Mass, Capacity and Temperature

Pick up a notebook in one hand and an eraser in the other. Which feels heavier? Mass tells how heavy something is. In everyday talk, you might ask, "How much does it weigh?"

Feel first, then check

Holding things to compare their masses is called hefting. Your hands can notice a big difference. They may not notice a small one. A balance scale helps you compare more carefully.

A balance has two pans on a beam. Before you start, check the empty pans. The beam must be level, with neither pan hanging lower. Adjust it, or ask an adult to help.

Put one object in each pan. Watch what happens:

• The heavier side goes down.
• The lighter side goes up.
• A level beam means the sides have the same mass.

Suppose a toy car is in the left pan. A toy boat is in the right pan. The boat's pan goes down. You can say, "The boat is heavier than the car." You can also say, "The car is lighter than the boat."

Looks can fool you

A big beach ball is lighter than a small rock. Size alone cannot tell you which is heavier. What a thing is made of matters too. Check a surprising guess with the balance.

Shape can change while mass stays the same. A ball of clay balances 10 matching cubes. Squash all that clay into a flat disk. It still balances 10 cubes: you kept all the clay. Adding or taking away clay would change its mass.

Put things in order

A book is heavier than a shoe. The shoe is heavier than a mitten. Start with the heaviest, then follow the comparisons: book, shoe, mitten. The book is heavier than the mitten too.

A balance with one object on each side tells you which is heavier. For a measurement, put matching cubes in the other pan. If 14 cubes balance the object, its mass is 14 of those cubes.

A bottle can be empty and still hold plenty when filled. Its capacity is how much fits when it is full. Its liquid volume is how much liquid is inside right now.

Fill and pour

To compare two containers, start with one full and the other empty. Pour all the water from the full one into the empty one. Watch the second container:

• If water spills over, the first container holds more.
• If space remains, the first container holds less.
• If the water fills it exactly, both hold the same amount.

For example, fill a small pitcher and pour it into an empty jar. The jar fills, and some water is left in the pitcher. The pitcher holds more than the jar.

You can describe a container as full, nearly full, half full, nearly empty or empty. These words tell you how much of its space is being used. A half-full bottle still has the same capacity as before.

Watch the shape

Pour water from a wide bowl into a narrow bottle. The water may reach much higher in the bottle. You have the same amount if none spills. A higher level in a different-shaped container does not mean more water.

For a fair water-level test, use two matching clear containers. They must have the same size and shape, and hold all the water. Fill the containers you want to compare. Pour each one's water into its own clear container. The higher water level now shows the greater capacity.

Compare more than two

Suppose a pail holds more than a jar. The jar holds more than a mug. From most to least, write: pail, jar, mug.

Capacity is not just for water. You can count how much rice, sand or dried beans fills a container too. Filling the whole space is what lets you compare capacities.

How could you tell a friend how much a bucket holds? You could fill it with cupfuls and count them. The cup is your unit: the amount you use again and again.

Keep each unit the same

Use the same cup for every pour. Fill it to the top each time. Count one for each full cupful. If six cupfuls fill the bucket, say, "The bucket holds 6 cups."

A half-filled cup cannot count as a full cup. Mixing full and partly filled cups makes the count unfair. Spilling water before it reaches the bucket also changes the result.

For mass, put an object on a balance. Add matching cubes to the other pan until the beam is level. A model dinosaur might balance 18 cubes. Write "18 cubes," with both the number and the unit. "18" alone does not tell your friend how heavy it is.

The unit changes the count

The same bowl might hold 3 big mugfuls or 6 small cupfuls. Both measurements describe the same capacity. Each mugful is larger, so fewer are needed.

This also helps you compare measurements. A toy balances 22 cubes. Another balances 17 of the same cubes. The first toy is heavier because it takes more matching cubes to balance it.

But suppose your friend uses bigger cubes. Your cube counts no longer make a fair comparison. You need matching units before comparing the numbers.

Agree on units

People's drinking cups come in many sizes. Two children may count different cupfuls for the same bucket. Standard units solve this problem. Their sizes are agreed on everywhere.

Grams and kilograms measure mass. Milliliters and liters measure capacity and liquid volume. Degrees measure temperature. A gram has the same size wherever you measure, so someone else can understand your result.

A pencil and a dog need very different mass measurements. Grams are useful for light things. Kilograms are useful for heavy things.

Learn the short forms

Write g for grams and kg for kilograms. Leave a space after the number: 8 g or 3 kg. Read "8 g" as "8 grams."

A paper clip has a mass of about 1 g. A nickel, the 5-cent coin, has a mass of 5 g. These small objects help you picture a few grams.

One kilogram is much heavier than one gram. 1,000 grams make 1 kilogram. Half a kilogram is 500 g. A full 1-liter bottle of water has a mass of about 1 kg, plus a little for the bottle.

Pick a useful unit

Think about the full water bottle. Is the thing much lighter than it? Grams will usually be useful. Pencils, strawberries, letters and apples are often weighed in grams. An apple might have a mass of about 150 to 200 g.

For a heavier thing, kilograms are often easier to use. A bag of potatoes, a dog or a large watermelon can be weighed in kilograms. A large watermelon can have a mass of about 5 kg.

Keep the number and unit together. "A pencil weighs about 5 g" sounds sensible. "A pencil weighs about 5 kg" would make it as heavy as a large watermelon!

Guess, then measure

An estimate is a sensible guess before measuring. Compare with something whose mass you know. A small orange feels far heavier than a paper clip. It feels much lighter than a full water bottle. You might estimate 200 g, then weigh it to check. Your guess does not need to be exact.

Equal masses are equally heavy, whatever the objects look like. A bag with 1 kg of feathers balances a bag with 1 kg of rocks. The feathers take up more space, but each side has the same mass.

A spoonful and a bucketful are very different amounts. Milliliters help you measure small amounts of liquid. Liters help you measure large amounts.

Read the labels

The short form for milliliter is mL. The short form for liter is L. Write 150 mL or 4 L, with a space after the number. Some books and labels use ml and l instead.

A teaspoon holds about 5 mL. Picture that little spoonful. One milliliter is about one-fifth of it. A juice box often holds about 200 mL, much more than one spoonful.

1,000 milliliters make 1 liter. Half a liter is 500 mL. Many large water bottles hold 1 L. A bucket might hold about 10 L.

Choose the unit

Use a 1-liter bottle as a guide. A small glass holds less than that bottle, so milliliters are useful. A bathtub or fish tank holds many bottles' worth, so liters are useful.

The unit changes what a number means. A teaspoon holds about 5 mL. Five liters would be enough to fill a 10-liter bucket halfway. Check the unit when an amount seems much too big or small.

Estimate a container's capacity

Picture pouring full 1-liter bottles into a watering can. If you think two would fill it, estimate about 2 L. Fill the can and measure its water with a measuring jug to check.

Capacity and the amount inside can differ. A jug has room for 2 L when full. It has only 1 L of juice inside, so it is half full. Drinking the juice changes the liquid volume. It does not change how much the jug can hold.

Look at a measuring jug or kitchen scale. Its marks make a scale, like a number line. Equal spaces stand for equal steps in the measurement.

Start with two numbers

Not every mark has a number beside it. Find two neighboring numbered marks. You can work out the steps between them:

1. Find the difference between their numbers.
2. Count the spaces between the marks.
3. Divide the difference by the number of spaces.

A jug shows 100 mL and 200 mL. There are five equal spaces between them. The whole increase is 100 mL.

Each space is a step of 20 mL. Starting at 100 mL, the marks show 120, 140, 160, 180 and 200 mL.

Count jumps, not lines

An interval is the step between one mark and the next. Imagine hopping along a number line. Count each hop across a space. Do not count the starting mark as a hop.

From 0 to 100 mL, four equal spaces give steps of 25 mL. There are three small marks inside that gap, but four jumps. Dividing by three would count the wrong thing.

Check by counting on

Skip-count using your step size. For the four-space scale, count 0, 25, 50, 75, 100. You land on the next printed number, so your step fits.

A different scale has 0 and 10 with five spaces. Its steps are 2, because 10 divided by 5 is 2. Scales can use steps of 1, 2, 5, 10, 20, 25, 50 or 100. Check each new scale instead of guessing that every little mark means one.

Find the unit too

Look for g, kg, mL, L or a temperature unit. A measuring cup may have milliliters on one side and other units on the other. A thermometer may show both °C and °F. Follow one set of marks with the unit you need.

Once you know the step size, you can read an unnumbered mark. Find a nearby number and count from there to the pointer or water level.

Count forward or back

A kitchen scale has steps of 20 g. Its pointer is three steps after 100 g. Start at 100 and count three jumps: 120, 140, 160. The object has a mass of 160 g.

You can count back when the pointer is near the next number. A pointer is one 25 g step before 500 g.

The reading is 475 g. Counting forward from 500 would move away from the pointer.

Find the middle

Halfway means right in the middle. Halfway between 200 mL and 300 mL is 250 mL. It is 50 mL from each end. Halfway between 2 kg and 4 kg is 3 kg.

Sometimes the water lies between marks. If it is much closer to 400 mL than 300 mL, read about 400 mL to the nearest 100 mL. The word "about" shows that the level is near the mark, not exactly on it.

Read around a dial

On a round kitchen dial, follow the numbers as they increase clockwise. The path curves, but the counting works in the same way.

Suppose 200 g and 300 g have four equal spaces between them. Each step is 25 g. The pointer is three steps after 200 g. Count 225, 250, 275. The reading is 275 g.

Keep track of the starting number

A jug has steps of 50 mL. Water reaches two steps above 300 mL. Count from 300 to 350, then 400 mL. The answer includes the starting amount and both jumps. "2" only counts the jumps; it does not give the amount of water.

Write the unit beside every reading. A pointer at 400 could mean 400 g on one tool or 400 mL on another.

Choose a tool for what you need to find. Use a balance or weighing scale for mass. Use a measuring jug, measuring cup or measuring spoon for liquid amounts. A thermometer measures temperature.

Balance with gram weights

Put the object in one pan of a level balance. Add gram weights to the other until the beam is level again. Add the masses written on the weights.

A small bag balances a 100 g weight, two 10 g weights and a 5 g weight.

The bag's mass is 125 g. You add the numbers on the weights, not just the number of weights.

Begin at zero

An empty kitchen scale must show 0. Check the pointer on a dial scale. On a digital scale, use the zero button, sometimes labeled tare.

For food in a bowl, put the empty bowl on first. Press zero while the bowl is there. Add the food. The reading now shows the food's mass alone.

If you forget to zero the bowl, the reading includes both. Suppose the bowl is 150 g and the bowl with oats is 420 g. Find the oats by subtracting:

The oats have a mass of 270 g.

Digital scales show a number on a screen. Read the unit too. Large scales, such as bathroom scales, can weigh heavy things like suitcases in kilograms.

Look across the water

Put a measuring jug on a flat table. Bend down until your eyes are level with the water. Looking down from above can make the level appear in the wrong place.

Water often curves upward where it touches the jug. Read at the bottom of that curve, in the middle. Match that height to the scale marks.

To measure out 300 mL, pour slowly as you near the 300 mL mark. Stop and check at eye level. If liquid is in a container without marks, pour all of it into a measuring jug. Read the jug to find how much was inside.

Temperature tells how hot or cold something is. You can describe it with words such as hot, warm, cool and cold. A thermometer gives you a measurement in degrees.

Check Celsius or Fahrenheit

Degrees Celsius are written °C. Read "20 °C" as "20 degrees Celsius." Degrees Fahrenheit are written °F. Many U.S. thermometers and weather reports use Fahrenheit.

These scales give different numbers for the same temperature. Check the C or F before deciding what a reading means.

The inside of a fridge is about 4 °C. These familiar temperatures help you judge other readings. A weather report of 30 °F describes a cold day, below water's freezing point. A report of 30 °C describes a hot day. The unit makes the difference.

Watch the liquid move

A liquid thermometer has colored liquid in a thin tube. When it gets warmer, the liquid moves up. When it gets cooler, the liquid moves down. The top of the liquid lines up with the temperature marks.

A digital thermometer shows the reading on a screen. You still need to look at its unit.

Never touch very hot water, an oven or a stove to test its temperature. Ask an adult to measure it with a thermometer.

Amount and temperature are different

Imagine water in a large pot. Pour some into a small cup. At the time of pouring, the water has the same temperature. The cup has less water, but less water does not mean a lower temperature.

Picture a thermometer as a number line standing up. Higher readings mean warmer temperatures on the same scale. Lower readings mean colder temperatures.

Find the step, then the top

A Celsius thermometer has five equal spaces between 10 °C and 20 °C. The gap is 10 degrees, so each step is 2 degrees.

The liquid ends two steps above 20 °C. Count 22, then 24. The reading is 24 °C. Keep your eyes level with the very top of the liquid.

Read Fahrenheit marks in the same way. A scale has five spaces between 60 °F and 70 °F. Each step is 2 degrees Fahrenheit. Three steps above 70 °F gives 72, 74, 76 °F.

Go below zero

A Celsius reading below 0 °C is below water's freezing point. The minus sign shows that the number is below zero. Read "−2 °C" as "minus two degrees Celsius" or "two degrees below zero."

With steps of one degree, go down from 0: −1, −2, −3, −4. Each step is colder. So −4 °C is colder than −1 °C. The 4 looks larger, but its position is lower on the thermometer.

To order temperatures, follow their positions from bottom to top. For example, from coldest to warmest: −6 °C, −1 °C, 3 °C, 15 °C.

Find a rise or fall

A morning reading is 11 °C. Later it is 19 °C.

It became 8 degrees warmer. To find a new temperature after a rise, add. After a fall, subtract. A fall of 5 degrees from 18 °C gives 13 °C.

For a change through zero, count in two parts. From −2 °C to 5 °C, go up 2 degrees to zero. Then go up another 5 degrees.

The temperature rose by 7 degrees. Zero joins the two parts; do not skip the distance below it.

Two bags can look alike but have different masses. Read each measurement, including its unit. When the units match, compare the numbers.

Compare place by place

One packet has a mass of 360 g. Another is 306 g. Both have three hundreds. Compare the tens next: 6 tens is more than 0 tens. The 360 g packet is heavier.

Use symbols to write comparisons:

• > means greater than.
• < means less than.
• = means equal to.

The open side faces the larger amount. For example, $360>306$, so write "360 g > 306 g." Two containers that each hold 4 L have equal capacities: "4 L = 4 L."

Make an ordered list

You have masses of 280 g, 208 g, 520 g and 250 g. Three have two hundreds, so compare their tens. The 520 g mass has five hundreds and is heaviest. From lightest to heaviest, the order is 208 g, 250 g, 280 g, 520 g.

Check the direction requested. For capacities of 7 L, 2 L and 5 L, most to least is 7 L, 5 L, 2 L. Least to most reverses that order.

The units matter

A larger number does not always mean a larger amount. Compare 2 kg and 700 g. One kilogram alone is 1,000 g, already heavier than 700 g. So 2 kg is heavier. In the same way, 3 L holds more than 800 mL: one liter alone is 1,000 mL.

Find how much more

A 480 g bag is heavier than a 320 g bag. To find how much heavier, subtract the smaller mass.

The difference is 160 g. If measurements come from scales, read each one first. Then compare or subtract using the readings, not the number of marks you counted.

Read a measurement story and picture what happens. Ask what you need to find. Check that the amounts use the same unit, then choose your calculation.

Put together or take away

Add to combine amounts. A snack mix uses 120 g of raisins and 240 g of cereal.

The mix has a mass of 360 g.

Subtract when some is taken away. A pitcher has 800 mL of juice. You pour out 250 mL.

There are 550 mL left. A drawing can help: mark the start at 800 mL, then show the amount falling by 250 mL.

Subtraction also finds how much more will fit. A tank holds 18 L when full. It has 11 L inside. The empty space is 7 L, because 18 minus 11 is 7.

Equal groups or equal shares

Multiply to combine equal groups. Five bags each contain 2 kg of soil.

Together the bags contain 10 kg. A row of five bag drawings can show the five equal amounts.

Divide to share a total equally. Share 20 L of water among five pails.

Each pail gets 4 L. Here you know the total and need the amount in each share.

Check the unit and the size

You can add 200 mL and 300 mL because both use milliliters. You cannot just add the numbers in 2 L and 300 mL. Those units have different sizes.

An estimate helps you check a calculation. For 198 g plus 203 g, think of 200 g plus 200 g: about 400 g. The exact total is 401 g. That is close to your estimate.

Also picture the answer. A bucket whose full capacity is only 9 mL would barely hold two teaspoonfuls. About 9 L is a sensible capacity for an ordinary bucket.

Finish with what the answer means: "Each pail gets 4 L." The unit tells how much, and the words tell whose amount you found.