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 ✗.

Given: Four whole shapes.

Concept: To show a quarter, divide the whole into 4 equal parts by drawing lines.

Step 1: For a square — draw one vertical line through the centre AND one horizontal line through the centre. This creates 4 equal smaller squares, each being one quarter.
Step 2: For a rectangle — similarly draw one vertical and one horizontal line through the centre.
Step 3: For a circle — draw two diameters perpendicular to each other (like a plus sign through the centre).

Answer: In each shape, draw 2 lines that cross at the centre, dividing the shape into 4 equal parts. Each part = one quarter of the whole.

Given: A shape where one quarter is already drawn/shown.

Concept: $1 \text{ whole} = 4 \text{ quarters}$. If 1 quarter is given, we need to draw 3 more equal quarters to complete the whole.

Step 1: Identify the size and shape of the given quarter.
Step 2: Draw 3 more identical pieces adjacent to the given quarter.
Step 3: Together, all 4 equal pieces form the complete whole.

Answer: Draw 3 more pieces, each exactly the same size and shape as the given quarter, to complete the whole shape. The finished shape should be a complete square, rectangle, or circle (depending on the original shape).

Given: Shapes with some quarters already shown (2 quarters or 3 quarters shown).

Concept: $1 \text{ whole} = 4 \text{ quarters}$.
- If 2 quarters are shown, draw 2 more.
- If 3 quarters are shown, draw 1 more.

Step 1: Count how many quarters are already drawn.
Step 2: Calculate how many more are needed: $4 - \text{(quarters shown)}$.
Step 3: Draw the remaining quarters, each equal in size to the ones already shown.

Answer: Complete each shape by drawing the missing quarters so that all 4 equal parts together form the whole shape.

Given: A group of birds. Shabnam and Mukta have each coloured some birds (as shown in the images).

Concept:
- Half = $\frac{1}{2}$ of the total (total ÷ 2)
- Quarter = $\frac{1}{4}$ of the total (total ÷ 4)
- Double = 2 times a number

Based on the standard version of this exercise (8 birds total):
- Total birds = 8
- Half of 8 = 4
- Quarter of 8 = 2

Shabnam coloured 4 birds = half of 8 birds.
Mukta coloured 2 birds = a quarter of 8 birds.
Shabnam coloured 4 birds, Mukta coloured 2 birds. $4 = 2 \times 2$, so Shabnam coloured double the number Mukta coloured.

Answer:
- Shabnam ☑ has coloured half of the birds.
- Mukta ☑ has coloured a quarter of the birds.
- Shabnam has coloured double the number of birds that Mukta has coloured.

Given: Lakshanya has 16 flowers. Peehu has 16 flowers.

Concept:
- Half of 16 = $16 \div 2 = 8$
- Quarter of 16 = $16 \div 4 = 4$
- Double of 4 = $4 \times 2 = 8$

Based on the standard exercise:
- Lakshanya tied 8 flowers = half of 16.
- Peehu tied 4 flowers = a quarter of 16.
- Lakshanya tied 8, Peehu tied 4. Since $8 = 4 \times 2$, Lakshanya tied double the number Peehu tied.

Answer:
- Lakshanya ☑ tied half of her flowers. ($16 \div 2 = 8$ flowers)
- Peehu ☑ tied a quarter of her flowers. ($16 \div 4 = 4$ flowers)
- Lakshanya ☑ tied double the number of flowers that Peehu tied. ($8 = 2 \times 4$)

Given: Several shapes with portions coloured.

Concept: Three-quarters means the whole is divided into 4 equal parts and 3 of those parts are coloured/shaded.

Step 1: Check if the shape is divided into 4 equal parts.
Step 2: Check if exactly 3 out of 4 equal parts are coloured.
Step 3: If both conditions are met, tick that shape.

Answer: Tick ☑ only those shapes where:
- The whole is divided into 4 equal parts, AND
- Exactly 3 parts (three-quarters) are coloured.

Shapes where only 1, 2, or 4 parts are coloured, or where parts are unequal, should NOT be ticked.

Given: Six shapes, each already divided into 4 equal parts. Instructions tell how many quarters to colour in each.

Concept: Each shape is divided into 4 equal parts. Colour the number of parts as instructed.

Solutions:
1. 2 quarters: Colour any 2 out of 4 equal parts. (This is the same as one-half.)
2. 1 quarter: Colour any 1 out of 4 equal parts.
3. 3 quarters: Colour any 3 out of 4 equal parts.
4. 4 quarters: Colour all 4 parts. (This is the complete whole.)
5. 3 quarters: Colour any 3 out of 4 equal parts.
6. 1 quarter: Colour any 1 out of 4 equal parts.

Answer: In each shape, count the total parts (4), then colour the required number of equal parts as instructed above.

Given: Six whole shapes (not yet divided). Instructions tell what fraction to show.

Concept: First draw lines to divide the shape into 4 equal parts, then colour the required number of parts.

Step 1: Draw 2 lines through the centre of each shape to create 4 equal parts.
- For a square/rectangle: one horizontal + one vertical line through the centre.
- For a circle: two perpendicular diameters.

Step 2: Colour the required number of parts:
1. 2 quarters → colour 2 out of 4 parts.
2. 1 quarter → colour 1 out of 4 parts.
3. 3 quarters → colour 3 out of 4 parts.
4. 4 quarters → colour all 4 parts (complete whole).
5. 3 quarters → colour 3 out of 4 parts.
6. 1 quarter → colour 1 out of 4 parts.

Answer: Draw lines first to make 4 equal parts, then colour the instructed number of parts in each shape.

Given: A rectangle divided in a particular way (as shown in the image).

Concept: A rectangle can be divided into quarters in different ways, not just by two straight lines through the centre.

Explanation:
A rectangle shows quarters when it is divided into 4 equal parts. This can be done by:
- Drawing one horizontal and one vertical line through the centre (giving 4 equal smaller rectangles).
- Drawing two horizontal lines dividing it into 4 equal horizontal strips.
- Drawing two vertical lines dividing it into 4 equal vertical strips.
- Drawing diagonal lines or other creative cuts, as long as all 4 parts are equal in area.

Answer: The rectangle shows quarters because it is divided into 4 equal parts. Each part is exactly the same size — it is one quarter of the whole rectangle. Together, all 4 parts make the complete whole rectangle ($4 \text{ quarters} = 1 \text{ whole}$).

Given: Four grids (square grids).

Concept:
- Half = 2 equal parts; colour or mark $\frac{1}{2}$ of the grid.
- Quarter = 4 equal parts; colour or mark $\frac{1}{4}$ of the grid.

Different ways to show halves in a grid:
- Colour the top half (all squares in the top rows).
- Colour the left half (all squares in the left columns).
- Colour a diagonal half.

Different ways to show quarters in a grid:
- Colour the top-left quarter.
- Colour the top-right quarter.
- Colour the bottom-left quarter.
- Colour the bottom-right quarter.
- Colour a non-rectangular arrangement of squares that equals $\frac{1}{4}$ of the total.

Answer: In each grid, colour the required number of squares:
- For half: colour exactly half the total squares in any arrangement where both halves are equal.
- For quarter: colour exactly one-quarter of the total squares in any arrangement where all four quarters are equal.

Each grid should show a different way of making the half or quarter.

Given: Fraction cards (cut-out pieces) from the perforated sheet at the back of the book — these include halves and quarters of various shapes.

Concept: $2 \text{ halves} = 1 \text{ whole}$ and $4 \text{ quarters} = 1 \text{ whole}$.

Step 1: Take out the fraction cards.
Step 2: Try combining:
- 2 half-pieces of the same shape → they should fit together to form 1 whole.
- 4 quarter-pieces of the same shape → they should fit together to form 1 whole.
- 1 half + 2 quarters of the same shape → they should also form 1 whole.

Step 3: Superimpose pieces to verify they are exactly equal in size.

Answer:
- 2 halves placed together = 1 whole
- 4 quarters placed together = 1 whole
- 1 half + 2 quarters = 1 whole

The number of pieces used: 2 pieces (halves) or 4 pieces (quarters) or 3 pieces (1 half + 2 quarters) all make one complete whole.