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Observing the relationship of number patterns over a given period of time is what allows scientists to make educated guesses, and is at the heart of making mathematical pattern analyses.
Understanding patterns will open doors for your students to understand more complex mathematical operations, but also, improve their ability to understand the world. This is why, in this article, we’ll share a number of tips on how to teach your students number sequences and patterns.
What Are Number Sequences and Patterns?
Children begin forming patterns from a very early age. For example, if you notice your child or student arranging color cubes in a repetitive pattern of blue-yellow-orange, they’re not simply engaging in meaningless child’s play, but they’re actively learning about pattern recognition.
This rule of arranging objects in a specific manner also applies to number patterns. In other words, even before you introduce the concept of number patterns and sequences to your lessons, children are likely to have acquired some knowledge about pattern recognition on their own.
A number pattern (or a number sequence) refers to a series of numbers that follow a certain rule.
For example, this is a simple number pattern that you can observe with your students: 2, 4, 6, 8, 10, 12, 14
They can easily come to the conclusion that this list of numbers follows a rule of skip counting by 2. In other words, the difference between any two consecutive numbers is 2. We have thus identified a number pattern of increasing by 2.
Why Are Number Sequences and Patterns Important?
Research indicates that a child’s understanding of patterns provides a foundation for additional types of mathematical thinking, among which:
- Geometry and many more.
This is why it is of overriding importance to make sure that your students (or children if you’re a homeschooling parent) have a solid understanding of patterns before leaping into more complex mathematical operations.
If your students are having a hard time understanding why the concept of number patterns is important, you can use draw analogies with real life.
Imagine that you can predict the future. Wouldn’t that be cool?
Well, this is what scientists are already doing nowadays. Granted, they’re unable to tell us who you’ll marry or if your child will grow to become a genius, but they are constantly doing complex predictions about what the future holds.
While they may not be using a crystal ball, their ‘clairvoyance’ often relies on another skill set – the ability to make observations about number patterns.
Let’s say a scientist would like to know how the Covid crisis will develop. One frequently-used method to make a prediction on this is to observe and analyze a series of number patterns and sequences in newly infected individuals in the previous weeks or months.
How to Learn Number Sequences and Patterns
Before starting to learn number sequences and patterns, it’s important that your student or child has mastered a few other basics. Otherwise, they might find themselves struggling with number patterns.
Review Cardinal & Ordinal Numbers
Start off by checking whether the child has a firm grasp of counting numbers and the number order. So do a few counting drills, engage in counting games, and complete various worksheets on number counting.
Make sure the child understands the difference between cardinal and ordinal numbers. In other words, check if they understand the difference between numbers denoting quantity (e.g.: 1, 2, 3) and those that represent the specific position in a given order of numbers (e.g.: 1st, 2nd, 3rd).
Build on Easier Number Patterns
It is often advisable to begin with easier number patterns. For instance, try concentrating on a few number pattern worksheets with “1 more” or “1 less” patterns. After completing those, move on to worksheets with “2 more” or “2 less”.
Then extend the pattern to “3 more” and “4 more”, and slowly move on to bigger quantities and more complex number patterns. It is important to monitor the child’s progress throughout the process and move at their pace.
Capitalize on Visualization
Traditionally, teachers tend to shy away from exploring visual patterns and place more emphasis on numerical patterns instead. And yet, the ability to visualize a pattern is essential while learning number patterns.
Therefore, it’s advisable to bring worksheets with visual patterns or even diverse manipulatives for hands-on activities. For example, you can bring green lego blocks in class. Remember to choose same-sized blocks to make it easier for the students. Arrange them in a given pattern.
Start with an easy one, like:
3 blocks, 6 blocks, 9 blocks, 12 blocks
Allow time for the students to observe the visual representation of the bocks, then explain the number pattern.
To make the lesson more fun, repeat the exercise with other objects, such as:
- Toy cars
- Colored popsicle sticks
Leave No Room for ‘I Just Know’
It’s the job of any good educator to have the students explain the thought process behind identifying a certain number pattern. Don’t accept answers like ‘I just know’. Ask the students to explain how they reached a specific conclusion.
Start by demonstrating your own thought process. For example, write a number pattern on the whiteboard, such as:
100, 87, 74, 61, 48
Now ask the students to simply observe the pattern and analyze if the numbers are increasing or decreasing in this particular sequence. State that if the numbers are decreasing, then this could be a pattern of subtracting a given number. Then you can demonstrate your thought process in the following way:
“How can I find this number?
I will try to see what the difference is between 2 consecutive numbers in the list of numbers. 100-87 = 13. Could 13 be the pattern that I am looking for? I will try to find the difference between the other numbers, 87-74 = 13.
Yes, the difference between all consecutive numbers is 13, so I can safely conclude that the pattern in this sequence of numbers is 13”.
Try to present your thinking process aloud several times so that it becomes second nature to students.
Discover the Fibonacci Sequence in Nature
If you can embark on a walk outside the classroom to discover number patterns in nature, don’t think twice – children will love the idea. This activity may be easier if you’re a homeschooling parent, but it’s certainly not impossible for school teachers.
The aim of teaching in nature is to help children understand that number patterns exist all around us, including nature. A powerful example of this is the Fibonacci Sequence, expressed as:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34…
In other words, each number is the sum of the two numbers that precede it (0+1 = 1; 1+1 = 2, etc.).
The Fibonacci Sequence is visible in many settings in nature, such as the branching in trees or the pattern in which leaves are arranged on a stem. Put on your hiking shoes and attempt to find the Fibonacci Sequence in nature together with your students!
One caveat though: don’t introduce this activity at the very beginning of the lesson, as the Fibonacci Sequence may not be so simple to understand for beginners.
Practice Skip Counting
Skip counting means counting by skipping a number in between. The important thing is to add the same number each time. The technique can be helpful for a variety of mathematical operations such as learning addition, subtraction, multiplication, and division, and can reinforce number pattern recognition.
For instance, when doing skip counting by 2s, the students will count to 10 by shouting out every other number, that is 2, 4, 6, 8, 10.
To make the activity more playful, you can turn it into a simple game. Tell your students to sit in a circle. Then shout out a random number and have students skip count by that number by going around the circle.
If the Child Is Still Struggling…
Take a break. Take a breather. Be patient. And remember, kids learn at a different pace and even the best of students can sometimes struggle when faced with a novel concept.
You may want to go back to the process of familiarizing the child with patterns. This can be done with different hands-on activities, such as:
- Classifying socks by color – if you’re a homeschooling parent, ask your child to help you sort out all the socks by color. Black ones in one pile, brown ones in another pile, and white ones in a third pile. Practising classification will help them sharpen up their analytical skills.
- Sort food by flavor – bring some peanuts, pistachios, and several types of candy. Ask the child to sort them into two categories – ‘savory food’ and ‘sweet food’. Again, you’re working on the development of analytical skills here, even though the activity is not directly focused on number patterns.
- Arranging fruits – arrange two types of fruits in a specific pattern. For example, use an ABBA pattern, banana, orange, orange, banana, orange, orange, banana, etc.
In this article, we provided an overview of the meaning of number sequences and patterns and discussed their importance. We also explored several tips that you can use in your classroom or home when teaching number sequences and patterns.
If you’d like to learn more about teaching math to children, make sure to check out our comprehensive set of math curricula, as well as our blog. You’ll find plenty of math resources for all ages that will get your students excited about learning math!
Not sure yet? Here’s a freebie of our middle school math curriculum just so you can see what we mean.