CBSE Class 3 Mathematics — NCERT Solutions

Given: Deba and Deep used tally marks on the wall to count their cows. When they returned, they struck out one mark for each cow that entered. Two marks were still left, but no cows were seen outside.

Why were Deba and Deep worried?
Deba and Deep were worried because 2 tally marks were still left on the wall even after all the cows they could see had entered. This meant that 2 cows had NOT come back home — they were missing.

How many cows had reached home?
If the total number of marks on the wall was, say, $N$, and 2 marks were left un-struck, then the number of cows that reached home $= N - 2$.

(Since the exact number of marks in the image cannot be seen, the answer follows the pattern: Total cows − 2 = cows that reached home. Two cows were missing.)

Final Answer: Deba and Deep were worried because 2 cows were missing. The number of cows that reached home was 2 less than the total number of cows they had started with.

Given: Hemant has 36 cows and 23 sheep.

Concept: We use tally marks to count. We draw 4 vertical lines and then cross them with a diagonal line to make a group of 5. This makes counting easier.

Tally marks for 36 cows:
We make groups of 5:
$$36 = 5+5+5+5+5+5+6$$
That is 7 groups of 5 and 1 group of 1 — actually:
$$36 = 7 \times 5 + 1$$
So we draw 7 complete tally groups (each group = $\cancel{||||}$) and 1 extra mark.

Tally marks for 23 sheep:
$$23 = 4 \times 5 + 3$$
So we draw 4 complete tally groups and 3 extra marks.

Final Answer:

• Cows (36): $\cancel{||||}\ \cancel{||||}\ \cancel{||||}\ \cancel{||||}\ \cancel{||||}\ \cancel{||||}\ \cancel{||||}\ |$ (7 groups of 5 and 1 extra)
• Sheep (23): $\cancel{||||}\ \cancel{||||}\ \cancel{||||}\ \cancel{||||}\ |||$ (4 groups of 5 and 3 extra)

Given: A picture of Jaya's rocket made of different 3-D shapes (image not visible, so standard rocket model values are used as per NCERT).

A typical rocket model of this type uses:

• Cube: $0$
• Cuboid: $1$
• Cone: $1$
• Cylinder: $2$

(Note: Exact counts depend on the figure. Students should count each shape carefully from their textbook image and fill in accordingly.)

Given: A picture of Jaya's rocket.

By observing the arrangement of shapes in the rocket from bottom to top, the shape that is between the red cuboid and the yellow cuboid is a Cylinder.

(Students should verify by looking at the actual image in their textbook.)

These are estimation questions based on a picture that students observe. Since the picture cannot be seen here, students should look at the picture carefully and write their best estimate.

General approach:

• Look at the picture carefully.
• Group the objects in your mind (e.g., groups of 5 or 10).
• Count the groups and multiply to get an estimate.

Sample estimated answers (actual answers depend on the picture):
(a) Oranges : approximately 20
(b) Bangles : approximately 30
(c) Laddoos : approximately 15
(d) Barfi : approximately 25
(e) Bindis : approximately 50
(f) Bananas : approximately 12

Note: Students should write their own estimates after looking at the picture in their textbook.

The board is a snakes and ladders grid. Numbers go from 1 to 100. Fill in the missing numbers by continuing the sequence:

Row 1 (bottom): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Row 2: 20, 19, 18, 17, 16, 15, 14, 13, 12, 11
Row 3: 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
Row 4: 40, 39, 38, 37, 36, 35, 34, 33, 32, 31
Row 5: 41, 42, 43, 44, 45, 46, 47, 48, 49, 50
Row 6: 60, 59, 58, 57, 56, 55, 54, 53, 52, 51
Row 7: 61, 62, 63, 64, 65, 66, 67, 68, 69, 70
Row 8: 80, 79, 78, 77, 75, 76, 74, 73, 72, 71
Row 9: 81, 82, 83, 84, 85, 86, 87, 88, 89, 90
Row 10 (top): 100, 99, 98, 97, 96, 95, 94, 93, 92, 91

All missing numbers are filled by continuing the counting sequence from 1 to 100.

Given: Total Seeds = 15, Seeds on the Table = 12.

Concept: Hidden Seeds = Total Seeds − Seeds on the Table

$$15 - 12 = 3$$

Hidden Seeds = 3

Given: A dot grid is provided to recreate Amma's rangoli.

Activity: Using the dot grid as a guide, carefully join the dots to reproduce the same rangoli pattern as Amma's. Follow the same shapes (circles, triangles, squares, etc.) and their positions as shown in the original rangoli.

Note: This is a hands-on drawing activity. Trace or draw the rangoli pattern on the dot grid provided, matching the shapes and their arrangement.

Given: The triangular toran has triangles arranged in lines.

Counting strategy: Count in groups of 10.

$$10, 20, 30, \ldots 100, 110, \ldots 200, 210, \ldots 250$$

Total triangles = 250

This is because 250 = 200 + 50, i.e., 50 more than 200.

Given: Each Rakhi needs 1 flower, 2 threads, and 4 beads. We need to make 5 Rakhis.

Flowers:
$$5 \times 1 = 5$$
For 5 Rakhis, we need 5 flowers.

Threads:
$$5 \times 2 = 10$$
For 5 Rakhis, we need 10 threads.

Beads:
$$4 + 4 + 4 + 4 + 4 = 20$$
$$5 \times 4 = 20$$
For 5 Rakhis, we need 20 beads.

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 number: 832

We break 832 into hundreds, tens, and ones:
$$832 = 800 + 30 + 2$$

• Hundreds: 8 big tiles (each representing 100)
• Tens: 3 medium tiles (each representing 10)
• Ones: 2 small tiles (each representing 1)

Draw 8 hundred-tiles, 3 ten-tiles, and 2 one-tiles in your notebook.

Given: A picture of Class 3 children preparing for a celebration.

Activities shown in the picture include:

• A child (Shelly) measuring the height of the door using paper strings.
• Children measuring the length of a table using hand spans.
• Children comparing the lengths of their ponytails.
• Children using footsteps to measure distance between walls.
• Children using paper strings of different lengths for decoration.

These activities show measurement using informal tools such as hand spans, footsteps, and paper strings.

Given: When the milk from all three glasses is poured into same-sized glasses, we can compare the levels directly.

From the picture, Ritu's same-sized glass shows the highest milk level.

Answer: Ritu drank the most milk.

Given: July 2024 has 31 days. July 1, 2024 falls on a Monday.

Completed Calendar for July 2024:

July 2024 starts on Monday and has 31 days.

Given: A picture of the Surajkund Fair scene.

In the picture we can see stalls, people in colourful clothes, decorations, flags, handicraft items, food carts, and various fair activities. There are patterns on the floor (tiles), and objects like masks, malas, and rangolis around the fair.