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Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 1.0 Knowledge of Algebra, Patterns, and Functions

Topic A. Patterns and Functions

Indicator 2. Identify, describe, extend, and create non-numeric growing or repeating patterns

Objective a. Represent and analyze growing patterns using symbols, shapes, designs, or pictures

Assessment limit: Start at the beginning, show at least 3 levels but no more than 5 levels, and ask for the next level

Clarification

A non-numeric pattern is represented with manipulatives, symbols, pictures, or anything in the pattern that is not numbers. A growing pattern involves a progression from one step to the next. Each new step is related to the previous step as defined by the pattern.
The change from step to step can be made by adding on to or expanding the previous step.
The overall pattern should be discussed in two important ways:

  • Appearance (How will the next step look?)
  • Numerically (How many will be in the next step?)

Note: In growing patterns "steps" may also be referred to as "terms".

Classroom Example 1

Creating growing patterns with manipulatives helps students realize what is "added" in each step to get the next step.

geometric figures

  • Use cubes to show Step 1.
  • What do you add to Step 1 to get Step 2? [two cubes]
  • What do you add to Step 2 to get Step 3? [two cubes]
  • What would you add to Step 3 to get Step 4? [two cubes]
  • How many cubes do you add each time?
  • How many cubes would be in Step 1? Step 2? Step 3? Step 4? Step 5?

Complete the table below for each step. Some have been done for you.

chart

Classroom Example 2

Growing patterns may have a position component, as well as a numeric component. In the following example, the number of triangles increases by one from one step to the next step. Each triangle added in the new step is horizontal flip of the previous triangle.

geometric figures

If the pattern continues what would be the next step?

  • How many triangles are in the next step?
  • What will the next step look like?

Classroom Example 3

Growing patterns may also expand from the center of the representation rather than from adding on to the end of the previous representation. In this example they may also include alternating colors.

geometric figures

  • Use color tiles to show Step 1.
  • What do you add to Step 1 to get Step 2? [four red tiles]
  • What do you add to Step 2 to get Step 3? [four blue tiles]
  • What would you add to Step 3 to get Step 4? [four red tiles]
  • How many tiles do you add each time?
  • How many would be in Step 1? Step 2? Step 3? Step 4? Step 5?

Complete the table below for each step. Some have been done for you.

chart

Classroom Example 4

Indicator Connection:
Connect this non-numeric pattern with the numeric pattern created by skip counting by 4 starting with 1.

What comes next in the pattern below?

1, 5, 9, _______

Classroom Example 5

triangles

If the pattern continues, what would come next?

How many triangle s are in Step 1? Step 2? Step 3? Step 4?

Complete the table below for each step. Some have been done for you.

chart

Note: The next term in this pattern is not obtained by adding the same number each time. This type of pattern cannot be linked to numeric patterns obtained by skip counting like the example before. It is important that students see patterns of this type so that they can develop a concept about growing patterns that includes ones whose terms are obtained by adding more than a constant increase.
/instruction/clarification/mathematics/grade3/xml/1A2a.xml
Resources for Objective 1.A.2.a:
CLARIFICATIONS | Lesson Seeds | Sample Assessments |