Grade 6Mathematics

Multiplication

Multiplying up to 4-digit by 2-digit numbers (1.2, 6 lessons).

📖 8 min read · 4 worked examples · 8 practice questions

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The lesson

Specifically, we will learn how to multiply numbers that are up to four digits by two digits. This is a very useful skill. This lesson is part of the Kenyan KICD curriculum, Strand 1.2, which is all about numbers and operations. Why do we learn this? Think about someone selling tomatoes or maize at the market. They need to multiply the price per kilo by the number of kilos to get the total cost. Or, when you take a matatu. You might pay 50 shillings per trip. If you take 15 trips in a month, how much does that cost? That's multiplication! Even in construction. If a builder needs 120 bricks per wall, and is building 25 walls, they need to figure out the total. This skill is everywhere in real life.

We'll start with a very important review of the times tables, from one to twelve. These are our key review points. First, quick recall. We need to know these facts automatically, like we know our own names. Second, we must spot patterns. For example, you see here: 'Doubles, Triples'. What does that mean? If you know 4 x 4 is 16, you can quickly find 8 x 4 is double that, which is 32. Using patterns saves us time and mental effort. Let's focus on a key area. The larger products, like those from 6 times 7 and above, often take a bit more practice to remember. These are our 'Focus Area'. Here you see the key products we should have at our fingertips. 6 x 7 is 42. 7 x 8 is 56. 8 x 9 is 72. These are very common in calculations. Why are they so important? Because once you know them well, they become building blocks for larger problems, like the long multiplication we will do later. Take a moment to look down the table. Find one product that you always remember easily, and one you sometimes mix up. Keep that in mind. I want to share one of my favourite mental shortcuts. Here: 7 x 8 = 56, and it has this little rhyme '5-6-7-8'. The numbers 5, 6, 7, 8 are in order! This is a fun trick to help you lock it in your memory. Are there any other patterns or tricks you use to remember tricky tables? Let's share ideas.

Class, let's continue with our multiplication unit. We just covered basic multiplication, and now we are moving to the Long Multiplication Method. Specifically, we'll learn how to multiply a four-digit number, like 2475, by a two-digit number, like 62. It's a step-by-step process. First, look at this chart. It shows us the visual flow of the four steps we'll follow. Step one, step two, step three, step four. Step one is crucial: Write the numbers aligned correctly. You must line up the place values. The tens digit of the two-digit number goes directly above the ones digit. Step two: Multiply by the ones digit. Multiply every digit of the four-digit number by the ones digit of the bottom number. Write your first partial product. Step three: Multiply by the tens digit. Remember, because this is the tens digit, you shift your second partial product one place to the left. It's like multiplying by ten. Finally, step four: Add the partial products. You combine the two rows you've written to get your final answer. We'll walk through applying these four steps to this problem. To recap: Align correctly, multiply by ones, multiply by tens, then add. Once you master these steps, you can handle any large multiplication.

Let's wrap up our lesson by summarizing the key takeaways for long multiplication. First, always remember the core method: the Long Multiplication Method. Step one is crucial: align your numbers neatly by their place value. If the digits are out of line, your answer will be wrong. Step two: multiply by each digit from the bottom number. This is where knowing your multiplication tables from Standard 3 comes in handy. Step three: don't forget to add those placeholder zeros! Each new row of partial products must be shifted one place to the left. Finally, step four: add up all those partial products to get your final answer. Double-check your addition. Why is this skill so important? Because you use it in real Kenyan life every day. For example, if you and four friends take a matatu and the fare is 50 shillings each, you need to multiply to find the total fare. Or when budgeting: if a pen costs 30 shillings and you need ten for the term, that's another multiplication problem. Even with mobile money, if your mum sends you 200 shillings via M-Pesa each day, you multiply to know the total for a week. Practice regularly. Keep those multiplication tables sharp. A little practice each day will make you a multiplication master. In our next lesson, we'll build on this foundation and learn how to divide large numbers. You're doing great work, class. Keep it up.

Worked examples

Matatu Fares

A worked example that brings multiplication into our everyday lives. We'll solve a realistic Kenyan word problem. The problem is here: a real scenario we might encounter. The matatu, our shared taxi, charges 150 Kenyan shillings per person. We have 47 passengers. We need to find the total fare. Step 1 is to set up the equation. The total fare equals the fare per person multiplied by the number of passengers. We write that as 150 times 47. Step 2: We multiply using place value. We break 47 into 40 and 7. First, 150 multiplied by 40 gives us 6,000. Next, 150 multiplied by 7 gives us 1,050. 6,000 plus 1,050 equals 7,050. Our answer is clear: The total fare collected by the matatu driver is 7,050 Kenyan shillings.

Market Quantities

This is Worked Example Two. The problem: A farmer buys 124 bags of maize. The cost per bag is 2,350 shillings. What is the total cost? To find the total cost, we must multiply the price per bag by the number of bags. That is 2,350 multiplied by 124. The first step is to set up the multiplication correctly. We must align the numbers by place value. The key here is handling the zeros in 2,350. Notice the strategy. We break down 124 into 100, 20, and 4. Then we multiply 2,350 by each part separately: by 100, by 20, and by 4. This makes the calculation easier to manage. First, 2,350 times 100. Since it's times one hundred, we just shift the digits: 235,000. Then, 2,350 times 20 gives us 47,000. 2,350 times 4 gives us 9,400. The crucial part: adding these products. We must handle zeros carefully and ensure we add the place values correctly. 235,000 plus 47,000 is 282,000. Then add 9,400 to get 291,400. The total cost for the farmer is 291,400 shillings. That's a significant amount, so accuracy is very important. Remember the tip: always check your place values and add zeros carefully. In Kenyan markets, farmers and traders rely on accurate calculations for their business. This example shows how multiplication is used in everyday life. A quick check: if the price per bag increased to 2,500 shillings, how would the total change? Think about it.

M-Pesa Transactions

Let's apply our multiplication skills to a real-life situation that might be very familiar to many of us in Kenya. This is Worked Example 3, all about M-Pesa. Here is our problem. Let's all read it carefully. You need to send three thousand, eight hundred and twenty-five shillings each day for twenty-eight days. The question asks: what is the total amount sent? Think about that for a moment. This is how you'd figure out a monthly cost or total spending. Let's work through the solution together, step by step. The first and most important step is to set up our equation. The total equals 3,825 multiplied by 28. We have our starting point. A smart strategy to make 28 easier to multiply is to break it into 20 and 8. First, we multiply 3,825 by 20. Remember, multiplying by 20 is like multiplying by 2 and then by 10. 3,825 times 20 gives us 76,500. Second step, we multiply the same number, 3,825, by 8. Let's calculate that. 3,825 times 8 equals 30,600. Final step, very important. We add the two results we found. 76,500 plus 30,600 equals 107,100. There's our final answer. You would send a total of 107,100 shillings over the 28 days. This is exactly how multiplication helps us plan and understand costs in everyday life, like with M-Pesa.

s from Kenyan Contexts

Let's put our skills into practice with some real-life problems you might face right here in Kenya. Problem one is about school uniforms. A shirt costs 350 Kenyan shillings and trousers cost 480. Your task is to find the total cost. At the numbers: 350 and 480. Think about what operation you need to perform. Moving to problem two. This is about water. A pump fills a tank at a rate of 12 litres per minute. We need to find out how long it takes to fill a given amount. This involves rate, which is another word for speed. If you know the total litres and the litres per minute, you can work backwards to find the time. Problem three is from construction. One bag of cement costs 850 shillings. If a project needs five bags, what's the total cost? This is a straightforward multiplication problem. You have the cost of one item and the number of items you need. Finally, problem four involves a savings club, like a chama. Eight members each contribute 200 shillings. We need the total savings. Think: is this repeated addition, or can you see it as a multiplication problem? Both will give you the same answer. Your job is to solve each of these step by step. Show your working clearly. Remember to write your final answer with the correct unit, like 'Ksh' for money or 'minutes' for time. Take a moment to start working on the first one.

Practice questions

  • What is the product of 9 and 7? This is testing your recall of multiplication tables.
  • Second question is about setting up numbers correctly. When multiplying 43 by 25 using the lattice or vertical method, how should the numbers be aligned?
  • Finally, the last question asks: You are solving 312 × 4 using long multiplication. What is the first step?
  • The first question: 'A school bus makes 14 trips each week. It carries 48 students on every trip.
  • For the second one: 'At a school sports day.
  • Is interesting: 'A farmer collects eggs.
  • The last one is a real Kenyan context: 'David is a delivery driver in Nairobi using a matatu to deliver 25 parcels per trip, 38 trips a month.
  • Take your time, calculate carefully, and show your work step by step.

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