pattern problem solving grade 5

• 5th Grade Math
• Number patterns & sequences

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 Questions

Patterns questions and answers are given here to help students understand how to solve patterns questions using simple techniques. Solving different pattern questions will be beneficial for a quick understanding of the logic in patterns. In this article, you will learn how to solve patterns in maths with detailed explanations.

What are Patterns in Mathematics?

In mathematics, a pattern is a sequence of numbers that are formed in a particular way. Every pattern contains a specific rule. For example, the sequence of even numbers is a pattern since each number is obtained by adding 2 to the previous number.

i.e., 2, 4, 6, 8, 10, 12, 14,….

Here, 2 + 2 = 4

8 + 2 = 10 and so on.

Also, check:

• Number patterns in Whole numbers
• Algebra as pattern

A pattern can be of numbers or figures, which means we can also observe patterns in a sequence of similar figures. Let’s have a look at the solved problems on the various number and figure patterns.

Patterns Questions and Answers

1. Identify the pattern for the following sequence and find the next number.

2, 3, 5, 8, 12, 17, 23, ____.

2, 3, 5, 8, 12, 17, 23, ____

The pattern involved in the given sequence is:

12 + 5 = 17

17 + 6 = 23

23 + 7 = 30

Therefore, the next number of the given sequence is 30.

2. Observe the below figure and identify the missing part.

Consider the question figure, where the design in each part will be obtained by rotating the previous design by 90 degrees in the clockwise direction.

So, the missing part will be option (b).

Hence, the complete figure is:

3. Write the next three numbers of the following sequence.

173, 155, 137, 119, 101

The pattern in the given sequence is:

173 – 18 = 155

155 – 18 = 137

137 – 18 = 119

119 – 18 = 101

So, the next three numbers can be written as:

101 – 18 = 83

83 – 18 = 65

65 – 18 = 47

Thus, the sequence is 173, 155, 137, 119, 101, 83, 65, 47.

4. Observe the following figure and choose the correct option.

Each part of the square box contains a triangle inscribed in the circle in the given figure. Also, the triangle in the next circle is the vertical image of the previous one.

Similarly, in the second row, the triangle in the missing part will be an image of the previous one.

Thus, the missing part is option (a).

5. What is the formula for the pattern for this sequence?

11, 21, 31, 41, 51, 61, 71

The numbers in this sequence are written as:

11 + 10 = 21, 21 + 10 = 31, 31 + 10 = 41, and so on.

This can also be expressed as:

11 = 10 + 1 = 10 × 1 + 1

21 = 20 + 1 = 10 × 2 + 1

31 = 30 + 1 = 10 × 3 + 1

41 = 40 + 1 = 10 × 4 + 1 and so on.

From this, we can write the formula for the above pattern as: 10n + 1, where n = 1, 2, 3, etc.

6. Find the pattern in the sequence and write the next two numbers.

10, 17, 36, 73, 134,…

Given sequence is:

10 = 1 3 + 9

17 = 2 3 + 9

36 = 3 3 + 9

73 = 4 3 + 9

134 = 5 3 + 9

So, the next number = 6 3 + 9 = 216 + 9 = 225

Again, the next number = 7 3 + 9 = 343 + 9 = 352

Therefore, the sequence is:

10, 17, 36, 73, 134, 225, 352.

7. Observe the pattern given below. Find the missing number.

In the given figure, we can observe that the sum of the four numbers is equal to the number written in the middle of the shape.

That means,

11 + 22 + 33 + 44 = 110

16 + 24 + 32 + 40 = 112

? + 23 + 34 + 12 = 114

? = 114 – 23 – 34 – 12 = 45

Therefore, the missing number is 45.

8. What is the next number of the following sequence?

20, 18, 21, 16, 23, 12, 25, 8, 27, 4, 33, ?

Given sequence:

20, 18, 21, 16, 23, 12, 25, 8, 27, 4, 33

Let us find the difference between two consecutive numbers of the sequence to identify the pattern.

18 – 20 = -2

21 – 18 = 3

16 – 21 = -5

23 – 16 = 7

12 – 23 = -11

25 – 12 = 13

8 – 25 = -17

27 – 8 = 19

4 – 27 = -23

33 – 4 = 29

Here, we can see that the differences are the prime numbers.

So, the number number = 33 – 31 = 2

9. Estimate the next number of the following sequence.

1, 2, 6, 15, 31, ?

Let’s write the difference between consecutive numbers.

2 – 1 = 1

6 – 2 = 4

15 – 6 = 9

31 – 15 = 16

Here, 1 = 1 2 , 4 = 2 2 , 9 = 3 2 , 16 = 4 2 .

Thus, the next number of the sequence will be obtained by adding 5 2 , i.e. 25, to the previous number.

Therefore, 31 + 5 2 = 31 + 25 = 56.

10. What will be the next number of the given sequence?

1, 5, 12, 22, 35, ?

Let’s write the difference between consecutive numbers.

5 – 1 = 4

12 – 5 = 7

22 – 12 = 10

35 – 22 = 13

The difference between these numbers follows a pattern that 3 is odd to the previous difference.

So, the next number will be obtained by adding 13 + 3, i.e. 16 to 35.

Hence, the next number = 35 + 16 = 51.

Practice Problems on Patterns

• Find the correct number to complete the pattern given below.

20, 21, 23, 26, 30, 35, 41, ___.

• Find the next number in the sequence, 12, 21, 23, 32, 34, 43.
• Write the missing numbers in the following.

60

54

x

42

36

30

y

18

12

6

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5th Grade Pattern Worksheets

In 5th grade Pattern worksheet, students can practice the questions on shapes and patterns. The questions are based on progressive patterns, number patterns, triangular numbers patterns, square numbers patterns.

I. Complete the given pattern:

(i) 5, 20, 10, 30, 15, 40, ……., ……., …….

(ii) 1, 3, 5, 7, 11, ……., ……., …….

(iii) 5, 8, 11, 14, 17, ……., ……., …….

(iv) 6, 95, 7, 90, 8, 85, ……., ……., …….

(v) 1, 5, 25, 125, ……., ……., …….

(vi) 800, 400, 200, 100, ……., ……., …….

(vii) 2, 6, 18, 54, ……., ……., …….

(viii) 1, 4, 9, 16, 25, ……., ……., …….

(ix) 99999, 9999, 999, ……., …….

(x) A, Z, BB, YY, CCC, ……., ……., …….

II. Draw the next figure to complete the pattern:

III. Complete the given Sudoko:

IV.  Complete the given Sudoko:

I. (i) 20, 50, 25

(ii) 13, 17, 19

(iii) 20, 23, 26

(iv) 9, 80, 10

(v) 625, 3125, 15625

(vi) 50, 25, 12.5

(vii) 162, 486, 1458

(viii) 36, 49, 64

(x) XXX, DDDD, WWWW

Math Patterns  

Math Homework Sheets   From 5th Grade Pattern Worksheets to HOME PAGE

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Number patterns

Here you will learn about number patterns, including how to find and extend rules for sequences, input/output tables and shape patterns.

Students will first learn about number patterns as part of operations and algebraic thinking in 4th and 5th grade. They continue to build on this knowledge in middle school and high school.

What are number patterns?

Number patterns are groups of numbers that follow rules. They can use input/output tables to create sequences .

Two types of sequences are arithmetic and geometric .

• An arithmetic sequence is a list of numbers where the same amount is either being added or subtracted every time.

Each sequence has a starting number, a rule and terms (the numbers that make up the sequence).

For example,

Rule: Subtract 6 each time.

There are also patterns, between the terms of two or more arithmetic sequences.

Both sequences start at 0. If you multiply the left column by 3, you get the terms in the right column.

This is because using the rule +9 is three times more than the rule +3.

Step-by-step guide:   Arithmetic sequence

• A geometric sequence is a number pattern where the rule is multiplication or division.

Rule: Multiply the previous term by 5.

Rule: Divide the previous term by 3.

Step-by-step guide:   Geometric sequence formula

Step-by-step guide:   Sequences

This page will highlight rules that involve whole numbers only.

[FREE] Number Patterns Worksheet (Grade 4 to 5)

Use this quiz to assess your grade 4 to 5 students’ understanding of number patterns. 10+ questions with answers on 4th and 5th grade number pattern topics to identify areas of strength and support!

• Input/output tables are tables that are used to show two sets of numbers that are related by a rule. The rule can be one step or multi-step, but has to work for each relationship shown in the table.

What is the rule for the table below?

To find the rule, look for the relationship between the input and the corresponding output.

Notice, 11 is being added to each input to get the output, so the rule is ‘add 11. ’

Step-by-step guide: Input/output tables

As students learn to work with number patterns, they can learn more about generalizing patterns by working with shape patterns.

• Shape patterns are any set of polygons, 3D shapes, letters or symbols that follow non-operational rules. There are repeating shape patterns and growing shape patterns .

A repeating pattern has a core that repeats over and over again.

The core of the pattern above is:

The core can be used to extend the pattern.

The next shape in the pattern would be:

because the last part of the core shown is:

• A growing pattern has parts that stay the same, but other parts that change.

• Changing – the left column starts with 0 and increases by 2.
• Staying the same – the 1 cube on the top right.

Step-by-step guide: Shape patterns

Common Core State Standards

How does this relate to 4th grade math and 5th grade math?

• Grade 4 – Operations and Algebraic Thinking (4.OA.C.5) Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3 ” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
• Grade 5 – Operations and Algebraic Thinking (5.OA.B.3) Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3 ” and the starting number 0, and given the rule “Add 6 ” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

How to use number patterns

There are a lot of ways to use number patterns. For more specific step-by-step guides, check out the pages linked in the “What are number patterns?” section above or read through the examples below.

Number patterns examples

Example 1: geometric sequence.

What are the next three terms in the pattern?

3, 6, 12, 24, 48…

Identify the rule.

Rule: Multiply the previous term by 2.

2 Use the rule to extend the pattern.

Multiply the last term by 2 to extend the pattern to the next three terms.

3 State and explain any patterns within the terms.

Except for the first term, all the terms are even.

The first term is odd, but multiplying it by 2 (even), makes the next term even.

From then on it is always an even term times 2 \rightarrow \text { even } \times \text { even }=\text { even }.

Example 2: compare arithmetic sequences

Compare the following sequences:

0, 2, 4, 6, 8… \, and \, 0, 12, 24, 36, 48…

Identify the rule of each sequence.

Find a pattern between the related terms of each sequence.

Look at the related terms for each sequence. What do you notice?

Both sequences start at 0. If you multiply the left column by 6, you get the terms in the right column.

Use the pattern to write a comparison statement.

The terms in the second sequence are 6 times the terms in the first sequence.

This is because using the rule +12 is six times more than using the rule +2.

Example 3: input/output table – identify the rule

What is the rule for the table?

Look at the relationship between the input and the corresponding output.

Looking from each input to output, see if you notice an obvious relationship. If not, use subtraction to find the difference between each input and the corresponding output.

Decide if the rule is add/subtract or multiply/divide.

Each output is 27 more than the input, so the rule is addition.

Write the rule.

Rule: Add 27 to the input.

Example 4: input/output table – find a missing value

Find the missing value in the table.

From each input to output, the difference is not the same, so the rule is not addition or subtraction.

Try to find a relationship that involves multiplying or dividing. Since the relationship from input to output is decreasing, try division.

Rule: Divide the input by 7.

*Note, the rule ‘Multiply the input by \, \cfrac{1}{7} \, ’ is also correct.

Use the rule to find the missing value(s).

70 \div 7=10

The missing value in the table is 10.

Example 5: 3D shape pattern, repeating

Create a rule for the pattern and find the next shape.

Identify the core – the part of the pattern that repeats.

This is a repeating pattern with cubes that go purple, purple, orange, purple, red, purple.

Notice that purple is repeated multiple times within the core. Always look at all the shapes given to confirm the pattern core.

Use the core to find and justify the next part in the pattern.

The next shape is:

Example 6: shape pattern, growing

Identify what is changing and what is staying the same.

• Changing – 0 triangles on the top and left side, 1 triangle on top and left side, 2 triangles on top and left side, 3 triangles on top and left side.
• Staying the same – The first triangle at the bottom is always there.

Create a rule based on Step 1.

Start with 1 triangle. Add 1 triangle to the top and 1 triangle to the left side each time.

Use the rule to find and justify the next part in the pattern.

The next part in the pattern is:

because 1 triangle is added to the top and 1 triangle is added to the side each time.

Teaching tips for number patterns

• There are many printable number patterns worksheets that can be used, but also give students the opportunity to create their own patterns. Then let their classmates find the rules and extend them. This helps keep students interested and deepens their understanding of patterns by challenging them to create and giving them opportunities to engage in discourse around patterns.
• Support students who are not yet confident in all operations by providing useful tools such as number lines, hundreds boards or counters. Completing calculations should not be a burden when working with patterns.
• Focusing on justifying pattern rules is as important as identifying them. Justification is not only a necessary mathematical practice, but doing it can teach students how to write better rules. Thinking about why a rule works, draws attention to the general parts of a pattern – how they are changing or staying the same, which is the basis of a valid mathematical generalization.

Easy mistakes to make

• Making an operational error Since finding the rule and extending the pattern require a calculation, this leaves room for mistakes to be made. Always double check your work and take time to think about if your answers are reasonable.
• Thinking there is only one way to write a growing shape pattern rule Often there is more than one way to describe what is changing and what is staying the same in a growing shape pattern. Encourage students to look for more than one way to describe their rule, as this is a helpful stepping stone to equivalent expressions.

Practice number patterns questions

1. What is the next number in the pattern?

4, 20, 100, 500, 2,500…

Multiply the last term by 5 to extend the pattern.

2. Starting number: 68

Rule: subtract 6 each time.

Which statement is true about the terms of the sequence described above?

All the terms are even

All the terms are odd

The terms alternate between even and odd

The first term is even and the rest are odd

Extend the sequence based on the starting number and the rule.

Since 6 (even number) is being subtracted each time, and even – even = even, all the terms are even.

3. What is the rule for the table?

Add 20 to the input

Multiply the input by 6

Multiply the input by 8

Add 25 to the input

Looking from each input to output, see if you notice an obvious relationship.

If not, use subtraction to find the difference between each input and the corresponding output.

Try to find a relationship that involves multiplying or dividing.

Since the relationship from input to output is increasing, try multiplication.

Rule: Multiply the input by 6.

4. Find the missing value in the table.

Each output is 12 less than the input, so the rule is subtraction.

Rule: Subtract 12 from the input.

Since the input is missing, thinking about what number subtracted by 12 will equal 83 :

The missing value in the table is 95.

5. What is the next shape in the pattern?

This pattern goes e, c, S, 8, o, e, 8 and then repeats.

6. What is the next part in the pattern?

Identify what is changing and what is staying the same:

• Changing – one purple in the middle and one green on either side, two purple in the middle and two green on either side, three purple in the middle and three green on either side.
• Staying the same – There is always a purple x with a green x beside it and below it at the top.

Rule: Start with a purple x with a green x to the right and below it. Repeat, adding the 1 st term again, but to the left and down one .

because it adds the first term again, but to the left and down one (shown in purple outline).

Number patterns FAQs

No, since students are most familiar with whole number operations, the standards start with these numbers. However, in middle school, sequences grow to include integers and other types of rational numbers. This also continues in later grades to include sequences with complex numbers.

Fibonacci’s sequence (or fibonacci numbers) and triangular numbers (pascal’s triangle) are two sequences that are commonly explored in upper level mathematics. Step-by-step guide : Triangular numbers (coming soon)

While shape patterns do not typically include fractions or decimals, they could be used in a way that does not involve calculations (for example in the repeating pattern \, \cfrac{1}{5} \, , \, \cfrac{1}{8} \, , \, \cfrac{1}{5} \, , \, \cfrac{1}{8} \, , \, \cfrac{1}{5} \, , \, \cfrac{1}{8} \, … ).

Yes, there are sequences that involve square numbers, cube numbers, and other more complex operations.

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Free Printable Number Patterns Worksheets for 5th Grade

Math Number Patterns: Discover a vast collection of free printable worksheets for Grade 5 students, designed to help them explore, understand, and master the intriguing world of number patterns in mathematics.

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Number Patterns worksheets for Grade 5 are an excellent resource for teachers looking to enhance their students' understanding of Math and Number Sense. These worksheets provide a variety of engaging activities and exercises that help students recognize, analyze, and predict number patterns. By incorporating these worksheets into their lesson plans, teachers can effectively develop their students' critical thinking and problem-solving skills. Furthermore, these worksheets are designed to align with Grade 5 curriculum standards, ensuring that students are receiving age-appropriate content that supports their academic growth. With Number Patterns worksheets for Grade 5, teachers can create a dynamic and interactive learning environment that fosters a strong foundation in Math and Number Sense.

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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 Number Patterns Quiz

Grade 5 questions on number patterns are presented along with their detailed Solutions

Number Pattern Worksheets 5th Grade

Number pattern worksheets 5th grade 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 5th Grade Number Pattern Worksheets

Number pattern worksheets 5th grade help students deal with various patterns like identifying the next picture, color, size, shape, increasing and decreasing number patterns, writing the pattern rule, etc. This worksheet comes with visuals which helps students visualize concepts and get a crystal clear understanding of the topic. With the help of a variety of questions, students can never get bored thus they can easily navigate through these worksheets in an engaging manner. The stepwise approach of these 5th grade math worksheets helps students understand concepts better and solidify their understanding of the topic.

Printable PDFs for Grade 5 Number Pattern Worksheets

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

Pattern analysis is a critical 21st century skill.

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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 (top)	1	1
2	3	4 (1 + 3 = 4)
3	5	9 (4 + 5 = 9)
4	7	16 (9 + 7 = 16)
5	9	25 (16 + 9 = 25)
6	11	36 (25 + 11 = 36)

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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Fifth Grade (Grade 5) Patterns Questions

You can create printable tests and worksheets from these Grade 5 Patterns questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

Games Refereed	3	4	5	6
Ariana's Pay ($)	60	80	100	120

• Divide the total number of games she referees by 20 to find the amount of money earned.
• Divide the total number of games she referees by 60 to find the amount of money earned.
• Multiply the total number of games she referees by 20 to find the amount of money earned.
• Multiply the total number of games she referees by 60 to find the amount of money earned.
• Both number values will be 20.
• Both number values will be less than 20.
• Both number values will be greater than 20.
• The Y value will be 20 and the X value will be more than 20.
• The X value will be 20 and the Y value will be more than 20.
• Each term in Pattern X is 4 less than the corresponding term in Pattern Y.
• Each term in Pattern Y is 8 more than the corresponding term in Pattern X.
• Each term in Pattern X is twice the corresponding term in Pattern Y.
• Each term in Pattern Y is twice the corresponding term in Pattern X.
• Each term in Pattern A is 4 more than the corresponding term in Pattern B.
• Each term in Pattern A is 6 more than the corresponding term in Pattern B.
• Each term in Pattern A is 3 times the corresponding term in Pattern B.
• Each term in Pattern A is [math]1/3[/math] times the corresponding term in Pattern B.
• Each term in Pattern A is 5 times the corresponding term in Pattern B.
• Each term in Pattern B is 5 times the corresponding term in Pattern A.
• Each term in Pattern B is 4 more than the corresponding term in Pattern A.
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Problem-Solving Strategies: Finding Patterns

In this lesson, we will learn different problem solving strategies to find patterns.

The following are some examples of problem solving strategies.

Explore it/Act it/Try it (EAT) method (Basic) Explore it/Act it/Try it (EAT) method (Intermediate ) Explore it/Act it/Try it (EAT) method (Advanced) Finding a Pattern (Basic) Finding a Pattern (Intermediate) Finding a Pattern (Advanced)

Find A Pattern (Advanced)

Here we will look at some advanced examples of “Find a Pattern” method of problem solving strategy.

Example: Each hexagon below is surrounded by 12 dots. a) Find the number of dots for a pattern with 6 hexagons in the first column. b) Find the pattern of hexagons with 229 dots.

1	12	12
2	12 + 16	28
3	12 + 16 + 21	49
4	12 + 16 + 21 + 26	75
5	12 + 16 + 21 + 26 + 31	106
6	12 + 16 + 21 + 26 + 31 + 36
7	12 + 16 + 21 + 26 + 31 + 36 + 41	183
	12 + 16 + 21 + 26 + 31 + 36 + 41 + 46	229

a) The number of dots for a pattern with 6 hexagons in the first column is 142.

b) If there are 229 dots then the pattern has 8 hexagons in the first column.

Example: Each member of a club shook hands with every other member who came for a meeting. There were a total of 45 handshakes. How many members were present at the meeting?

	●
	●	●
	●	●	●
	●	●	●	●
	●	●	●	●	●
	●	●	●	●	●	●
	●	●	●	●	●	●	●
	●	●	●	●	●	●	●	●
	●	●	●	●	●	●	●	●	●
	9	8	7	6	5	4	3	2	1

Solution: Total = 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 handshakes

There were 10 members

Example: In the figure, a pinball is released at A.

How many paths are there for it to drop from A to E?

Solution: from A to B: 2 B to C: 6 A to C: 2 × 6 = 12 C to D: 70 A to D: 12 × 70 = 840 D to E: 2 A to E: 2 × 840 = 1680

There are 1680 paths from A to E

Example: A group of businessmen were at a networking meeting. Each businessman exchanged his business card with every other businessman who was present.

a) If there were 16 businessmen, how many business cards were exchanged?

b) If there was a total of 380 business cards exchanged, how many businessmen were at the meeting?

Solution: a) 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 120 exchanges

120 × 2 = 240 business cards

If there were 16 businessmen, 240 business cards were exchanged.

b) 380 ÷ 2 = 190

190 = (19 × 20) ÷ 2 = 19 + 18 + 17 + … + 3 + 2 + 1

If there was a total of 380 business cards exchanged, there were 20 businessmen at the meeting.

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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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Our grade 5 math worksheets cover the 4 operations, fractions and decimals at a greater level of difficulty than previous grades. We also introduce variables and expressions into our word problem worksheets .  

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4 operations.

Place Value & Rounding

Add & Subtract

Multiply & Divide

Order of Operations

Add & Subtract Fractions

Multiply & Divide Fractions

Converting Fractions

Fractions to / from Decimals

Add & Subtract Decimals

Multiply Decimals

Divide Decimals

Data & Graphing

Word Problems

Sample Grade 5 Math Worksheet

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Patterns grade 5

Resource type.

5 .OA.3 5th Grade Number Patterns /Coordinate Plane/Ordered Pairs

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Ontario Guided Math Unit - PATTERNING - Patterns & Algebra - Grades 3,4, 5 , 6

Patterns of Power grades 1- 5 , the first 4 teaching units - Bundle

Grade 5 Ontario Math - Patterns & Equations Assessments - PDF+Google Slides

Patterns and Algebra Interactive Math Unit | Grade 4 and Grade 5

TEKS 5 .4C - 5th Grade Math - Numerical Patterns - Digital & Print

Grade 5 Patterning NEW Ontario Math DIGITAL Google Slides : C . Algebra

Grade 5 Math - Alberta - Patterns & Algebra - NEW 2022 Curriculum

Phonemic Awareness & Spelling Patterns for Grades 2- 5 Game and Word Sort Mats

Go Math Practice - 4th Grade Chapter 5 - Factors, Multiples, and Patterns

Common Core Math Task Cards (5th Grade ): Patterns and Rules CCSS 5 .OA.B.3

Patterning Test or Patterns Quiz - split grades 3, 4, 5 , 6

Patterns and Algebra Interactive Math Unit | Grade 5 and Grade 6

Two Fun Triangle Building & Pattern Challenges ( Grades 3- 5 +)

Grade 5 Patterning NEW Ontario Math : C1. Patterns & Relationships

Grade 5 -6 Patterning & Algebra (Ontario Math) Google, Printable, Forms

Math TEK 5 .4C ★ Numerical Patterns ★ 5th Grade STAAR Math Test Prep Task Cards

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Patterns and Algebra Unit Plans - Grade 5 /6 - Ontario

Text Structure Organizational Patterns Foldable Learning Guide ( Grades 5 -8)

Patterns and Equations Grade 5 Digital Escape Room - Algebra Review Activity

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