# Using the State Curriculum: Mathematics, Grade 3

 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

### 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 level to the next. Each new level is related to the previous level as defined by the pattern.
The change from level to level can be made by adding on to or expanding the previous level.
The overall pattern should be discussed in two important ways:

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

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

### Classroom Example 1

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

• 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.

### 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.

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.

• 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.

### 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

If the pattern continues, what would come next?

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

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

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.