**Title:** Patterns, Patterns, Everywhere

**Description:**
An interactive lesson on teaching about patterns and finding patterns in the environment.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**Standard(s): **

[MA2015] (3) 9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. [3-OA9]

**Subject:**Mathematics (3 - 4)

**Title:**Patterns, Patterns, Everywhere

**Description:**An interactive lesson on teaching about patterns and finding patterns in the environment. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**Title:** Shapes on the Way Home

**Description:**
This reproducible chart, from an Illuminations lesson, prompts students to search for and list shapes they find as they walk home from school. They record each shape's name, where it was found and whether it is a plane or solid figure.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**Shapes on the Way Home

**Description:**This reproducible chart, from an Illuminations lesson, prompts students to search for and list shapes they find as they walk home from school. They record each shape's name, where it was found and whether it is a plane or solid figure.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Hopping on the Number Line

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students generate products using the number line model. The order property is also introduced. In the lesson, students are encouraged to predict the products and to answer puzzles involving multiplication.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**Hopping on the Number Line

**Description:**In this lesson, one of a multi-part unit from Illuminations, students generate products using the number line model. The order property is also introduced. In the lesson, students are encouraged to predict the products and to answer puzzles involving multiplication.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Repeating and Growing Patterns

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students create and explore more complex patterns such as growing patterns, which have related but different relationships to repeating patterns. Students form generalizations, analyze, and describe growing patterns using connecting-cubes and then explore what happens when growing patterns double or split.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**Repeating and Growing Patterns

**Description:**In this lesson, one of a multi-part unit from Illuminations, students create and explore more complex patterns such as growing patterns, which have related but different relationships to repeating patterns. Students form generalizations, analyze, and describe growing patterns using connecting-cubes and then explore what happens when growing patterns double or split.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,PreK,1,2

**Title:** Geometric Solids and Their Properties

**Description:**
In this five-lesson unit from Illuminations, students analyze characteristics and properties of three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; and use visualization, spatial reasoning, and geometric modeling to solve problems. After being introduced to shapes, they look for patterns, construct a solid, and build a shape jacket.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**Geometric Solids and Their Properties

**Description:**In this five-lesson unit from Illuminations, students analyze characteristics and properties of three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; and use visualization, spatial reasoning, and geometric modeling to solve problems. After being introduced to shapes, they look for patterns, construct a solid, and build a shape jacket.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Looking for Patterns

**Description:**
This lesson, one of a multi-part unit from Illuminations, focuses on the properties of multiplication. Students skip count, examine multiplication patterns, and explore commutativity.
**Standard(s): **

[MA2015] (5) 3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. [5-OA3]

**Subject:**Mathematics

**Title:**Looking for Patterns

**Description:**This lesson, one of a multi-part unit from Illuminations, focuses on the properties of multiplication. Students skip count, examine multiplication patterns, and explore commutativity.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Understanding Distance, Speed, and Time Relationships

**Description:**
In this two-lesson unit, from Illuminations, students use a software simulation of two runners along a track. Students can control the speeds and starting points of the runners, watch the race and examine a graph of the time-versus-distance relationship. They examine graphs of related data and investigate scenarios involving constant rates of change.
**Standard(s): **

[MA2015] (5) 23: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., *x*-axis and *x*-coordinate, *y*-axis and *y*-coordinate). [5-G1]

**Subject:**Mathematics

**Title:**Understanding Distance, Speed, and Time Relationships

**Description:**In this two-lesson unit, from Illuminations, students use a software simulation of two runners along a track. Students can control the speeds and starting points of the runners, watch the race and examine a graph of the time-versus-distance relationship. They examine graphs of related data and investigate scenarios involving constant rates of change.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Playing with Patterns

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use objects and symbols to make repeating linear patterns. They also extend patterns and translate patterns from one modality (auditory, visual, and kinesthetic) to another.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics,Physical Education

**Title:**Playing with Patterns

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use objects and symbols to make repeating linear patterns. They also extend patterns and translate patterns from one modality (auditory, visual, and kinesthetic) to another.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,PreK,1,2

**Title:** The Fibonacci Series

**Description:**
The purpose of this lesson, from Science NetLinks, is to appreciate and investigate a numerical pattern and to look for evidence of mathematical patterns in nature. In this lesson, students explore the Fibonacci series. They identify the pattern among the Fibonacci numbers, look for applications of these numbers, and explore the ways that this pattern can be related to objects and shapes in both the natural and designed world.
**Standard(s): **

[MA2015] (7) 6: Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) [7-NS3]

**Subject:**Mathematics, Arts

**Title:**The Fibonacci Series

**Description:**The purpose of this lesson, from Science NetLinks, is to appreciate and investigate a numerical pattern and to look for evidence of mathematical patterns in nature. In this lesson, students explore the Fibonacci series. They identify the pattern among the Fibonacci numbers, look for applications of these numbers, and explore the ways that this pattern can be related to objects and shapes in both the natural and designed world.

**Thinkfinity Partner:**Science NetLinks

**Grade Span:**6,7,8

**Title:** Patterns That Grow

**Description:**
In this five-lesson unit, from Illuminations, students use logical thinking to create, identify, extend, and translate patterns. They make patterns with numbers and shapes and explore patterns in a variety of mathematical contexts. These lessons give students an opportunity to create and analyze numeric and geometric patterns. Particular emphasis is placed on growing patterns.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**Patterns That Grow

**Description:**In this five-lesson unit, from Illuminations, students use logical thinking to create, identify, extend, and translate patterns. They make patterns with numbers and shapes and explore patterns in a variety of mathematical contexts. These lessons give students an opportunity to create and analyze numeric and geometric patterns. Particular emphasis is placed on growing patterns.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Patterns That Grow: Looking Back and Moving Forward

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use logical thinking to create, identify, extend, and translate patterns. They make patterns with numbers and shapes and then explore patterns in a variety of mathematical contexts. The lesson includes a link to an interactive online shape tool.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**Patterns That Grow: Looking Back and Moving Forward

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use logical thinking to create, identify, extend, and translate patterns. They make patterns with numbers and shapes and then explore patterns in a variety of mathematical contexts. The lesson includes a link to an interactive online shape tool.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Many Ways to Create Patterns

**Description:**
This lesson, one of a multi-part unit from Illuminations, accommodates multiple learning styles as students create patterns using different forms. For example, students use body movement or kinesthetic experiences to create and copy patterns. Students use knowledge and skills in new situations to develop a solid understanding of the process for creating patterns, recognizing pattern sequences, and representing patterns in different ways.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**Many Ways to Create Patterns

**Description:**This lesson, one of a multi-part unit from Illuminations, accommodates multiple learning styles as students create patterns using different forms. For example, students use body movement or kinesthetic experiences to create and copy patterns. Students use knowledge and skills in new situations to develop a solid understanding of the process for creating patterns, recognizing pattern sequences, and representing patterns in different ways.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,PreK,1,2

**Title:** Exploring Other Number Patterns

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students analyze numeric patterns, including Fibonacci numbers. They also describe numeric patterns and then record them in table form.
**Standard(s): **

[MA2015] (5) 3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. [5-OA3]

**Subject:**Mathematics

**Title:**Exploring Other Number Patterns

**Description:**In this lesson, one of a multi-part unit from Illuminations, students analyze numeric patterns, including Fibonacci numbers. They also describe numeric patterns and then record them in table form.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Patterns on Charts

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students find, record, and analyze patterns on hundred and multiplication charts. They also use an interactive online shape tool and an online calculator to generate patterns and then record them on a chart.
**Standard(s): **

[MA2015] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5-MD2]

**Subject:**Mathematics

**Title:**Patterns on Charts

**Description:**In this lesson, one of a multi-part unit from Illuminations, students find, record, and analyze patterns on hundred and multiplication charts. They also use an interactive online shape tool and an online calculator to generate patterns and then record them on a chart.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** What Comes Nex_?: A Lesson in Patterns and Sorting

**Description:**
This lesson, from Illuminations, deals with patterns and the importance of looking at data from more than a single perspective. Students work to extend patterns and classify items as they investigate a series of items that appear to be ordered in some obvious ways.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**What Comes Nex_?: A Lesson in Patterns and Sorting

**Description:**This lesson, from Illuminations, deals with patterns and the importance of looking at data from more than a single perspective. Students work to extend patterns and classify items as they investigate a series of items that appear to be ordered in some obvious ways.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** What's Next?

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students begin their study of growing patterns by making linear patterns with pattern block shapes using several pattern cores. They extend a partner s pattern and find the missing element in a pattern.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**What's Next?

**Description:**In this lesson, one of a multi-part unit from Illuminations, students begin their study of growing patterns by making linear patterns with pattern block shapes using several pattern cores. They extend a partner s pattern and find the missing element in a pattern.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Pattern Pizzazz

**Digital Tool:**
Interactivate Pattern Generator **Web Address URL:**
http://www.shodor.org/interactivate/activities/PatternGenerator/ **Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]**Digital Tool Description:** This activity is an excellent reinforcement activity for students to explore patterns using shapes, letters, and numbers. The activity can be used individually or in groups of 2 or 3 students.
This learning activity was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.

**Title:**Pattern Pizzazz

**Digital Tool:**Interactivate Pattern Generator

**Digital Tool Description:**This activity is an excellent reinforcement activity for students to explore patterns using shapes, letters, and numbers. The activity can be used individually or in groups of 2 or 3 students. This learning activity was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.

**Title:** Ten Marks Personalized Math

**Digital Tool:**
Ten Marks **Web Address URL:**
http://www.tenmarks.com/ **Standard(s): **

[MA2015] (7) 6: Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) [7-NS3]**Digital Tool Description:** Ten Marks provides multiple choice questions for students in 2nd grade through Geometry. With a minimum of ten math subtopics per grade level, this tool can be used as an whole group or individual. The teacher manages the assignments and is able to view individualized reports. Students are guided through questions and have on screen access to audio/video instruction. When the assignment is complete, students receive immediate feedback and explanations for review. Access is available 24 hours/day, seven days per week.

**Title:**Ten Marks Personalized Math

**Digital Tool:**Ten Marks

**Digital Tool Description:**Ten Marks provides multiple choice questions for students in 2nd grade through Geometry. With a minimum of ten math subtopics per grade level, this tool can be used as an whole group or individual. The teacher manages the assignments and is able to view individualized reports. Students are guided through questions and have on screen access to audio/video instruction. When the assignment is complete, students receive immediate feedback and explanations for review. Access is available 24 hours/day, seven days per week.

**Title:** How Do You Unlock a Secret Code?

**Description:**
Cryptologists study secret codes. Being able to read encoded German and Japanese communications enabled the Allies to achieve victory in World War II., Join us as we explore how the code was cracked. By the end of this wonder, you may be making and breaking secret codes, too!
**Standard(s): **

[MA2015] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6-SP5]

**Subject:**Cross-Disciplinary - Informal Education , Arts - Glass , Arts - Sculpture , Arts - Woodworking , Science - Earth science , Science - Geology , Informal Education - Zoo/Aquarium/Nature Center Education

**Title:**How Do You Unlock a Secret Code?

**Description:**Cryptologists study secret codes. Being able to read encoded German and Japanese communications enabled the Allies to achieve victory in World War II., Join us as we explore how the code was cracked. By the end of this wonder, you may be making and breaking secret codes, too!

**Thinkfinity Partner:**Wonderopolis

**Grade Span:**K,PreK,1,2,3,4,5

**Title:** Number and Operations Web Links

**Description:**
This collection of Web links, reviewed and presented by Illuminations, offers teachers and students information about and practice in concepts related to arithmetic. Users can read the Illuminations Editorial Board's review of each Web site, or choose to link directly to the sites.
**Standard(s): **

[MA2015] (5) 26: Classify two-dimensional figures in a hierarchy based on properties. [5-G4]

**Subject:**Mathematics

**Title:**Number and Operations Web Links

**Description:**This collection of Web links, reviewed and presented by Illuminations, offers teachers and students information about and practice in concepts related to arithmetic. Users can read the Illuminations Editorial Board's review of each Web site, or choose to link directly to the sites.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,1,2,3,4,5,6,7,8,9,10,11,12

**Title:** Learning Geometry and Measurement Concepts by Creating Paths and Navigating Mazes: Hiding Ladybug

**Description:**
This stand-alone applet is part of the Illuminations lesson titled '' Helping Ladybug Hide with Arrows and Angles.'' In the lesson, students use this applet to hide a ladybug under a leaf.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**Learning Geometry and Measurement Concepts by Creating Paths and Navigating Mazes: Hiding Ladybug

**Description:**This stand-alone applet is part of the Illuminations lesson titled '' Helping Ladybug Hide with Arrows and Angles.'' In the lesson, students use this applet to hide a ladybug under a leaf.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,PreK,1,2

**Title:** Communicating about Mathematics Using Games: Playing Fraction Tracks

**Description:**
Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. This e-example from Illuminations contains an interactive version of a game that can be used in the grades 3-5 classroom to support students' learning about fractions. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.
**Standard(s): **

[MA2015] (5) 26: Classify two-dimensional figures in a hierarchy based on properties. [5-G4]

**Subject:**Mathematics

**Title:**Communicating about Mathematics Using Games: Playing Fraction Tracks

**Description:**Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. This e-example from Illuminations contains an interactive version of a game that can be used in the grades 3-5 classroom to support students' learning about fractions. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Learning about Number Relationships and Properties of Numbers Using Calculators and Hundred Boards: Displaying Number Patterns

**Description:**
Building on students' intuitive understandings of patterns and number relationships, teachers can further the development of number concepts and logical reasoning as described in the Number and Operations and Reasoning and Proof Standards. In this two-part example from Illuminations, virtual hundred boards and calculators furnish a visual way of highlighting and displaying various patterns and relationships among numbers. Using calculators and hundred boards together, teachers can encourage students to communicate their thinking with others, as discussed in the Communication Standard.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**Learning about Number Relationships and Properties of Numbers Using Calculators and Hundred Boards: Displaying Number Patterns

**Description:**Building on students' intuitive understandings of patterns and number relationships, teachers can further the development of number concepts and logical reasoning as described in the Number and Operations and Reasoning and Proof Standards. In this two-part example from Illuminations, virtual hundred boards and calculators furnish a visual way of highlighting and displaying various patterns and relationships among numbers. Using calculators and hundred boards together, teachers can encourage students to communicate their thinking with others, as discussed in the Communication Standard.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,1,2

**Title:** How Do You Unlock a Secret Code?

**Description:**
Cryptologists study secret codes. Being able to read encoded German and Japanese communications enabled the Allies to achieve victory in World War II., Join us as we explore how the code was cracked. By the end of this wonder, you may be making and breaking secret codes, too!
**Standard(s): **

[MA2015] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6-SP5]

**Subject:**Cross-Disciplinary - Informal Education , Arts - Glass , Arts - Sculpture , Arts - Woodworking , Science - Earth science , Science - Geology , Informal Education - Zoo/Aquarium/Nature Center Education

**Title:**How Do You Unlock a Secret Code?

**Description:**Cryptologists study secret codes. Being able to read encoded German and Japanese communications enabled the Allies to achieve victory in World War II., Join us as we explore how the code was cracked. By the end of this wonder, you may be making and breaking secret codes, too!

**Thinkfinity Partner:**Wonderopolis

**Grade Span:**K,PreK,1,2,3,4,5

**Title:** Creating, Describing, and Analyzing Patterns to Recognize Relationships and Make Predictions: Extending Pattern Understandings

**Description:**
This is part three of a three-part e-example from Illuminations that highlights different aspects of students' understanding and use of patterns. This part, Extending Pattern Understandings, demonstrates ways in which students begin to create a '' unit of units,'' or a grouping that can be repeated, and begin to relate two patterns in a functional relationship. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math Investigations.
**Standard(s): **

[MA2015] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4-OA5]

**Subject:**Mathematics

**Title:**Creating, Describing, and Analyzing Patterns to Recognize Relationships and Make Predictions: Extending Pattern Understandings

**Description:**This is part three of a three-part e-example from Illuminations that highlights different aspects of students' understanding and use of patterns. This part, Extending Pattern Understandings, demonstrates ways in which students begin to create a '' unit of units,'' or a grouping that can be repeated, and begin to relate two patterns in a functional relationship. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math Investigations.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,PreK,1,2