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What’s Next?

  • Lesson
Pre-K-2,3-5
1
Algebra
Grace M. Burton
Location: unknown

In this lesson, students make patterns with objects, read patterns and find patterns in the environment. They should be encouraged to classify patterns by type (i.e. AAB, ABC). They continue learning about patterns by extending a given pattern, identifying missing elements in a pattern, and recording a pattern.

Begin the lesson by displaying a piece of fabric or wallpaper with a pattern. Ask the students to describe the pattern in words (for example, red, green, blue, red, green, blue) and then to record the pattern using crayons. Then ask the students to look around the room to see what other patterns they can find. You might want to suggest that they look at classmate's clothing. Next, ask the students what patterns they found at their house. Ask students to compare one another's patterns. Provide them with the appropriate pattern names, such as ABA and AAB).

Then put the students into pairs and distribute materials such as buttons, pretty pasta, or color tiles. Ask each student to make a pattern of at least 3 repeats. When all the students have done this, ask them to add 2 repeats to their partner’s pattern. (You may wish to provide rubber stamps or stickers in addition to, or in place of, real objects.)

Next make a pattern with overhead color tiles or some other overhead manipulatives on the overhead projector, and ask for volunteers to extend the pattern. For example, if you laid out buttons in the pattern red, red, green, red, red, green, you would expect students to extend the pattern using a core of two reds and a green (an AAB pattern).

Then, tell the students that you are going to play the "One Away" game. Turn off the overhead projector and remove one tile from the pattern. For instance, you might take away one red tile; or, as shown below, a sticker of a flask has been removed from the pattern flask, flask, atom. Then turn the projector back on and have the students tell you what was removed. When the students suggest what was removed, place the piece they name in the pattern and ask them to read the pattern aloud to verify their answer. Repeat this several times. Now ask the students to play the "One Away" game with a partner by using their materials to make a pattern and taking away one object while their partner’s eyes are closed.

 

585 pattern

 

As a concluding activity, have students record their patterns with crayons, stickers or rubber stamps, leaving a little space between each element. Now have them make a "One Away" puzzle by covering one button, sticker or stamp by taping a small piece of paper over it. An interesting bulletin board can be created from their pattern puzzles.

  • Fabric or wallpaper sample
  • Buttons, tiles or other patterning material
  • Overhead projector and manipulatives
  • Paper
  • Crayons
  • Tape
  • Stickers or rubber stamps (optional)

Assessments 

  1. Make notes about students’ patterns. Next to each student’s name on a class roster, record the date, the pattern type, the number of iterations the student made, and a check or X to indicate whether the student made any mistakes. Throughout the unit, continue to record students’ pattern types to assess whether students are able to create a variety of patterns.
  2. Collect students’ "One Away" puzzles.
  3. Make a pattern on the overhead projector with one object missing. Have students draw your pattern and insert the missing object. Note that this activity can be especially rich if you use a pattern and remove an element that could be replaced by several different objects. Then, students can suggest multiple answers, but the assessment comes in the justification.
    585 one away assessment
     
  4. For instance, the pattern above shows a missing third element. The sequence might represent an ABB pattern if shape is considered: circle, square, square. On the other hand, it could represent an ABC pattern if color is considered: red, green, blue. Either answer could be considered correct, depending on a student's reason.

 
Extensions   
  1. During math rotations or centertime, place students at the computer on the Color Patterns website. Students will extend computer-generated patterns.
 

Questions for Students 

1. What will come next in the pattern blue, yellow, yellow, blue yellow, yellow?
 

[Blue will come next.]

2. What patterns can you find on the clothes that students are wearing? Do you see any other patterns in the room?

[Answers will vary.]

3. How are these two patterns alike?

[Answers will vary, but one possibility is that they are both ABC patterns.]

4. Suppose you want to make an AB pattern. How could you do that? Who could do it a different way?

[You could use two colors, such as red, blue, red, blue. A different answer might use different colors or objects.]

5. How would you make an ABB pattern? How is it like an AB pattern? How is it different from an AB pattern?

[You could use red, blue, blue, red, blue, blue, for example. Like the AB pattern, it has two colors or objects, but the second color is repeated.]

6. How would you explain to a friend how to find out what is missing in a pattern?

[You have to find what is being repeated first. Then you can see what is missing.]

Teacher Reflection 

  • Which pairs worked most effectively together? Which pairs were less effective? Why?
  • Which students can make a pattern? What activities are appropriate for those who cannot do this yet?
  • Can most of the students read a pattern? What extension activities are appropriate for those who do this well?
  • Which students can extend a pattern? What activities are appropriate for those who can and those who cannot do this yet?
  • Which students can identify the missing element in a pattern? What activities are appropriate for those who cannot do this yet?
  • Which students recorded their patterns accurately? What additional experiences will help those who did not?
 
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Algebra

Order, Order

Pre-K-2

In this lesson students seriate objects and review the meaning of ordinal numbers. They describe orderings in words and in pictures. [This lesson gives you an opportunity to review or teach vocabulary such as before, after, and next.] At the conclusion of the lesson, students make an entry in their portfolios. A Science extension is suggested.

[At this point you may wish to make pretty pasta for the students to use in this unit. Simply place uncooked pasta of various shapes in a plastic bag; add a few drops of food color and a few drops of rubbing alcohol. Shake the bag until the pieces are coated, then spread them out to dry.]

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Algebra

Sorting Time

Pre-K-2
Students sort objects and symbols and make patterns with sorted objects. They make Venn diagrams and use their sortings to create linear patterns. They extend a pattern created by the teacher. Students will begin identifying pattern cores and reading patterns. A Social Studies connection is suggested as an extension.
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Algebra

Playing With Patterns

Pre-K-2
Students use objects and symbols to make repeating linear patterns. They extend patterns and translate patterns from one modality (auditory, visual, and kinesthetic) to another. A Physical Education connection is suggested as an extension. This lesson is intended to take two class periods to ensure that all students have multiple opportunities to create original patterns.
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Algebra

More Patterns

Pre-K-2
Students extend their knowledge of linear patterns by recognizing and discussing familiar patterns. Students make auditory and visual patterns from names. An art activity is suggested as an extension.
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Algebra

Multiple Patterns

Pre-K-2
Students explore patterns which involve doubling. They use objects and numbers in their exploration and record them using a table.
Algebra

Exploring Other Number Patterns

Pre-K-2, 3-5
Students make and extend numerical patterns using hundred charts. They also explore functions at an intuitive level. This lesson integrates technology.
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Algebra

Growing Patterns

Pre-K-2, 3-5
Students explore growing patterns. They analyze, describe, and justify their rules for naming patterns. Since students are likely to see growing patterns differently, this is an opportunity to engage them in communicating about mathematics.
Algebra

Looking Back and Moving Forward

Pre-K-2
This final lesson reviews the work of the previous lessons. Students explore patterns in additional contexts and record their investigations. Students will rotate through center activities. Teachers may add other centers they feel will benefit the students.

Learning Objectives

Students will:

  • Identify and read patterns
  • Extend patterns
  • Create linear patterns
  • Record patterns in pictorial form
  • Identify the missing element in a pattern
 

Common Core State Standards – Mathematics

Grade 4, Algebraic Thinking

  • CCSS.Math.Content.4.OA.C.5
    Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule ''Add 3'' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP7
    Look for and make use of structure.
  • CCSS.Math.Practice.MP8
    Look for and express regularity in repeated reasoning.