4th Grade Unit 2: Patterns and Algebraic Reasoning

Unit Driving Question 

How does identifying patterns help you solve real-world problems?      

Essential Questions 

1. In what ways does organizing data aide in identifying patterns?

2. What are ways to describe numerical patterns?

3. How can we use mathematical expressions with unknowns to describe geometric patterns?

Big Ideas

1. Number patterns can be represented by mathematical expressions and displayed in input/output tables. 
2. Growing geometric patterns can be represented by mathematical expressions. 

Technology Resources

Launch Task 

1 Lesson 

The Handshake Problem:  In this task, students explore a mathematics classic, the Handshake Problem.  The question is, “If each person in a group shakes hands with every other person exactly one time, how many handshakes will take place?”  Students will experiment with groups of different sizes, and try to identify a pattern.  Here is a link to an adaptation of this problem situation for 4th-grade students.

Big Ideas for Development Lessons 

2 Weeks (approximately 1 week per big idea) 

Big Idea 1: Number patterns can be represented by mathematical expressions and displayed in input/output tables.

Collaborative Engagement 

1. The Banquet Table Problem - In this hands-on task, students must discover the number of tables needed to seat all of the guests at a banquet.  Students will create t-tables to organize their data and identify rules that fit the patterns they develop.

Key Resources 

1. Analyzing Number Patterns - In this collaborative activity, students work with peers to analyze patterns, identifying the rule on which a pattern is based, create their own patterns, and analyze patterns created by their peers.
2. What’s My Rule? Intro to Function Tables  - This lesson introduces input/output tables, and provides multiple opportunities to create and analyze them. (source:  BetterLesson.com)
3. What’s My Rule?  The Game - After students have been introduced to input/output tables, this game is a great way to practice working with them all year long. 
4. Determining the Rule in Input/Output Tables (source:  BetterLesson.com) - The Direct Instruction portion of this lesson has an excellent, very thorough explanation of input/output tables, and gives students 5 specific steps to use when analyzing these tables and finding the rule.  Tables to match the Direct Instruction portion of the lesson are available here.  The lesson also contains a student practice assignment (see ‘IND Lesson 8’ at the above link).
5. Patterns and Functions (source:  BetterLesson.com) Lesson contains lots of practice working with number patterns in a variety of formats. 

Big Idea Formative Assessment 

1. Here is an exit ticket for analyzing number patterns, identifying the rule, and finding missing pattern elements. 
2. Here is an exit ticket for determining the rule for Input/Output Tables. 

Evidence of Understanding  

• Analyze number patterns

• Identify the rule on which the pattern is based; express the rule in the form of a mathematical expression (i.e., x + 4)

• Extend the pattern using the identified rule  

• Create input/output charts or tables to represent number relationships

• display number pairs from which the rule may be generalized

• apply the rule to identify additional number pairs and extend the pattern

• Analyze input/output tables and function machines

• identify the rule for the given number pattern

• describe the rule using a mathematical expression

Big Idea 2: Growing geometric patterns can be represented by mathematical expressions.

Collaborative Engagement 

1. Growing Patterns with Toothpicks and Tiles - Students will practice building a variety of geometric patterns and find the mathematical rule on which each pattern is based.  (Lesson adapted from ‘Growing Patterns and Sequences’, http://www.doe.virginia.gov/testing/solsearch/sol/math/6/mess_6-17.pdf)

Key Resources 

1. One Grain of Rice - In this folktale lesson, students will work together to make estimates based on a geometrically growing pattern.  The lesson is based on the book of the same title, which can be found at most libraries.  (lesson source:  University of North Carolina at Chapel Hill, School of Education)
2. Growing Patterns - In this NCTM Illuminations lesson, students explore growing patterns and see what patterns they can discover in Pascal’s Triangle.  

Big Idea Formative Assessment 

Using pattern blocks students will be assessed on repeating and growing patterns.

Evidence of Understanding  

• Analyze growing geometric patterns

• identify the rule on which the pattern is based

• express the rule in the form of a mathematical expression

• Create an input/output table or function machine to model the extension of a growing geometric pattern

Unit Closure