What is a Sequence of Figures?

S1-SA5-0212

Grade Level:

Class 4

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

A sequence of figures is a list of shapes or pictures arranged in a specific order, following a certain rule or pattern. Each figure in the sequence changes or progresses in a predictable way from the previous one.

Simple Example

Quick Example

Imagine you have a stack of rotis, each one slightly smaller than the one below it. If you arrange them from largest to smallest, you've created a sequence of figures (the rotis) where each figure follows a size-decreasing pattern.

Worked Example

Step-by-Step

Let's look at this sequence of matchstick figures: Figure 1 has 3 matchsticks (forming a triangle). Figure 2 has 5 matchsticks (forming two triangles joined). Figure 3 has 7 matchsticks (forming three triangles joined).

Step 1: Observe Figure 1. It has 3 matchsticks.
---Step 2: Observe Figure 2. It has 5 matchsticks. The difference from Figure 1 is 5 - 3 = 2 matchsticks.
---Step 3: Observe Figure 3. It has 7 matchsticks. The difference from Figure 2 is 7 - 5 = 2 matchsticks.
---Step 4: Identify the pattern. Each new figure adds 2 matchsticks to the previous figure.
---Step 5: Predict Figure 4. Since Figure 3 has 7 matchsticks, Figure 4 will have 7 + 2 = 9 matchsticks.
Answer: The next figure in the sequence will have 9 matchsticks.

Why It Matters

Understanding sequences of figures helps you spot patterns everywhere, from designs to data trends. This skill is vital for careers in engineering, where you design repeating structures, or in computer science, where you predict how systems will grow. Even game developers use patterns to create engaging levels!

Common Mistakes

MISTAKE: Only looking at the first two figures to guess the pattern, which might be wrong for later figures. | CORRECTION: Always check the pattern across at least three or four figures to confirm it truly holds for the entire sequence.

MISTAKE: Confusing the number of items in a figure with the change between figures. | CORRECTION: Clearly identify what is changing (e.g., number of sides, number of items, orientation) and by how much, rather than just counting everything.

MISTAKE: Not considering different types of changes (size, rotation, addition, subtraction). | CORRECTION: Think about all possible ways a figure can transform: Is it getting bigger? Rotating? Are parts being added or removed? Is it flipping?

Practice Questions

Try It Yourself

QUESTION: A sequence shows squares. Figure 1 has 1 square. Figure 2 has 4 squares (a 2x2 grid). Figure 3 has 9 squares (a 3x3 grid). How many squares will Figure 4 have? | ANSWER: 16 squares (a 4x4 grid)

QUESTION: A sequence of arrows points: Up, Right, Down, Left. What direction will the next arrow point? | ANSWER: Up

QUESTION: Look at a sequence of stars. Figure 1 has 1 star. Figure 2 has 3 stars. Figure 3 has 6 stars. How many stars will Figure 4 have? (Hint: The number added each time increases by 1) | ANSWER: 10 stars (1+2=3, 3+3=6, 6+4=10)

MCQ

Quick Quiz

Which of these is a sequence of figures?

A group of different colored balls

A list of numbers: 2, 4, 6, 8

Pictures of a plant growing over several days, showing its height increase

All the students in your class standing randomly

The Correct Answer Is:

Option C shows figures (pictures of a plant) arranged in order, following a pattern of growth over time. Options A and D are just collections, and Option B is a sequence of numbers, not figures.

Real World Connection

In the Real World

Imagine you're watching a cricket match and the commentator shows a graphic of a batsman's runs over the last few overs: 5 runs, then 8 runs, then 11 runs. This is a sequence of numbers, but the graphic itself (like a bar chart getting taller) is a sequence of figures showing a pattern. Meteorologists also use sequences of weather maps to predict how a storm will move, looking for patterns in its path.

Key Vocabulary

Key Terms

SEQUENCE: A set of things arranged in a particular order | FIGURE: A shape, picture, or drawing | PATTERN: A regular, repeated way in which something happens or is done | RULE: The specific instruction or logic that defines the pattern

What's Next

What to Learn Next

Great job understanding sequences of figures! Now that you can spot patterns in shapes, you're ready to learn about 'Number Sequences'. This will help you find patterns in numbers, which is super useful for solving many math problems and understanding data.