Flipped Math
Sequences
To say it explicitly—put the terms in order. Pupils learn about the two main sequences, arithmetic and geometric and discover the general explicit formulas for both types. Using the formulas, learners then calculate specific terms of the...
CK-12 Foundation
Arithmetic Series Sums: Adding Arithmetic Sums
Sum up the shortcuts. The interactive allows pupils to discover a shortcut in finding a partial sum of an arithmetic series. Learners use the shortcut to find other sums and to verify the process.
CK-12 Foundation
Arithmetic Sequences: Paying of a Loan
How long does it take to pay off a loan? Pupils use a graph to model the sequence associated with paying off a loan. Using the graph, learners determine the initial value and the common difference of the arithmetic sequence. The learners...
EngageNY
Modeling from a Sequence
Building upon previous knowledge of sequences, collaborative pairs analyze sequences to determine the type and to make predictions of future terms. The exercises build through arithmetic and geometric sequences before introducing...
EngageNY
Integer Sequences—Should You Believe in Patterns?
Help your class discover possible patterns in a sequence of numbers and then write an equation with a lesson plan that covers sequence notation and function notation. Graphs are used to represent the number patterns.
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...
Mathed Up!
Sequences
Explicitly talk to the class about sequences. A segment of a review series for the General Certificate of Secondary Education math assessment provides a review of arithmetic sequences. Pupils watch a video showing how to find terms given...
Virginia Department of Education
Arithmetic and Geometric Sequences and Series
Examine the importance of sequence and series through contextual situations. Here, learners partake in a five-day unit that begins with the basics of arithmetic and geometric sequences and series. As it progresses, pupils apply the...
Shodor Education Foundation
Sequencer
Take the first step into graphing sequences. Learners set the starting number, multiplier, add-on, and the number of steps for a sequence. Using the inputs, the interactive calculates and plots the sequence on the coordinate plane. Users...
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...
Mathematics Vision Project
Module 1: Sequences
Sequences are all about recognizing patterns. A module of 11 lessons builds pupils' understanding of sequences through pattern analysis. The practice connects the analysis to linear and exponential equations. This is the first module in...
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...
CK-12 Foundation
Sequence: The Sequence Calculator
Work through a sequence in discovering number patterns. Using the interactive, pupils explore arithmetic and geometric sequences by setting the initial value and the common difference or ratio. Learners distinguish between the two types...
CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 2)
What does it mean if young mathematicians cannot put the squeeze on a sequence? Learners investigate a divergent sequence and find the formula for the nth term. Using the definition of a limit of a sequence, pupils try to find the limit...
CK-12 Foundation
Explicit Formulas: Tiles for Writing nth Term in a Sequence
Build an explicit formula using tiles. Pupils develop a tile representation of a term within a sequence given figures of previous terms. Using the diagrams, learners develop the explicit formula by recognizing the common difference and...
Mathematics Vision Project
Module 1: Sequences
Take steps into sequences. An 11-lesson unit builds upon pupils' previous understanding of writing expressions to develop the idea of sequences. The resource explores both arithmetic and geometric sequences using recursive and explicit...
Shmoop
Building Functions Worksheet 2
If your test scores go up five points every problem you complete on this worksheet, is that an arithmetic or geometric sequence? Learners practice through four straightforward sequence questions and then finish with six word problems and...
Concord Consortium
Boards III
Learn to visualize mathematical patterns as a folded pattern. Beginning with a visual display, the task encourages pupils to view sequences as a folded table. The pattern of the table then becomes a formula in a spreadsheet that...
Concord Consortium
Boards IV
Build a connection between algebraic sequences and spreadsheets. Learners examine a specific folding pattern and convert the pattern into a spreadsheet. The goal of the spreadsheet is to produce a sequence of a specific pattern modeled...
Flipped Math
Explicit Formulas
Find a faster way to determine the 100th term of a sequence. Learners watch a video providing instruction on a way to find the nth term of a sequence—without writing down all the previous terms. Scholars create explicit formulas for...
Flipped Math
Recursive Formulas
Write formulas that depend upon previous terms. Individuals watch a video that explains how to create a recursive formula based on a sequence of numbers. Learners find out how to determine whether a sequence is geometric or arithmetic...
Shodor Education Foundation
Recursion
Perform the operation ... and then do it again. Scholars investigate recursive formulas by creating and graphing them. Using the interactive, pupils set the variable, determine the initial value, and type in a recursive formula.The...
Flipped Math
Series
Add it all together. Pupils learn how Gauss was able to add the numbers from 1 to 100 so quickly and arrive at a formula to find the sum of a given number of terms of an arithmetic series. Scholars learn the formula to find the sum for a...
Bowland
Patchwork Cushions
Find out if there are enough squares. Given diagrams for the first four figures in a sequence, pupils try to determine the next figure. Individuals find the number of square and triangle pieces of fabric that are required to make...
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