Numbers Live On A Line

You already use numbers like street signs. Page numbers. Scores in a game. Stickers in a pack. Today we put those numbers in one place so we can see how they relate.

Start with the numbers from $0$ to $20$. They are small, friendly, and they show a big idea. Every number has a spot, and the spots come in a steady order. Once you can picture that order, you can answer questions like Which is bigger, $7$ or $12$? and How far is $6$ from $10$?

Numbers we meet every day

Think about counting. You begin at $0$, then $1$, then $2$, and you keep going one more each time until $20$. Nothing fancy is happening. You are just adding one.

Here are a few you might bump into a lot.

• $0$ means none. No stickers. No points.
• $10$ often means a full set of ten fingers.
• $20$ can mean a full score in some games, or twenty items in a box.

The key is that each number is exactly one step away from the next counting number. From $8$ to $9$ is one more. From $19$ to $20$ is one more. That one more feeling is what the number line will show with equal spaces.

Left is smaller, right is bigger

Imagine the numbers as houses on a straight street. House $0$ is on the left. Then house $1$ is just a little to the right. Then house $2$, and so on, each one evenly spaced.

When you look at this street, a pattern pops out.

Order on a number line means numbers to the left are smaller, and numbers to the right are bigger.

So if $5$ is left of $9$, then $5$ is smaller than $9$. If $14$ is right of $11$, then $14$ is bigger than $11$.

Try placing the numbers so they sit like houses in order from $0$ to $20$.

A useful check is to count forward. If you can start at one number and count up to reach another, the one you reach later is bigger.

Distance means how far

Now use the street idea for how far you walk. If you stand on $7$ and walk to $10$, you take one step to $8$, one step to $9$, and one step to $10$. That is $3$ steps.

Distance on a number line is just how many steps between two numbers when you move one space at a time.

Look at a few more.

Start at $10$ and walk to $10$. You do not move. That is $0$ steps.

Start at $9$ and walk to $10$. That is $1$ step.

Start at $13$ and walk back to $10$. You go $13 \to 12 \to 11 \to 10$. That is $3$ steps again. The direction changed, but the how far stayed the same.

Pick a number from $0$ to $20$ and see how many steps it takes to reach $10$ on the line.