Sharing and Measuring

Given: A sheet of paper is to be shared between Ikra and Samina. The choices are one half ($\frac{1}{2}$) or two quarters ($\frac{2}{4}$).

Concept: $\frac{1}{2} = \frac{2}{4}$ because when a whole is divided into 4 equal parts, two of those parts together equal one half.

Answer: Both choices give exactly the same amount of paper. $\frac{1}{2} = \frac{2}{4}$. So it does not matter which one you choose — you get the same area of paper either way. A student may say they would choose either one, as long as they understand both are equal.

Given: Ikra offered Samina two quarters and kept one half for herself.

Concept: $\frac{2}{4} = \frac{1}{2}$. Two quarters of a whole equal one half of the same whole.

Working: If a paper is divided into 4 equal parts, each part is $\frac{1}{4}$. Two such parts = $\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$.

Answer: Yes, Ikra shared the paper equally. Both sisters got exactly half the paper. Samina received two quarters ($\frac{2}{4}$) and Ikra kept one half ($\frac{1}{2}$), and these are equal.

Given: The paper is divided into two portions.

Concept: Equal division means both parts have the same area/size.

Answer: We can check equal division by folding one part over the other. If both parts overlap exactly (one covers the other completely), the paper has been divided equally. We can also measure the length or area of each part — if they are the same, the division is equal.

Given: Samina was offered a choice between 'one half' and 'two quarters'.

Reason: Samina is young and does not yet know that $\frac{2}{4} = \frac{1}{2}$. The phrase 'two quarters' sounds like a bigger amount because the number 2 is greater than 1, and 'quarters' sounds like more pieces. She thought she was getting more paper by choosing two quarters.

Answer: Samina chose two quarters because she thought two pieces would be more than one piece. She did not realise that $\frac{2}{4}$ and $\frac{1}{2}$ are equal amounts.

Given: Several figures divided into two parts.

Concept: A figure is divided into halves correctly only when both parts are exactly equal in size and shape.

Method: For each figure, check whether the dividing line creates two parts of equal area. If both parts are equal, the figure is divided into halves correctly and should be coloured.

Answer: Colour only those figures where the line divides the shape into two equal (congruent) parts. Figures where one part is larger than the other are NOT halves and should not be coloured. (Since the actual figures are in the textbook image, students should apply the above rule to each figure shown.)

Given: Various shapes (rectangle, circle, triangle, etc.).

Concept: To divide a shape into halves, draw a line that splits it into two equal parts.

Method:
- Rectangle: Draw a line through the middle either horizontally or vertically.
- Circle: Draw a line through the centre (diameter).
- Triangle: Draw a line from one vertex to the midpoint of the opposite side (median).
- Square: Draw a line through the centre horizontally, vertically, or diagonally.

Answer: Draw a straight line through the centre/middle of each shape so that both resulting parts are equal in size. (Students should draw the line on the shapes given in their textbook.)

Given: Various shapes to be divided into 4 equal parts.

Concept: When a whole is divided into 4 equal parts, each part is called a quarter and is written as $\frac{1}{4}$.

Method:
- Rectangle/Square: Draw one horizontal and one vertical line through the centre, creating 4 equal parts.
- Circle: Draw two diameters perpendicular to each other.

Answer: Draw lines to divide each shape into 4 equal parts. Each part represents $\frac{1}{4}$ of the whole. (Students should draw the lines on the shapes given in their textbook.)

Think answer: If an object is divided into 5 equal parts, each part is written as $\frac{1}{5}$ (one-fifth). The denominator (bottom number) tells us the total number of equal parts, and the numerator (top number) tells us how many parts we are considering.

Given: A rectangular piece of paper.

Concept: A rectangle can be folded into two equal halves in multiple ways.

Different ways:
1. Fold along the horizontal centre line (landscape fold) — top half meets bottom half.
2. Fold along the vertical centre line (portrait fold) — left half meets right half.
3. Fold along one diagonal — creates two equal triangles.
4. Fold along the other diagonal — creates two equal triangles.

Answer: There are at least 4 different ways to fold/cut a rectangle into two equal halves. Each fold must result in two parts that are exactly equal in size.

Given: A rectangle to be divided into 4 equal parts.

Concept: Each of the 4 equal parts is $\frac{1}{4}$ (one quarter) of the whole.

Five different ways:
1. Two horizontal lines dividing the rectangle into 4 equal horizontal strips.
2. Two vertical lines dividing the rectangle into 4 equal vertical strips.
3. One horizontal and one vertical line through the centre (making 4 equal rectangles).
4. One diagonal and one line perpendicular to it through the centre.
5. Fold into half vertically, then fold that half horizontally (or vice versa).

Answer: Draw 5 rectangles and show a different way of dividing each into 4 equal parts. Each part in every drawing should be $\frac{1}{4}$ of the whole rectangle.

Given: Parts of shapes and their corresponding wholes are shown in the textbook image.

Concept: A part of a shape, when repeated the correct number of times, makes the complete whole shape.

Method: Look at each part and identify which whole shape it belongs to by checking the shape, size, and the fraction it represents.

Answer: Match each part to the whole it belongs to by identifying the shape and checking that the part fits exactly into the whole the correct number of times. (Students should draw lines matching each part to its whole as shown in the textbook figures.)

Given: Each time a new guest arrives, the dhokla is shared equally among more people.

Observation: As more people share the dhokla, the number of equal parts increases, so each person's share becomes smaller.

Answer: Sumedha observes that as each new guest arrives and the dhokla is shared among more people, her share of the dhokla keeps getting smaller. More people sharing the same whole means each person gets a smaller fraction.

Given: Dhokla shared among 9 people gives each person $\frac{1}{9}$; shared among 11 people gives each person $\frac{1}{11}$.

Concept: When the same whole is divided into more parts, each part is smaller. So \frac{1}{9} > \frac{1}{11}.

Answer: Sumedha will get more dhokla when it is shared among 9 people, because $\frac{1}{9}$ is greater than $\frac{1}{11}$. Fewer people sharing means a bigger piece for each person.

Given: The dhokla is divided into 6 equal parts, each part = $\frac{1}{6}$.

Concept: The number of equal parts needed to make a whole equals the denominator.

Working: $\frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{6}{6} = 1$ (complete whole).

Answer: 6 pieces of $\frac{1}{6}$ would make a complete dhokla.

Given: The dhokla is shared among 5 people (Sumedha, Vinayak, Kumar, Paridhi, Idha), so each person gets $\frac{1}{5}$. Idha and Vinayak give their shares to Sumedha.

Working: Sumedha's own share = $\frac{1}{5}$
Idha's share = $\frac{1}{5}$
Vinayak's share = $\frac{1}{5}$

Total Sumedha gets = $\frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{3}{5}$

Answer: Sumedha would get $\frac{3}{5}$ (three-fifths) of the dhokla.

Given: One whole dhokla shared equally.

Case 1 — 6 people:
Each person gets $\frac{1}{6}$ (one-sixth) of the dhokla.
Draw a circle divided into 6 equal parts; each part = $\frac{1}{6}$.

Case 2 — 8 people:
Each person gets $\frac{1}{8}$ (one-eighth) of the dhokla.
Draw a circle divided into 8 equal parts; each part = $\frac{1}{8}$.

Comparison: Since 6 < 8, dividing among 6 people gives bigger pieces.
\frac{1}{6} &gt; \frac{1}{8}

Answer: Each person gets $\frac{1}{6}$ when shared among 6 people, and $\frac{1}{8}$ when shared among 8 people. The people sharing among 6 will get bigger pieces because \frac{1}{6} &gt; \frac{1}{8}.

Given: Dhokla shared among different numbers of people.

Method: For each number of people $n$, Sumedha's share = $\frac{1}{n}$.
- 2 people: shade $\frac{1}{2}$ of the circle
- 3 people: shade $\frac{1}{3}$ of the circle
- 4 people: shade $\frac{1}{4}$ of the circle
- 5 people: shade $\frac{1}{5}$ of the circle, and so on.

Why fractions get smaller: The whole dhokla stays the same size. As we divide it among more people, each person's share becomes a smaller piece. The denominator (number of people) increases, making each fraction smaller.

Answer: Shade the appropriate sector in each circle diagram. The fractions get smaller because the same whole is being divided into more and more equal parts — more parts means each part is smaller.

Observations using the fraction kit:
- The whole (1) is the largest piece.
- $\frac{1}{2}$ pieces are the next largest — 2 of them make the whole.
- $\frac{1}{3}$ pieces are smaller than $\frac{1}{2}$ — 3 of them make the whole.
- As the denominator increases ($\frac{1}{4}, \frac{1}{5}, \frac{1}{6}$, etc.), each piece gets progressively smaller.
- The piece with the largest denominator is the smallest piece.
- Any set of equal pieces with the same denominator, when combined to equal the denominator count, makes one whole.

Example: Compare $\frac{1}{4}$ and $\frac{1}{6}$.

Place both pieces side by side. The $\frac{1}{6}$ piece is shorter/smaller than the $\frac{1}{4}$ piece.

Reason: Both fractions are parts of the same whole. The whole is divided into more parts for $\frac{1}{6}$ (6 parts) than for $\frac{1}{4}$ (4 parts). More parts from the same whole means each part is smaller.

Answer: \frac{1}{6} &lt; \frac{1}{4}. The piece with the larger denominator is always smaller (when comparing unit fractions of the same whole).

Yes, I agree with Sumedha.

Explanation: When the same whole is divided into more equal parts, each part must be smaller because the total size stays the same but is shared among more pieces.

Example: \frac{1}{2} &gt; \frac{1}{3} &gt; \frac{1}{4} &gt; \frac{1}{5} &gt; \frac{1}{6} &gt; \frac{1}{7} &gt; \frac{1}{8}

This can be verified with the fraction kit — the $\frac{1}{8}$ strip is much smaller than the $\frac{1}{2}$ strip, even though both are parts of the same whole.

Given: 5 pieces each of size $\frac{1}{5}$.

Working: $\frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{5}{5} = 1$ (one whole)

Verification with fraction kit: Take 5 pieces of the $\frac{1}{5}$ strip and place them together. They will exactly cover the whole strip.

Answer: Yes, Sumedha is correct. Joining 5 pieces of $\frac{1}{5}$ makes exactly one whole.

Given: A shape/strip where one part out of three equal parts is shown (refer to textbook image).

Concept: A fraction $\frac{1}{3}$ means the whole is divided into 3 equal parts and we are considering 1 part.

Answer: Sumedha is saying the part is one-third ($\frac{1}{3}$) because the whole has been divided into 3 equal parts and the shaded/shown part is exactly 1 of those 3 equal parts. Since all 3 parts are equal in size and together they make the whole, each part is $\frac{1}{3}$ of the whole.

Given: Two fractions $\frac{1}{4}$ and $\frac{1}{5}$ from the same whole.

Concept: For unit fractions (fractions with numerator 1), the one with the smaller denominator is greater.

Working: 4 < 5, so \frac{1}{4} &gt; \frac{1}{5}.

Answer: $\frac{1}{4}$ is greater than $\frac{1}{5}$.

Given: Two fractions $\frac{1}{9}$ and $\frac{1}{6}$.

Concept: For unit fractions, smaller denominator means larger fraction.

Working: 6 < 9, so \frac{1}{6} &gt; \frac{1}{9}.

Answer: $\frac{1}{6}$ > $\frac{1}{9}$.

Given: Compare $\frac{1}{6}$ and $\frac{1}{8}$.

Concept: For unit fractions, smaller denominator = larger fraction.

Working: 6 < 8, so \frac{1}{6} &gt; \frac{1}{8}.

Answer: $\frac{1}{6}$ > $\frac{1}{8}$.

Concept: For unit fractions, the one with the larger denominator is smaller.

Example answer: $\frac{1}{7}$ is smaller than $\frac{1}{3}$.

Reason: 7 > 3, so when the whole is divided into 7 parts, each part is smaller than when divided into 3 parts. Therefore \frac{1}{7} &lt; \frac{1}{3}.

Given: The garden is divided into 5 equal parts. Rose occupies 2 parts ($\frac{2}{5}$), Mogra occupies 1 part ($\frac{1}{5}$), Marigold occupies 1 part, Jasmine occupies 1 part.

Answer:
Marigold in $\frac{1}{5}$ (one-fifth) part of the garden.
Jasmine in $\frac{1}{5}$ (one-fifth) part of the garden.

Given: Garden divided into 5 equal parts. Rose occupies 3 parts = $\frac{3}{5}$. The remaining 2 parts are for Mogra and Marigold (1 each).

Answer:
Mogra in $\frac{1}{5}$ part.
Marigold in $\frac{1}{5}$ part.

Given: Garden divided into 5 equal parts. Rose occupies 4 parts = $\frac{4}{5}$. The remaining 1 part is for Marigold.

Answer: Marigold in $\frac{1}{5}$ part.

Given: Garden divided into 7 equal parts.
- Marigold: $\frac{1}{7}$ → 1 part
- Rose: $\frac{3}{7}$ → 3 parts
- Hibiscus: $\frac{3}{7}$ → 3 parts

Check: $\frac{1}{7} + \frac{3}{7} + \frac{3}{7} = \frac{7}{7} = 1$ ✓

Answer: Divide the garden strip into 7 equal parts. Colour/label 1 part as Marigold, 3 parts as Rose, and 3 parts as Hibiscus. (The remaining seeds — Mogra, Jasmine, Lily, Periwinkle — are not planted in this arrangement.)

Given: Garden divided into 7 equal parts.
- Lily: $\frac{3}{7}$ → 3 parts
- Marigold: $\frac{2}{7}$ → 2 parts
- Periwinkle: $\frac{2}{7}$ → 2 parts

Check: $\frac{3}{7} + \frac{2}{7} + \frac{2}{7} = \frac{7}{7} = 1$ ✓

Answer: Divide the garden strip into 7 equal parts. Label 3 parts as Lily, 2 parts as Marigold, and 2 parts as Periwinkle.

Given: Garden divided into 7 equal parts.
- Mogra: $\frac{5}{7}$ → 5 parts
- Hibiscus: $\frac{2}{7}$ → 2 parts

Check: $\frac{5}{7} + \frac{2}{7} = \frac{7}{7} = 1$ ✓

Answer: Divide the garden strip into 7 equal parts. Label 5 parts as Mogra and 2 parts as Hibiscus.

Given: The dosa is divided into parts (refer to textbook image). Based on the image description, the dosa appears to be divided into 4 equal parts with 2 toppings shown.

Note: The exact shading is in the textbook image. Applying the concept that the dosa is divided into equal parts:

If the dosa is divided into 4 equal parts and Chilli paneer covers 2 parts and Classic potato covers 2 parts:
1) Chilli paneer = $\frac{2}{4}$ (or $\frac{1}{2}$)
2) Classic potato = $\frac{2}{4}$ (or $\frac{1}{2}$)

(Students should count the actual shaded parts in their textbook image and write the fraction as: number of parts with that topping ÷ total number of equal parts.)

Given: The dosa is divided into equal parts with 3 toppings (refer to textbook image).

Concept: Fraction = $\frac{\text{number of parts with that topping}}{\text{total equal parts}}$

If the dosa is divided into 4 equal parts with each topping getting some parts:
Example answer (students verify with their image):
1) Tangy tomato = $\frac{1}{4}$
2) Classic potato = $\frac{2}{4}$
3) Spicy onion = $\frac{1}{4}$

Check: $\frac{1}{4} + \frac{2}{4} + \frac{1}{4} = \frac{4}{4} = 1$ ✓

Given: The dosa is divided into equal parts with 2 toppings (refer to textbook image).

Concept: Fraction = $\frac{\text{number of parts with that topping}}{\text{total equal parts}}$

Example answer (students verify with their image):
1) Spicy onion = $\frac{3}{4}$
2) Tangy tomato = $\frac{1}{4}$

Check: $\frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1$ ✓

Given: The dosa is divided into equal parts with 3 toppings (refer to textbook image).

Concept: Fraction = $\frac{\text{number of parts with that topping}}{\text{total equal parts}}$

Example answer (students verify with their image):
1) Tangy tomato = $\frac{2}{6}$
2) Classic potato = $\frac{3}{6}$
3) Spicy onion = $\frac{1}{6}$

Check: $\frac{2}{6} + \frac{3}{6} + \frac{1}{6} = \frac{6}{6} = 1$ ✓

Given: Dosa to be divided into 3 equal parts.
- Spicy onion: $\frac{2}{3}$ → 2 parts out of 3
- Classic potato: $\frac{1}{3}$ → 1 part out of 3

Check: $\frac{2}{3} + \frac{1}{3} = \frac{3}{3} = 1$ ✓

Answer: Draw a circle (dosa) and divide it into 3 equal parts. Shade/label 2 parts as Spicy onion and 1 part as Classic potato.

Given: Dosa to be divided into 8 equal parts.
- Classic potato: $\frac{3}{8}$ → 3 parts
- Chilly paneer: $\frac{1}{8}$ → 1 part
- Tangy tomato: $\frac{4}{8}$ → 4 parts

Check: $\frac{3}{8} + \frac{1}{8} + \frac{4}{8} = \frac{8}{8} = 1$ ✓

Answer: Draw a circle (dosa) and divide it into 8 equal parts. Label 3 parts as Classic potato, 1 part as Chilly paneer, and 4 parts as Tangy tomato.

Given: Total cookies = 12.

Concept: When 12 cookies are shared equally among $n$ children, each child gets $\frac{12}{n}$ cookies, and each child's share as a fraction of the whole is $\frac{1}{n}$.

a) 3 children:
Each child gets $\frac{12}{3} = 4$ cookies.
Fraction each child gets = $\frac{1}{3}$ of the total (i.e., 4 out of 12).
Circle groups of 4 cookies each.

b) 6 children:
Each child gets $\frac{12}{6} = 2$ cookies.
Fraction each child gets = $\frac{1}{6}$ of the total (i.e., 2 out of 12).
Circle groups of 2 cookies each.

c) 2 children:
Each child gets $\frac{12}{2} = 6$ cookies.
Fraction each child gets = $\frac{1}{2}$ of the total (i.e., 6 out of 12).
Circle groups of 6 cookies each.

d) 4 children:
Each child gets $\frac{12}{4} = 3$ cookies.
Fraction each child gets = $\frac{1}{4}$ of the total (i.e., 3 out of 12).
Circle groups of 3 cookies each.

Given: A group of friends (refer to textbook image for the number). $\frac{1}{3}$ of them receive hairbands.

Method: Count the total number of friends shown. Divide that number by 3. The result is the number of friends who get hairbands.

Example: If there are 9 friends shown:
$\frac{1}{3}$ of 9 = $9 \div 3 = 3$ friends get hairbands.

Answer: Divide the friends into 3 equal groups. Place hairbands on 1 group (one-third of the total). (Students should count the friends in their textbook image and apply this method.)

Given: A number of pots shown in the textbook image.

Method: Count the total number of pots. Divide by 5. Draw flowers in that many pots.

Example: If there are 10 pots:
$\frac{1}{5}$ of 10 = $10 \div 5 = 2$ pots should have flowers drawn in them.

Answer: Count the pots, divide by 5, and draw flowers in that many pots. (Students should count the actual pots in their textbook image and apply this method.)

Given: Total barfis = 16. Divided into 4 equal parts.

Working:
$$\frac{1}{4} \text{ of } 16 = 16 \div 4 = 4$$

Draw 16 barfis arranged in 4 equal groups of 4.

Answer: Each part contains $\mathbf{4}$ barfis. $\frac{1}{4}$ of 16 = 4.

Given: Mohan's ribbon length is shown in the textbook. Mohan's ribbon = $\frac{1}{4}$ of Rohan's ribbon.

Concept: If Mohan's ribbon = $\frac{1}{4}$ of Rohan's ribbon, then Rohan's ribbon = 4 × Mohan's ribbon.

Method: Measure Mohan's ribbon length. Multiply by 4 to get Rohan's ribbon length.

Example: If Mohan's ribbon = 3 cm, then Rohan's ribbon = $4 \times 3 = 12$ cm.

Answer: Rohan's ribbon is 4 times as long as Mohan's ribbon. Draw Rohan's ribbon as 4 copies of Mohan's ribbon placed end to end.

Given: A rectangle folded into 3 equal parts; 1 part is coloured = $\frac{1}{3}$.

Step 1: Fold into 3 equal parts → coloured part = $\frac{1}{3}$
Step 2: Fold in half (now 6 equal parts) → coloured part = $\frac{2}{6}$
Step 3: Fold in half again (now 12 equal parts) → coloured part = $\frac{4}{12}$
Step 4: Fold in half again (now 24 equal parts) → coloured part = $\frac{8}{24}$
Step 5: Fold in half again (now 48 equal parts) → coloured part = $\frac{16}{48}$

All these fractions are equal to $\frac{1}{3}$ — they are called equivalent fractions.

Answer: $$\frac{1}{3} = \frac{2}{6} = \frac{4}{12} = \frac{8}{24} = \frac{16}{48}$$

Observation: Each time we fold in half, both the numerator and denominator double, but the value of the fraction stays the same.

Given: A rectangle folded into 2 equal parts; 1 part is coloured = $\frac{1}{2}$.

Step 1: Fold into 2 equal parts → coloured part = $\frac{1}{2}$
Step 2: Fold in half (now 4 equal parts) → coloured part = $\frac{2}{4}$
Step 3: Fold in half again (now 8 equal parts) → coloured part = $\frac{4}{8}$
Step 4: Fold in half again (now 16 equal parts) → coloured part = $\frac{8}{16}$
Step 5: Fold in half again (now 32 equal parts) → coloured part = $\frac{16}{32}$

All these are equivalent fractions equal to $\frac{1}{2}$.

Answer: $$\frac{1}{2} = \frac{2}{4} = \frac{4}{8} = \frac{8}{16} = \frac{16}{32}$$

Given: Fraction chart showing $\frac{1}{2}$ and $\frac{1}{4}$ strips.

Working: $\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$

Answer: Two pieces of $\frac{1}{4}$ are equal to $\frac{1}{2}$.

Given: Compare $\frac{2}{3}$ and $\frac{1}{2}$.

Method using fraction chart: Place two $\frac{1}{3}$ pieces against one $\frac{1}{2}$ piece.

Working: $\frac{2}{3}$ means 2 out of 3 equal parts. $\frac{1}{2}$ means 1 out of 2 equal parts.
Converting to same denominator: $\frac{2}{3} = \frac{4}{6}$ and $\frac{1}{2} = \frac{3}{6}$.
Since \frac{4}{6} &gt; \frac{3}{6}, we have \frac{2}{3} &gt; \frac{1}{2}.

Answer: $\frac{2}{3}$ is greater than $\frac{1}{2}$.

Working: $\underbrace{\frac{1}{10} + \frac{1}{10} + \cdots + \frac{1}{10}}_{10 \text{ times}} = \frac{10}{10} = 1$

Answer: True. Ten pieces of $\frac{1}{10}$ make exactly one complete whole, because $\frac{10}{10} = 1$.

Working:
Three pieces of $\frac{1}{6}$: $\frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$

Two pieces of $\frac{1}{8}$: $\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$

Since $\frac{1}{2} \neq \frac{1}{4}$, the statement is false.

Answer: False. Three pieces of $\frac{1}{6}$ equal $\frac{1}{2}$, while two pieces of $\frac{1}{8}$ equal $\frac{1}{4}$. These are not equal.

Working: We need to find $n$ such that $n \times \frac{1}{8} = \frac{1}{4}$.
$$n = \frac{1}{4} \div \frac{1}{8} = \frac{1}{4} \times 8 = 2$$

Verification: $\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$ ✓

Answer: 2 pieces of $\frac{1}{8}$ make $\frac{1}{4}$.

Using the fraction chart, here are some combinations:

- $\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$ (two quarters make a half)
- $\frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$ (three sixths make a half)
- $\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$ (two eighths make a quarter)
- $\frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$
- $\frac{1}{4} + \frac{1}{8} + \frac{1}{8} = \frac{2}{8} + \frac{1}{8} + \frac{1}{8} = \frac{4}{8} = \frac{1}{2}$

Answer: Many combinations of smaller pieces can be put together to make a bigger piece. The key is that the fractions must add up to equal the bigger piece.

Given: Several squares divided in different ways (refer to textbook images).

Concept: A square is cut into equal parts only when all resulting pieces have the same size and shape.

Method: For each square:
1. Check if all parts are equal in size.
2. If yes, circle it and write the fraction: $\frac{\text{number of shaded parts}}{\text{total equal parts}}$.
3. If parts are unequal, do not circle it.

Answer: Circle only the squares where all parts are equal. For each circled square, count the total parts and the shaded parts, then write the fraction. (Students apply this rule to each square shown in their textbook image.)

Given: Six pictures with shaded parts and children's claims about the fractions.

Concept: A fraction is correct only if (a) the shape is divided into equal parts, and (b) the number of shaded parts matches the numerator while the total equal parts match the denominator.

Method for each picture:
1. Check if all parts are equal.
2. Count total parts (= denominator).
3. Count shaded parts (= numerator).
4. Compare with the child's claim.

General guidance (students verify with their textbook images):
- If the shape is divided into 3 equal parts and 1 is shaded → $\frac{1}{3}$ is correct.
- If parts are unequal, the fraction claim is incorrect regardless of the numbers.
- You can draw additional lines to make parts equal and then verify.

Answer: Circle the claims that match the actual equal division and shading. Cross out claims where either the parts are unequal or the fraction does not match the shading. (Students should examine each image carefully.)

Given: Six pictures with coloured parts (refer to textbook images).

Concept: Fraction = $\frac{\text{number of coloured parts}}{\text{total number of equal parts}}$

Method: For each picture, count the total equal parts and the number of coloured parts, then write the fraction.

Answer: (Students count the parts in each image and write the fraction.)
Example answers based on typical textbook figures:
- Figure 1: $\frac{1}{2}$
- Figure 2: $\frac{2}{4}$ or $\frac{1}{2}$
- Figure 3: $\frac{3}{6}$ or $\frac{1}{2}$
- Figure 4: $\frac{1}{3}$
- Figure 5: $\frac{2}{5}$
- Figure 6: $\frac{3}{8}$

(Actual answers depend on the specific images in the textbook.)

Given: Six pictures with blue parts (refer to textbook images).

Concept: Fraction of blue parts = $\frac{\text{number of blue parts}}{\text{total equal parts}}$

Method: Count the total equal parts in each figure and the number of blue parts. Write the fraction.

Answer: (Students count the blue parts and total parts in each image.)
Example answers:
- Figure 1: $\frac{1}{4}$
- Figure 2: $\frac{2}{6}$ or $\frac{1}{3}$
- Figure 3: $\frac{3}{8}$
- Figure 4: $\frac{2}{5}$
- Figure 5: $\frac{1}{3}$
- Figure 6: $\frac{3}{4}$

(Actual answers depend on the specific images in the textbook.)

Given: Four shapes to be divided and shaded.

a) Shade $\frac{2}{3}$:
Divide the shape into 3 equal parts. Shade any 2 of the 3 parts.

b) Shade $\frac{4}{6}$:
Divide the shape into 6 equal parts. Shade any 4 of the 6 parts.
Note: $\frac{4}{6} = \frac{2}{3}$, so this is the same amount as (a).

c) Shade $\frac{1}{4}$:
Divide the shape into 4 equal parts. Shade 1 part.
To also show $\frac{1}{8}$: Divide the shape into 8 equal parts. Shade 1 part (which is half the size of $\frac{1}{4}$).

d) Shade $\frac{3}{4}$:
Divide the shape into 4 equal parts. Shade 3 of the 4 parts.

Answer: Draw the dividing lines carefully to ensure all parts are equal, then shade the required number of parts as described above.