NCERT Class 4 Mathematics Maths Mela Chapter 13 The Transport Museum PDF Download

Chapter 13: The Transport Museum

Mystery Matrix

Fill the yellow boxes with 1-digit numbers (multiplicands and multipliers) such that you get the products given in the white boxes.

Fill the remaining white boxes with appropriate products.

[Figure: A multiplication matrix with yellow boxes for multiplicands and multipliers, white boxes for products, and one example showing 32, 42, 45, and 21 in some boxes]

The product of the numbers in each row is given in the orange boxes. The product of the numbers in each column is given in the blue boxes. Identify appropriate numbers to fill the blank boxes.

[Figure: A multiplication matrix showing row products (56, 54, 42, 50) in orange boxes and column products (63, 48, 60, 35) in blue boxes]

Times-10

Match each problem with the appropriate pictorial representation and write the answer.

1. \( 2 \times 10 = \) 2 Tens = ______
2. \( 5 \times 10 = \) _____ Tens = ______
3. \( 8 \times 10 = \) _____ Tens = ______

[Figure: Pictorial representations of tens using beads or dots arranged in groups]

10 Tens 10 Tens 1 Hundred = 100

What is \( 10 \times 10 = \) ____ Tens = _______

Constructing Tables

How many pebbles are there in this arrangement? _______

[Figure: An arrangement of pebbles in a 5 × 15 grid]

This is a \( 5 \times 15 \) arrangement. There is an easy way to find this product by splitting the arrangement.

\( 5 \times 15 = 5 \times 10 \) and \( 5 \times 5 \) = ______ + ______ = ______

Recall the times-tables that we created in Grade 3. Now construct a times-15 table. You may use the arrangement given below and split the columns into 10 and 5 for ease of counting, as shown on the previous page.

[Figure: An arrangement showing 15 columns and 10 rows of pebbles]

How can we find \( 1 \times 15 \), \( 2 \times 15 \), ..... with this?

What times-table is this? ____ How did we get this?

15 - 5 = 10 30 - 10 = 20 45 - 15 = 30 ____________ ____________ ____________ ____________ ____________ ____________ ____________

1. What patterns do you see in this table?
2. Compare the times-15 table with the times-5 table. What similarities and differences do you notice?
3. Construct other times-tables for numbers from 11 to 20, as you did for 15.
4. As you compared the times-5 table with the times-15 table, compare the times-1 table with the times-11 table, the times-2 table with the times-12 table, and so on. Share your observations.

Teacher's Note

When you compare the times-5 and times-15 tables, you will see that every term in the times-15 table is exactly 3 times the corresponding term in the times-5 table (because \( 15 = 3 \times 5 \)). This pattern works for other pairs too: the times-12 table is always 6 times the times-2 table. Look for this relationship when comparing any two times-tables.

Making tables by splitting into equal groups

Here is an arrangement of wheels. To count the total number of wheels, Tara splits them into two equal groups.

[Figure: An arrangement showing 3 rows of 14 wheels, split into two groups of 7 wheels each]

\( 3 \times 14 = 3 \times 7 \) and \( 3 \times 7 \) = 21 + 21 = double of 21 = 42

Similarly, \( 6 \times 14 \) can be obtained by splitting the arrangement into two equal groups.

[Figure: An arrangement showing 6 rows of 14 wheels, split into two groups of 7 wheels each]

\( 6 \times 14 = \) Double of \( 6 \times 7 \) Why?

\( 6 \times 14 = 6 \times 7 \) and \( 6 \times 7 \) = 42 + 42 = double of 42 = 84

We have seen how to calculate \( 3 \times 14 \) and \( 6 \times 14 \) by splitting and doubling. Can we construct the times-14 table by splitting and doubling? Try!

What other times-tables can be constructed by splitting into equal groups and doubling? Give examples.

Teacher's Note

When you split a number like 14 into \( 7 + 7 \), you can write \( 3 \times 14 = 3 \times (7 + 7) = (3 \times 7) + (3 \times 7) \). This is the distributive property of multiplication: you multiply each part and add the results. You can use this idea to split any even number and double a known times-table to find a new one.

Multiples of 10

[Figure: A visual showing 14 × 10 as 10 Tens and 4 Tens combined, using grid squares]

\( 14 \times 10 = 14 \) Tens = 10 Tens + 4 Tens = 100 + 40 = 140

Find the answers to the following:

1. \( 15 \times 10 = \) _____ Tens = _____
2. \( 16 \times 10 = \) _____ Tens = _____
3. \( 19 \times 10 = \) _____ Tens = _____
4. \( 20 \times 10 = \) _____ Tens = _____

\( 10 \times 10 = \) ____

2 times (i.e., double of) \( 10 \times 10 = \) ____

Discuss in grade what happens when we take several groups of 10.

Note for Teachers

Support the learners in understanding multiplication when group size is a multiple of 10. Language of 'tens' is a useful way to think about this. For example: \( 16 \times 10 = 16 \) Tens is 160 \( 16 \times 20 = 16 \times 2 \) Tens = 32 Tens = 320

Key Points

• When you multiply any number by 10, you can think of it as that many groups of 10, or "tens". For example, \( 14 \times 10 = 14 \) Tens \( = 140 \).
• To find products of numbers like 14 or 15, you can split them into parts you already know (like \( 14 = 7 + 7 \) or \( 15 = 10 + 5 \)) and use addition or doubling.
• Times-tables for larger numbers are related to times-tables for smaller numbers. For example, the times-15 table is exactly 3 times the times-5 table, because \( 15 = 3 \times 5 \).
• You can split an even number into two equal parts and use doubling to find its times-table quickly, using what you already know about related times-tables.

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