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.
EngageNY
Recursive Challenge Problem—The Double and Add 5 Game
As a continuation of a previous lesson, this activity builds on the concept of calculating the terms of a sequence. Pupils are challenged to determine the smallest starting term to reach a set number by a set number of rounds. Notation...
Balanced Assessment
Local and Global Behavior
Create rules for numerical sequences. Pupils develop local rules and recursive rules for number sequences. The sequences are linear, quadratic, and cubic in nature. Scholars find that some local rules do not work, no matter where in 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...
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
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.
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...
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...
Curated OER
Introduction to Fractals: Infinity, Self-Similarity and Recursion.
This instructional activity introduces students to the ideas involved in understanding fractals. They develop a sense of infinity, self-similarity and recursion and
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.
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
The Mandelbrot Set
Students are introduced to the notion of a complex number and function iteration in order to motivate the discussion of Julia sets and the Mandelbrot set.
Curated OER
Introduction to Arithmetic and Geometric Sequences
Students examine the concept of sequences. Students create a sequence using varied starting numbers, multipliers, and add on values. Students practice determining the starting values to use in order to produce a desired sequence.
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...
Inside Mathematics
Hexagons
Scholars find a pattern from a geometric sequence and write the formula for extending it. The worksheet includes a table to complete plus four analysis questions. It concludes with instructional implications for the teacher.
Curated OER
Properties of Fractals
Students build a working definition of a regular fractal, they measure the concepts of dimensions and scale, they explore the concept of a logarithm and they attempt to solve simple exponential equations for the exponent both by trial...
Curated OER
Irregular Fractals
Middle schoolers study and research irregular fractals and construct a few based on their research. Students practice pattern recognition skills and plane geometry skills calculating dimensions on the Fractured Pictures activity.
Curated OER
Making Number Patterns
In this number patterns worksheet, students make number patterns for sets of rules given. Answers and a reference website are included.
Curated OER
Making Number Patterns
For this number patterns worksheet, learners 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.
Inside Mathematics
Conference Tables
Pupils analyze a pattern of conference tables to determine the number of tables needed and the number of people that can be seated for a given size. Individuals develop general formulas for the two growing number patterns and use them to...
Curated OER
Converge or Diverge?
Students prepare for the calculus concepts of limits by examining sequences that converge and diverge. By using an Excel program that generates sequences, students manipulate the starting number, multiplier and add-on values, and examine...
Curated OER
Math TODAY Challenge - New Color of Money
Students read about the changes in the "new money" and then create a graph to represent various combinations of currency produced.
Curated OER
Discovering the Linear Relationship between Celsius and Fahrenheit
Middle schoolers discover the linear relationship between degrees Farenheit and degrees Celsius. They manually compute the slope and y-intercept of the line passing through points. They convert Celsius to Fahrenheit degrees.
Curated OER
Making Number Patterns
For 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.