Using Models to Add Up to 100

When numbers get bigger than ten, it helps to see them instead of just saying them. A model is a picture or a set of objects that stands in for a number so you can watch what happens when two amounts are put together. For addition up to 100, the most common models are base ten blocks, place value charts, hundred charts, and number lines. This lesson focuses on base ten blocks because they show place value directly: a long rod stands for a group of ten, and a small cube stands for one single unit.

Using a model matters because it turns an abstract equation like \( 34 + 28 = 62 \) into something you can build, move, and regroup with your hands or on paper. Once you can see why the answer is 62, the written method for adding digits up to 100 makes a lot more sense.

Every two-digit number can be broken into tens and ones. The number 34 is made of 3 tens and 4 ones, and 28 is made of 2 tens and 8 ones. In a base ten block model, each ten is drawn as a tall rod and each one is drawn as a small square.

To add \( 34 + 28 \) with the model, follow three moves.

Step 1: Build both numbers separately with rods and cubes, as shown above.

Step 2: Push all the tens rods together and all the ones cubes together. That gives 3 rods plus 2 rods, which is 5 rods, and 4 cubes plus 8 cubes, which is 12 cubes.

Step 3: Since 12 ones is more than a full group of ten, trade 10 of those ones cubes for 1 new tens rod. This step is called regrouping, and it is the key idea the block model makes visible.

This is exactly the same regrouping idea used when you line up digits in columns, but the model lets you see the trade happening instead of just following a rule. If you want more practice recognizing when totals cross a ten, the lesson on addition strategies covers several ways to spot regrouping quickly.

Base ten blocks are not the only model. A hundred chart, a 10 by 10 grid of numbers from 1 to 100, lets you start at one addend and count forward the value of the second addend, moving down a row for each ten and across for each one. A number line works the same way: start at the first number, make one big jump of ten for each ten in the second number, then smaller jumps of one for the remaining ones. Both models rely on the same place value idea as base ten blocks, just drawn differently.

Try modeling \( 47 + 35 \). Build 47 as 4 tens and 7 ones, and 35 as 3 tens and 5 ones. Combine the tens: \( 4 + 3 = 7 \) tens. Combine the ones: \( 7 + 5 = 12 \) ones. Since 12 ones is more than a ten, trade 10 ones for 1 new ten, leaving 7 + 1 = 8 tens and 2 ones. The model shows \( 47 + 35 = 82 \).

Once modeling two addends feels comfortable, the same block and regrouping ideas extend naturally to problems with more terms, such as adding with 3 numbers up to 100.

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