Class-5, Mathematics, Can You See the Patterns? worksheet | Live ... - Free Printable

Let's solve the worksheet step by step.

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Question 1: What is the growth interval for the following sequences?

We are to find the pattern (either increasing or decreasing) in each sequence and determine how much each number changes from one to the next.

#### (a) 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
- Let’s check the difference between consecutive numbers:
- 4 – 2 = 2
- 6 – 4 = 2
- 8 – 6 = 2
- And so on...
- The numbers grow by 2.

✔ Answer: These numbers grow by 2

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#### (b) 45, 40, 35, 30, 25, 20, 15, 10, 5
- Difference between terms:
- 40 – 45 = –5
- 35 – 40 = –5
- 30 – 35 = –5
- So, it reduces by 5 each time.

✔ Answer: These numbers reduce by 5

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#### (c) 5, 10, 15, 20, 25, 30, 35, 40, 45
- Differences:
- 10 – 5 = 5
- 15 – 10 = 5
- 20 – 15 = 5
- Pattern continues...

✔ Answer: These numbers grow by 5

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#### (d) 27, 24, 21, 18, 15, 12, 9, 6, 3
- Differences:
- 24 – 27 = –3
- 21 – 24 = –3
- 18 – 21 = –3
- So, it reduces by 3

✔ Answer: These numbers reduce by 3

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✔ Summary of Question 1:

- (a) Grow by 2
- (b) Reduce by 5
- (c) Grow by 5
- (d) Reduce by 3

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Question 2: Complete the pattern

We need to identify the pattern and choose the correct option to fill the box.

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#### a) Smiley faces

Sequence:

1. 😊 (happy face)
2. 😐 (neutral face, eyes closed)
3. 🙂 (smile with closed mouth)
4. □ (to be filled)

Now look at the options:
- (i) 😐 (same as second one)
- (ii) 🙂 (same as third one)

Let’s analyze the pattern:

- First: 😊 — happy, open mouth
- Second: 😐 — neutral, no smile, dots for eyes
- Third: 🙂 — smiley, but closed mouth

Wait — actually, let’s re-express them clearly:

- First: 😊 → two dots for eyes, wide U-shaped mouth
- Second: ( : ) → two dots, colon-like mouth (no curve), but inverted — maybe it's a frown?
Wait, actually, it's drawn like this: `( : )` — that looks like a frowning face, but with dots for eyes?

Wait, looking closely:
- First: 😊 → standard happy face
- Second: `(:)` → This is likely meant to be a frowny face, but with eyes represented as dots and a colon mouth (which is usually a smile). Hmm — perhaps it's a silly face?

Alternatively, think about rotation or transformation.

But wait — perhaps it's about rotating the face?

Let’s consider the possibility that the face is rotating.

Look again:

1. 😊 — normal orientation
2. `(:)` — rotated 90° clockwise? Or upside down?

Actually, the second face has the mouth pointing upward? No — if you look at the drawing:
- First: 😊 — mouth up, eyes above
- Second: `(:)` — mouth is colon, eyes are dots, but the whole face seems flipped vertically? Or rotated?

Wait — better idea: The facial expressions are changing in a cycle.

Let’s list them:

- (1) 😊 — smiling (mouth up)
- (2) `(:)` — appears to be a frowning face (mouth down) — but drawn as colon?
Actually, `(:)` is often used to represent a sad face, but here it might be a neutral or inverted face.

Wait — perhaps it's not emotion-based, but symmetry or rotation?

Let’s examine the shapes:

- First: 😊 → two dots (eyes), curved line (mouth) — standard
- Second: `(:)` → two dots (eyes), colon (mouth) — but the colon is vertical, so it looks like vertical mouth, meaning the face is turned sideways?

Ah! Here's a clue:

Look at the third face: it's a smile with a horizontal line — like `:-)` but without the dash?

Wait, the third face is drawn as:

```
o o
-
```

So it's a smile with horizontal mouth, eyes above.

Compare:
- Face 1: 😊 → mouth curved upward
- Face 2: `(:)` → mouth is colon (vertical), eyes are dots — could be rotated 90° clockwise
- Face 3: 🙂 → mouth is horizontal line (like a flat smile), eyes above

Wait — maybe the faces are being rotated?

Let’s try interpreting:

- Face 1: Normal face — upright
- Face 2: Rotated 90° clockwise → so the mouth becomes vertical, eyes become side-by-side horizontally? But in the image, it's shown as `(:)` — which might mean the face is now sideways.

Then Face 3: Rotated another 90° → now upside down?

But Face 3 has a horizontal mouth again, but the eyes are still above — doesn't match.

Alternative idea: Pattern based on mouth shape and eye position

But let’s look at the options:

- (i) `(:)` — same as second face
- (ii) `:)` — a standard smiley

But the third face is already `:)` — so if we’re going:

1. 😊 → full smile
2. `(:)` → frown or neutral
3. `:)` → smile

That doesn’t make sense.

Wait — perhaps the pattern is alternating?

But the sequence is:

1. 😊
2. `(:)`
3. `:)`
4. ?

Wait — maybe the first and third are similar?

First: 😊 → two dots, curved mouth

Third: `:)` → two dots, curved mouth

Second: `(:)` → two dots, colon mouth

So maybe it's alternating between curved mouth and straight/colon mouth?

But first: curved → second: straight → third: curved → fourth: should be straight?

But both (i) and (ii) are given.

Option (i): `(:)` — colon mouth (straight vertical)

Option (ii): `:)` — curved mouth

But third is already `:)`, so if it's alternating, fourth should be `(:)`?

But then the pattern would be:

- 1: curved
- 2: straight
- 3: curved
- 4: straight → so answer is (i)

But wait — the second face is `(:)` — which is not a smile, but a frown? Or just a different style?

Alternatively, think about mirror images or rotations.

Another idea: The faces are rotating 90 degrees clockwise.

Let’s test:

- Face 1: normal → upright
- Face 2: rotated 90° clockwise → mouth becomes vertical (so colon), eyes become horizontal — matches `(:)` — yes!
- Face 3: rotated another 90° → now upside down → mouth horizontal, but upside down — but the third face is `:)` — which is upright, not upside down.

No — doesn’t match.

Wait — perhaps the pattern is emotional expression?

1. Happy 😊
2. Sad `(:)` — frown
3. Happy `:)`
4. Should be Sad again?

So pattern: Happy → Sad → Happy → Sad → ?

Then the next should be Sad, i.e., `(:)`

So answer is (i)

Yes! That makes sense.

So the pattern is alternating emotions:

- Happy → Sad → Happy → Sad

Therefore, the missing face should be sad, which is option (i)

✔ Answer for 2a): (i)

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#### b) Arrow patterns

Sequence:

1. ←→ (left-right arrow)
2. ↑↓ (up-down arrow)
3. ↔ (double-headed right-left arrow) — wait, no — third one is T-shaped?

Wait — look carefully:

- First: ←→ — left and right arrows joined
- Second: ↑↓ — up and down arrows joined
- Third: ↔ — but it's drawn as a double-headed arrow pointing left and right, but the middle is connected?

Wait — actually, the third one is:

```
<--->
```

But in the image, it's shown as a horizontal double arrow, like ←→

But second is ↑↓ — vertical

Third is ←→ again? No — wait:

Looking at the image:

- First: ←→ (horizontal)
- Second: ↑↓ (vertical)
- Third: ↔ — but it's drawn as a horizontal double arrow, same as first?

Wait — no — third one is shown as:

```
<--->
```

But it's labeled as "T" — no, it's actually a double-headed arrow pointing left and right, same as first.

But that can’t be — unless it’s repeating.

Wait — look again:

Actually, the third one is:

It's a horizontal double arrow, but with the arrowheads on both ends, same as first.

But second is vertical.

So sequence:

1. Horizontal double arrow (←→)
2. Vertical double arrow (↑↓)
3. Horizontal double arrow (↔)

So it alternates: horizontal → vertical → horizontal → ?

So next should be vertical?

But the options are:

- (i) ↓↑ (down-up) — vertical, but reversed
- (ii) ←→ — horizontal

So if the pattern is: horizontal → vertical → horizontal → vertical

Then next should be vertical

Between (i) and (ii), (i) is vertical (but direction reversed — but that’s fine), (ii) is horizontal.

So (i) is vertical, so it fits.

But is it the same as second?

Second was ↑↓ — up-down

(i) is ↓↑ — down-up — same thing, just reversed.

In such patterns, direction reversal may not matter.

So likely, the pattern is alternating between horizontal and vertical double arrows.

So:

1. Horizontal
2. Vertical
3. Horizontal
4. Vertical

So answer is (i)

✔ Answer for 2b): (i)

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✔ Final Answers:

#### Question 1:
(a) Grow by 2
(b) Reduce by 5
(c) Grow by 5
(d) Reduce by 3

#### Question 2:
(a) (i)
(b) (i)

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