Minds On
Mass or capacity
Which metric units would you use to estimate the mass or capacity of the following examples? Why?
How can we create a proper estimate of mass or capacity of an object or container?
Record your ideas in a notebook or a method of your choice.
Action
Mass and capacity
Choosing a proper metric unit depends on what you are planning to measure.
Mass is the amount of matter in an object and usually is measured in grams and kilograms.
Capacity is the greatest amount a container can hold and usually is measured in millilitres and litres. We can use a scale to measure mass and capacity.
Benchmarks for mass
If we are trying to determine the mass of a small item like a pencil or a carton of blueberries, we could use grams. If we are trying to determine the mass of a larger item like watermelon, table, or even a car, we could use the larger unit, kilograms.
When we estimate, we can use benchmarks for these metric units to make the most accurate guesses.
Consider some examples that you know that measure about 1 gram (g) and 1 kilogram (kg). Then compare them to the following benchmarks.
For example, 1 paper clip is about 1 gram in mass, so 1,000 paper clips are about 1 kilogram in mass.
A baker’s benchmarks
If a baker is measuring the mass of items in their kitchen, they might have their own benchmark measurements to estimate mass before they measure their ingredients.
For example, 1 block of butter, loaf of bread and 3 oranges all measure approximately 500 grams in mass.
Using those benchmarks, the baker knows that 2 blocks of butter would equal 1 kilogram.
Benchmarks for capacity
If we are trying to determine the capacity of a small item like a spoonful of honey or a small carton of juice, we could use millilitres. If we are trying to determine the capacity of a larger item like a large carton of milk, a tank of gas for a car, we could use the larger unit, litres.
Consider some examples that you know that measure about 1 millilitre (ml) and 1 litre (L) and then compare them to the following benchmark.
For example, a few drops of milk in a teaspoon equals 1 millilitre. You would need 1,000 spoons of milk to make up 1 litre of milk.
Creating our own benchmark
If we wanted to create our own benchmark, we can use a container whose capacity we know.
For example, if we had a can of pop that held 355 mL then we can estimate that about 3 cans of pop are approximately 1,000 ml.
We can check our estimation by multiplying the capacity of the pop can by 3.
355 × 3 = 1,065
1,065 mL = 1.65 L
Based on the relationship 1,000 mL = 1 L we know that 3 cans of pop contain approximately 1 L.
Estimating mass and capacity
Using your understanding of benchmarks for mass and capacity, identify which of the following examples are measured in mass or capacity and choose the appropriate metric unit.
Using the benchmarks explored in Action, and your own prior knowledge, create an estimate for each example. Explain your reasoning. Record your answers using the following table or a method of your choice.
Press the ‘Activity’ button to access Estimating Mass and
Capacity table.
Activity
(Open PDF in a new window)
You may use the following multiple choice questions to check if you have selected the appropriate metric unit.
When you have completed the activity, press ‘Answer’ to access possible estimates and explanations to compare your answers with.
A stack of pencil crayons
- Possible estimate: If one paperclip is equal to 1 gram, then I will estimate that a pencil is 6 grams. If one pencil is 6 grams, and there are approximately 12 pencils in the image, I will estimate that the stack of pencils is 72 grams.
A spoonful of honey being taken from a jar of honey
- Possible estimate: I know that I am measuring capacity since I am measuring the amount of liquid in the container (spoon). Based on the benchmark for millilitres, my estimate is 5 millilitres.
A glass of milk
- Possible estimate: I know that I am measuring capacity since I am measuring the amount of liquid in the container (glass). I know that in the benchmark for litre, 1 large container of milk equals 1 L. My estimate for the glass of milk based on its size next to the carton of milk is 500 ml.
A pineapple
- Possible estimate: I know that three oranges weigh approximately 500 grams. I think a pineapple would be approximately twice that amount, so my estimate is 1 kg.
A water bottle
- Possible estimate: I know that I am measuring capacity since I am measuring the amount of liquid in the container (water bottle). I know that a carton of milk is about 1 L, and I think this bottle of water is about half of the size. My estimate is 500 ml.
A watering can
- Possible estimate: I know that I am measuring capacity since I am measuring the amount of liquid in the container (watering can). I think the watering can is larger than a carton of milk. My estimate is 1.5 L.
A basket of strawberries
- Possible estimate: I know that I am measuring mass since the strawberries are solid and not a liquid. I think this basket of strawberries would have a similar mass to three oranges. My estimate is 500 grams.
Two loaves of bread
- Possible Estimate: I know that I am measuring mass, because I am measuring the amount of matter in a loaf of bread. Based on the Baker’s Benchmark I will estimate that these loaves of bread are about 1 kg.
A stack of books
- Possible estimate: I know that I am measuring mass, because I am measuring the amount of matter in a book. I know that a container of 1,000 paperclips equals 1 kg. I think 1 kg is approximately the mass of 1 thick book. There are 7 books of different sizes, 2 are larger than others. My estimate is 9 kg for this stack of books.
Word problem: Artist’s paints
An artist has 6 bottles of paint and would like to open them all up and pour them into a large jug. If each bottle holds 250 mL and the jug has a capacity of 2 L, will all of the paint from 6 bottles fit into the jug? Will there be any leftover capacity? Explain your answer.
Record your ideas in a notebook or a method of your choice.
When you have completed the word problem, press ‘Answer’ to access a possible solution to compare your answers.
Possible estimation and solution: I know that 200 mL is about (benchmark) goes into 1,000 mL 5 times. I know that 4 times 50 would be 200. Therefore, I know that 250 mL would go into 1 L 4 times. This means, I would need to add two more bottles of paint, and that would be half of a litre. I estimate that there will be leftover capacity in the large jug.
Calculation:
250 × 6 = 1,500
1,500 mL = 1.5 mL
2 L = 1.5 L = 0.5 L
There would half a litre or 0.5 litres capacity leftover in the large jug.
Consolidation
Mass and capacity word problems
Problem 1
Designing a children’s play area
A city worker is pouring buckets of water into a half filled pool
A city worker just started to fill an outdoor pool, but the hose stopped working. The pool holds 20,000 L of water when full. There’s a creek about 100 m away. They have two buckets that hold 10 L each. How many trips would they need to make to the creek and back if they use both buckets for each trip? Is this a reasonable way to fill up the pool? Suggest an alternate strategy. Explain, and describe your process.
Record your ideas in a notebook or a method of your choice.
When you have completed the word problem, press ‘Answer’ to access a possible solution to compare your answers.
Possible solution
I can divide the total amount of water the pool holds (20,000 L) by the amount of what 2 buckets (2 × 10 L) can carry to figure out the number of trips required.
20,000 L ÷ (2 × 10 L) = 1,000 trips
It takes 1,000 trips to fill up the pool. This is unreasonable because it is way too many trips and quite a far distance that the city worker has to travel.
Another strategy could be to get a truck to transport the water from the creek to the pool.
Problem 2
How much sugar?
A loaf of bread is about 500 g. A chef is helping bring some groceries into the restaurant from a grocery run. They carry in a bag with 10 loaves of bread. On their next trip they carry a bag of sugar that has about the same mass. What mass is likely written on the bag of sugar?
Record your ideas in a notebook or a method of your choice.
When you have completed the word problem, press ‘Answer’ to access a possible solution to compare your answers.
Possible Solution
Since I know the mass of 1 loaf of bread is 500 g, I can figure out the mass of 10 loaves of bread which will be about the same mass as the sugar.
500 g × 10 = 5,000 g = 5 kg
Therefore, the mass that is likely written on the bag of sugar is 5 kg.Think about your learning
Why is it important to understand the relationships between different metric units when measuring mass and capacity?
How does using benchmarks help us to improve our estimation skills?
Record your ideas in a notebook or a method of your choice.
Reflection
As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.
I feel...
Now, record your ideas using a voice recorder, speech-to-text, or writing tool.