Grade 6Mathematics

Mass

Tonnes, kilograms, grams; relationships between mass units (2.4, 14 lessons).

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

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The lesson

This is an exciting part of our mathematics journey. Let's move into a very practical topic: Strand 2.4, Measurement, specifically focusing on Mass. What is mass? At its core, it's simply a measure of how much 'stuff' or matter an object has. The more 'stuff', the greater the mass. Think about a small mango versus a big watermelon – the watermelon has more mass. This idea of mass is incredibly important in our everyday life here in Kenya. First, think about buying goods at the market. When you buy rice, sugar, or maize flour, you're buying a certain mass of it. The price is often based on that mass – like per kilogram. Another big application is in transporting crops. Farmers loading their produce, like avocados or cabbages, onto a lorry or truck need to know the mass. This ensures the vehicle isn't overloaded for safety and helps calculate costs. It's not just about buying and selling. Mass matters at home too. Cooking recipes, for example, often specify mass – 'add 250 grams of flour'. Even checking your own weight involves measuring mass. As we can see, understanding mass helps us in buying, selling, transporting, and cooking.

Far we've been exploring measurements. Last time we discussed length and how we measure it. Let's build on that and focus on measuring something different. Mass is how much 'stuff' is in an object, and we use these three main units, from the heaviest down to the lightest, to measure everything. This is the 'Tonnes', or 't' for short. We use this for objects that are extremely heavy. Here are some excellent examples from our daily lives. A 'lorry', or truck, delivering goods is measured in tonnes. Also, the 'sacks of maize' you might see at the market — a full lorry-load of maize is many tonnes. Next, the unit you and I use all the time: the 'Kilogram', or 'kg'. This is our go-to unit for weighing everyday items. At these examples. A 'bag of sugar' from the shop is often 1 or 2 kilograms. Of course, when you step on a scale, your own body weight is measured in kilograms. Finally, for the smallest and lightest items, we use 'Grams', written as 'g'. This unit is perfect for things that weigh very little. Think about a 'tomato' you buy at the market. A single tomato might weigh about 100 grams. Or the 'spices' your mother uses for cooking — just a pinch or a small spoonful is measured in grams. To really bring this home and help you remember, let's look at some specific 'Examples from Kenya'. Let's examine this table. It shows us real objects we see around us in Kenya and which unit of mass is best for measuring them. We have an elephant — that's measured in tonnes. A school bag is measured in kilograms. A mobile phone? That's measured in grams.

Let's get very clear on the relationship between these three units: tonnes, kilograms, and grams. It's all about scale and conversion. The first key relationship is this: one tonne equals one thousand kilograms. One thousand! If you have a big lorry carrying sand, and it weighs one tonne, that's the same as one thousand of the kilogram weights we use in the market. The next relationship is similar: one kilogram equals one thousand grams. That bag of maize flour that's one kilogram? Inside, it's made up of one thousand tiny gram units. Think about this. If one tonne is a thousand kilograms, and one kilogram is a thousand grams... How many grams are in one tonne? Let's follow the chain. It's one thousand kilograms times one thousand grams per kilogram. That gives us... One million grams! One tonne equals one million grams. That's a huge jump in scale. At this chart. It shows the scale visually, from the biggest unit, the tonne, down to the kilogram, and finally to the gram. The arrows and numbers show the conversion factors. You can see it's a pyramid, getting wider as the units get smaller, because you need more of them. Remember the flow: from big to small. Tonne to kilogram to gram. Each step, you multiply by one thousand. This visualisation helps us see that moving down the scale means the numbers get much, much larger.

Let's summarize the key takeaways so we're all clear on what mass means and how to work with it. First, the most important concept: Mass is simply a measure of how much matter, or 'stuff', is in an object. That's it! Whether it's a sack of maize or a new phone, we're measuring the amount of material inside. We use three main units. Tonnes, for very heavy things like a lorry load of sand. Kilograms, for everyday items like your school bag or a bag of sugar. Grams, for smaller things like a packet of milk or a pencil. The relationship between them is crucial. Remember this formula: One tonne equals one thousand kilograms. One kilogram equals one thousand grams. The relationships are clear: 1 tonne equals 1000 kilograms, and 1 kilogram equals 1000 grams. This is the key to converting between units. It's all about multiplying or dividing by 1000. A practical skill: Always read scales carefully. At the units marked and the intervals between numbers. When a problem gives you mass in one unit but asks for the answer in another, you must convert using the relationships we just covered. Finally, and this is the exciting part, you now have the skills to apply this knowledge in real Kenyan situations! You can figure out if a 5-tonne lorry can carry 6000 kilograms of bricks, or how many 500-gram packets of flour make up 2 kilograms. Great work today, everyone. You've grasped the concept of mass, its units, and how to use them. Keep practicing, and you'll be mass measurement experts in no time.

Worked examples

Buying Maize

Building on what we just covered about units, let's apply it. Here's a real problem. A farmer buys 2 tonnes of maize. The question is: how many kilograms is this? Step one is always to recall the relationship. We know 1 tonne equals 1000 kilograms. Step two is the multiplication. We have 2 tonnes, so we multiply 2 by 1000 kilograms per tonne. 2 multiplied by 1000 gives us 2000. A very straightforward calculation. Our final answer: 2 tonnes of maize equals 2000 kilograms. Excellent work, everyone. This is the exact process we'll use for all conversion problems.

Loading a Lorry

Everyone, next, let's tackle another worked example. This one is called 'Loading a Lorry'. Here's our problem statement: a lorry carries 1500 kilograms of fertilizer. Then, workers add three sacks. Each sack weighs 50 kilograms. Our task is to find the total mass, but we need to give the answer in tonnes. What is the total mass in tonnes? We'll break this into three clear steps. First, Step 1: calculate the mass of the sacks that were added. How many sacks? Three. Each is 50 kilograms. We multiply: 3 times 50 equals 150 kilograms. Step 2: add this extra mass to the lorry's initial load. We need to find the total in kilograms before we convert. The lorry started with 1500 kilograms. We add the 150 kilograms from the sacks. 1500 plus 150 gives us 1650 kilograms. Step 3 is crucial: we convert kilograms to tonnes. Remember, 1 tonne is equal to 1000 kilograms. That's our conversion rule. We have 1650 kilograms. To get tonnes, we divide by 1000. 1650 divided by 1000 equals 1.65 tonnes. Always keep this conversion in mind: 1 tonne = 1000 kilograms. It's the key to solving many mass problems. Great job following those steps. The total mass after loading the lorry is 1.65 tonnes.

Market Produce

This one is called Market Produce. Our problem says Mama Njugu buys 2 kilograms of potatoes and 500 grams of tomatoes. What is the total mass in grams? We have two different units here: kilograms and grams. We cannot add them directly, can we? Step one is the most important: convert the kilograms to grams. Remember our rule: 1 kilogram equals 1000 grams. 2 kilograms is 2 multiplied by 1000. This calculation gives us 2000 grams for the potatoes. For step two. Our potatoes are 2000 grams, and our tomatoes are 500 grams. We add them together: 2000 plus 500. The sum is 2500 grams. Step three gives us our final answer. The total mass of Mama Njugu's vegetables is 2500 grams. Great work, everyone. This is a very common type of problem you'll see in real life, at the market. Always remember: if you have kilograms and grams, convert the kilograms to grams first.

Solving Word Problems: A Step-by-Step Guide

Excellent work on those practice problems. Let's build on those skills and tackle a very important topic: solving word problems. Word problems can seem tricky, but with a clear strategy, you can solve any of them. Here is our general strategy, a step-by-step guide. This is your toolkit for tackling mass word problems, especially ones with real contexts we see here in Kenya, like the weight of maize sacks or the load on a lorry. Step one is the most important: read carefully. Don't rush. Identify the objects involved. What are we weighing? Is it bags, animals, people? Also, identify all the units mentioned. Are we mixing grams and kilograms? Step two: draw a picture or make a list. Note down every mass given in the problem. A quick sketch of a lorry with sacks labelled with their weights can make everything much clearer. Step three: convert. This is a critical skill. Before you can add or compare, all masses must be in the same unit. If you have 2 kg and302 g, you must convert one so they are both kilograms or both grams. Step four: calculate. You perform the operation the problem asks for. Is it addition to find a total? Subtraction to find a difference? Follow your plan from step two and use your converted numbers from step three. Finally, step five: check. Ask yourself, is my answer reasonable? If the problem is about the weight of a chicken, does your answer make sense? Could a chicken weigh 200 kilograms? This step catches silly mistakes. To solve any mass word problem: Read, List, Convert, Calculate, and Check. This five-step process will guide you. Let's commit these steps to memory and see how they work in our next example.

Practice questions

  • Please read each question carefully. These questions will test your ability to convert between tonnes, kilograms, and grams, and to choose the right unit for a real-world situation, like buying rice or measuring a lorry's load.
  • For the first two questions, remember our conversions: 1 tonne equals 1000 kilograms, and 1 kilogram equals 1000 grams. Converting 5 tonnes means we multiply by 1000, giving us 5000 kilograms.
  • Think about the scale. A single bag of cement is heavy, but a lorry carries many, many bags.
  • For the short answer question, imagine your family at the market. A 2 kg bag of rice is a typical size.

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