Illuminations: Powerful Patterns

Powerful Patterns

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Lesson 5

Lesson 6

Lesson 7

Lesson 8

Lesson 9

Multiple Patterns

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

Learning Objectives

Students will:

copy patterns
use a table to record the results of doubling

Materials

Crayons
Pattern blocks (or paper shapes and glue)

Instructional Plan

Begin this lesson by asking the students to play Follow the Leader. Then ask them, “How did you know what to do?”

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 Candy

Mix 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 Needed for 10 Balls	Amount Needed for 20 Balls
Milk	9	18
Peanut Butter	10	20
Honey	5	10

You may wish to add columns to record other amounts.

Questions for Students

Listen to this pattern (clap, clap, stamp feet). Can you copy it? Can you translate it into a pattern with pattern blocks?

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.]

(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.]

(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.]

Assessment Options

Collect students "doubled" patterns.
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.

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?

NCTM Standards and Expectations

Algebra Pre-K-2

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.

This lesson prepared by Grace M. Burton.

1 period

NCTM Resources

Principles and Standards for School Mathematics

Activities

Shape Tool


More and Better Mathematics for All Students