Repeating Patterns Study Guide

A repeating pattern is a sequence of elements that repeats in a predictable manner. In mathematics, repeating patterns are often found in geometry, algebra, and number sequences.

Types of Repeating Patterns:

Geometric Patterns: These patterns involve shapes or designs that repeat in a regular sequence.
Numeric Patterns: These patterns involve number sequences that have a recurring order or rule.
Algebraic Patterns: These patterns involve algebraic expressions or equations that exhibit a repetitive structure.

Identifying Repeating Patterns:

To identify a repeating pattern, look for a consistent sequence of elements that repeats with a regular interval. This could be a specific color sequence, shape sequence, or number sequence.

Describing Repeating Patterns:

When describing a repeating pattern, you can use terms such as "unit of repeat," "core," and "period." The unit of repeat is the smallest sequence that, when repeated, creates the entire pattern. The core is the essential part of the pattern that is repeated, and the period is the number of elements in the unit of repeat.

Examples of Repeating Patterns:

Here are some examples of repeating patterns:

Geometric Pattern: A sequence of squares, circles, and triangles arranged in a regular order.
Numeric Pattern: The sequence 2, 4, 6, 8, 10, where each number increases by 2.
Algebraic Pattern: The sequence 2n, where n is a natural number, creating the pattern 2, 4, 6, 8, ...

Practice Problems:

Try solving the following problems to test your understanding of repeating patterns:

Identify the core and period of the following pattern: red, blue, green, red, blue, green, ...
Write the next three terms in the numeric pattern: 3, 6, 9, 12, ...
Create an algebraic expression for the pattern: 5, 10, 15, 20, ...

Conclusion

Repeating patterns are important in mathematics and have applications in various fields. By understanding the characteristics and properties of repeating patterns, you can analyze and create patterns in a variety of contexts.

◂Math Worksheets and Study Guides Eighth Grade. Displaying data

Organizing & Displaying Data

The resources above cover the following skills:

Data Analysis and Probability (NCTM)

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

Select and use appropriate statistical methods to analyze data.

Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.

Develop and evaluate inferences and predictions that are based on data.

Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.

Grade 8 Curriculum Focal Points (NCTM)

Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets

Students use descriptive statistics, including mean, median, and range, to summarize and compare data sets, and they organize and display data to pose and answer questions. They compare the information provided by the mean and the median and investigate the different effects that changes in data values have on these measures of center. They understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center. Students select the mean or the median as the appropriate measure of center for a given purpose.

Connections to the Grade 8 Focal Points (NCTM)

Data Analysis: Building on their work in previous grades to organize and display data to pose and answer questions, students now see numerical data as an aggregate, which they can often summarize with one or several numbers. In addition to the median, students determine the 25th and 75th percentiles (1st and 3rd quartiles) to obtain information about the spread of data. They may use box-and-whisker plots to convey this information. Students make scatterplots to display bivariate data, and they informally estimate lines of best fit to make and test conjectures.