Mathematics: Class 4 — Chapter 13: The Transport Museum

13.1 Mystery Matrix & Times-10

This section introduces multiplication concepts through puzzles and visual representations of tens.

Mystery Matrix

A grid puzzle where students find 1-digit multiplicands and multipliers to match given products, and fill in the remaining products.

Times-10

Understanding multiplication by $10$ as counting groups of tens:

$2 \times 10 = 2 \text{ Tens} = 20$
$5 \times 10 = 5 \text{ Tens} = 50$
$8 \times 10 = 8 \text{ Tens} = 80$
$10 \times 10 = 10 \text{ Tens} = 100$ (which is equal to $1 \text{ Hundred}$)

13.2 Constructing Tables by Splitting

Larger multiplication tables can be constructed easily by splitting numbers into smaller, manageable groups.

Splitting into 10 and 5

To find a product like $5 \times 15$, we can split the arrangement into $10$ columns and $5$ columns:

$5 \times 15 = (5 \times 10) + (5 \times 5)$
$5 \times 15 = 50 + 25 = 75$

Splitting into Equal Groups (Doubling)

Multiplication can also be solved by doubling a known smaller product:

$3 \times 14 = (3 \times 7) + (3 \times 7) = 21 + 21 = 42$ (Double of $21$)
$6 \times 14 = (6 \times 7) + (6 \times 7) = 42 + 42 = 84$ (Double of $42$)

13.3 Multiples of 10 and 100

Rules and patterns for multiplying numbers by multiples of $10$ and $100$.

Multiples of 10

$14 \times 10 = 14 \text{ Tens} = 140$
$16 \times 20 = 16 \times 2 \text{ Tens} = 32 \text{ Tens} = 320$
$26 \times 10 = 26 \text{ Tens} = 260$

Multiples of 100

$3 \times 100 = 3 \text{ Hundreds} = 300$
$11 \times 100 = 11 \text{ Hundreds} = 1100$
$11 \times 200 = 11 \times 2 \text{ Hundreds} = 22 \text{ Hundreds} = 2200$
$80 \times 50 = 4000$

13.4 Area/Grid Method of Multiplication

A visual method to multiply multi-digit numbers by breaking them down into place values.

2-Digit by 2-Digit: $15 \times 14$

Split $15$ into $10 + 5$ and $14$ into $10 + 4$:

$10 \times 10 = 100$
$10 \times 4 = 40$
$5 \times 10 = 50$
$5 \times 4 = 20$
Total Product: $100 + 40 + 50 + 20 = 210$

3-Digit by 2-Digit: $64 \times 152$

Split $64$ into $60 + 4$ and $152$ into $100 + 50 + 2$:

$60 \times 100 = 6000$, $60 \times 50 = 3000$, $60 \times 2 = 120$
$4 \times 100 = 400$, $4 \times 50 = 200$, $4 \times 2 = 8$
Total Product: $6000 + 3000 + 120 + 400 + 200 + 8 = 9728$

13.5 Division and Remainders

Understanding division as repeated subtraction or grouping, and introducing leftovers.

The Concept of Remainder

When a number cannot be divided equally, the leftover amount is called the remainder.

Example: $324 \div 14$

$14 \times 10 = 140$ (Remaining: $324 - 140 = 184$)
$14 \times 10 = 140$ (Remaining: $184 - 140 = 44$)
$14 \times 1 = 14$ (Remaining: $44 - 14 = 30$)
$14 \times 2 = 28$ (Remaining: $30 - 28 = 2$)
Quotient: $10 + 10 + 1 + 2 = 23$
Remainder: $2$

Dividing by 10 and 100

$60 \div 10 = 6$
$600 \div 10 = 60$
$600 \div 100 = 6$
$400 \div 20 = 20$
$400 \div 200 = 2$