## Multiple Patterns

Pre-K-2
1

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

Next, put the students into pairs and give each pair some pattern blocks (or paper shapes) and some plain paper. Ask the students to make and record a linear pattern with 3 repeats by tracing the pattern blocks or gluing the paper shapes on the paper. After the students have had a chance to make and record the patterns, ask them to write the number of objects in their pattern at the end of the pattern. Then have them trade patterns and make an identical pattern directly under their partner’s pattern. When they have recorded the pattern, have them write at the end of the pattern the number of shapes in it. Then ask the students to find and record the total number of shapes in all.

When the students are finished, call on a volunteer to describe the pattern that he or she copied, and ask how many shapes there were in all. (In the sample shown above, the total is 24.) Ask if anyone else’s pair of patterns had the same number of shapes. Then ask if anyone made a pattern and its copy that had a different total number of shapes. Record the responses in a table on the blackboard or overhead. (See example below.)

 Number of Shapes In One Pattern In Two Patterns 12 24 9 18

Now ask the students if they have heard the word "double." You may wish to explain the concept  doubling  as it is used in cooking. Then display a copy of the following recipe for Peanut Butter Candy.

 Peanut Butter CandyMix together: 9 tablespoons nonfat dry milk 10 tablespoons peanut butter (creamy or crunchy) 5 teaspoons honey Then gradually blend the ingredients together, and roll the batter into ten small balls.This candy does not need refrigeration.

Explain that the recipe will make 10 peanut butter balls. Ask how they could make 20 peanut butter balls. Record their responses in a table.

 Ingredient Amount Neededfor 10 Balls Amount Neededfor 20 Balls Milk 9 18 Peanut Butter 10 20 Honey 5 10

You may wish to add columns to record other amounts.

• Crayons
• Pattern blocks (or paper shapes and glue)

Assessment Options

1. Collect students "doubled" patterns.
2. Write another "Number of Shapes" table for doubling patterns. Write how many shapes in one pattern or how many shapes in two patterns, and have the students use that information to fill in the blanks. For example, if you write 10 in the column for number of shapes in two patterns, students must figure out that there are 5 shapes in one pattern.
Extension
Move on to the next lesson, Exploring Other Number Patterns.

Questions for Students

1. Listen to this pattern (clap, clap, stamp feet). Can you copy it? Can you translate it into a pattern with pattern blocks?
2. If I make a pattern with 2 repeats that has 6 shapes in all, how many shapes would there be in all if I copied it?

[There will be 12 shapes in all.]

3. (Point to the first row in the Peanut Butter Candy table.) What does this row in the table tell us?

[It tells us how much dry milk we have to use.]

4. (Point to the second column in the Peanut Butter Candy table.) What does this column tell us?

[It tells us how much we need to make 20 balls.]

Teacher Reflection

• Which students had difficulty copying a pattern? What was the nature of their errors? What instructional experiences do they need next?
• Which students were successful in copying a pattern? What experiences would be appropriate for them?
• Which students had difficulty using a table? What caused their difficulty? What instructional experiences do they need next?
• Which students were successful in using a table? What experiences would be appropriate for them?
• What other recipes might I use in the lesson?
• What adjustments would I make the next time I teach this lesson?

### 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.

### 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.

### What’s Next?

Pre-K-2, 3-5
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.

### 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.

### 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.

### 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.

### 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.

### 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:

• Copy patterns.
• Use a table to record the results of doubling.

### NCTM Standards and Expectations

• Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
• Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
• Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.