Critical Thinking Worksheet Grades K-2: Mathematical Concepts ... - Free Printable

Let's solve each of these math analogies step by step. These are visual analogies where we need to determine the relationship between the first two figures and apply that same relationship to the third figure to find the missing fourth figure.

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1)

```
○ : ◯½ :: □ : ?
```

- First shape: a full circle.
- Second shape: a circle with half shaded (i.e., half-filled).
- The relationship is: "whole to half" — the circle has been split in half, and one half is shaded.
- Now, apply this to the square: a full square → what would be its "half" version?

→ The answer should be a square with half shaded.

✔ Answer: A square with one half shaded (like the half-circle).

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2)

```
△ : □ :: △ : ?
```

- First shape: a triangle.
- Second shape: a square.
- Third shape: a triangle, but it's divided into two smaller triangles (by a line from top vertex to base).
- So the relationship seems to be: "shape to a divided version of itself"?

Wait — let’s look carefully:

First pair: Triangle : Square — they are different shapes. That doesn’t seem like a transformation.

But second pair: Triangle : ? — the triangle on the left is solid, and the one on the right is divided into two parts.

Wait — perhaps it's about how the shape is divided?

Let’s re-analyze:

Actually, looking at the pattern:

- First: solid triangle
- Second: solid square
- Third: triangle split vertically into two halves
- Fourth: ?

Wait — maybe the analogy is:

Solid triangle : Solid square :: Split triangle : ?

That suggests: if the triangle becomes split, then the square should become split too?

But that might not make sense.

Alternatively, think of it as:

Triangle → Square (change in shape), then Split triangle → ?

But the third shape is a split triangle, so maybe the relationship is "the first shape is transformed into the second by splitting"?

Wait — no, triangle to square isn't splitting.

Let’s consider another idea:

Perhaps the analogy is:

Whole triangle : Whole square :: Half-divided triangle : ?

But the second shape is not split.

Wait — maybe it's about number of sides? Triangle (3 sides) → Square (4 sides). But then triangle → ?

No, the third shape is a triangle again.

Wait — look again:

The first shape is a solid triangle
The second shape is a solid square
Then the third shape is a triangle with a vertical line down the middle (split into two small triangles)

So the third shape is the same as the first, but divided.

So the analogy is:

Solid triangle : Solid square :: Divided triangle : ?

So the relationship is: "If you divide the first shape, what do you get for the second?"

But the second shape is a square, not a divided triangle.

This seems confusing.

Wait — perhaps the analogy is not about transformation, but matching the pattern of division?

Another idea:

Look at the structure:

It might be:

Triangle : Square :: Triangle (with line) : ?

Maybe the rule is: "The first shape is changed to a different shape, and the third shape is the same as the first but modified — so the fourth should be the second shape modified similarly."

So:

- Triangle → Square (a change in shape)
- Then, a divided triangle → ? → should be a divided square?

Yes! That makes sense.

So the analogy is:

Original shape : New shape :: Divided original shape : Divided new shape

So:
- Triangle → Square
- Divided Triangle → Divided Square

✔ Answer: A square with a vertical line through it (split into two halves).

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3)

```
Fish with mouth open : Fish with mouth closed :: Face with eyes and mouth open : ?
```

- First fish: mouth open
- Second fish: mouth closed
- Third: face with eyes and mouth open
- We need to find what the face becomes when following the same rule.

So the rule is: "mouth opens → mouth closes" or "from open to closed"

So the face has mouth open → should become mouth closed

But what about the eyes?

The fish don't have eyes changing — just mouth.

The face has eyes and mouth both open.

But in the fish, only the mouth changes.

So likely, the mouth is the key feature.

So the face with open mouth → should become face with closed mouth

But the eyes stay the same?

Yes — since the fish’s eyes don’t change.

So the analogy is: "Mouth state changes from open to closed"

Therefore, the fourth image should be the same face, but with mouth closed

✔ Answer: A face with eyes open, but mouth closed

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4)

```
Nest with 3 eggs : 3 eggs outside nest :: Nest with 2 eggs : ?
```

- First: nest with 3 eggs
- Second: 3 eggs outside the nest
- Third: nest with 2 eggs
- Fourth: ?

So the relationship: eggs move from inside the nest to outside

In the first pair: 3 eggs in nest → 3 eggs out of nest

So the transformation is: "eggs removed from nest"

Now, apply to the third: nest with 2 eggs → what should be outside?

Likely: 2 eggs outside the nest

So the fourth image should show 2 eggs outside the nest

✔ Answer: Two eggs outside the nest (no nest shown, just the eggs)

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✔ Final Answers:

1) Square with half shaded
2) Square split vertically into two parts
3) Face with eyes open, mouth closed
4) Two eggs outside the nest

These follow the patterns of transformation: shading, division, facial expression change, and object location.

Let me know if you'd like a visual sketch description!