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  1. 1st Grade Math
  2. Measuring Length by Laying Objects End to End

1ST GRADE MATH • MEASUREMENT & DATA

Measuring Length by Laying Objects End to End

Learn how to find out how long something is by using smaller things lined up in a row!

SECTION 1

Why Do We Measure Things?

Have you ever wanted to know how long your desk is? Or how tall your friend is? People have always wanted to measure things! A very long time ago, there were no rulers. So people used parts of their bodies — like their feet or their hands — to measure. That is where the word "foot" comes from!

Let's look at how people learned to measure over time.

Long, Long Ago
People in ancient Egypt used their arms and hands to measure. They would stretch out their arm and call that a "cubit." But everyone's arm is a different size!
Hundreds of Years Ago
A king said, "Use MY foot to measure!" People started using one person's foot size so everyone would get the same answer.
Later On
People made rulers and tape measures so everyone could measure the same way. They used inches, feet, and centimeters.
Today — Your Turn!
Now YOU get to learn to measure! You will use small objects — like paper clips or cubes — and line them up to find how long something is. This is the same big idea people have used for thousands of years!

The big question is: How can we use little things to find out how long a big thing is? That is exactly what this lesson is about!

SECTION 2

The Big Ideas

Before we start measuring, let's learn four important rules. These rules will help you measure the right way every time!

1

Use the Same Object

Pick ONE kind of small object. Use that same object every time. If you start with paper clips, use paper clips the whole time. Do not mix paper clips and crayons!
2

No Gaps!

Put each small object right next to the one before it. Do not leave any space between them. They should touch end to end.
3

No Overlaps!

Do not let the small objects pile on top of each other. Each one should be flat and next to the last one — not on top of it.
4

Line Up Straight

Put the small objects in a straight line. Do not let them go in a wiggly or curvy path. A straight line gives the right answer!
✦ KEY TAKEAWAY
Think of it like building a train! 🚂 Each little object is a train car. You put the train cars right next to each other, touching end to end, in a straight line. Then you count how many train cars you used. That number tells you how long the big thing is!
SECTION 3

See How It Works!

Let's look at a picture. Here is a pencil. We want to know how long it is. We will use small cubes to measure it. Watch how we lay the cubes end to end along the pencil.

Measuring a Pencil with Cubes✏️ PENCILSTART HERE1234566 cubes long!no gapno gapno gap

Do you see what happened? We put 6 cubes in a row under the pencil. Each cube touches the next one — no gaps and no overlaps! They go in a straight line from one end of the pencil to the other end. So the pencil is 6 cubes long.

The cube is our length unit. A length unit is the small thing we use to measure. We can say: "The pencil is 6 length units long."

SECTION 4

How to Measure Step by Step

Here are the steps you follow every time you measure something. Let's learn them one at a time!

Step 1: Pick Your Length Unit

Choose a small object. It could be a paper clip, a cube, a crayon, or even your thumb! Make sure you have many copies of the same object.

Step 2: Line Them Up

Put the first small object at one end of the thing you are measuring. Put the next one right next to it. Keep going until you reach the other end.

Step 3: Count!

Count how many small objects you used. That number is your measurement!

HOW WE WRITE IT
The book is 5 paper clips long.
You say the number first, then the name of the small object.
ANOTHER EXAMPLE
The shoe is 8 cubes long.
We counted 8 cubes from one end to the other.

Notice that the answer is always a whole number. That means a counting number like 1, 2, 3, 4, 5, and so on. We do not use pieces of numbers (like 2 and a half). We use the whole number of objects we can fit!

✦ KEY TAKEAWAY
Measuring is like counting! 🔢 You line up your small objects end to end, and then you count them. The number you get is how long the big thing is. It is that easy!
SECTION 5

Different Objects, Different Numbers!

Here is something really interesting. If you measure the same thing with different small objects, you will get different numbers! That is because some objects are bigger than others. Let's see this in a picture.

Same Crayon — Two Different Length Units!CRAYONBIG CUBES123= 3 big cubesVSSAME CRAYONSMALL CUBES123456= 6 small cubesBigger length unit → smaller numberSmaller length unit → bigger number

Look! The same crayon is 3 big cubes long. But it is also 6 small cubes long. The crayon did not change — only the size of the cube changed!

Here is the rule: when you use bigger objects to measure, you need fewer of them. When you use smaller objects, you need more of them.

THING WE MEASUREDLENGTH UNITHOW MANY?
CrayonBig cube3
CrayonSmall cube6
BookPaper clip5
BookEraser3
SECTION 6

Let's Measure Together!

Let's try a full example from start to finish. We want to measure how long a ribbon is using paper clips.

Measuring a Ribbon with Paper Clips

Step 1 — Choose Your Length Unit

We pick paper clips. We have a big pile of paper clips that are all the same size. Good!

Step 2 — Start at One End

Put the first paper clip at the very beginning of the ribbon. Line it up with the edge.

Step 3 — Add More Paper Clips

Put the second paper clip right next to the first one. No gap! No overlapping! Keep adding paper clips in a straight line. We put one, then another, then another…

Step 4 — Stop at the Other End

We stop when we reach the other end of the ribbon. The last paper clip lines up with the end of the ribbon.

Step 5 — Count All the Paper Clips

Let's count: 1… 2… 3… 4… 5… 6… 7!

Step 6 — Say Your Answer

The ribbon is 7 paper clips long. 🎉
We write: The ribbon = 7 paper clips.
SECTION 7

Tips and Common Mistakes

Even grown-ups can make mistakes when measuring! Let's learn what to watch out for so you always get the right answer.

RIGHT WAY ✅WRONG WAY ❌WHY IT MATTERS
All objects are the same sizeMix of big and small objectsYou cannot count them fairly if they are different sizes
Objects touch end to endGaps between objectsGaps make you miss some length, so your number is too small
Objects do not overlapObjects stacked or overlappingOverlapping makes your number too small because you are double-counting space
Straight lineWiggly or curvy lineA curvy path is longer than a straight one, so your number would be too big
Start at one endStart in the middleYou will miss part of the thing you are measuring
✦ KEY TAKEAWAY
Think of laying down train tracks! 🛤️ Each piece of track has to touch the next piece, or the train will fall through. The track pieces are all the same size and go in a straight line. If you build your tracks right, you can count how many pieces you used and know exactly how long the path is!
SECTION 8

What Comes Next?

Right now you are measuring with objects like paper clips and cubes. That is wonderful! But soon you will learn to measure with rulers. A ruler has little marks called inches or centimeters. Those marks are just like tiny cubes all in a row — but they are already printed on the ruler for you!

Everything you are learning today is the same idea. Whether you use paper clips, cubes, or a ruler, you are always asking: How many of the small thing fits along the big thing?

WHAT YOU DO NOWWHAT COMES LATER
Use paper clips, cubes, or other objectsUse rulers with inches and centimeters
Count the objects yourselfRead the number on the ruler
Answer is a whole numberYou might get half-inches and more
Measure short thingsMeasure long things like rooms and hallways

You are building the foundation right now. Once you understand end to end and counting, everything else will be easy! 💪

SECTION 9

Practice Time!

Try these problems! Think carefully, then click "Show Answer" to check.

PROBLEM 1 — WHAT DO YOU KNOW?
When we measure something with paper clips, why do we put them end to end with no gaps?
PROBLEM 2 — COUNT AND MEASURE
Sam puts cubes along his marker. He uses 4 cubes and they go from one end to the other end with no gaps. How long is the marker?
PROBLEM 3 — THINK ABOUT IT
Emma measures her book with big erasers. She uses 3 erasers. Then she measures the same book with small paper clips. She uses 9 paper clips. Why did she get a bigger number with paper clips?
PROBLEM 4 — REAL LIFE
You want to find out how long your desk is. You have a box of crayons that are all the same size. Describe what you would do, step by step.
PROBLEM 5 — CHALLENGE
Lila measured a string with cubes and got 5 cubes. Her friend Max measured the same string with the same cubes and got 7 cubes. One of them made a mistake. What could Max have done wrong?
SUMMARY

Let's Remember What We Learned!

Today you learned how to find the length of an object by using smaller objects called length units. You lay many copies of the same small object end to end in a straight line with no gaps and no overlaps. Then you count how many you used. That number is a whole number that tells you how long the object is.

You also discovered that using a bigger length unit gives you a smaller number, and using a smaller length unit gives you a bigger number. This same idea is used by rulers and tape measures — you are building the skills that will help you measure everything around you!

Varsity Tutors • 1st Grade Mathematics (Common Core) • Measurement and Data