Growing Patterns

Objectives•Discover and use familiar

children’s songs and literature to promote the

understanding of repeated patterns and growing

patterns.

Course of Study Standards

•Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from representation to another.

•Analyze how both repeating and growing patterns are generated.

Questions to Think About

• Why is it important to have students explain how they are interpreting patterns they have created?

• In what ways are such discussions helpful in building mathematical vocabulary?

What is a Pattern?

A pattern is…..

• a sequence or order of objects that repeat or grow.

Pattern Vocabulary

• The pattern rule is the relationship between number or objects in a pattern.

• The core is the main unit of the pattern that is repeated.

• A term is each one of the parts making up the pattern.

ABABAB

The core of this pattern would be A, B.

There are two terms in each core of this pattern.

There are six terms in the pattern.

What’s My Rule?

• Introduce patterns by playing “What’s My Rule?”

Create patterns using manipulatives or pictures with the children. Ask them to describe the pattern and its parts. What makes it a pattern?

Create a repeating pattern and a growing pattern. Ask the children to describe the patterns. Make several more patterns and ask the students to tell whether they are repeating or growing patterns.

Children’s Literature with Growing Patterns

• Ten Black Dots by Donald Crews• The Very Hungry Caterpillar by Eric Carle• Rooster’s Off to See the World By Eric Carle

• The Hunter by Pat Hutchins • Six Dinner Sid by Inga Moore• Bat Jamboree by Kathee Apelt• Counting Crocodiles by Judy Sierra• Over in the Grasslands by Anna Wilson• Fiddle I Fee by Melissa Sweet• Warthogs in the Kitchen by Pamela Edwards

Songs with Growing Patterns• There was an Old Lady Who Swallowed a Fly

• The Green Grass Grew All Around• B-I-N-G-O• Had a Little Rooster• Today is Monday• Don’t throw Your Junk In my Backyard• When We All Go Out To Play• Tarzan Songs that have a growing pattern with motions: • My Granny Went to the County Fair• Mother Gooney Bird• My Name is Joe and I work in a Button factory• http://games.greenghoulie.com/songs/mynameisjoe.htm• Tootie Tah• My Hands on My Head

Websites to explore Virtual Manipulatives creating Patterns

• http://pbskids.org/cyberchase/games/patterns/patterns.html 

• http://www.shodor.org/interactivate/activities/ 

• http://www.arcytech.org/java/patterns/patterns_j.shtml

Pattern Center Time

• Select a tool and create a growing pattern. Draw a line under the core element, label the pattern with numbers, and translate the pattern using a different tool.

• When finished, present the various representations to the class and explain what was thought before creating the pattern.

Questions for Students• What would come next in your pattern? Why?

• Are there songs that you know that include patterns?

• How does singing a pattern help you recognize and remember it?

• What kinds of things did you have to think about to create your pattern?

• If you were to add one more repeat to your pattern (or extend it), what objects would you need to that?

• What kinds of problems did you have when creating your pattern? What caused these problems?

• How could you describe what you did to make your pattern?

Teacher ReflectionsWhich students have difficulty recognizing "what comes next" in patterns? What instructional experiences do they need before moving to the next lesson?

Were the students able to extend patterns easily? If not, what questions could I ask to guide them to think about ways to do so?

Which students were able to translate freely among the different representations of the same pattern? What challenges are appropriate for them now?

Which students demonstrated limited understanding of patterns and ways to analyze, create, describe, extend, or interpret patterns

For Further Instruction

• Revisit repeating patterns as they naturally occur in the course of daily instruction to reaffirm the fact that patterns define order in the world.

• For example, you might note the arrangement of petals on a flower, leaves on a stem, or colors and patterns in floor tiles.

• Keep your notes for future reference and to share with students, their parents, and others as appropriate.

1. What problems did the students have completing the activities in this lesson? What learning experiences would address these problems?2.  Which tools did most students select for creating their patterns? 3.  Are there other ways to represent patterns that occur naturally in the curriculum? 4.  What vocabulary did the students use when describing their patterns? What additional vocabulary do the students need to learn? How can I teach that vocabulary with meaning and purpose? 5. What problems did the students have completing the activities ? What learning experiences would address these problems?

Looking Back1. Which students met all the objectives? What extension

activities are appropriate for those students?

2.      Which students are still having difficulty with the objectives? What additional instructional experiences do they need?

3.      Did all the students display understanding of the relationship between the core elements within a pattern? What is my evidence for this?

4.      What were the greatest challenges for the students? Which portions were the students most motivated

to complete? Why?

Moving Forward

1. How can I help the students extend their understanding of patterns and the relationships among the elements of a pattern?

2. What experiences can I provide so that the students will remember how to identify and describe patterns?

3. What experiences can I plan so that the students will have a genuine need to recognize and use patterns in everyday experiences?

4. What learning experiences would help the students not yet comfortable with the concepts of patterns?