CK-12 Foundation
Recursive Formulas: Fibonacci Sequence
Explore the building blocks of the Fibonacci Sequence. Given the lengths of sides of squares, pupils deduce the pattern to determine the lengths of two more squares. Learners continue to work with recursive formulas to generate numerical...
EngageNY
Recursive Formulas for Sequences
Provide Algebra I learners with a logical approach to making connections between the types of sequences and formulas with a lesson that uses what class members know about explicit formulas to develop an understanding of recursive formulas.
Balanced Assessment
Stick Patterns
Sticks and stones may break my bones, but these sticks will make me smarter. Pupils examine arrays of sticks to determine the next array in a pattern. They use the number of sticks added to each previous array to determine a recursive...
Curated OER
Solving a Legend- Exponents, Recursive and Explicit Equations.
Eighth graders play a game to solve problems. In this exponents and scientific notations lesson, 8th graders play a game in small groups to move colored disks from location A to location C. Students identify recursive patterns to solve...
Curated OER
Toothpick Triangles
Explore patterns, variables, and mathematical relationships when you examine patterns with toothpicks and determine the next sequence of figures. Your class writes and justifies a formula based on the sequence. An answer key is included.
K20 LEARN
Didn’t We Already Learn That Pattern? Functions/Arithmetic Sequences
Just how many toothpicks does the pattern take? After watching a video of someone building a pattern with toothpicks, groups create methods to find the number of toothpicks needed to accomplish that task. Groups either use explicit...
Curated OER
Exploring Pascal's Triangle and Other Recursive Patterns
Students explore patterns in everyday life and in the mathematic world. They create various concrete examples of patterns and verbally describe these patterns to a fellow student.
Curated OER
Arithmetic Sequences
Twenty-eight problems, two pages, and an answer key all related to number patterns, recursive formula, and arithmetic sequence. Leaners find the next number in the pattern or sequence and determine the arithmetic formula to go with the...
PBS
Adventures With The Fish Pond: Population Modeling
Build up from the previous activity where your learners charted the population growth and decay of a fish pond with M&Ms®. Have them look at the data from that activity and create a Now-Next, or recursive equations, to predict the...
Kenan Fellows
Dinner Party: Using Pattern Trains to Demonstrate Linear Functions
Nothing fancy here ... just your run-of-the-mill Algebra party! Learners explore the patterns of linear functions while designing seating arrangements for a dinner party. Comparing the number of tables to the perimeter of the combined...
Curated OER
Making Number Patterns
In this number patterns activity, learners make number patterns for sets of rules given. Answers and a reference website are included.
Curated OER
Making Number Patterns
In this number patterns worksheet, students follow instructions to create number patterns with given starting numbers. A website reference for additional resources and answer key are provided.
Curated OER
Making Number Patterns
In this number patterns instructional activity, students make number patterns for sets of rules given. A website reference for additional resources is provided. A website reference for additional resources and answers is provided.
Mathematics Vision Project
Quadratic Functions
Inquiry-based learning and investigations form the basis of a deep understanding of quadratic functions in a very thorough unit plan. Learners develop recursive and closed methods for representing real-life situations, then apply these...
Inside Mathematics
Hexagons
Scholars find a pattern from a geometric sequence and write the formula for extending it. The learning exercise includes a table to complete plus four analysis questions. It concludes with instructional implications for the teacher.
Curated OER
Introduction to Fractals: Infinity, Self-Similarity and Recursion
Students think about several of the concepts from fractals, including recursion and self similarity. They use mathematical concepts of line segments, perimeter, area and infinity are used, and skill at pattern recognition is practiced.
Curated OER
Tile Patterns that Grow
Students explore how a pattern built with square tiles grows and describe the change from stage to stage. They predict later stages of a tile design sequence and create math equations related to the growth of tile designs.
Curated OER
Amazing Fibonacci
Students integrate the patterns of Fibonacci into music. For this geometry lesson, students apply the concepts of recursion, pattern and Phi or Golden Ratio to composing and playing music on various instruments. They lesson is co-taught...
EngageNY
Arithmetic and Geometric Sequences
Arithmetic and geometric sequences are linear and geometric patterns. Help pupils understand the relationship and see the connection with an activity that asks them to write the rules and classify the patterns correctly. A sorting...
Curated OER
Introduction to Fractals: Geometric Fractals
Students study and observe the patterns made by the areas of the Sierpinski Triangle. Students use the computer to draw two or three iterations to discover the number patterns. Students complete worksheets based on Geometric Fractals.
Curated OER
Finding Patterns in Tiles
Learners explore perimeter and area of rectangles. In this rectangular lesson, students use tiles to discover the formulas for perimeter and area. Learners solve for area.
Mathematics Vision Project
Module 3: Arithmetic and Geometric Sequences
Natural human interest in patterns and algebraic study of function notation are linked in this introductory unit on the properties of sequences. Once presented with a pattern or situation, the class works through how to justify...
Curated OER
Susita's Account
Your algebra students double their money monthly in this task based on a checking account balance. Learners write an equation to model the situation and then use their model to answer contextual questions.
EngageNY
Algebraic Expressions—The Distributive Property
Do your classes truly understand the distributive property? Use a demonstrative lesson to represent the distributive property in various ways. Learners solidify understanding by creating a geometric pattern for distributive property, and...