the First Round Table.24 Have students search the Internet for information about Pi or direct them to appropriate Web sites such as http://www.joyofpi.com/, which includes basic information about Pi, Pi history, fun with Pi, Pi links, and more. Visit the Web site of the Goudreau Museum of Mathematics in Art and Science (New Hyde Park, NY), http://www.mathmuseum.org/, for information about their annual Pi Day Contest. A "Pi Trivia Game" is available at http://eveander.com/trivia/. As of February 2004, Pi Day greeting cards were available at http://www.bluemountain.com/kwsearch.pd?strSearch=pi+day&btnsearch.x=17&btnsearch.y=6. Attractive Pi t-shirts are available online at http://www.scienceteecher.com.
The Plane (grades 4-5)
Help students learn to plot points on the coordinate plane. Define terms such as line, plane, axis, and quadrant. The version of this activity available at http://mathforum.org/cgraph/cplane/plane.html includes the plane, finding points, graphing points, scale, glossary, links, and a "for grownups" section.
Platonic Solids (grades 4-5)
Discuss the Platonic solids (cube and regular tetrahedron, octahedron, dodecahedron, and icosahedron) and develop the concepts of edges, faces, and vertices-noting that all faces are regular polygons. Use nets to construct the shapes. Make a chart to determine the relationship between the number of edges, vertices, and faces (Euler's formula).
Playground Grids (grades 4-5)
Mark off a grid with X- and Y-axes on the playground. Have students walk to points on the grid by traveling along the grid lines, starting from (0,0) and following directions to the appropriate locations. Have students start at other points on the grid and describe how they could get to a different location. In a classroom with square floor tiles, have students move around the room following verbal directions to reinforce the concept of coordinates.
Plotting Pictures (grades 4-5)
Have students plot and connect sets of coordinates that result in various shapes, such as a sailboat, a chimney, or a palm tree.25 For example, if students plot and connect the points (1,2), (2,3), (3,3), (4,2), (3,1), and (2,1), it forms a hexagon. Have students draw shapes on graph paper and then list the coordinates; give other students the coordinates for these designs to graph.
Pumpkin Pi (grade 5)
Give each student a small pumpkin and have students measure the circumference of the circle at the middle of the pumpkin using a tape measure or string. Cut horizontally through the center of each pumpkin so students can measure the diameter. Record the circumferences and diameters on a chart on the overhead or on large paper. Have students calculate the quotient of the circumference divided by the diameter. Record the quotients in the chart and find the average, so students can see that their results approximate pi.
Regular Polygons (grades 4-5)
Have students use flexible straws (or K'NEX) to make regular polygons by placing the short end of the flexible straw into the long end (this will ensure that all sides will be of equal length). Have students attempt to make each interior angle the same measure so that the resulting shapes are regular polygons. Discuss the attributes of the shapes.
Rope Polygons (grades 3-5)
Have three students make a triangle using rope or string. Have other students direct the three students to move to create different types of triangles (right, equilateral, isosceles). Have students create other polygons and determine how many students are needed for each polygon.
Scale Drawings (grades 4-5)
Use scale drawings to develop the concept of similarity. Have students make scale drawings of their classroom so they can see the relationships between sizes and shapes. One square on the graph paper can represent one square floor tile or a one-foot by one-foot square students make. Have students measure the lengths of sides of objects in the room and the corresponding sides of the scale drawing of the object. Ask, "What is the ratio of the measures of corresponding sides in each instance?" (All ratios should be equal or almost equal.) Have students look at the interior angles of a two-dimensional representation of an object in the room and the corresponding interior angles of the scale drawing of the object. (The corresponding angles should have the same measure.)
Shape Journals (grades 2-4)
Have students name a polygon on each page of their journal (include the different types of triangles and quadrilaterals) and then draw it. Have students look in magazines to find a picture of an object that closely resembles the polygon (a stop sign is an octagon; a candy bar is a rectangle), cut it out, and paste it into the journal.
Shape Puzzles (grades 3-5)
Enlarge and cut out the shapes below. Put the pieces into an envelope and draw the final shape on the outside of the envelope. Have students arrange the pieces into the shape shown on the envelope. Have students make shape puzzles for others to solve.
Simply Symmetrical (grades 1-5):
This activity is available at the Web site of the U.S. Department of Education, http://www.ed.gov/pubs/parents/Math/mathhome.html. Adaptations of this for the classroom are:
Traveling on a Grid (grades 2-3)
Have students use large block graph paper to draw city streets and buildings. Have students describe how many blocks you would have to travel east-west (left-right) or north-south (up-down) to move from one building to another. Have students draw their own cityscapes and list distances from one location to another.
Tree Measurement (grades 4-5):
Working in pairs with string and a ruler, students learn a method for measuring the height of a tree that is too tall to measure directly and are introduced to the concept of circumference. This activity is available at
Using Geometric Software to Explore Triangles (grade 5)
Have students use dynamic geometric software (such as the Geometer's Sketchpad®) to draw a triangle. Have students measure the interior angles and the lengths of the sides. Grab a vertex of the triangle and move the vertex to create a new triangle. Have students create an equilateral triangle, isosceles triangle, scalene triangle, acute triangle, obtuse triangle, and right triangle. Lead students to discover the triangle inequality property- that the sum of the lengths of any two sides must be larger than the length of the third side. Have students determine that the sum of interior angles of a triangle is always 180 degrees.
Using Maps (grades 3-5)
Make copies of road maps (from an atlas or from various Web sites) for students. Have students measure the distances between cities and describe the directions from one city to another. Have students find the shortest distance between two cities by traveling on roads.
"Who Am I" Riddles (grades 2-4)
Prepare "Who Am I" riddles for students to solve, such as: "I am a polygon; I have four sides of equal length, but the four angles are not of equal measure. Who am I?" Have students make up riddles and share them with each other.
Winter Shapes (grades K-3)
Cut various two-dimensional shapes from construction paper and have students use the shapes to make all the winter objects they can think of, such as trees from triangles, snowmen from circles, and houses from rectangles and triangles. Make these objects the focus of the class bulletin board.
Writing Stories (grades 1-5)
Have students write stories using as many geometric terms as possible. Encourage them to be creative. Suggest a general topic or theme for their story or relate them to what you are teaching in language arts, science, or social studies.