Patterns:  Regularities in situations such as those in nature, events, shapes, designs, and sets of numbers (e.g., spirals on pineapples, geometric designs in quilts, the number sequence 3, 6, 9, 12,…).

Pattern Unit:  The part of a pattern that repeats.

Students will develop strategies or determining geometric and numeric patterns.  Students will:

• Create, read, and extend a given linear pattern
• Identify missing elements of a linear pattern
• Recognize and record the pattern unit, sequence, and rule
• Describe growing numeric and geometric patterns
• Analyze number patterns on hundreds charts

Visual and Number Patterns Unit (Lessons 1-3): Each lesson can take between 30-45 minutes, and may take several days to complete the entire unit.  Breakup procedures and review as needed.  Total unit duration is approximately 90-135 minutes.

 Materials:

• Thinkfinity – http://www.thinkfinity.org
• pattern blocks or Shape Tool (interactive)
• Hundreds Chart (interactive and/or worksheet)
• Multiplication Chart (interactive and/or worksheet)
• Calculator and Hundreds Board Tool or calculators
• number line
• "The House that Jack Built" by Mother Goose
• Exploring Pascal's Triangle (interactive)
• construction paper
• crayons

T = These lessons include working as a class, in groups, and individually. It includes teacher modeling, hands-on activities, and technology.  To enrichment these lessons introduce the students to Pascal’s triangle by opening Exploring Pascal's Triangle. Ask students to name any patterns that they see.   Have them relate the patterns they discovered to the activities they did throughout the lessons.  They should be applying the vocabulary terms to their findings and refelcting upon their new understanding.  You can also extend the lesson by using more challenging visual and number patterns that have multiple rules which students can debate the validity of the pattern rule.  For example, the pattern        1, 1, 2, 3, 5, 8, 13, 21.  Use the the Growing Patterns Activity Sheet to display these patterns.

O = These lessons begin with concrete relationships, transition into more abstract exploration, recordings, and creation.  Students find and create patterns, explore their growth, predict their continuation, establish its rule, and share their findings.                                                                                                                        

        Lesson 1 – What’s Next

W = During this unit, students use logical thinking to create, identify, extend, and translate patterns using geometric blocks.  They can also practice this skill using the Shape Tool.

• Using pattern blocks, make a pattern with at least three repeats of the pattern unit (example variety of two- and three- dimensional figures.                                                           INTERVENTION - use less shape variation in each pattern unit and provide students with descriptive geometric language and accompanying picture

H = Students have the opportunity to make patterns with numbers and shapes and explore patterns in a variety of mathematical contexts.

• Then ask a volunteer to read the pattern. Repeat with other patterns and other volunteers. Next place the students in pairs and give each pair several pattern blocks. (If you do not have pattern blocks, you might supply the students with paper shapes.) Ask each student to make a pattern with at least three repeats. Then call on volunteers to read their patterns and ask if anyone else has a similar pattern. Encourage several students to read their patterns using both descriptive geometric language and attributed letter pattern (AAB).  What is the pattern unit and how did you find figure it out?  How can you explain the pattern unit using letters?
• For additional practice, show students the Shape Tool.  Model how to make a linear pattern with the online shapes. As you demonstrate, you may wish to have the students copy the pattern with pattern blocks or draw it on paper. Allow volunteers to make a pattern on the Web site and read it to the class. Then encourage the students to use the site during math-center or free-choice times.  Finally, ask students to record one pattern by drawing with crayons on blank pieces of construction paper. 

Lesson 2 – Patterns on Charts

E = Students explore patterns by using hundreds charts identifying patterns in place value, multiplication, and even/odd numbers.  Patterns can run vertical or diagonal, allowing students to predict the growth of the pattern.

• After the students have made and recorded the patterns, call them together to describe their patterns.  After finding the pattern unit, what are the next three shapes in the pattern?
• Now show the Web site, Calculator and Hundreds Board Tool.
• Ask a volunteer to enter 2, +, 2, =, =, =, = into the online calculator and to describe what he or she sees on the calculator display. Ask another student to describe what happened on the online hundred chart.
• Next, place the students in pairs, and give each pair one copy of the Hundreds Chart and some crayons.  Have students circle the patterns they find on their paper hundred chart. When the groups have located several patterns, call on volunteers to describe patterns they found. Encourage the students to find skip-counting patterns for 2’s, 5’s, and 10’s [a preparation for multiplication] and the pattern of odd and even numbers. Also encourage them to notice patterns in the tens and ones places.  For independent practice, give students copies of the Multiplication Chart and ask them to color any number patterns that they notice.   What did you notice about the relationship between the number pattern and the numbers skipped on the hundreds chart?  When skip-counting by a number, you skip one less than that number.  For example, when skip-counting by 4s, you skip three numbers.                                                                               INTERVENTION - using the multiplication chart for independent practice, offer suggestions of patterns to explore

Lesson 3 – Growing Patterns

• To begin the lesson, recite "The House that Jack Built" by Mother Goose. Then ask the students to tell what happened in the story.
• Next explain that students will be exploring patterns that grow according to a rule. Display the “bowling pin” pattern (which is a “counting-on” pattern):

           •
           •   •
           •   •   •
           •   •   •   •

• Then ask, “What will come next in this pattern?”  When students give the correct answer [a row of five dots], ask them to explain how they got that answer. Repeat with several more rows. Then ask the students to state the rule that they would use to add more figures to the pattern. Encourage alternate expressions of the rule.
• Next display the pattern below, and ask students what they might call the pattern [a T pattern.]  

• Then repeat the steps used in the counting-on pattern above with the new pattern below.

R = Students engage in discussion to reflect on pattern findings and work together on growing patterns.

E = Students apply what they learned by creating, analyzing, and sharing their own pattern that grows and the accompanying rule utilized.  The rule can be increasing or decreasing in value and can show a relationship to mathematical functions such as addition, subtraction, and multiplication.

• Have the students make patterns that grow and exchange them with a friend to extend. At the end of the class, ask for volunteers to share their growing patterns and their rules.  What is the pattern rule?  Explain.  After finding the pattern rule, what is the missing number in the pattern?  

Intervention Strategies used throughout the lessons:

• use less shape variation in each pattern unit
• provide students with descriptive geometric language and accompanying picture
• using the multiplication chart for independent practice, offer suggestions of patterns to explore 

It is important for students to know how to:

• make, extend, and record a linear patterns;
• find the missing element in a linear pattern;
• find and analyze patterns on a chart;
• create, describe, and analyze growing patterns;
• recognize the pattern unit, sequence, and rule.

Math Problem-Solving Patterns Assessment Rubric

• http://rubistar.4teachers.org/index.php?screen=ShowRubric&rubric_id=1180656&

(click Find Rubric, Search Keywords (patterns), and Find Math - Problem Solving: Patterns)

Specific Questions to Assess Formative Assessment:

• What is the pattern unit and how did you find figure it out?
• How can you explain the pattern unit using letters?
• After finding the pattern unit, what are the next three shapes in the pattern?
• What did you notice about the relationship between the number pattern and the numbers skipped on the hundreds chart?  When skip-counting by a number, you skip one less than that number.  For example, when skip-counting by 4s, you skip three numbers.
• What is the pattern rule?  Explain.
• After finding the pattern rule, what is the missing number in the pattern?  

Materials and Resources:

• "Http://illuminations.nctm.org/ActivityDetail.aspx?ID=35." Web.  1 Mar. 2010. <htttp://www.thinkfinity.org/>.
• "Http://illuminations.nctm.org/lessons/HundredsChart.pdf." Web.  1 Mar. 2010. <htttp://www.thinkfinity.org/>.
• "Http://illuminations.nctm.org/lessons/MultiplicationChart.pdf." Web.  1 Mar. 2010. <htttp://www.thinkfinity.org/>.
• "Http://standards.nctm.org/document/eexamples/chap4/4.5/index.htm." Web.  1 Mar. 2010. <htttp://www.thinkfinity.org/>.
• "Http://illuminations.nctm.org/lessons/3-5/patterns/jackhouse.pdf." Web.  1 Mar. 2010. <htttp://www.thinkfinity.org/>.
• "Http://mathforum.org/workshops/usi/pascal/pascal_middisc.html>." Web  1 Mar. 2010. <htttp://www.thinkfinity.org/>.
• "Http://illuminations.nctm.org/lessons/PowerPatterns/PowerfulPatterns-AS-Growing.pdf." Web.  1 Mar. 2010. <htttp://www.thinkfinity.org/>.