The Mathematics of Wallpaper

Classroom Activities

1. Introductory Activity Ideas for Integrated Learning

The introduction of pattern recognition will begin with read-alouds from the collection of student resources, reading first Patterns – Math Counts by Henry Arthur Pluckrose. The pictures show basic objects in our lives and will promote discussion. The text is simple and straightforward and the students will begin to develop vocabulary for discussing patterns. Include in this set of terms location words – before, after, beside, up, down; attribute words – colors, size, shapes.

Each day will include one or more of these activities to allow for repeated experience. They can take place during the morning meeting on the rug, preparing for a transition, and as a beginning component to the daily math lesson.

Objective: The students will practice generating patterns through a variety of opportunities for experiential learning.

Procedure: Organize the students in groups or a circle. Choose an activity to practice for approximately 5 minutes.

Clap patterns - fast, fast, slow, fast, fast, slow (AAB pattern)

Actions - hop, hop, clap, clap, hop, hop, clap, clap (AABB pattern)

Drama activities - swirl arms like the wind, arms up like the sunshine as you say: windy,

windy, sunshine; windy, windy, sunshine

Line up at the door in patterns - boy, girl, boy, girl (AB pattern) Let the students recognize that these patterns could continue forever, or are examples of frieze patterns.

Introduce and practice translations – line students up and step forward one giant step, sideways left one giant step, sideways one giant step, backwards one giant step – notice we are all still next to the same students

Introduce and practice rotations – stand and face one direction, turn 90 degrees, turn again 90 degrees, turn again 90 degrees, and again, back to the "identity", or original position. Repeat only reverse the direction. Come back to original position.

Introduce and practice reflections – stand facing another student and repeat arm, leg and body motions to show reflections

2. Math Center Activities

Objectives: The students will use hands-on experiences to understand pattern and sequence, recognizing the fundamental domain and demonstrating the ability to generate the repeat.

Materials: pattern blocks, counting bears, attribute blocks, crayons, pencils, objects from nature (acorns, shells, pebbles, leaves), coins,

Procedure: The math center activities will allow the student to explore. Each activity should include appropriate materials contained in baskets or tubs. Students may work in groups or singly to show their knowledge of patterns. The students should have sufficient quantity of the materials to repeat the pattern several times. These activities should take about 10 minutes and there should be opportunities for each student to participate in all the centers at some point.

1. Create color patterns with materials – example: red crayon, blue crayon, red crayon, blue crayon. Change materials each day or rotation of centers to objects such as colored counting bears, pine cones and acorns, shells, etc.
2. Put pattern blocks in the pocket chart or on mats – example: hexagon, hexagon, triangle, hexagon, hexagon, triangle. Provide exploration tubs of pattern blocks to allow students to create frieze patterns and to begin to explore wallpaper patterns. There should be exploration and discovery occurring.
3. Diagrams or drawings – example: draw big apple, big apple, small apple; repeat. This activity should include simple, recognizable items or shapes for the drawing. The center should include only the drawing and writing materials needed to complete the pattern - any additional choices may be confusing. If the pattern includes the colors red and green, offer only those two colors.
4. Letters and words - put letters or words in the pocket chart or on mats. AA BB, AA BB or cat, cat, dog; cat, cat, dog

Assessment: Students will share with the teacher and/or the class their patterns, using descriptive words to show understanding.

3. Exploratory Activities

Objective: The students will use a variety of materials to examine and generate a variety of strip or wallpaper patterns with those materials.

Procedure: Read aloud Lots and Lots of Zebra Stripes: Patterns in Nature by Stephen Swinburne. Engage the students to discuss the patterns they notice on each page. Encourage them to use descriptive words to explain what they see. How do they know it is a pattern? What would come next?

The students should work in teams of two for these activities. The students will work together trading roles as "designer" and "repeater". This should be approached as cooperative learning, allowing for exploration and student interaction with limited involvement of the teacher. The following

a. Create their own patterns at various difficulty levels use a selection of cutout shapes of construction paper (for example, from an Ellison or other die cut machine)

red, blue, red, blue...

• red, blue, yellow,…
• red, red, blue, red, red, blue....
• red, blue, yellow, yellow, yellow…

b. Copy patterns that others have made

c. Extend patterns that others have started

d. Tell what is missing if part of a pattern is hidden

For activities a, b, and c – The students can use pattern blocks, cutouts, small objects, etc. This should be differentiated for the students to create patterns based on their level of understanding so including a small variety of choices would be appropriate. Keep the collections of objects in separate container or tubs to encourage success and not confusion. Each pattern activity should use only one tub at a time. Cooperative learning should occur as students work together to create their own patterns.

Objective: The students will recognize patterns exist naturally in our environment.

Materials – chart paper, markers, read aloud book

Procedure: Read aloud Patterns Everywhere. Students will recognize the objects and places in the book. Use this as a basis for the students to:

a. Compare and talk about patterns that arise from their daily experiences to understand that our lives have patterns. This is a good opportunity to share sequencing. An example may be how we brush our teeth and discuss the order of events, first the toothbrush, then the toothpaste, brushing, rinsing, etc. If the pattern has changes, then the activity would not work the same way. Have the students continue with other patterns or sequences of activity and discuss the need for order for that particular activity

b. Recognize patterns in the environment – example: fence posts: short, tall, short, tall... Use the classroom (windows, desks), hallway (doorways, tile), school grounds (playground equipment) and generated an on-going list to keep posted in the classroom

c. Use patterns to describe the world around them and to solve problems – discuss how "knowing what comes next" helps understand order in the world (patterns in the tile with no gaps or overlaps keeps the floor level, windows would be missing if the patterns are not complete, have students discover other patterns and problems they can solve and keep an on-going list of solutions they discover posted in the classroom.

d. Identify a pattern – describing the pattern, what they see and what makes it a pattern. Encourage the use of vocabulary that is clear. Keep an on-going list of vocabulary that the students use for describing.

4. Culminating Activity

The class will create a wallpaper design for the classroom using handprints. This will require a large paper from a roll, enough to cover an area on an available wall or bulletin board. Working together, the class and teacher will determine design and colors. Although the wallpaper will be the student's work, it will be necessary for the teacher to be quite involved with the painting process. The teacher will paint the hands (one at a time!) and help the students locate the correct spot for their handprint (color and orientation). As the teacher is working one on one with the student, on-going assessment can take place. Questions such as "What color will you need?" and "Where should you add your handprint?" will provide the teacher with a level of each student's understanding.