Last Updated on October 30, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 6 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 6 maths. In this article, you will find case study questions for CBSE Class 8 Maths Chapter 1 Patterns in Mathematics. It is a part of Case Study Questions for CBSE Class 6 Maths Series.

Chapter | Patterns in Mathematics |

Type of Questions | Case Study Questions |

Nature of Questions | Competency Based Questions |

Board | CBSE |

Class | 6 |

Subject | Maths |

Useful for | Class 8 Studying Students |

Answers provided | Yes |

Difficulty level | Mentioned |

Important Link | Class 6 Maths Chapterwise Case Study |

### Case Study Questions on Patterns in Mathematics

**Questions**

**Passage 1: **

Patterns can become more intricate as we explore them further. In mathematics, patterns can follow multiple rules, combining arithmetic, geometric, and even shape-based changes. Recognizing patterns requires careful observation and analysis of the relationship between the numbers, objects, or shapes.

For example, consider the number pattern:

2, 5, 10, 17, 26, …

Here, the difference between consecutive numbers is increasing. To get from 2 to 5, we add 3. To get from 5 to 10, we add 5. To get from 10 to 17, we add 7, and so on. This is an example of a pattern where the differences between numbers increase by a constant amount.

Now, let’s look at a shape pattern:

○, △, □, ○○, △△, □□, …

In this sequence, not only are the shapes repeating, but each shape is doubling in number as the pattern progresses. Such patterns combine both geometric growth and alternating shapes.

(i) In the pattern 2, 5, 10, 17, 26, __, __, find the next two numbers in the sequence. Explain the rule.

(ii) A pattern starts with 1 and follows this rule: multiply the number by 2, then subtract 1 to get the next number. Write the first five numbers of the sequence.

(iii) Identify the next two shapes in the following pattern: ○, △, □, ○○, △△, □□, ○○○, __, __.

(iv) Find the missing numbers in the pattern: 3, 9, 18, __, 45, 63. Identify the rule.

(v) The first number in a pattern is 4, and the rule is to add 4 to the first number, then multiply the result by 2 to get the next number. Write the first four numbers of the pattern.

**Solutions:**

1. In the pattern 2, 5, 10, 17, 26, __, __, find the next two numbers in the sequence. Explain the rule.**Solution:**

The differences between consecutive terms are increasing by 2:

- 5 – 2 = 3
- 10 – 5 = 5
- 17 – 10 = 7
- 26 – 17 = 9

The next difference should be 11, so: - 26 + 11 = 37

The next difference should be 13, so: - 37 + 13 = 50

The next two numbers are:**37 and 50**.

2. A pattern starts with 1 and follows this rule: multiply the number by 2, then subtract 1 to get the next number. Write the first five numbers of the sequence.

**Solution:**

We start with the number 1 and apply the rule: multiply by 2, then subtract 1 to get the next number.

**First number: 1**- 1 × 2 = 2
- 2 – 1 = 1

So, the first number is**1**.

**Second number: 1**- 1 × 2 = 2
- 2 – 1 = 1

So, the second number is**1**.

**Third number: 1**- 1 × 2 = 2
- 2 – 1 = 1

So, the third number is**1**.

**Fourth number: 1**- 1 × 2 = 2
- 2 – 1 = 1

So, the fourth number is**1**.

**Fifth number: 1**- 1 × 2 = 2
- 2 – 1 = 1

So, the fifth number is**1**.

3. Identify the next two shapes in the following pattern: ○, △, □, ○○, △△, □□, ○○○, __, __.

**Solution:**

This pattern alternates between circles (○), triangles (△), and squares (□). The number of shapes increases by 1 in each set.

- First: ○ (1 circle)
- Second: △ (1 triangle)
- Third: □ (1 square)
- Fourth: ○○ (2 circles)
- Fifth: △△ (2 triangles)
- Sixth: □□ (2 squares)
- Seventh: ○○○ (3 circles)

Following this alternating pattern:

- Eighth: △△△ (3 triangles)
- Ninth: □□□ (3 squares)

The next two shapes in the pattern are **△△△ (3 triangles)** and **□□□ (3 squares)**.

4. Find the missing numbers in the pattern: 3, 9, 18, __, 45, 63. Identify the rule.

**Solution:**

Let’s look at the differences between the consecutive numbers:

- 9 – 3 = 6
- 18 – 9 = 9
- 45 – 18 = 27
- 63 – 45 = 18

Notice that the differences are increasing by multiples of 3: 6, 9, 18, 27.

The difference between 18 and the missing number should follow this pattern, which is 18.

Therefore, the missing number is:

- 18 + 18 =
**36**

So, the complete pattern is: 3, 9, 18, **36**, 45, 63.

5. The first number in a pattern is 4, and the rule is to add 4 to the first number, then multiply the result by 2 to get the next number. Write the first four numbers of the pattern.

**Solution:**

Start with the first number, 4, and apply the rule: add 4 and then multiply by 2.

- First number = 4
- 4 + 4 = 8; 8 × 2 = 16 (Second number)
- 16 + 4 = 20; 20 × 2 = 40 (Third number)
- 40 + 4 = 44; 44 × 2 = 88 (Fourth number)

The first four numbers in the pattern are: 4, 16, 40, 88.

### Topics from which case study questions may be asked

- Patterns in Numbers
- Visualising Number Sequences
- Relations among Number Sequences
- Patterns in Shapes
- Relation to Number Sequences

Mathematics is largely about searching for patterns and understanding why they exist. These patterns are present everywhere—in nature, daily activities, and even celestial movements. They appear in tasks like cooking, playing games, or using technology. Exploring these patterns can be fun and creative, which is why mathematics is seen as both an art and a science. The goal of mathematics is not only to identify patterns but also to explain them, often leading to applications beyond the original context, helping to advance humanity.

Understanding patterns in the motion of stars, planets, and their satellites has led to the development of gravitational theory, enabling us to launch satellites and send rockets to the Moon and Mars. Similarly, recognizing patterns in genomes has advanced the diagnosis and treatment of diseases, among many other significant applications.

Case study questions from the above given topic may be asked.

### Understanding Patterns in Mathematics

- Mathematics may be viewed as the search for patterns and for the explanations as to why those patterns exist.
- Among the most basic patterns that occur in mathematics are number sequences.
- Some important examples of number sequences include the counting numbers, odd numbers, even numbers, square numbers, triangular numbers, cube numbers, Virahānka numbers, and powers of 2.
- Sometimes number sequences can be related to each other in beautiful and remarkable ways. For example, adding up the sequence of odd numbers starting with 1 gives square numbers.
- Visualizing number sequences using pictures can help to understand sequences and the relationships between them.
- Shape sequences are another basic type of pattern in mathematics. Some important examples of shape sequences include regular polygons, complete graphs, stacked triangles and squares, and Koch snowflake iterations. Shape sequences also exhibit many interesting relationships with number sequences.

### Frequently Asked Questions (FAQs) on Patterns in Mathematics Case Study

#### Q1: What is a pattern in mathematics?

A1: A pattern in mathematics is a sequence or arrangement of numbers, shapes, or objects that follows a particular rule or set of rules. Patterns help us predict what comes next and can be used to identify trends or relationships. They can be found in numbers, shapes, colors, and many real-life situations.

#### Q2: What are the different types of patterns in mathematics?

A2: The different types of patterns in mathematics include:**Number patterns:** These are sequences of numbers that follow a specific rule, like adding, subtracting, multiplying, or dividing.**Shape patterns:** These involve repeating or growing sequences of shapes, which change based on size, color, or arrangement.**Geometric patterns:** These involve shapes that follow a rule, such as increasing in size or rotating.**Algebraic patterns:** These patterns involve the use of variables and mathematical expressions to identify relationships.

#### Q3: How do we identify the rule of a pattern?

A3: To identify the rule of a pattern:

Look at the sequence carefully.

Find how one element changes to the next.

Check if the changes involve adding, subtracting, multiplying, dividing, or rotating shapes.

Apply the same rule to the next elements in the pattern to ensure consistency.

For example, in the pattern 2, 4, 6, 8, 10, the rule is to add 2 to each number to get the next one.

#### Q4: What is the importance of learning patterns in mathematics?

A4: Learning patterns is important because:**Improves logical thinking:** Recognizing patterns helps develop critical thinking and problem-solving skills.**Enhances prediction skills:** Patterns allow us to make predictions based on observed trends.**Forms the basis for algebra:** Identifying patterns is a foundational skill in algebra and higher-level mathematics.**Real-life application:** Patterns are everywhere in real life, such as in nature, art, and architecture, helping us understand the world around us.

#### Q5: How can we create a pattern?

A5: To create a pattern, you need to:**Decide the type of pattern:** Choose whether it’s a number, shape, or color pattern.**Select a rule:** This could be adding, subtracting, multiplying, or arranging shapes in a particular way.**Follow the rule:** Apply the chosen rule consistently to generate more elements in the pattern.

For example, if you start with the number 3 and decide to add 5 each time, the pattern would be 3, 8, 13, 18, and so on.

#### Q6: **What are symmetrical patterns?**

A6: A symmetrical pattern is one where one half is the mirror image of the other half. These patterns can be found in many shapes, such as butterflies, leaves, and human faces. In geometry, symmetrical shapes are those that can be divided into two equal halves, where each half looks exactly like the other.

#### Q8: **Are there any online resources or tools available for practicing **Patterns in Mathematics **case study questions?**

A8: We provide case study questions for CBSE Class 6 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.