"Looking for patterns trains the mind to search out and discover the similarities that bind seemingly unrelated information together in a whole. . . . A child who expects things to 'make sense' looks for the sense in things and from this sen develops understanding. A child who does not see patterns often does not expect things to make sense and sees all events as discrete, separate, and unrelated."
- Mary Baratta-Lorton(1)

Children should construct, recognize and extend patterns with pattern blocks, cubes, toothpicks, beans, buttons and other concrete objects. Children in kindergarten can recognize patterns in motion, color, designs, sound, rhythm, music, position, sizes and quantities. They are very aware of sound and rhythm, and can clap out patterns that repeat, such as clap-clap-clap-pause, clap-clap-clap-pause, etc. They can sit in a circle and wear colored hats which make a pattern, such as red-white-blue, red-white-blue, etc. One child can walk around the circle and tap successive children in an arm-shoulder-head pattern. The teacher may ask the class who the next person to be tapped on the head would be if the pattern were to be continued. In addition to repeating patterns, students should have experiences with growing patterns. They can indicate such a pattern by using motion: skip-jump-turn around, skip-jump-jump-turn around, skip-jump-jump-jump-turn around, and so on. Songs are excellent examples of repetition of melody or of words as well as of rhythmic patterns. Children's literature abounds with stories which rely on rhythm, rhyming, repetition and sequencing. As students move on to first and second grade, they should start to create their own patterns and transform patterns using concrete objects into pictorial and symbolic representations of those patterns. The transition will be from working with patterns using physical objects to using pictures, letters, numbers, and geometric figures in two and three dimensions to using symbols (words and numbers) to represent patterns.

Also important for students in the primary grades are categorization and classification. Students in kindergarten should have numerous opportunities to sort, classify, describe, and order collections of many different types of objects. For example, students might be asked to sort attribute shapes, buttons, or boxes into two groups and explain why they sorted them as they did. This area offers an excellent opportunity for students to integrate learning in mathematics and science as they sort naturally-occurring shapes such as shells or leaves.

Primary-grade students should also use patterns to discover a rule. Kindergartners might look at Anno's Counting House(2) to see if they can figure out the pattern that is used in moving from one set of pages to the next. (The people in this book move, one by one, from one house to another.) Older students might try to find the pattern in a series of numbers, like 1, 3, 5, 7, 9, ...

Often, students will be looking for patterns in input-output situations. For example, they might look at the pictures in Anno's Math Games II(3) to find out what happens to objects as the elves put them into the magic machine. (Sometimes the number of objects doubles, sometimes the objects grow eyes, and sometimes each object turns into a circle.)

Establishing the habit of looking for patterns is exceedingly important in the primary grades. By studying patterns, young children can learn to become better learners of mathematics as well as better problem solvers. In addition, patterns help students to appreciate the beauty of mathematics and to make connections within mathematics and among mathematics and other subject areas.

(2) Anno's Counting House by Mitsumasa Anno. New York: Philomel Books, 1982.

(3) Anno's Math Games II by Mitsumasa Anno. New York: Philomel Books, 1982.

Experiences will be such that all students in grades K-2:

A. reproduce, extend, create, and describe patterns and sequences using a variety of materials.

• Students make a collage with examples of patterns in nature.
• Students create visual patterns with objects, colors, or shapes using materials such as buttons, macaroni, pattern blocks, links, cubes, attrilinks or attribute blocks, toothpicks, beans, or teddy bear counters. They challenge other students to describe or extend their patterns.
• Students sort objects such as leaves, buttons, animal pictures, and blocks, using categories corresponding to characteristics like number of holes, number of sides, or thickness.
• One child walks around the outside of a circle and taps successive children in a head-shoulder-shoulder-head pattern. The teacher asks who the next person to be tapped on the head would be if the pattern were to be continued. The children sing and act out the song, "Head, shoulders, knees and toes."
• Students describe patterns made from circles, triangles, and squares and select the next shape in the pattern.
• Students make patterns with letters and extend the sequence.
• Students use letters to identify patterns they have created with objects -- for example, RRBRRB for red-red-blue-red-red-blue.
• Students connect the dots to make a picture by following a number sequence, such as 2, 4, 6, 8.
• Students create one more and one less patterns.
• Students create patterns with the calculator. They enter any number such as 10, and then add 1 for 10+1= ,=, =. The calculator will automatically repeat the function and display 11, 12, 13, 14, etc. Some calculators may need to have the pattern entered twice: 10+1=11 +1=, =, =, etc. Other calculators will need 1++, 10=, =, =, etc. Students may repeatedly add (or subtract) any number.
• Students use squares placed in two rows to reproduce odd and even number patterns. They also describe odd and even by using the sum of the dots on dominoes.
• Students name things that come in pairs (or 4s or 5s): eyes, ears, hands, arms, legs, mittens, shoes, bicycle wheels, etc. They work in pairs to find how many people there are if there are 20 eyes.
• Students count by 2, 5, and 10 using counting objects or creating color patterns with Unifix or linker cubes; they repeat this counting on a number line.
• Students use skip counting or calculators to color multiples of numbers on the hundreds chart. Linking cubes or Unifix cubes can be used to build towers or trains with every other cube or every third cube, a certain color to illustrate, recognize and practice skip counting patterns.
• Students write their first name repeatedly on a 10x10 grid then color the first letter of their name to create a pattern. They discuss the patterns formed.
• Students identify the same pattern in a variety of contexts. For example, black-white-black-white is like sit-stand-sit-stand and ABAB and up-down-up-down and straight-curve-straight-curve.
• Students identify patterns on a calendar using pictures or numerals. For example, in November, even dates might be marked with a snowflake, and odd dates with a picture of a turkey. Or, they might identify the day(s) of the week.
• Students describe a pattern made by using various stamp blocks or picture designs.
• Students use or create patterns with geometric figures (circles, triangles, squares, pentagons, hexagons, etc.) and record how many of each shape exist after each repeating cluster.
• Students create a mosaic design (tessellation) made of different shapes using objects such as pattern blocks. They color congruent shapes of a mosaic design with the same color.

• Students fill in a table given several starting numbers and a verbal rule.
• Students describe the pattern illustrated by the numbers in a table by using words (e.g., one more than), and then the teacher helps them to represent it with symbols in an open sentence ([] = * + 1).
• Students use colored squares to make a graph showing the multiples of 3 and relate this to a table and an expression involving a variable, such as 3 x [].
• Students describe how the distance from school changes as they are walking to school and draw a picture that illustrates this situation.

• Students put numbers into Max the Magic Number Machine and read what comes out. (The teacher acts as Max.) Then they describe what Max is doing to each number.
• Students investigate a hole-making machine that puts 4 holes in buttons. They make a table that shows the number of buttons and the number of holes for different numbers of buttons. Then they write a sentence that describes how the total number of holes changes as new buttons are added to the pattern.
• Students play "Guess my Rule." The teacher gives them a starting number and the result after using the rule. She continues giving examples until students discover the rule.
• Students count the number of pennies (or nickels) in 1 dime, 2 dimes, 3 dimes and record their results in chart form. They study the patterns and discuss the "rules" observed.
• Students consider the cost of two or three candies if one candy costs one dime. They make a chart using the information.
• Students count the number of lifesavers in an assorted pack. They make a table showing the number of each color and the total number in one pack. Then they look at the number of each color and the total for two, three, or more packs.

• Students discuss how ice changes to water as it gets hotter. They talk about how it snows in January or February but rains in April or May.
• Students plant seeds and watch them grow. They write about what they see and measure the height of their plants as time passes. They discuss how changes in time bring about changes
• in the height of the plant. They also talk about how other factors might affect the plant, such as light and water.

• Students go on a pattern hunt around the classroom and the school, discussing the patterns they see.
• Students sing and act out songs like "Rattlin' Bog" (Bird on the leaf, and the leaf on the tree, and the tree in the hole, and the hole in the ground, . . .) and "Old MacDonald Had a Farm."
• In reading, students recognize patterns in rhythm, in rhyming, in syllables and in sequencing. Stories such as Ten Black Dots by Donald Crews, Five Little Monkeys Jumping on a Bed by Eileen Christelow, Little Red Hen, Jump, Frog, Jump by Robert Kalan, Six Dinner Sid by Inge Moore, and Dr. Seuss books offer such opportunities. Visual patterns can be shown using picture representations for children's books such as 1 Hunter by Pat Hutchins, Rooster's Off to See the World, The Patchwork Quilt by Valerie Flournoy, and The Keeping Quilt by Patricia Polacco.
• Students identify every third letter of the alphabet; every fourth letter, etc.
• Students choose a day. They identify the name of the next day; of the previous day; and also the name of the day two days (or more) before and after. They select a date, and give the date of the next day and of the previous day; the name of the month, of the next month, and of the previous month. They give the name of the date 2 days before and after, 3 days (or more) before and after.
• Students graph daily weather patterns, showing sunny, cloudy, rainy or snowy days. Then they discuss monthly or seasonal patterns.
• In social studies, students identify traffic patterns such as how many cars, trucks, or buses pass the front of the school during five minutes at different times of the day. They keep records for five days, organizing the information in chart form.
• In art, students observe patterns in pictures, mosaics, tessellations, Escher-like drawings as well as in wallpaper, fabric and floor tile designs. They learn that it is important to match patterns when a part is used for the whole, such as in sewing or wallpapering.

• Students draw pictures of faces and make a table that shows the number of faces and the number of eyes. The teacher writes a sentence on the board that the class composes, describing the patterns that they find.
• Students observe that there are 12 eggs in a carton of eggs. These are called a dozen. They explain how to find the number of eggs in 2 cartons (dozen).
• Students write a sentence or more telling about the patterns they have observed in a particular activity. They may use pictures to describe or generalize what they have observed. For example, after students have colored multiples of a certain number on the hundreds chart, they write about the pattern they observe on the chart.