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Math Pattern Worksheets

Working with mathematical patterns and sequences can be difficult for students. We look at various strategies students can use to solve these in our lesson and worksheet series. We start out with basic concepts and slowly progress to more difficult outlets of understanding.

Introduction (For Beginners)

What's Missing? - Using basic shapes, we find a single missing shape. Breathe in the pattern to fully comprehend what it is doing. Don't jump at the answer, let it come to you.

Complete the Shape Pattern Simple - They have to trust the pattern that is presented. You are asked to figure out what comes next in line. The worksheet assumes that everything is cyclical.

Patterns with 5s and 10s (Skip Counting) - We start very basic. Students start to understand patterns from counting sequences. We work on our 5s and 10s. A great intro to times tables and multpliying by 5 and 10.

Patterns with 20s and 100s (Skip Counting) - The sequences grow and so do the matching skills. Skip by twenties and hundreds to complete all the sequences. This is a great introduction to sequencing.

What Comes Before and After - A kindergarten worksheet. What numbers come before and after the number that you are presented with. A simple yet effective set of tasks.

What's Between Us - Fill in the missing number that fits into the sequence. This is a really nice move away from skip counting and heading towards recognizing patterns.

Missing Odds and Ends Numbers - Fill in any missing numbers in the even-odd matrix. Simple worksheet to get students set into a frame of mind that best suits their learning curve. We work with even and odd numbers in a matrix.

Intermediate Work

Patterns as a Cycle - This follows the basic national assessments you will see today. We now put you in a basic testing format and ask you to explain a repeating pattern and what it will reveal in future iterations of the pattern.

What Letter Comes Next? - Given a sequence of letters, figure out what comes next. We suggest you convert the pattern to a standard numeric code to help you understand the sequence and what comes next.

Circle the Next Picture - We move to visual pictures and see if students can make the transition. Determine the sequence that is taking place and then decide what comes next in the pattern that you are working with.

Complete the Pattern - 10 pages in total. Find the last two parts of the sequence. As the title indicates there are 10 pages. 5 pages of worksheets, 5 pages of answers. The answers explain each pattern in detail. So this can be very helpful.

Complete the Number Pattern - Fill in missing parts of the numeric sequences. They are randomly found. At first, this seems like an easy task for anyone. That is until you realize that some of these patterns are very tricky.

You Complete Me (Shuffle Patterns) - We have students determine the rule that each pattern is following.

Identify the Pattern in Numeric Form - Convert the letters to numbers and then proceed. A great introduction on how to convert patterns to something that is understandable regardless of the variable or expression that you encounter.

Pattern Based Word Problems - All are real world problems that are frequently featured on assessments. We would recommend you draw what is presented to you. At times it can be very confusing without a clearly drawn picture.

Make a Numeric Pattern - You are given shapes. Make sense of them with numbers. Convert each shape pattern to a rhythmic numeric pattern. It can make things very easy for you to use this strategy often.

Smiley Faces and Sad Faces - This one is neat! Make sense of all the crazy happy and sad faces. Can you see the patterns in the faces? This is a very unique pattern sheet. Have fun with this one!

Complete Math Sequences - Find the missing numbers in the sequence using all of your math skills. We give you mixd math sequence. Sometimes it's adding, other times it's repeated products. Figure out what numbers are missing.

Solving Division Sequences - This one focuses in on finding missing quotients. Everything here is division based. Find out what numbers are missing in each sequence.

Patterns of Sums - Each pattern is based on a sum of the numbers in the set. All the sequences are sums of the previous two integers. This makes it easy, but hard at the same time. See how you do!

Advanced Work

Continue the Pattern (Hard) - Things get a bit more tricky with this set. We use sums and differences. Take time to understand the makeup of each pattern. Then determine what the next three slots of the sequence is.

Double Missing Items (Repeater Pattern) - You will see a repeating pattern. Just figure out where it starts and ends. Find the missing shapes. We suggest you back up a bit and number the pattern first to make it much easier on yourself.

Which Item Doesn't Belong? - At first this one seems very easy, but then it really turns up the heat! We ask you to consider a group of items and which items stick out like sore thumbs. It is your basic compare and contrast with an explanation.

Multiplication Sequences - These numbers really get big. Figure out what products are missing in the this battle of multiplication.

How to Determine a Math Pattern

Some arithmetic problems are simple to solve, while others are a bit more challenging. Math patterns are a form of mathematical problem that several individuals find interesting to complete. It requires some reasoning, attention skills, and basic math skills to decipher. You can probably answer a couple of the simpler patterns in your head. If you come across a particularly challenging sequence, you may need to use pen and paper to solve it. Read on to learn how to decipher a math pattern.

Mathematical Patterns

In mathematics, a pattern is a recurring organization of numbers, forms, colors, and so forth. The pattern may be applied to any form of object or event. It is a series of integers that are connected to one another in a specified way. Patterns are also referred to as sequences and at times they can be endless.

For instance, in a math pattern, 1, 3 5, 7 …. each number is growing by a factor of two. As a result, the final number in this math sequence will be 7 + 2 = 9

Here are a few samples of numerical patterns.:

- Fibonacci numbers pattern -: 1, 1, 2, 3, 5, 8 ,13 ... - Odd numbers pattern -: 3, 5, 7, 9, 11, 13 ... - Even numbers pattern -: 2, 4, 6, 8, 10, 12 ... Numerical Patterns

Numerical patterns are a series of numbers, which adhere to a specific order. Numerical patterns can be Fibonacci patterns, geometric patterns, algebraic patterns, and so on. Let's have a look at the following distinct patterns here. Arithmetic Sequence

This algebraic pattern is another name for the arithmetic pattern. The patterns of an arithmetic sequence are formed by the addition or subtraction of numbers. If we have more than one value in the sequence, we can identify the mathematical pattern by using addition or subtraction.

For instance, we have the sequence 30, 25, 20,_, 10, _.

In this number sequence, we have to figure out the third last, and last value.

The rule employed in the pattern is "subtract 5 from the previous number to get the next number in the sequence".

By that rule, the third last value in the above-mentioned math pattern will be:

20 - 5 = 15 => third value

And the last value will be

10 - 5 = 5 => last value

Fibonacci Sequence

The Fibonacci sequence can be described as a numerical sequence where each value is formed by applying the addition operation on two values before it, beginning with the integers 0 and 1. The Fibonacci math sequence is as follows:

0, 1, 1, 2, 3, 5, 8, ...

To simplify:

3rd number = 1st number + 2nd number = 0+1 = 1

4th number = 2nd number + 3rd number= 1+1 = 2

5th number= 3rd number + 4th number = 1+2 = 3

Last number = 6th number + 7th number = 5 + 8 = 13

Geometric Sequence

The geometric sequence is described as a series of integers dependent on multiplication and division operations. If more than one integers in the sequence are available, we may quickly discover the unknown components in the sequence by multiplying or dividing the values within the sequence.

For the following geometric sequence: 3, 9, 27, ...

Each value in the series can be computed by multiplying 3 with the value before it.

Second Value = 3 x 3 = 9

Third Value = 9 x 3 = 27

Fourth Value = 27 x 3 = 81 Types of Sequences

There are three types of sequences in basic Mathematics: - Rising: If the values are in ascending order, the pattern is called a rising pattern. For instance 2, 4, 6, 8, ..

- Shirking: The pattern in which the values are in the descending order is the shrinking pattern. For instance, 10, 8, 6, 4, ...

- Repeating: A repeating sequence is a pattern where the rule repeats itself again and again.

Benefits of Solving Math Patterns

When students strive to tackle various types of pattern difficulties, they gain a multitude of health advantages. Several advantages have been discovered in numerous research on pattern-solving activities. It aids in the development of a child's vocabulary and logical reasoning.

It is highly beneficial for students when they answer various types of sequence activities and tests regularly. It not only broadens their vocabulary and knowledge but also vastly enhances their reasoning abilities. Here are some of the primary advantages of pattern recognition:

1. Inspires Educational Learning

One of the primary advantages of identifying patterns is that it improves a child's analytical reasoning, research, and cognitive skills. Dealing with puzzles like Sudoku, which are equally enjoyable, requires logical thought. As a result, it aids in stimulating learning.

2. It Keeps the Mind Healthy and Active

It exhibits the mind's ability to become involved in circumstances that need a great deal of patience, focus, and contemplation. It is also stated that if we keep our brain busy, we'll feel energetic the whole time. Furthermore, it also aids in the lowering of anxiety levels and weariness.

3. Increased Productivity

Solving math sequence questions aids in the development of critical abilities that boost productivity.

4. Increases IQ

Among the most significant advantages of solving sequence questions is that it raises an individual's IQ. Patterns undoubtedly aid in the development of memory, cognitive skills, general knowledge, and problem-solving abilities.

5. Cognitive Skills Strengthen

Answering math pattern questions improves visual performance significantly. Students' cognitive ability may be considerably improved by recognizing fundamental patterns, shapes, and colors. Math patterns also enable higher levels of thinking.

6. Enhanced Levels of Concentration

Concentration is essential for a kid's education and is also required in daily situations. Patterns need logical reasoning and, as a result, a great deal of attention and persistence. Students can only solve a pattern if they concentrate. And the long-term advantage is that it has a significant influence on attentiveness.

Wrapping Up

Solving math patterns can be fun and beneficial at the same time. They help keep students engaged and aid in the development of skills like pattern recognition, logic, critical thinking, and analytical skills that can help a student grow and prosper in the future.

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Unit 8: Arithmetic patterns and problem solving

About this unit.

Math isn't just about numbers - it's about patterns, too! In this unit, you'll figure out how to spot patterns in different types of problems and learn cool strategies to solve them. You'll tackle word problems, master estimation, and learn to write expressions like a pro.

2-step expressions

• Order of operations (2-step expressions) (Opens a modal)
• 2-step expressions Get 5 of 7 questions to level up!

Estimation word problems

• 2-step estimation word problems (Opens a modal)
• 2-step estimation word problems Get 3 of 4 questions to level up!

One and two-step word problems

• Setting up 2-step word problems (Opens a modal)
• 2-step word problem: truffles (Opens a modal)
• 2-step word problem: running (Opens a modal)
• 2-step word problem: theater (Opens a modal)
• Represent 2-step word problems with equations Get 3 of 4 questions to level up!
• 2-step word problems Get 3 of 4 questions to level up!

Patterns in arithmetic

• Finding patterns in numbers (Opens a modal)
• Recognizing number patterns (Opens a modal)
• Intro to even and odd numbers (Opens a modal)
• Patterns with multiplying even and odd numbers (Opens a modal)
• Patterns in hundreds chart (Opens a modal)
• Patterns in multiplication tables (Opens a modal)
• Arithmetic patterns and problem solving: FAQ (Opens a modal)
• Math patterns Get 5 of 7 questions to level up!
• Patterns with even and odd Get 3 of 4 questions to level up!
• Patterns in hundreds chart Get 3 of 4 questions to level up!
• Patterns in multiplication tables Get 5 of 7 questions to level up!

Patterns are sequences or arrangements that repeat in a predictable manner. They can be found in numbers , shapes , and events. Understanding patterns is important in advancing in mathematics and problem-solving.

Types of Patterns

There are different types of patterns:

• Numeric Patterns : These are patterns found in number sequences , such as 2, 4, 6, 8, 10, where each number increases by the same amount.
• Geometric Patterns : These are patterns found in shapes and designs, such as a sequence of triangles or squares .
• Repeating Patterns : These are patterns that repeat in a specific sequence, such as circle , square , triangle , circle , square , triangle .
• Function Patterns : These are patterns found in mathematical functions, where a rule or operation is applied to a number to generate the next number.

Identifying Patterns

To identify a pattern, look for repetition or a consistent rule. Here are some steps to identify patterns:

• Observe the Sequence: Look at the given sequence of numbers , shapes , or objects.
• Look for a Rule: Try to find a rule that describes how the sequence is changing or repeating.
• Predict the Next Term: Use the rule to predict the next term in the sequence.

Study Guide

To master patterns, you can follow these study guide steps:

• Practice Number Sequences : Work on solving number sequences and identifying the pattern in the sequence.
• Explore Geometric Patterns : Look for patterns in shapes and designs. Try to create your own geometric patterns .
• Work with Repeating Patterns : Create and identify repeating patterns using objects or shapes .
• Understand Function Patterns : Practice working with mathematical functions and identifying the patterns within them.
• Challenge Yourself: Solve pattern puzzles and try to predict complex patterns.

Understanding patterns is essential for higher-level math and problem-solving. By mastering patterns, you can develop strong analytical and critical thinking skills.

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Grade 5 math fun & engaging number patterns and sequences worksheets

Are you ready to explore the amazing world of number patterns and sequences? If your students are in 5th grade, they probably already know some basic facts about numbers, such as how to add, subtract, multiply, and divide them. But do they know that numbers can also form beautiful and fascinating patterns and sequences that can help them understand math better and have fun simultaneously? We’ll discover all with these Grade 5 math fun & engaging number patterns and sequences worksheets .

In this section of MathSkills4Kids, we will show you what number patterns and sequences are, how to teach them in grade 5, why they are fun and easy to learn, how to use them to solve problems and puzzles, and where to find them in nature, art, and music.

We will also give you some tips and tricks to help 5 th graders master them quickly and some activities and games to practice with their friends. And as a bonus, we will share with you some exciting number patterns and sequences resources that will boost your students’ learning and make them love math even more!

So let's get started!

What are Number Patterns?

A number pattern is a set of numbers that follows a specific rule or order. For example,

look at this number pattern: 2, 4, 6, 8, 10, ...

Can you guess what the rule is? That's right; it's adding 2 to the previous number. So the following number in the pattern would be 12, then 14, then 16, and so on.

Number patterns can also be more complex, such as: 1, 4, 7, 10, 13, 16 ...

Do you see the rule here? It's not as obvious as the previous one, but if you look closely, you will notice that the rule here is skip counting by 2 plus 1 . So the following number would be 19 (16, 18 + 1) , then 19 (19, 21 + 1) , then 22 (22, 24 + 1) , and so on.

Number patterns can help you discover exciting properties of numbers, such as divisibility rules , prime numbers , factors , multiples, and more. They can also help you make predictions and generalizations based on patterns.

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Start practice on Fifth Grade here

How to teach number patterns in grade 5.

Teaching number patterns in grade 5 can be fun and engaging using diverse methods and resources. Here are some suggestions:

• Use visual aids such as charts, tables, graphs, diagrams, or manipulatives to show how number patterns work and how they relate to other math concepts.
• Use concrete examples from real life or other subjects such as science or social studies to show how number patterns are helpful and relevant.
• Use games and puzzles such as Sudoku, magic squares, crosswords, or logic problems to challenge students to find and complete number patterns.
• Use songs or poems with number patterns like "One Potato Two Potato" or "Twinkle Twinkle Little Star" to help students remember and enjoy number patterns.
• Use calculators, computers, or apps to generate or explore number patterns.
• Use inquiry-based learning where students ask questions, make hypotheses, test their ideas, and share their findings about number patterns.
• Use cooperative learning, where students work in pairs or groups to investigate or create number patterns.

What are number sequences?

A number sequence is a list of numbers that follows a specific rule or order. For example, 1, 2, 3, 4, and 5 is a simple number sequence that follows the rule of adding 1 to the previous number.

Number sequences are similar to number patterns, but they have some differences. Number sequences usually have a starting and ending point, while number patterns can continue forever. Number sequences also have specific terms or positions, while number patterns can have any number of terms. For example,

1st term: 1

2nd term: 2

3rd term: 3

4th term: 4

5th term: 5

This is a way of describing the terms or positions of the number sequence above.

Number sequences can help you learn about arithmetic sequences (where each term is obtained by adding or subtracting a constant value), geometric sequences (where each term is obtained by multiplying or dividing by a constant value), Fibonacci sequence (where each term is the sum of the two previous terms), triangular numbers (where each term is the sum of all the natural numbers up to that term), square numbers (where each term is the square of a natural number), cube numbers (where each term is the cube of a natural number), and more.

Why number patterns and sequences are fun and easy to learn

Number patterns and sequences are fun and easy to learn because they appeal to our natural curiosity and sense of beauty. They also help us develop our logical thinking and problem-solving skills. Here are some reasons why number patterns and sequences are fun and easy to learn :

• They are everywhere . You can find number patterns and sequences in nature, such as the petals of a flower, the spirals of a shell, the spots of a leopard, or the rings of a tree. You can also find them in art, such as the symmetry of a painting, the rhythm of a song, the rhyme of a poem, or the shape of a sculpture. You can also find them in everyday life, such as the calendar, the clock, the phone number, or the license plate.

Or did you know that if you add up all the digits of any multiple of 9, you will always get 9? This is called the digital root of 9, a property of divisibility by 9.

Or you can make a sequence using your name, birthday, or hobbies. You can also use different operations or rules to make your patterns and sequences more exciting or challenging.

How to use number patterns and sequences to solve problems and puzzles

Number patterns and sequences can help you solve problems and puzzles by giving you clues, strategies, or shortcuts. Here are some ways to use number patterns and sequences to solve problems and puzzles :

• Look for patterns or sequences in the given information or answer choices . For example, if you are asked to find the next term in a sequence, you can look for a pattern or a rule that connects the given terms. Or, if you are asked to choose the correct answer from a list of options, you can look for a pattern or a sequence that matches the question.

Or, if you are asked to find how many times a specific digit appears in a large number, you can use the pattern or sequence of digits to find the answer.

• Use patterns or sequences to check your answers or find mistakes . For example, if you are asked to add or multiply two large numbers, you can use the pattern or sequence of digits to check if your answer is correct. Or, if you are asked to find a missing term in a sequence, you can use the pattern or rule to check if your answer fits.

Examples of number patterns and sequences in nature, art, and music

Number patterns and sequences are useful for math and enable us to appreciate the beauty and harmony of nature, art, and music. Here are some examples of number patterns and sequences in nature, art, and music :

The Fibonacci sequence is related to another number pattern called the golden ratio, a unique proportion that makes things look pleasing to the eye. The golden ratio is about 1.618, and you can find it in many natural shapes, such as the human face, a butterfly's wings, and the wave's curve.

Another artist who used number patterns and sequences was Piet Mondrian. He was inspired by geometry and used rectangles of different sizes and colors to create abstract paintings. He followed a rule that each rectangle had to be horizontal or vertical and that each color had to be red, yellow, blue, black, or white. He also used the golden ratio to arrange his rectangles nicely.

A typical rhythm pattern is called 4/4 time, which means that each measure has four beats, and each beat has a quarter-note value. You can count this pattern as 1-2-3-4 or clap along with it.

Another typical rhythm pattern is called 3/4 time, which means that each measure has three beats, and each beat has a quarter-note value. You can count this pattern as 1-2-3 or clap along with it. Some songs use different rhythm patterns to create variety and contrast.

As you can see, number patterns and sequences are fun, easy to learn, and excellent ways to understand and appreciate the world around us. Above all, they help us see the beauty and order in nature, art, and music.

Mathskills4kids’ Tips and tricks to master Grade 5 fun and engaging number patterns and sequences worksheets

Grade 5 students might think that number patterns and sequences are hard to learn, but they are easy and fun once you know the tricks! Here are some tips and tricks from Mathskills4kids.com that are helpful to master Grade 5 math fun and engaging number patterns and sequences worksheets :

Sometimes the rule is simple, like adding or multiplying by a constant. Other times, the rule is more complex, like using two operations or alternating between two rules. The key is to look for the pattern and figure out the rule.

They can make a table with two columns: one for the term number (n) and one for the term value (a). Then they can fill the table with the given terms and look for a pattern in the second column. They can also use a chart to plot the terms of a number pattern or sequence on a coordinate plane and see how they change as n increases.

They can also use variables and expressions to write a general formula for a number pattern or sequence, such as a(n) = 2n + 1 for the pattern 3, 5, 7, 9, ...

They can also use logic and common sense to see if their answers make sense. For example, if you find that the next term of a pattern is negative, but all the given terms are positive, you might have made a mistake.

Activities and games for 5 th graders to practice number patterns and sequences with their friends

Learning number patterns and sequences is easy, fun, and very useful. We can use them to solve problems and puzzles, create art and music, and explore nature and science. Here are some activities and games that your students can do with their friends to practice number patterns and sequences :

They can also make variations of this game by using different starting numbers or rules for generating the sequence.

Students can make a bingo game using this triangle by making cards with different numbers from Pascal's triangle. Then they can draw numbers from a hat or a bag and call them out loud. The first person who has five numbers in a row on their card wins.

Please encourage your students to challenge their friends to make their magic squares using different numbers or different sizes of grids. They can also try to find magic squares with other properties, such as being symmetric or having only prime numbers.

Bonus: Interesting number patterns and sequences resources to boost your learning

If you want to learn more about number patterns and sequences, there are many resources that you can explore online or offline. Here are some of them:

• [Math is Fun] ( https://www.mathsisfun.com/puzzles/number-sequences-solution.html ): This website explains making magic squares. It also has interactive activities and puzzles that you can try.
• [Khanacademy] ( https://www.khanacademy.org/math/arithmetic-home/arith-review-patterns ): This website has videos and exercises that teach you how to identify and extend number patterns and sequences.
• [Splashlearn] ( https://www.splashlearn.com/math/number-patterns-games-for-5th-graders ): This website has games and quizzes that test your skills on number patterns and sequences.

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

Conclusion: applying number patterns and sequences to real-life situations

Number patterns and sequences are fun to learn and useful in real-life situations. We can use them to:

• Predict future events or trends based on past data. For example, we can use number patterns and sequences to forecast the weather, the stock market, or the population growth.
• Create codes or passwords that are hard to crack. For example, we can use number patterns and sequences to make secret messages or encryption keys.
• Solve problems or puzzles that involve logic, reasoning, or creativity. For example, we can use number patterns and sequences to crack codes, find hidden clues, or make art.

Number patterns and sequences are everywhere in the world around us. They are beautiful, fascinating, and powerful. They can help us understand nature, science, art, music, and more. They can also help us improve our math skills, our thinking skills, and our problem-solving skills. They are fun and easy to learn with the right tips and tricks.

So what are you waiting for? Visit Mathskills4kids.com and download premium Grade 5 math fun & engaging number patterns and sequences worksheets and start practicing with your students today while having fun.

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Patterns Worksheets

Patterns worksheets help students develop a higher understanding of the formation of patterns and help students visualize different types of patterns. These are great resources for students as they can help students recognize different patterns and variations.

Benefits of Patterns Worksheets

Patterns worksheets help students deal with various patterns like identifying the next picture, color, size, and shape, increasing and decreasing number patterns, writing the pattern rule, and more. This worksheet comes with visuals which helps students visualize concepts and get a crystal clear understanding of the topic.

Pattern worksheets can boost the problem-solving skills of a student. These worksheets also deal with the logical and reasoning aspect of mathematics and help students in real-life scenarios as well.

Download Patterns Worksheet PDFs

With the help of a variety of questions, students will never get bored. They can easily navigate through these worksheets in an engaging manner. The stepwise approach of these worksheets helps students understand concepts better and solidify their understanding of the topic.

These pattern worksheets can be downloaded for free in PDF format.

determining pattern rules Worksheets

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Fun teaching resources & tips to help you teach math with confidence

Math Strategies: Problem Solving by Finding a Pattern

One important math concept that children begin to learn and apply in elementary school is reading and using a table. This is essential knowledge, because we encounter tables of data all the time in our everyday lives! But it’s not just important that kids can read and answer questions based on information in a table, it’s also important that they know how to create their own table and then use it to solve problems, find patterns, graph equations, and so on. And while some may think of these as two different things, I think problem solving by making a table and finding a pattern go hand in hand!

–>Pssst! Do your kids need help making sense of and solving word problems? You might like this set of editable word problem solving templates ! Use these with any grade level, for any type of word problem :

Finding Patterns in Math Problems: 

So when should kids use problem solving by finding a pattern ? Well, when the problem gives a set of data, or a pattern that is continuing and can be arranged in a table, it’s good to consider looking for the pattern and determining the “rule” of the pattern.

As I mentioned when I discussed problem solving by making a list , finding a pattern can be immensely helpful and save a lot of time when working on a word problem. Sometimes, however, a student may not recognize the pattern right away, or may get bogged down with all the details of the question.

Setting up a table and filling in the information given in the question is a great way to organize things and provide a visual so that the “rule” of the pattern can be determined. The “rule” can then be used to find the answer to the question. This removes the tedious work of completing a table, which is especially nice if a lot of computation is involved.

But a table is also great for kids who struggle with math, because it gives them a way to get to the solution even if they have a hard time finding the pattern, or aren’t confident that they are using the “rule” correctly.

Because even though using a known pattern can save you time, and eliminate the need to fill out the entire table, it’s not necessary. A student who is unsure could simply continue filling out their table until they reach the solution they’re looking for.

Helping students learn how to set up a table is also helpful because they can use it to organize information (much like making a list) even if there isn’t a pattern to be found, because it can be done in a systematic way, ensuring that nothing is left out.

If your students are just learning how to read and create tables, I would suggest having them circle their answer in the table to show that they understood the question and knew where in the table to find the answer.

If you have older students, encourage them to find a pattern in the table and explain it in words , and then also with mathematical symbols and/or an equation. This will help them form connections and increase number sense. It will also help them see how to use their “rule” or equation to solve the given question as well as make predictions about the data.

It’s also important for students to consider whether or not their pattern will continue predictably . In some instances, the pattern may look one way for the first few entries, then change, so this is important to consider as the problems get more challenging.

There are tons of examples of problems where creating a table and finding a pattern is a useful strategy, but here’s just one example for you:

Ben decides to prepare for a marathon by running ten minutes a day, six days a week. Each week, he increases his time running by two minutes per day. How many minutes will he run in week 8?

Included in the table is the week number (we’re looking at weeks 1-8), as well as the number of minutes per day and the total minutes for the week. The first step is to fill in the first couple of weeks by calculating the total time.

Once you’ve found weeks 1-3, you may see a pattern and be able to calculate the total minutes for week 8. For example, in this case, the total number of minutes increases by 12 each week, meaning in week 8 he will run for 144 minutes.

If not, however, simply continue with the table until you get to week 8, and then you will have your answer.

I think it is especially important to make it clear to students that it is perfectly acceptable to complete the entire table (or continue a given table) if they don’t see or don’t know how to use the pattern to solve the problem.

I was working with a student once and she was given a table, but was then asked a question about information not included in that table . She was able to tell me the pattern she saw, but wasn’t able to correctly use the “rule” to find the answer. I insisted that she simply extend the table until she found what she needed. Then I showed her how to use the “rule” of the pattern to get the same answer.

I hope you find this helpful! Looking for and finding patterns is such an essential part of mathematics education! If you’re looking for more ideas for exploring patterns with younger kids, check out this post for making patterns with Skittles candy .

And of course, don’t miss the other posts in this Math Problem Solving Series:

• Problem Solving by Solving an Easier Problem
• Problem Solving by Drawing a Picture
• Problem Solving by Working Backwards
• Problem Solving by Making a List

One Comment

I had so much trouble spotting patterns when I was in school. Fortunately for her, my daughter rocks at it! This technique will be helpful for her when she’s a bit older! #ThoughtfulSpot

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Pattern Problem Solving: Teach Students to Find a Pattern in Math Problems

Pattern analysis is a critical 21st century skill.

Need more tips and tricks for teaching math? You can find them in our math resources center .

Pattern problem solving

In this article, we’ll delve into the concept of pattern problem solving, a fundamental mathematical strategy that involves the identification of repeated sequences or elements to solve complex problems.

This method is instrumental in enhancing logical thinking and mathematical comprehension among students. Let's explore how this works, why it's important, and how to teach this critical skill effectively.

What is pattern problem solving? 

Pattern problem solving is a mathematical strategy in which students look for patterns in data to solve a problem. To find a pattern, students search for repeated items, numbers, or series of events.

The following problem can be solved by finding the pattern:

There are 1000 lockers in a high school with 1000 students. The first student opens all 1000 lockers; next, the second student closes lockers 2, 4, 6, 8, 10, and so on up to locker 1000; the third student changes the state (opens lockers that are closed, closes lockers that are open) of lockers 3, 6, 9, 12, 15, and so on; the fourth student changes the state of lockers 4, 8, 12, 16, and so on. This continues until every student has had a turn. How many lockers will be open at the end?

For the answer, visit  The Locker Problem from the Math Doctors

Why is pattern problem solving important? 

Pattern problem solving is an important strategy for students as it encourages them to observe and understand patterns in data, which is a critical aspect of mathematical and logical thinking.

This strategy allows students to predict future data points or behaviors based on existing patterns. It helps students understand the inherent structure of data sets and mathematical problems, making them easier to solve.

Pattern recognition also aids in the understanding of multiplication facts, for example, recognizing that 4 x 7 is the same as 7 x 4. Overall, pattern problem solving fosters analytical thinking, problem-solving skills, and a deeper understanding of mathematics.

How to teach students to find the pattern in a math problem (using an example)

In the upcoming section, we will break down the steps on how to find a pattern in a math problem effectively. We will use a practical example to illustrate each step and provide helpful teaching tips throughout the process.

The goal is to offer a clear and comprehensible guide for educators teaching students about pattern problem solving in math.

Sample question:  If you build a four-sided pyramid using basketballs and don't count the bottom as a side, how many balls will there be in a pyramid that has six layers?

Helpful teaching tip:  Use cooperative learning groups to find solutions to the above problem. Cooperative learning groups help students verbalize their thinking, brainstorm ideas, discuss options, and justify their positions. After finding a solution, each group can present it to the class, explaining how they reached their solution and why they think it is correct. Or, students can explain their solutions in writing, and the teacher can display the solutions. Then students can circulate around the room to read each group's solution.

1. Ensure students understand the problem 

Demonstrate that the first step to solving a problem is  understanding  it. This involves identifying the key pieces of information needed to find the answer. This may require students to read the problem several times or put the problem into their own words.

Sometimes you can solve a problem simply through pattern recognition, but more often you must extend the pattern to find the solution. Making a number table will help you see the pattern more clearly.

In this problem, students understand:

The top layer will have one basketball. I need to find how many balls there will be in each layer of a pyramid, from the first to the sixth. I need to find how many basketballs will be in the entire pyramid.

2. Choose a pattern problem solving strategy 

To successfully find a pattern, you need to be sure that the pattern will continue.

Have students give reasons why they think the pattern is predictable and not based on probability. Problems that are solved most easily by finding a pattern include those that ask students to extend a sequence of numbers or to make a prediction based on data.

In this problem, students may also choose to make a table or draw a picture to organize and represent their thinking.

3. Solve the problem

Start with the top layer of the pyramid, one basketball. Determine how many balls must be under that ball to make the next layer or a pyramid. Let students use manipulatives if needed— they can use manipulatives of any kind, from coins to cubes to golf balls. Let students also draw pictures to help solve the problem, if needed.

If your students are in groups, you may want to have each group use a different manipulative and then compare their solutions. This will help you understand if different manipulatives affect the solution.

Helpful teaching tip:  If students are younger, solve this problem with only three layers.

If it helps to visualize the pyramid, use manipulatives to create the third layer. Record the number and look for a pattern. The second layer adds 3 basketballs and the next adds 5 basketballs. Each time you add a new layer, the number of basketballs needed to create that layer increases by 2.

1 1 + 3 = 4 4 + 5 = 9

Continue until six layers are recorded. Once a pattern is found, students might not need to use manipulatives. 9 + 7 = 16

16 + 9 = 25 25 + 11 = 36

Then add the basketballs used to make all six layers.

The answer is 91 balls .

Look at the list to see if there is another pattern. The number of balls used in each level is the square of the layer number.  So the 10th layer would have 10 x 10 = 100 balls .

4. Check your students' answers

Read the problem again to be sure the question was answered:

Yes, I found the total number of basketballs in the six-layer pyramid.

Also check the math to be sure it’s correct:

1 + 4 + 9 + 16 + 25 +36 = 91

Determine if the best strategy was chosen for this problem, or if there was another way to solve the problem:

Finding a pattern was a good way to solve this problem because the pattern was predictable.

5. Explain 

Students should be able to explain the process they went through to find their answers. Students must be able to talk or write about their thinking. Demonstrate how to write a paragraph describing the steps they took and the decisions they made throughout.

I started with the first layer. I used blocks to make the pyramid and made a list of the number of blocks I used. Then I created a table to record the number of balls in each layer. I made four layers, then saw a pattern. I saw that or each layer, the number of balls used was the number of the layer multiplied by itself. I finished the pattern without the blocks, by multiplying the number of balls that would be in layers 5 and 6. Then I added up each layer. 1 + 4 + 9 + 16 + 25 +36 = 91. I got a total of 91 basketballs

How can you stretch this pattern problem solving strategy? 

Math problems can be simple, with few criteria needed to solve them, or they can be multidimensional, requiring charts or tables to organize students' thinking and to record patterns.

In using patterns, it is important for students to find out if the pattern will continue predictably. Have students determine if there is a reason for the pattern to continue, and be sure students use logic when finding patterns to solve problems.

• For example, if it rains on Sunday, snows on Monday, rains on Tuesday, and snows on Wednesday, will it rain on Thursday?
• Another example: If Lauren won the first and third game of chess, and Walter won the second and fourth game, who will win the fifth game?
• Another example: If a plant grew 13 centimeters in the first week and 10 centimeters in the second week, how many centimeters will it grow in the third week?

Because these are questions of probability or nature, be sure students understand why patterns can't be used to find these answers.

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Problem Solving Worksheets

Customize problem solving worksheets.

What is Problem Solving?

It is the cognitive process of identifying, analyzing, and finding solutions to challenges or issues. It involves using logical and creative thinking to address obstacles that occur, make decisions, and achieve goals. Consider the five problem-solving steps: identifying the problem, generating possible solutions, evaluating options, selecting the best solution, and implementing it. Understanding the steps is crucial for navigating complex challenges with clarity and efficiency.

What are Problem Solving Worksheets?

These worksheets are structured in such a way that encourages solution-based thinking. Engaging in interactive problem-solving activities can help develop critical thinking skills and creative approaches to overcoming obstacles. While these skills are used in a variety of aspects of life, our worksheets focus on problem solving in mathematics. Printable worksheets provide practice for any child who is learning to master new skills they are taught in class. They are perfect for any level, and can be applied to any type of mathematical problem or unit of study.

Why are They Important and How are They Best Used?

They are great for ensuring that students practice what they have yet to master, since they can be customized by the teacher to meet the class and individual needs. They can be used to practice all kinds of word problems involving addition, subtraction, multiplication, division, and so much more.

In a world where challenges are inevitable, the ability to tackle problems effectively is a valuable skill that can be applied across all subjects and age groups. Problem-solving skills are the generator of success. They empower individuals to navigate complex situations, identify triggers, and develop plans to overcome obstacles. From the classroom to the boardroom, these skills are in high demand.

Tailoring Problem-Solving Worksheets for Different Subjects

Mathematics.

Math problem-solving worksheets can be a playground for nurturing critical thinking. Through word problem worksheets, students not only practice calculations but also apply math concepts to real-world scenarios.

Scientific problem-solving worksheets ignite curiosity. They prompt students to hypothesize, design experiments, collect data, and draw conclusions, fostering a scientific mindset.

Language Arts

Language skills and critical thinking intertwine in language arts problem-solving worksheets. Analyzing literature, engaging in creative writing prompts, and correcting grammar offer a holistic approach.

Social Studies

History comes to life through problem-solving worksheets. Encourage students to ponder over historical dilemmas and global challenges, nurturing their ability to think beyond the surface.

Math Worksheet Activity Ideas

• "Math Detective" Challenge: Create a set of worksheets featuring a fictional mystery storyline. Each worksheet presents a clue that requires students to solve a math problem to unveil the next piece of the puzzle. This engaging activity encourages critical and sequential thinking.
• "Math Menu" Project: Design a menu-style worksheet with various math problems categorized by difficulty levels. Allow students to choose a certain number of problems from each category to complete, giving them autonomy and catering to their individual skill levels.
• "Design Your Dream House" Activity: Provide a worksheet that guides students through designing their dream house layout. They need to calculate room dimensions, total area, and even budget constraints. This hands-on activity integrates math into real-life scenarios.
• "Math Art Gallery" Exhibition: Assign each student a famous artwork and create a worksheet that involves geometric calculations related to the art's dimensions and shapes. Students can then present their findings in a "Math Art Gallery" exhibition.
• "Math in the News" Analysis: Collect recent news articles that involve math-related concepts, such as statistics, percentages, or data analysis. Provide worksheets that require students to analyze the math behind the news and discuss its implications.
• "Budgeting for Vacation" Project: Design a project-based worksheet where students plan a vacation, considering expenses like transportation, accommodations, and activities. They must budget and calculate costs while staying within a specified budget.
• "Math Around the World" Exploration: Create a worksheet that presents math problems related to different countries' cultures, currencies, and measurements. Students solve problems like converting currencies or calculating time zone differences.
• "Mathopoly" Board Game: Design a problem-solving board game where players move through spaces by solving math problems. This interactive approach adds an element of fun while reinforcing math skills.
• "Math Olympiad Simulation" Practice: Prepare a set of challenging math problems similar to those in Math Olympiad competitions. Have students work on these problems individually or in teams to sharpen their skills.
• "Math Interview" Project: Assign each student a famous mathematician or scientist and provide a worksheet that guides them to research and create interview-style questions. This encourages exploration of math history and its relevance.
• "Math Escape Room" Challenge: Develop a series of interconnected math problems that lead students through a virtual "escape room." They must solve each problem correctly to advance to the next step and eventually "escape."
• "Data Analysis Report" Assignment: Provide students with a dataset related to a topic of interest, such as sports statistics or environmental data. They must analyze the data, create graphs, and present their findings in a structured report.
• "Math and Music Fusion" Project: Combine math with music by providing a worksheet that explores concepts like rhythm, frequency, and ratios in music. Students can calculate beats per minute, analyze musical patterns, and even compose their own melodies.
• "Math Recipe Creation" Challenge: Ask students to create a new recipe by adjusting ingredient quantities based on serving sizes. They must calculate ratios, proportions, and conversions to ensure the recipe's success.

Designing Effective Problem-Solving Worksheets

Creating successful problem-solving worksheets involves careful planning. Here are some ideas to consider:

• Define the Learning Objective: Clarify the specific mathematical concept you want to reinforce with the worksheet. Outline the steps involved and determine how this worksheet will contribute to improving their skills.
• Select a Problem Type: Choose a math problem type that aligns with the learning objective. It could involve algebraic equations, geometry calculations, or even practical scenarios related to everyday life.
• Structure the Steps: Break down the problem-solving process into logical steps. Ensure that each step reflects the problem solving steps you want students to follow, such as understanding the problem, planning, solving, and verifying.
• Incorporate Interactive Elements: Integrate interactive elements like multiple-choice questions, fill-in-the-blanks, or even drawing areas to encourage problem solving exercises within the worksheet.
• Utilize Graphic Organizers: Introduce a visual problem solving graphic organizer to help students map out their thinking. This can include spaces for writing down given information, variables, and equations.
• Provide a Problem Solving Template: Offer a structured template that guides students through the problem-solving process. Include prompts and placeholders for each step to provide clear direction.
• Encourage Exploration: Inspire students to explore different types of techniques to arrive at solutions. Encourage them to think critically and try various strategies before settling on an approach.

By incorporating these elements, you can create a comprehensive problem solving worksheet for kids that not only teaches mathematical concepts but also equips them with transferable skills. Whether you're focusing on basic arithmetic or more advanced mathematical principles, this approach ensures an engaging and educational experience for young learners.

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How to Make a Problem Solving Worksheet

Choose one of the premade templates.

We have lots of templates to choose from. Take a look at our example for inspiration!

Click on “Copy Template”

Once you do this, you will be directed to the storyboard creator.

Give Your Worksheet a Name!

Be sure to call it something related to the topic so that you can easily find it in the future.

Edit Your Worksheet

This is where you will include directions, specific images, and make any aesthetic changes that you would like. The options are endless!

Click "Save and Exit"

When you are finished, click this button in the lower right hand corner to exit your storyboard.

From here you can print, download as a PDF, attach it to an assignment and use it digitally, and more!

Happy Creating!

Frequently Asked Questions About Problem Solving Worksheets

How can math problem-solving worksheets show students how to improve problem-solving skills.

They provide structured exercises that guide students through real-world scenarios. By actively engaging in these worksheets and activities, children can practice the problem solving process, enhancing their critical thinking and logical reasoning abilities.

What strategies can I use to teach problem-solving skills using math worksheets?

Incorporate helpful math problem solving worksheets for kids into your lessons. Support and encourage students to work through the problem-solving steps: understanding the problem, devising strategies, making calculations, and verifying their solutions. Provide examples, guidance, and feedback to nurture their problem-solving skills.

How can I ensure that students grasp the problem-solving process effectively?

Provide clear instructions in your math problem-solving worksheets that guide students through each step of the process. Offer examples and encourage them to discuss their approaches. By nurturing a supportive and collaborative environment, you can help both younger kids and older kids build confidence in their problem solving skills.

What are specific examples of how to teach problem-solving skills in math using pre-answered solution worksheets?

Teaching problem-solving skills in math using pre-answered solution worksheets can be exemplified through scenarios like quadratic equations. Present the class with a quadratic equation and a pre-answered solution that breaks down the steps of factoring or using the quadratic formula. This guides them to understand the process, identify key components, and apply appropriate methods. Similarly, for geometry, offer a challenging problem involving angles or area calculations, along with a pre-answered solution that demonstrates the application of relevant geometric principles. As students work through the problem and compare their reasoning with the pre-answered solution, they grasp problem-solving strategies, logical sequences, and the importance of meticulous calculations. In both cases, these worksheets instill confidence, reinforce systematic approaches, and enhance students' problem-solving skills while navigating mathematical complexities.

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Solving word problems using patterns

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SOLVING PROBLEMS WITH PATTERNS

Example 1 :

For the following matchstick pattern, find the number of matches M required to make the 

(a) 8 th figure

(b) n th figure

By observing the figures

Number of matchstick in the 1 st figure = 4.

Number of matchstick in the 2 nd figure = 10.

Number of matchstick in the 3 rd  figure = 16.

Number of matchsticks in every figure is 2 less than the multiple of 6.

So, creating formula for this

number of matchstick in n th figure = 6n - 2

(a) using the formula

Number of match sticks in 8th figure :

(b) Number of matchstick in n th figure = 6n - 2.

Example 2 :

Consider the pattern :

S 1  = 1/(1×2)

S 2  = 1/(1×2) + 1/(2×3)

S 3  = 1/(1×2) + 1/(2×3) + 1/(3×4)

.....................

a) Find the values of S 1 , S 2 , S 3 , and S 4

b) write down the value of :

(i) S 10   (ii) S n

S 1  = 1/(1 x 2) = 1/2

S 2  = 1/(1 x 2) + 1/(2 x 3) = 1/2 + 1/6 = 4/6 = 2/3

S 3  = 1/(1x2) + 1/(2x3) + 1/(3x4)

= 1/2 + 1/6 + 1/12

= (6 + 2 + 1)/12

Observing the results it is in the form n/(n + 1)

S n  = n/(n + 1)

(where n is natural number)

(a)  

(b) (i)  If n = 10,

S 10  = 10/(10 + 1)

S 10  =  10/11

(ii)  S n  = n/(n + 1)

Example 3 :

S 1  = 1 2

 S 2  = 1 2 + 2 2

 S 2  = 1 2 + 2 2 + 3 2 , …………

a) Check that the formula

S n  = [n(n + 1)(2n + 1)]/6

is correct for n = 1, 2, 3 and 4.

b) Assuming the formula in a is always true, find the sum of

1 2  + 2 2  + 3 2  + 4 2  + 5 2 + ………… + 100 2  

which is the sum of the squares of the first one hundred integers.

(a) W hen n  =  1,

S 1  = 1(1 + 1)(2 + 1)]/6

S 1  = 1

It can be written as 1 2 .

When n = 2,

S 2  = [2(2 + 1)(4 + 1)]/6

S 2  = 5

It can be written as 1 2 + 2 2 .

When n = 3,

S 3  = [3(3 + 1)(6 + 1)]/6

S 2  = 84

It can be written as 1 2 + 2 2 + 3 2 .

Hence its verified.

(ii) Given :

1 2  + 2 2  + 3 2  + 4 2  + 5 2  + ………… + 100 2  

Here, n = 100.

S 100  = [100(100 + 1)(200 + 1)]/6

S 100  = 338350

Example 4 :

N 1  = 1 3  

N 2  = 1 3 + 2 3

 N 3  = 1 3 + 2 3 + 3 3 , …………

a) Verify that the formula

N n  = [n 2 (n + 1) 2 ] /4

is correct for n = 1, 2, 3 and 4

b) Use the above formula to find the sum of

1 3  + 2 3  + 3 3  + 4 3  + ………… + 50 3

c) Find the sum : 2 3  + 4 3  + 6 3  + 8 3  + ………… + 100 3

(a) W hen n = 1,

N n  = [n 2 (n + 1) 2 ]/4

N 1  = [1 2 (1 + 1) 2 ]/4

N 1  = 1

It can be written as 1 3 .

N 2  = [2 2 (2 + 1) 2 ]/4

N 2  = 9

It can be written as 1 3 + 2 3 .

N 3  = [3 2 (3 + 1) 2 ] /4

N 3  = 36

It can be written as 1 3 + 2 3 + 3 3 .

Hence, its verified.

(b)  1 3  + 2 3  + 3 3  + 4 3  + ………… + 50 3

here, n = 50.

S n  = n 2 (n + 1) 2 ] /4

S 50  = (50) 2 (50 + 1) 2 ] /4

S 50  = 1625625

c) 2 3  + 4 3  + 6 3  + 8 3  + ………… + 100 3

Factoring 2 3  from the series.

=  2 3 (1 3 + 2 3 + 3 3 + 4 3 + ………… + 50 3 )

= 2 3 (1625625)

= 8(1625625)

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