Build Whole Numbers With Base-Ten Blocks

A price tag says 123 cents. A meter stick shows 123 centimeters. The number looks the same in both places, but it is doing a job. It is telling you how many hundreds, tens, and ones are in the amount.

Think about 123 cents. You could hand someone 123 pennies, but you would probably group them. You might use 1 dollar coin for 100 cents, then 2 dimes for 20 cents, then 3 pennies for 3 cents. The total is still 123 cents, but now you can see the parts.

The same idea happens with length. 123 centimeters can be thought of as 1 group of 100 centimeters, plus 2 groups of 10 centimeters, plus 3 single centimeters.

Try a few money and length examples where you decide what the hundreds, tens, and ones are in the number 123.

Making new units by grouping 10

Counting one by one works, but it gets messy fast. Base ten is a way to keep things tidy by making bundles.

Start with ones. Imagine 10 single cubes. When you snap them into one rod, you have not changed how much you have. You just made a new unit that is easier to count. That trade is the whole idea.

Here is the key trade in words.

Ten ones can be traded for 1 ten.

Now do the same thing again. If you have 10 tens rods, you can trade them for one flat.

Ten tens can be traded for 1 hundred.

A common confusion is to think a ten rod is just one more block like the others. It is one block you can hold, but it stands for 10 ones. That is why trading changes the number of pieces, but not the total amount.

Play with small amounts and practice trading 10 ones for 1 ten, then 10 tens for 1 hundred.

Building numbers and watching the parts

When you build a number with blocks, you can read it two ways. You can read the total, like 146. You can also read the parts, like 1 hundred, 4 tens, and 6 ones.

Build 146. Start with the biggest place.

Take 1 hundred block. That is 100. Add 4 ten rods. That is 40 more. Add 6 ones cubes. That is 6 more.

Now you can say the number as a sum. This is called expanded form because it expands the number into its parts.

$$146=100+40+6$$

Expanded form helps you check yourself. If you accidentally used 6 tens instead of 6 ones, you would get $100+40+60=200$, which is not 146.

Build several numbers from 0 to 300 and watch how the expanded form changes as you add or trade blocks.