NCDPI AIG Instructional Resource: Background Information s4

NCDPI – AIG Instructional Resource: Background Information

Resource Title: Fluffy the Snake

Subject Area/Grade Level (s): Math/4 Time Frame: Two-three days

Common Core/Essential Standard Addressed: Operation and Algebraic Thinking Generate and analyze patterns. 4.OA.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. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 8. Look for and express regularity in repeated reasoning.

Additional Standards Addressed: NA

Brief Description of Lesson/Task/Activity: In this task, students will observe a snake’s length during its first three years of life. Students will analyze patterns, make generalizations, and formulate function rules for determining the snake’s length at any year of its life.

Type of Differentiation for AIGs (include all that apply): Enrichment x Extension x Acceleration

Adaptations for AIGs: x Content x Process x Product

Explanation of How Resource is Appropriate for AIGs: Fourth grade standards require students to generate a number or shape pattern that fits a given rule. Then, students are asked to observe features in the pattern. This task requires students to extend fourth grade standards by having them create charts or tables to organize information, examine recursive patterns, and explore functional relationship between quantities. Then, students are asked to generate function rules using natural and symbolic language. This task focuses on understanding concepts and making generalizations. The abstractness and complexity of this task makes it ideal for AIG students.

PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project Needed Resources/Materials • Color tiles • graph paper • Fluffy the Snake poster

Sources: NA

TEACHER NOTES: NA

NCDPI AIG Curriculum Resource Outline

STAGE ONE: ENGAGE

Did you know that snakes have can live up to 40 years or longer? Additionally, a snake continues to grow throughout its entire life. A forty year old snake must be huge!

Let’s examine this snake that is for sale at Pete’s Pet Store (show the Fluffy the Snake poster). Pete said that that Fluffy the Snake will continue to grow at the same rate throughout its entire life. How long will Fluffy be after four years? Five years? How do you know? How can we organize the information that we are collecting?

STAGE TWO: ELABORATE

As a courtesy to Fluffy’s future owner, create a sign explaining that the snake will continue to grow throughout its life. On the sign, provide an equation that the owner can use to determine the length of the snake at any age. Use symbols to represent the unknown quantities. Justify your equation using charts, tables, pictures, symbols, or words.

Before students begin working, ask students to silently think about the following questions:  What is this problem asking us to do?  What tools will you need to solve this problem?  How much will Fluffy grow each year?  How can you organize the information that you will collect?  How long will Fluffy be after 5 years? 10 years?  How can we determine Fluffy’s length at any age?

PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project As students work, it may be necessary to elicit thinking by asking the following questions:  Describe what happens to Fluffy each year?  How can you use a chart or table to organize this information?  Look at the right column in your chart (see sample chart in teacher notes). What is the pattern you notice? Fluffy’s length increases by 3 units each year.  What is the relationship between the quantity in the first column and the quantity in the second column? The size of the snake is three times the year, plus one more unit for the head.  How can you use an equation to represent the relationship between the first and second column? E.g., 3a+1=l

Once all students have completed their signs, compare and evaluate solution strategies. Revisit several of the above questions.

Extension: How can a customer determine the amount of green and red Fluffy will have at any given year? Each year Fluffy grows by one green unit, plus the green unit for his head (a+1=g). Each year, Fluffy grows by two red units (2a=r).

STAGE THREE: EVALUATE

Students will be evaluated on their ability to:  Observe patterns in Fluffy’s growth, and use patterns to predict future growth.  Organize data in a table or chart.  Identify recursive patterns. E.g., In the sample function table below, the numbers in the left column increase by one, the numbers in the right column increase by 3.  Use spoken or written words to describe the functional relationship between the left and right column. E.g., To get the number in the right column, multiply the number in the left column by three and add 1.  Generate an equation that can be used to determine the length of Fluffy at any age. E.g., 3a+1=l  Explain why this equation works. E.g., The “3a” represents that the body grows by three each year and the “+1” represents the head.

TEACHER NOTES: Sample Function Table: Age Length (a) (l) 1 4 2 7 3 10 4 13 5 16 6 19

PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project