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  1. 1st Grade Math
  2. Ordering Objects by Length & Comparing Indirectly

1ST GRADE MATH • MEASUREMENT AND DATA

Ordering Objects by Length & Comparing Indirectly

Learn how to put things in order from shortest to longest, and how to use one object to compare two others!

Section 1

Why Do We Measure Things?

People have always wanted to know how long things are. A long, long time ago — even before rulers were invented! — people used their hands, feet, and sticks to figure out which thing was longer or shorter. Let's look at how measuring grew up over the years.

Long, Long Ago
Cave people used their hands and arms to see how big something was. They held a rock next to a stick to see which one was longer!
Ancient Egypt
Egyptians used their forearms to measure. They called it a "cubit." They used cubits to build the huge pyramids!
King Henry's Time
A king said that one "foot" should be the length of his own foot. That's where the word "foot" for measuring comes from!
Today
Now we use rulers and tape measures with inches and centimeters. But first, we learn to compare and order things by looking!

Before you can use a ruler, you need to learn an important skill: looking at objects and telling which is longest, which is shortest, and which is in the middle. That's what this lesson is all about!

Section 2

Big Ideas About Length

Before we start ordering things, let's learn four important ideas. These will help you think like a measuring superstar! 🌟

1

Length = How Long Something Is

Length is the distance from one end of something to the other end. A pencil has a length. A shoe has a length. Even your arm has a length!
2

Line Up the Ends!

When you compare two things, always line up one end. Put both things on a table so one end is even. Then look at the other end to see which is longer.
3

Shortest, In Between, Longest

With three objects, one will be the shortest, one will be the longest, and one will be in between. You can put them in order!
4

Use a Helper Object

If you can't put two things side by side, you can use a third object to compare them. This is called indirect comparison.
✦ Key Takeaway
Think of it like this: if your crayon is longer than a paper clip, and the paper clip is longer than an eraser, then your crayon must be longer than the eraser too — even if you never put them side by side! The paper clip was your "helper" in the middle.
Section 3

See It! Ordering Three Objects

Let's look at three colored bars. They are different lengths. Can you tell which is the shortest and which is the longest? Look at the picture below!

Step 1: Look at the Three ObjectsLine up here!🖍️ Crayon← medium📎 Clip← short✏️ Pencil← long⬇Step 2: Put Them in Order!Shortest → Longest1📎 ClipSHORTEST2🖍️ CrayonIN BETWEEN3✏️ PencilLONGEST
Three bars ordered from shortest to longest: Clip, Crayon, Pencil

See how we lined up the left side of each bar? That makes it easy to see which one sticks out the farthest on the right side. The paper clip is the shortest. The crayon is in the middle. The pencil is the longest. We ordered them: shortest → in between → longest!

Section 4

How It Works: Using a Helper Object

Sometimes you can't put two objects next to each other. Maybe one is on a shelf and the other is on the floor! That's when we use indirect comparison. You use a third object — a helper — to figure out which one is longer.

The Big Rule
If A > B and B > C → then A > C
If A is longer than B, and B is longer than C, then A must be longer than C!

Let's see a picture of how this works. Imagine you have a ribbon taped to the wall and a shoe on the floor. You can't put them next to each other! But you have a piece of string you can carry around.

Step 1: Hold the string next to the ribbonWALL🎀 Ribbon🧶 StringString is LONGER ✓Step 2: Carry the string to the shoeFLOOR👟 ShoeString is LONGER ✓Step 3: What did we learn?The string is longer than the ribbon. ✓The string is longer than the shoe. ✓But what about ribbon vs. shoe?The ribbon is 240 long. The shoe is 200 long.🎀 Ribbon is LONGER than 👟 Shoe!
Using a string to indirectly compare a ribbon on a wall and a shoe on the floor

Did you see what happened? We used the string as our helper. We held it next to the ribbon and marked how long the ribbon was. Then we carried the string to the shoe and compared. The string showed us that the ribbon is longer than the shoe — without ever putting them next to each other!

Section 5

Sorting Chart: Words We Use

When we talk about length, we use special words. Here is a chart that shows the words and what they mean. These are the comparing words you need to know!

WordWhat It MeansExample
LongerHas more lengthA bat is longer than a ball.
ShorterHas less lengthA penny is shorter than a crayon.
LongestHas the most length of allThe jump rope is the longest of all three.
ShortestHas the least length of allThe eraser is the shortest of all three.
Same lengthBoth are equalThese two sticks are the same length.
Length Scale
Short
Medium
Long
← ShortestLongest →
✦ Key Takeaway
Think about standing in a line with your friends by height. The shortest person goes first, the in-between person goes in the middle, and the tallest person goes last. Ordering by length works the same way — line everything up from smallest to biggest!
Section 6

Worked Example

Let's do a full problem together, step by step! 📝

Maya's Desk: Ordering Three Objects

Problem

Maya has three things on her desk: a marker, a glue stick, and a ruler. She wants to put them in order from shortest to longest. The ruler is too long to pick up, so she uses a piece of yarn to help compare.

Step 1 — Compare the marker and glue stick

Maya puts the marker and glue stick side by side. She lines up one end. The marker sticks out farther. So the marker is longer than the glue stick.

Step 2 — Use yarn to compare the marker and the ruler

Maya cuts a piece of yarn the same length as the marker. Then she holds the yarn next to the ruler. The ruler is longer than the yarn! So the ruler is longer than the marker.

Step 3 — Think about the glue stick and the ruler

We know the ruler is longer than the marker, and the marker is longer than the glue stick. So the ruler must also be longer than the glue stick! We don't even need to compare them directly.

Step 4 — Put them in order!

Glue stick → Marker → Ruler
shortest → in between → longest
Section 7

Tips, Tricks & Common Mistakes

Here are some tips to help you get it right every time, and some mistakes to watch out for!

✅ Do This!❌ Watch Out!
Always line up one end of the objects evenly.Don't start one object farther ahead — that tricks your eyes!
Lay objects flat on a table or the floor.Don't hold things in the air — they might be tilted.
Use a straight helper (string, strip of paper, stick).Don't use a curvy helper — a curvy string looks shorter than it really is!
Check both ends of the objects.Don't just look at one end — you need to see where the other end stops too.
When ordering 3 things, compare pairs first.Don't try to guess all at once — compare two at a time!
✦ Key Takeaway
Think about a race. To see who wins, everyone starts at the same starting line. Comparing lengths is the same — you need a fair start! Always line up one end, then look at the other end to see who "wins" by being the longest. 🏁
Section 8

What Comes Next?

You are doing great! Once you can order objects and compare them using a helper, you'll be ready for even more cool measuring skills. Here's a peek at what's coming!

What You Learned TodayWhat You'll Learn Soon
Compare using your eyes and a helper.Measure with paper clips, cubes, or other small objects.
Use words like "longer" and "shorter."Use numbers to say exactly how long something is.
Order 3 objects by length.Order lots of objects and measure them with a ruler.
Indirect comparison with a helper object.Use inches and centimeters as standard helpers.

The skills you learned today — lining things up, comparing, and using a helper — are the building blocks for all measuring you'll ever do. In 2nd grade, you'll use rulers with numbers. In 3rd grade, you'll learn about inches and feet. It all starts right here! 🚀

Section 9

Practice Problems

Now it's your turn! Try each problem. Think carefully, then click "Show Answer" to check your work. You've got this! 💪

PROBLEM 1 — WHAT DOES IT MEAN?
What does "longer" mean when we talk about two objects?
PROBLEM 2 — PICK THE SHORTEST
Emma has a fork, a spoon, and a chopstick. The fork is shorter than the spoon. The spoon is shorter than the chopstick. Which one is the shortest?
PROBLEM 3 — USE THE HELPER
Jake can't move his bookshelf or his bed. He takes a jump rope and holds it next to the bookshelf. The bookshelf is shorter than the jump rope. Then he holds the jump rope next to the bed. The bed is longer than the jump rope. Which is longer — the bookshelf or the bed?
PROBLEM 4 — REAL-LIFE ORDERING
You have a green ribbon, a red ribbon, and a blue ribbon. You use a stick to compare. The stick is the same length as the green ribbon. The stick is longer than the red ribbon. The stick is shorter than the blue ribbon. Put all three ribbons in order from shortest to longest.
PROBLEM 5 — THINK HARD!
Mia says: "My pencil is longer than Sam's pencil, and Sam's pencil is longer than Lily's pencil. So my pencil must be longer than Lily's pencil." Is Mia right? Why or why not?
Summary

What We Learned

Today you learned how to compare the lengths of objects and put three objects in order from shortest to longest. You know to always line up one end of the objects so you can see which one sticks out farther. You learned the words longer, shorter, longest, and shortest to describe what you see.

You also learned a very powerful trick called indirect comparison. When you can't put two objects next to each other, you can use a third helper object — like a piece of string, a stick, or a strip of paper — to figure out which one is longer. If the helper is longer than Object A but shorter than Object B, then Object B must be longer than Object A. You're now a length-comparing superstar! ⭐

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