2,6,18,54 – Give a student these 4 numbers; chances are the student might be bewildered and perplexed seeing the numbers at first, they might see no correlation. But looking at the numbers closely, you might be able to derive a common ratio, that is number 3. This is what geometric sequencing is.

While this concept can be a tough nut to crack, the ultimate goal of any educator or teacher is to make it a concept that is as easy as a walk in the park. Then how do the teachers do so?

After an intriguing geometric Sequencing lecture, the teacher may have two options- give out homework assignments or make pupils’ learners indulge in the concept via games and activities. While both of these are effective, picks that ensure recreation may boost up engagement and may also ensure early feedback from instructors.

Hence, in this post, we will talk about some engaging activities that will help the children understand the concept better, by employing the same in the games and activities.

**Geometric sequence- Where factor determines succession!**

Numbers, when arranged in specific order governing a specific regulation, forms a sequence. Geometric succession is such progression, where numbers are depicted in such a way that the new number is derived by multiplying the previous number with a predetermined constant (factor).

Geometric succession has multiple real-life applications that most slip-on identifying. Say an employee has a fixed salary now, and this increases by a fixed percentage every year. The earnings after a few years can be derived today with concepts of geometric sequences. These notions can also be employed to determine the value of depreciation in a vehicle after a few years.

In 1994, J.R.Pollard^{[1]} used the concept of geometric sequence to describe multiple conductance levels of ion channels accurately. Being versed with such significant real-life applications, mastering these skills may look obligatory.

To use these skills freely and fluently later, one needs to have a proper understanding of it right from school days. To strengthen and smoothen this procedure, enticing games and activities may be employed.

**Games and activities- For practicing the geometric sequence**

Sequences may seem serene but may be taxing to calculate when the number of entries increases. For this reason, serving lectures with games and activities can oblige students with multifaceted learning.

**1. Stick it up**

Calculating geometric sequences in groups can make it facile to learn. To start with, the teacher procures sticky notes, a pen, and a ribbon. Next, the instructor opens a ribbon and places it on the ground just like a path, and sticks three sticky papers with numbers on it. Now the students are given a minute of time to see and find out the factor.

Now, a student comes and writes the next number of sequences and sticks it beside the other three. The same cycle repeats till all the students have taken their turn of estimating and sticking.

This activity may improve interest with the employment of manipulatives like sticky papers and ribbons. This activity can be performed with a single student as well.

**2. Sequence Auctions**

Auctions is the process where members of the group speak out in higher numbers to buy an entity. In this activity, the students make auctions to win rewards at the end.

To start with, the teacher procures a gift that is well-liked by students, say a Chocolate box. The instructor asks to make an auction for this box with a geometric sequence, with a certain factor. Now, the students grab the chance to reckon numbers and make calls as a try to win the reward.

The one with the largest number at the end wins the auction and the gift. For example, if the factor is 2, then the teacher says 4 to start. Then, one student raises their hand, saying 8, then the other says 16, and so on. The one with the largest number is the winner.

This activity makes sure the lesson is learned by ensuring roleplaying. Further, students may be exhilarated to win the reward.

**3. Build the Chain**

The build of a chain is unique- an arrangement of circles. Inducing the numbers of the sequence on the front side can be a fair idea.

Before starting this game, the instructor arranges a lot of paper strips, glue bottles, and markers. The student needs to build a chain of sequential numbers with these. To start with, each student is provided with 20 strips, glue, and a marker. Then, the mentor gives them a factor on which the geometric sequence is to be woven.

Students need to write the number on strips and then glue it to form a ring; next, they write another number on strip and glue it intersecting the previous ring in such a way that they form a chain. All the students start at once, and thereby the one who finishes the chain of 20 rings is the winner of the game.

This game includes tactile movement of children to accomplish, assisting all-around development and not just geometric sequence.

**4. Roll Number**^{th} Term

^{th}Term

This activity offers distinct questions to each student. First, the students are asked to note down their roll number/registration number on a sheet of paper. Now, the teacher writes four geometric sequences on the board. The learner needs to find their roll number^{th }term of the sequence.

For instance, if the roll number is 8, and the sequence is 2, 12, 72…., then here the factor is 6. Now the students calculate the 8^{th} term of the sequence by applying formal:

**A**_{n}**=AR**^{n-1}**, **here the solutions will be 2*6^{7} .

Here the answer would be 559872. This activity creates a divergent practice. Additionally, the learners can all grasp implementing formulas.

**5. Deck and Dice**

This can be a simple yet effective self-practicing pick for children. To start with, the students need to get a pack of cards and dice. To start with, the cards are well-shuffled, and one random deck is picked up. This is considered the first number of sequences. Note, the learner rolls the dice, the number that appears here is the factor. For example, if the number on the picked deck is 3 and the dice show 6, then 3 is the base, and 6 is the factor.

Now, based on these values, they can calculate and write sequences up to say ten to 15 places. Later, they can repeat this cycle to continue. This activity has a large number of combinations, thereby rigorous practice may be warranted.

**6. Key to Heaven**

A board game based on the geometric sequence can be a fair take in. In this recreation, the instructor creates a path to heaven with a few doors in between to unlock.

To start with, the mentor creates a board game on paper with start and endpoints, along with dice and task cards. The endpoint here is heaven, and the path is divided into various grids for the player to move forward in steps. The mentor also creates five doors on the way.

As the game starts, the student rolls the dice and moves forward. When they reach the door, they need to pick a task card. This card will have a sequence with a missing number in between. The player needs to find it out and fill it to open the door and move forward. The first one who reaches the endpoint (heaven) is the winner.

Board games make a good time for refreshment; mixing up learning into this evidently assists in additional practice.

**7. Sort those cups**

Sorting and sequencing can be linked up using this activity. To start, the teacher procures 20 cups and writes geometric sequences on them. Thereby, the 20 cups will have 20 numbers of the sequence. Now, the mentor keeps the first three cups in sequence and shuffles the rest, and keeps it aside. Now, they call upon to start the activity.

The learner looks and estimates the factor of the sequence and then sorts the other cups to form a geometric sequence. To add complexity, the teacher may also set a time limit for the task to complete. This activity preaches multiple notions along with sequencing like sorting and time management in estimation.

**8. Rapid Quiz Charades**

Rapid-fire, quiz, and dumb charades – three games that we all have played as kids, and loved! But how about mixing up all of these three and amalgamating them with the concept of geometric sequencing! This fun activity can be used as a classroom activity, birthday party game, or even during the activity hour.

Basically, students or children need to divide themselves into groups. Next, they need to use paper, or the blackboard and write a few numbers which have a geometric sequence. The opponent team now needs to rapidly answer what the progression is using the formula. The dumb charade concept can be used in an enticing manner where the students can whisper the numbers to one person of the opponent team rather than writing it down.

This activity can be a fun way to test the reflexes of the students, and strengthen the concept of geometric sequencing.

**Concluding thoughts **

Sequences may be a crucial part of math notions, especially for middle school students. For multiple complex concepts in higher grades, these skills may act as the foundation. Consequently, having a gripping mastery of geometric sequence and other similar progressions enhances fluency in the sphere of math.

For schoolers, who are at their best phase to learn innovatively, games and activities often turn evident as a fascinating pedagogy. Accordingly, opting for these strategies for better implementation and solving various types of problems related to it may take learners a step closer to number expertise.

**References:**

- Pollard, J. R., Arispe, N., Rojas, E., & Pollard, H. B. (1994). A geometric sequence that accurately describes allowed multiple conductance levels of ion channels: the” three-halves (3/2) rule”.
*Biophysical journal*,*67*(2), 647-655.

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,