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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, analyze, and create a non-numeric growing or repeating pattern

Objective a. Generate a rule for the next level of the growing pattern

Assessment limit: Use at least 3 levels but no more than 5 levels

Clarification

When generalizing a rule for a growing pattern, students need to be able describe the change from level to level within the pattern. Students should then be able to generalize a rule that is consistent with the pattern and apply it by finding the next level or any level along the way. The generalizations of these patterns provide the foundation for developing the concept of function. The charts that are used to record levels and the number of items at each level will become function tables.

Classroom Example 1

Look at the pattern below.

pattern

Record and the number of stars in each level in the chart below.

table

  • How does level 2 differ from level 1? (2 more stars)
  • How does level 3 differ from level 2? (2 more stars)
  • Does this difference continue to level 4? (Yes)
  • What rule describes the change from level to level? (Rule: +2 to each level to get the next level)
  • How many stars would be in the next level? (9)

Classroom Example 2

Look at the pattern below.

pattern

How could you describe the pattern? How else could you describe the pattern?

  • Some students might notice that the levels are 1 × 1, then 2 × 2, then 3 × 3, and 4 × 4. These are the level numbers times themselves.
  • Other students might say that each time, a row and a column are added, making sure there is the same number of rows as columns.

Students should record the level number and total number of circles in the chart below to help them see the relationship between the level and the number of circles.

table

This helps students see the relationship between the level and the total number of circles.

Classroom Example 3

Look at the pattern below.

pattern

Complete the chart below that shows the representation, the level and number of dots in each level.

chart

How could you describe the pattern? How else could you describe the pattern?

Possible responses:

  • Some students might notice that the pattern is 10 dots, 14 dots, 18 dots.
  • Some students might see that the rule is +4 to each level to get the next level.
  • Other students might say that each time the row is moved down by one and the column is moved over by one.
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