Length and Height: Measuring with Standard Units

You can tell someone a pencil is short. Measuring tells them more: how much space lies between its two ends.

Which length do you mean?

Length tells how long something is from end to end. Height tells how tall it is, from bottom to top. Height goes straight up. You measure a plant's height from its base to its top.

Width tells how wide something is, from side to side. You might measure a book's width across its cover. Distance tells how far it is from one place to another.

Use words to compare things: "My pencil is shorter than your ruler." For heights, say, "The tree is taller than the fence." Two things can also be the same length.

Turn your pencil so it points another way. Its length stays the same. You have moved it, but its ends are still the same distance apart. A string keeps its length when it curls. To measure along it easily, straighten it without stretching it.

Why share a unit?

You may have measured with cubes or hand spans before. You repeat the same unit along a length and count. The units touch end to end, with no gaps or overlaps.

Mia measures a table using 6 hand spans. Her dad uses only 4. His hand spans are bigger, so fewer fit along the table. Both can measure carefully and get different numbers.

A standard unit has the same size for everyone. A centimeter on your ruler is the same length as a centimeter on another ruler. People can share measurements because their units match.

Say both parts

A measurement needs a number and a unit. "12 centimeters" gives both parts. "12" alone leaves you wondering how long each unit is. Twelve feet would be a very different length!

You can write unit names in a short way. For example, "12 cm" means "12 centimeters." Leave a space between the number and the unit.

Look at a ruler labeled cm. Those letters stand for centimeters. A centimeter is a small unit for measuring length.

Find a centimeter

On a ruler numbered in centimeters, the space from 0 to 1 is 1 centimeter. The space from 1 to 2 is another centimeter. These spaces have equal lengths.

Your little finger is about 1 centimeter wide. A small cube from a base-ten block set is usually 1 centimeter across. You can picture that cube to help you remember the size.

Centimeters suit small things, such as a toy car or pencil. A crayon might be about 9 centimeters long. You can write that as "about 9 cm."

The word about means close to a length. Crayons come in different sizes, so measuring your own gives you its length.

Picture a meter

A meter is much bigger than a centimeter. Its short form is m. A meter stick is exactly 1 meter long.

One hundred centimeters laid end to end match 1 meter. Look along the centimeter scale of a meter stick. Starting at 0, it reaches 100 at the far end. Those 100 small spaces fill the stick's length.

A grown-up's big step is about 1 meter long. A doorknob is often about 1 meter above the floor. A door is about 2 meters tall. These familiar sizes help you picture meters.

Meters suit longer things, such as a classroom or hallway. A meter stick covers much more of the floor in one go than a single centimeter does.

Check the letters

Read "2 m" as "2 meters." Read "2 cm" as "2 centimeters." The numbers match, but the lengths are very different. Two centimeters is a tiny length, about two finger widths. Two meters reaches about as high as a door.

When you write a measurement, picture its size. That helps you catch a missing or extra letter in the unit.

A ruler may also have an inch scale. Inches, feet, and yards are three more standard units you can use.

An inch and a foot

An inch is a small unit, written in. The dot helps you spot the unit name. A quarter coin is almost 1 inch across. The top part of a grown-up's thumb is about 1 inch long.

Use inches for small things, such as a book or crayon. Check the ruler's label before reading. The centimeter edge and inch edge have different spaces.

A foot is bigger than an inch. A foot ruler is exactly 1 foot long. Twelve inches fit end to end along that length. A regular sheet of printer paper is 11 inches long, just shorter than a foot ruler.

The short form of foot is ft. Say "1 foot" and "2 feet." Your own foot has its own size. A shoe cannot take the place of a foot ruler: the standard unit is always 12 inches long.

Feet suit bigger things, such as a desk or a person's height. Many children your age are about 4 feet tall.

A yard

A yard is longer than a foot. Its short form is yd. Three foot rulers laid end to end match one yardstick.

Picture a grown-up taking a big step. That step is about 1 yard long. You might use yards to describe a long playground or a playing field. A football field is 100 yards long between its two goal lines.

Put the units in size order

From smallest to biggest, the five units go like this:

centimeter, inch, foot, yard, meter.

An inch is longer than a centimeter. About two and a half centimeters fit along one inch. A yardstick is a little shorter than a meter stick.

Try picturing the tools side by side. A foot ruler fits along a yardstick three times. The meter stick reaches a little farther than that yardstick.

Before you measure, look at the thing in front of you. Is it small or long? Is it straight or curved? Your choice of tool can make the job easier.

Choose the tool

A ruler works well for a pencil or book. You can lay it flat beside a short, straight edge. Many school rulers are 30 centimeters or 12 inches long.

A meter stick or yardstick reaches farther. Use one along a table or rug. You need fewer moves than you would with a short ruler.

A tape measure is long and bendy. It can reach across a room. A soft tape can also bend around a tree trunk. A straight stick cannot follow that curve.

Choose the unit

Use centimeters or inches for a small eraser. A meter is so large that it tells you little about an eraser's length: the eraser is much shorter than one.

Meters, feet, or yards work well across a room. Counting that long distance in centimeters would give a much bigger number.

One strip, two counts

A strip of paper is 6 inches long. On the centimeter scale, it is about 15 centimeters long. The strip has stayed the same size. Only the measuring unit has changed.

Centimeters are smaller, so more fit along the strip. Inches are bigger, so fewer fit. For the same length, bigger units give a smaller count.

Think about covering a path with long sticks or short sticks. Each long stick covers more ground. You need more short sticks to reach the same end.

Compare with matching units

A book is 10 inches long. A ribbon is 20 centimeters long. You cannot decide which is longer just by choosing the bigger number. Each number counts a different unit.

Measure both in centimeters, or measure both in inches. With the same unit, you can compare the numbers fairly.

Put a pencil beside a ruler. The ruler needs to follow the pencil's length, with both lying straight and still.

Line up and read

1. Find the unit label. Use the edge marked cm for centimeters.
2. Line up one pencil end with the 0 line.
3. Look straight down at the other pencil end.
4. Read the number there and say its unit.

If the pencil reaches 14, it is 14 centimeters long. Write "14 cm." For inches, use the inch edge and follow the same steps.

Look closely at the start of your ruler. The 0 line may sit a little way in from the plastic edge. Start at that line. Starting at the edge leaves an extra bit before the measured spaces begin.

Why zero matters

The space from 0 to 1 is one unit. From 1 to 2 is one more. When an object starts at 0, the number at its other end tells how many unit spaces it covers.

Starting at 1 changes the reading. A pencil from 1 to 9 covers 8 centimeter spaces. Calling it 9 centimeters counts a space before the pencil even starts. Move the pencil to 0 to read its length directly.

An end between marks

Some objects end between whole-unit marks. Look at the two nearest whole numbers. Choose the closer one and say about.

A crayon ends between 8 and 9 centimeters, nearer 9. Say, "The crayon is about 9 centimeters long." You are giving the nearest whole centimeter.

If the end is exactly halfway between 8 and 9, say, "About 8 and a half centimeters." The small marks can help you see where the end lies, but focus on the whole units you are measuring.

Measure a small height

Stand a toy on a table. Hold the ruler straight up beside it. Put 0 at the tabletop and read the mark at the toy's top. Keep the toy and ruler on the same flat surface.

A slanted ruler does not follow the straight height. Hold it upright, and look straight at the top mark.

A short ruler cannot reach across every object. For a table, hallway, or person's height, use a longer stick or tape.

Read marks without numbers

A long scale may show numbers such as 10, 20, and 30. There are marks between them too. Find what each space is worth before you count.

On a centimeter scale, find the marks spaced 1 centimeter apart. There are 10 of those spaces between 60 and 70. A table ends 4 of these spaces past 60. Count on: 61, 62, 63, 64. The table is 64 centimeters long.

Other scales may number marks in 2s, 5s, or 10s. The numbers alone do not tell you the value of each space. Look at how many equal spaces lie between two labeled marks. For example, five equal spaces between 15 and 20 are worth 1 each. Two spaces past 15 then show 17.

Move a stick along a length

For something longer than your stick, mark where the stick ends. Move its start exactly to that mark. Keep counting each full stick length.

A yardstick fits along a hallway exactly 5 times. The hallway is 5 yards long. Leave no gap between placements: a gap skips part of the floor and gives too small a count. An overlap counts some floor twice and gives too large a count.

A rug may take 2 meter sticks and a little more. Say, "A little more than 2 meters." If the last part is nearly a whole meter stick, say, "About 3 meters."

Measure straight up

For your height, take off your shoes and stand against a wall. Keep your heels, back, and head against it, and look ahead. A helper holds a flat book level on your head. They mark the wall under the book.

Measure from the floor to that mark. Put the tape's 0 at the floor. Many children your age are taller than a meter stick, so use a tape that reaches past 100 centimeters.

For a table's height, measure from the floor to the tabletop. For a straight floor length, keep the tape straight and pulled tight. A sagging tape follows a longer path.

You can use ruler marks to choose both ends of a line. You can also find a length when its first end is away from 0.

Draw 7 centimeters

Lay the centimeter ruler flat on your paper. Hold it still.

1. Make a dot at 0.
2. Make another dot at 7.
3. Draw along the ruler edge to join the dots.
4. Measure your line to check it.

Starting at 1 and stopping at 7 would fill only 6 centimeter spaces. Check the start as well as the end.

For a line 4 inches long, use the inch scale. Place dots at 0 and 4, then join them along the ruler.

A feather away from zero

A feather lies from 3 to 10 on a centimeter ruler. Its far end is at 10, but its length is not 10 centimeters. The feather does not cover the spaces before 3.

Count the jumps between its two ends:

3 to 4, 4 to 5, 5 to 6, 6 to 7, 7 to 8, 8 to 9, 9 to 10.

There are 7 jumps. The feather is 7 centimeters long. The first jump lands on 4; the starting mark is not a jump.

You can find the same length by subtracting:

10 − 3 = 7.

The ending number minus the starting number gives the length between them.

Spaces, not marks

From 3 through 10, you can name 8 marks. But those marks have only 7 spaces between them.

This method helps when a ruler's zero end is broken. Line up with a clear mark, read both ends, and find the distance between them.

How long do you think a shelf is? An estimate is a careful guess made before you measure. A length you know can help you make that guess.

Pick a benchmark

A benchmark is a familiar length you can picture. A 30-centimeter ruler is one. A meter stick is another. Your little finger is about 1 centimeter wide.

Choose a benchmark that suits the size of the thing. A finger width can help with a tiny object. A meter stick is easier to picture along a big room.

You can also use a foot ruler, a yardstick, or a common 3-inch square sticky note. A grown-up's big step is about a meter or a yard. Body lengths are rough guides, so use the word "about."

Picture repeats

A shelf looks as long as three school rulers. Each ruler is 30 centimeters long. Picture them touching end to end.

Count on: 30, 60, 90. Your estimate is about 90 centimeters.

You have a reason for that number: three known lengths seem to fit. Write your estimate before measuring the shelf.

A book might look as long as three 3-inch sticky notes. Add their lengths: 3 + 3 + 3 = 9. You would estimate the book at about 9 inches long.

Estimate a height

Picture a door about 2 meters tall. A cupboard reaches about halfway up that door. Half of that height is about 1 meter. You can estimate, "The cupboard is about 1 meter tall."

The useful benchmark is the door's height from floor to top. Compare the cupboard from the floor too, so the heights start together.

Make your guess clear

Say "about," then a number and a unit. "About 30 centimeters" tells someone the size you picture. "About 30" leaves the size of each unit unknown.

After making your estimate, measure the thing. The ruler or tape lets you check how well your pictured lengths fitted.

Your estimate and your measurement may be different. Keeping both helps you learn how close your guess was.

How close were you?

Leo estimates his book at about 20 centimeters. He then measures 23 centimeters. The book is longer than his guess.

Find the gap: 23 − 20 = 3. His estimate was 3 centimeters too short. It was close, even though it did not match exactly.

Keep the first estimate on your page. Write the measured length beside it. Changing the guess after measuring would hide what you learned.

If your guesses often come out too long, try picturing a smaller number of benchmarks next time. If they often come out too short, picture a few more. Check by measuring again.

Does the unit make sense?

Someone writes, "The door is 2 centimeters tall." Picture 2 centimeters: only about two finger widths. That cannot be the height of an ordinary door. A door is about 2 meters tall.

Now picture a pencil labeled "15 meters long." Fifteen meters would stretch farther than a whole classroom. A pencil about that familiar size is measured in centimeters. The wrong unit has changed the meaning of the number.

Check a surprising reading

If your reading is far from your estimate, measure again before changing the estimate. Look for a simple measuring mistake:

• Did the object start at the 0 line?
• Did you use the edge for the unit you wanted?
• Was the ruler or tape straight?
• Did moving the stick leave any gaps or overlaps?

A careful second reading helps you decide whether the guess or the measuring needed work.

Put two pencils beside each other. Line up their starting ends. The pencil that reaches farther is longer.

Make a fair comparison

If one pencil starts farther along the table, its tip may reach farther even though it is shorter. Move the starting ends together before looking at the far ends.

You can also compare recorded measurements. First check that both use the same unit. Then the bigger number tells the longer length.

A blue ribbon is 35 centimeters long. A red ribbon is 28 centimeters long. Both use centimeters, and 35 is bigger than 28. The blue ribbon is longer.

If one measurement uses inches and another uses centimeters, measure both again in one unit. Bigger numbers alone cannot settle a comparison with different units.

Write a comparison sign

You can write "35 cm > 28 cm." Read it as "35 centimeters is longer than 28 centimeters."

Turn the order around and write "28 cm < 35 cm." Now it says the shorter length first. The open side of either sign faces the larger number.

The equals sign means the lengths match: "30 cm = 30 cm."

Find the extra part

"How much longer?" asks for the difference between the lengths. Picture the two ribbons with their starts together. The blue ribbon has an extra part after the red one ends.

Subtract the shorter length from the longer:

35 − 28 = 7.

The blue ribbon is 7 centimeters longer. Answering "35 centimeters" would give the whole blue ribbon, including the part that matches the red one.

You can count on instead. From 28 to 30 is 2. From 30 to 35 is 5. Add the jumps: 2 + 5 = 7 centimeters.

Heights work in the same way. Sam is 52 inches tall and Lily is 48 inches tall. The difference is 52 − 48 = 4 inches. Sam is 4 inches taller; Lily is 4 inches shorter.

You can arrange several things by their lengths. First find out which direction the order should go.

Shortest to longest

Three pencils measure 14 centimeters, 9 centimeters, and 17 centimeters. All three use the same unit.

Start with the smallest number, 9. Of the two left, 14 is smaller than 17. The order is:

9 cm, 14 cm, 17 cm.

The 14-centimeter pencil goes in the middle. You can check both neighbors: it is longer than 9 centimeters and shorter than 17 centimeters.

When numbers look alike, check the tens first. Compare 47 and 74. Four tens is less than seven tens, so 47 centimeters comes first in shortest-to-longest order. If the tens match, compare the ones.

Tallest to shortest

For the other direction, start with the biggest number. Three plants are 63 inches, 45 inches, and 28 inches tall. The tallest-to-shortest order is:

63 in., 45 in., 28 in.

Read the direction before you answer. Putting the right measurements in reverse order answers a different question.

Two equal lengths tie. Place them next to each other. Neither one is longer, so either of the tied objects can come first.

Use what you already know

Sometimes you can order things without measuring every one. A rope is longer than a ribbon. The ribbon is longer than a string. The rope must be longer than the string too.

From longest to shortest, put them like this: rope, ribbon, string. The ribbon links the two comparisons.

If measurements use different units, measure all the objects again in one unit before sorting their numbers.

Two pieces laid end to end make one longer length. When you know the piece lengths, add them to find the whole.

Join two pieces

One piece of tape is 25 centimeters long. Another is 14 centimeters long. Their ends touch, with no overlap.

Picture a line with a mark where the two pieces meet. The first part is 25 centimeters. The next part adds 14 more.

Write an equation with a question mark for the total:

25 + 14 = ?

Add 10 to 25 to reach 35. Add the other 4 to reach 39. The whole strip is 39 centimeters long.

Show jumps on a line

Draw a line like a ruler. Start at 0. Make a jump of 25 to land on 25. Make another jump of 14 to land on 39. The landing number shows the total length from the start.

The second jump begins where the first jump ends. Starting that jump back at 0 would put the pieces on top of each other in your drawing.

Height stories work this way too. Jack has a tower 46 centimeters tall. He puts a 12-centimeter block on top. Add 46 + 12 = 58. The new tower is 58 centimeters tall.

Add three lengths

A path has parts of 20 meters, 15 meters, and 30 meters. You can add the easy pair first:

20 + 30 = 50, then 50 + 15 = 65.

The whole path is 65 meters long. Changing the order you add the parts does not change their total.

Check the total

Check that all piece lengths use the same unit. Two centimeter lengths give a total in centimeters. Keep that unit in your answer.

The total should be longer than each piece you joined. You can also estimate: 25 + 14 is close to 25 + 15, which is 40. A total of 39 centimeters is close to that check.

A story may give you the whole length and ask about just one part. Subtract the known part to find what is missing.

A piece is cut off

Ana starts with 60 centimeters of ribbon. She cuts off 25 centimeters. Picture the whole ribbon split into the cut piece and the piece left.

60 − 25 = 35.

There are 35 centimeters left. Check by putting the lengths back together: 35 + 25 = 60.

Find growth

A plant was 14 inches tall. Now it is 22 inches tall. Its growth is the extra height, not its whole new height.

22 − 14 = 8.

The plant grew 8 inches. The old 14 inches and the new 8 inches make its height of 22 inches.

Find a missing piece

Two pieces make a 50-centimeter stick. One piece is 32 centimeters. Write what you know:

32 + ? = 50.

Count on from 32. Eight more reaches 40. Ten more reaches 50. Together, those jumps are 18. The missing piece is 18 centimeters long.

You can also subtract 50 − 32 = 18. Add back to check: 32 + 18 = 50.

Choose from the story

A rope is 40 meters long. Another is 25 meters long. "How many more meters?" asks for the extra part of the longer rope.

40 − 25 = 15.

The first rope is 15 meters longer. The word "more" can ask for a difference, so read the whole question before choosing to add.

Count on across a ten

For 52 − 37, count from 37 to 40: 3. Then count from 40 to 52: 12. Add the jumps: 3 + 12 = 15.

Do not take each small digit from whichever large digit is nearby. Taking 2 from 7 and 3 from 5 would give 25, which fails the check: 37 + 25 is 62. The correct check is 37 + 15 = 52.