Lesson Notes By Weeks and Term v3 - Primary 6
Multiplication
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Multiplication
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Subject: General Mathematics
Class: Primary 6
Term: 3rd Term
Week: 2
Theme: Basic Operations
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Multiply a 3-digit number by a 3-digit number. Apply multiplication to the daily life activities Solve problems on quantitative aptitude on multiplication. Multiply decimal by decimal (to one decimal place). Multiply fractions by fraction Calculate square of numbers up to
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0. Calculate the square roots of perfect squares.
This involves extending the standard multiplication algorithm. The process entails multiplying the multiplicand by each digit of the multiplier, starting from the units digit, then the tens digit, and finally the hundreds digit. Partial products are then added together.
Steps: Multiply the multiplicand by the units digit of the multiplier. Multiply the multiplicand by the tens digit of the multiplier, placing a zero in the units column of the partial product. Multiply the multiplicand by the hundreds digit of the multiplier, placing zeros in the units and tens columns of the partial product. Add the three partial products to obtain the final product.
Worked Example 1 (Nigerian Context): A farmer planted 245 rows of maize, and each row contained 132 maize plants. How many maize plants are there in total?
Problem: $245 \times 132$ Solution: ``` 245 x 132 490 (245 x 2 <-- units digit of multiplier) 7350 (245 x 30 <-- tens digit of multiplier) 24500 (245 x 100 <-- hundreds digit of multiplier) 32340 ``` Therefore, there are 32,340 maize plants in total. This process is a systematic extension of multiplying by 1-digit and 2-digit numbers, using the standard long multiplication algorithm. It involves three partial products, which are then summed.
Example 1: Calculate $487 \times 235$ Multiply by the units digit (5): $487 \times 5 = 2435$ (Write 2435 in the first row of partial products, aligned to the right)
Multiply by the tens digit (30): $487 \times 30 = 14610$ (Write 14610 in the second row, starting with a zero in the units place, aligned under the tens column of the first partial product)
Multiply by the hundreds digit (200): $487 \times 200 = 97400$ (Write 97400 in the third row, starting with two zeros in the units and tens places, aligned under the hundreds column of the first partial product)
Add the partial products: ``` 487 x 235 2435 (487 x 5) 14610 (487 x 30) 97400 (487 x 200) 114445 ``` Therefore, $487 \times 235 = 114,445$. Nigerian Context
Example: A textile company produces 365 yards of Ankara fabric daily. If they operate for 125 days in a year, how many yards of Ankara fabric would they produce?
Problem: $365 \times 125$ Solution: ``` 365 x 125 1825 (365 x 5) 7300 (365 x 20) 36500 (365 x 100) 45625 ``` They would produce 45,625 yards of Ankara fabric. Multiplication is vital for solving problems involving repeated addition, scaling, and calculating total quantities or costs. Quantitative aptitude problems test the ability to apply mathematical concepts to real-world situations, often requiring critical thinking and multiple steps. Worked Example 2 (Nigerian Context - Daily Life Application): A market vendor buys 150 crates of eggs. If each crate contains 30 eggs, and each egg sells for N80, how much money will the vendor make if all the eggs are sold?
Solution: Total number of eggs: $150 \text{ crates} \times 30 \text{ eggs/crate} = 4500 \text{ eggs}$ Total money made: $4500 \text{ eggs} \times N80/\text{egg} = N360,000$ The vendor will make N360,
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0. Worked Example 3 (Nigerian Context - Quantitative Aptitude): If a driver travels 75 km in one hour, how far will the driver travel in 4 hours if the speed is consistent? If the driver maintains this speed for 3 days, driving 8 hours each day, what is the total distance covered?
Solution: Distance in 4 hours: $75 \text{ km/hour} \times 4 \text{ hours} = 300 \text{ km}$ Total driving hours in 3 days: $3 \text{ days} \times 8 \text{ hours/day} = 24 \text{ hours}$ Total distance in 3 days: $75 \text{ km/hour} \times 24 \text{ hours} = 1800 \text{ km}$ The driver will cover 1800 km in 3 days. This involves translating real-world scenarios into mathematical multiplication problems and solving them. Quantitative aptitude problems often present a situation that requires a sequence of logical steps, including multiplication, to arrive at a solution.
Nigerian Context Example 1 (Daily Life): A school needs to buy new desks for 15 classrooms. If each classroom requires 25 desks, and each desk costs N7,500, what is the total cost for all the desks?
Solution: Number of desks needed: $15 \text{ classrooms} \times 25 \text{ desks/classroom} = 375 \text{ desks}$ Total cost: $375 \text{ desks} \times N7,500/\text{desk} = N2,812,500$ The total cost for all the desks is N2,812,
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0. Nigerian Context Example 2 (Quantitative Aptitude): A transport company charges N150 per passenger for a trip from Ibadan to Lagos. If a bus has 45 seats and completes 4 trips a day, what is the maximum amount of money the company can make in 5 days, assuming all seats are filled for every trip?
Solution: Money per trip (full bus): $45 \text{ passengers} \times N150/\text{passenger} = N6,750$ Money per day (4 trips): $N6,750/\text{trip} \times 4 \text{ trips/day} = N27,000$ Money in 5 days: $N27,000/\text{day} \times 5 \text{ days} = N135,000$ The company can make a maximum of N135,000 in 5 days.
Market and Commerce (Economy): Multiplication is essential for calculating the total cost of multiple items. For instance, a trader at Onitsha market needs to calculate the cost of 25 bags of rice at N35,000 per bag. Similarly, a customer buying 3 metres of fabric at N1,200 per metre uses multiplication. This directly relates to budgeting and financial literacy in everyday Nigerian life. Agriculture and Farming (Community/Economy): Farmers use multiplication to estimate yields (e.g., if one yam mound produces 5 yams, 500 mounds will produce 2500 yams) or to calculate the amount of fertilizer needed for a large farm plot. Understanding squares helps in calculating the area of rectangular or square plots of land, which is vital for planning planting and harvesting. Construction and Design (Community/Environment): Builders and architects use multiplication for various measurements. For example, calculating the number of tiles needed for a floor (area calculation), the cost of multiple bags of cement, or scaling designs. The concept of squares and square roots is fundamental in calculating areas and determining side lengths for square spaces.
Resource Management (Environment): Calculating water usage (e.g., if a household uses 20 litres of water daily, how much is used in 30 days?), or projecting waste generation over time for environmental planning.