Fair Share

Given: A whole paratha and several pictures showing it cut in different ways.

Concept: When a whole is cut into two equal halves, both pieces must be exactly the same size and shape. You can check by folding one piece over the other — if they match perfectly, the cut is equal.

Answer: Tick ☑ the paratha that is cut straight through the middle so that both pieces are exactly the same size. (The paratha divided by a straight line passing through the centre, giving two equal pieces, is the correct one.)

Given: Several shapes, some with a portion coloured.

Concept: Half means the whole is divided into 2 equal parts and exactly one of those equal parts is coloured.

Step 1: For each shape, check whether the coloured part and the uncoloured part are equal in size.
Step 2: If both parts are equal AND exactly one part is coloured, that shape shows one-half coloured.

Answer: Circle only those shapes where the coloured region is exactly equal to the uncoloured region (i.e., the shape is divided into 2 equal parts and one part is coloured). Shapes where the coloured portion is more or less than the uncoloured portion should NOT be circled.

Note: Since the actual images are not visible, apply the rule — colour covers exactly $\frac{1}{2}$ of the whole shape.

Given: Several whole shapes (rectangle, circle, square, irregular shape).

Concept: To show one-half, draw a line that divides the whole shape into 2 equal parts. Both parts must be exactly the same size and shape.

Step 1: For a rectangle — draw a straight line either horizontally through the middle or vertically through the middle.
Step 2: For a circle — draw a straight line (diameter) passing through the centre.
Step 3: For a square — draw a line through the centre (horizontally, vertically, or diagonally).
Step 4: For any shape — ensure the line creates two mirror-image equal parts.

Answer: Draw a straight line through the exact centre/middle of each shape so that both resulting parts are equal. Each part = one-half of the whole.

Given: Shabnam has eaten chikki from 3 sides of a rectangular/square chikki piece.

Concept: If pieces are eaten from 3 sides, more than half of the chikki has been eaten, so what remains is less than half.

Step 1: Imagine a whole chikki (rectangle or square).
Step 2: Eating from 3 sides means a large portion around three edges has been consumed.
Step 3: The remaining piece (in the middle/one corner) is smaller than half.

Answer: ☑ (a) less than half

The chikki left is less than half because eating from 3 sides removes more than half of the whole chikki.

Given: A whole chikki (square or rectangular shape). It has been eaten from 2 sides, leaving exactly half.

Concept: Half means exactly $\frac{1}{2}$ of the whole is remaining. Eating from 2 sides (two adjacent or opposite sides) can leave exactly half.

Step 1: Look at the chikki grid/shape provided.
Step 2: If eaten from 2 opposite sides equally, the remaining middle strip = half.
Step 3: Colour exactly half of the chikki shape to show the eaten portion (or the remaining portion, as instructed).

Answer: Colour exactly half of the chikki shape. For example, if the chikki is a $2 \times 4$ grid, colour 4 squares (half of 8 total squares) in an L-shape or strip along 2 sides to show the eaten part. The coloured half and uncoloured half must be equal.

Given: Four identical shapes (squares or rectangles).

Concept: A half can be made in many ways as long as the line divides the shape into 2 perfectly equal parts.

Different ways to draw a half in a square:
- Way 1: Draw a vertical line through the centre (left half and right half).
- Way 2: Draw a horizontal line through the centre (top half and bottom half).
- Way 3: Draw a diagonal line from top-left corner to bottom-right corner.
- Way 4: Draw a diagonal line from top-right corner to bottom-left corner.

Answer: In each of the four shapes, draw one of the above lines. Each line must pass through the centre and create two equal parts. All four lines should be different, showing that there are many ways to make a half.

Given: Three pictures, each showing only one half of a shape or figure.

Concept: If one half is given, the other half is its mirror image. Drawing the mirror image of the given half completes the whole.

Step 1: Identify the line of symmetry (the fold line / dividing line) in each picture.
Step 2: For each point or line in the given half, draw its mirror image on the other side of the fold line.
Step 3: The completed drawing should look like a whole, symmetrical shape.

Answer: Draw the mirror image of each given half on the empty side. For example:
- If the left half of a butterfly is shown, draw the right wing as a mirror image.
- If the top half of a shape is shown, draw the bottom half as a mirror image.
The result is a complete, whole picture.

Given: Pairs of numbers. We need to identify whether the smaller number is 'half' of the larger, or the larger is 'double' of the smaller.

Concept:
- Half of a number = that number divided by 2. If $A = B \div 2$, then A is half of B.
- Double of a number = that number multiplied by 2. If $A = B \times 2$, then A is double of B.

Solutions:

1. $4 = 8 \div 2$, so 4 marbles are half of 8 marbles.

2. $8 = 4 \times 2$, so 8 marbles are double of 4 marbles.

3. $10 = 5 \times 2$, so 10 marbles are double of 5 marbles.

4. $5 = 10 \div 2$, so 5 marbles are half of 10 marbles.

5. $6 = 12 \div 2$, so 6 marbles are half of 12 marbles.

6. $12 = 6 \times 2$, so 12 marbles are double of 6 marbles.

7. Double of $7 = 7 \times 2 = 14$. Distance of 13 from 14 on the number line $= 14 - 13 = \mathbf{1}$. So 13 is 1 step away from the double of 7.

8. Half of $14 = 14 \div 2 = 7$. Distance of 5 from 7 on the number line $= 7 - 5 = \mathbf{2}$. So 5 is 2 steps away from half of 14.

Given:
- Clue 1: Less than the double of 3 marbles.
- Clue 2: More than the half of 8 marbles.

Step 1: Find double of 3.
$$3 \times 2 = 6$$
So the number must be less than 6.

Step 2: Find half of 8.
$$8 \div 2 = 4$$
So the number must be more than 4.

Step 3: The number must satisfy: more than 4 AND less than 6.
$$4 < \text{number} < 6$$
The only whole number that fits is 5.

Step 4: Check options:
- (a) 4 marbles: $4 > 4$? No. ✗
- (b) 5 marbles: $5 > 4$? Yes. $5 < 6$? Yes. ✓
- (c) 6 marbles: $6 < 6$? No. ✗

Answer: ☑ (b) 5 Marbles

Given:
- Clue 1: Less than the double of 4 marbles.
- Clue 2: More than the half of 10 marbles.

Step 1: Find double of 4.
$$4 \times 2 = 8$$
So the number must be less than 8.

Step 2: Find half of 10.
$$10 \div 2 = 5$$
So the number must be more than 5.

Step 3: The number must satisfy: more than 5 AND less than 8.
$$5 < \text{number} < 8$$
Possible whole numbers: 6 or 7.

Step 4: Check options:
- (a) 8 marbles: $8 < 8$? No. ✗
- (b) 6 marbles: $6 > 5$? Yes. $6 < 8$? Yes. ✓
- (c) 3 marbles: $3 > 5$? No. ✗

Answer: ☑ (b) 6 Marbles

Given: A chikki (square/rectangular piece) shared among 4 children equally (as shown in the context of the image).

Concept: When a whole is divided into 4 equal parts, each part is called one quarter (or one-fourth).

Answer:
- Each child gets one quarter of the chikki.
- There are 4 quarters in a whole.

$$1 \text{ whole} = 4 \text{ quarters}$$

Given: Several objects/shapes, some divided into 4 equal parts and some not.

Concept: Quarters means the whole is divided into exactly 4 equal parts. Each part must be the same size.

Step 1: Check each object — is it divided into 4 parts?
Step 2: Are all 4 parts equal in size?
Step 3: If yes to both, tick that object.

Answer: Tick ☑ only those objects/shapes that are divided into 4 equal parts. Objects divided into unequal parts or into a number other than 4 parts should NOT be ticked.

Note: Since images are not visible, apply the rule: 4 equal parts = quarters ✓; unequal parts or not 4 parts = not quarters ✗.