decimals and base ten blocks

2 min read 30-11-2024

Decimals can be tricky, but using base ten blocks makes learning about them much easier! Base ten blocks are a hands-on tool that visually represent place value, helping you grasp the concept of decimals and how they relate to whole numbers.

What are Base Ten Blocks?

Base ten blocks are a set of manipulatives used to teach math concepts, especially place value. They consist of different sized blocks representing ones, tens, hundreds, and beyond. For decimals, we extend this to tenths, hundredths, and thousandths.

Cube: Represents 1 (one)
Long (Rod): Represents 10 (ten)
Flat: Represents 100 (one hundred)
Large Cube: Represents 1000 (one thousand)
Unit Cube: Represents 0.1 (one tenth)
Small Flat: Represents 0.01 (one hundredth)
Small Cube: Represents 0.001 (one thousandth)

Image of base ten blocks showing ones, tens, hundreds, tenths, hundredths, and thousandths

Representing Decimals with Base Ten Blocks

Let's explore how to represent decimal numbers using these blocks. Imagine you want to represent the number 2.35.

The '2' in the ones place is represented by two large cubes.
The '3' in the tenths place is represented by three unit cubes.
The '5' in the hundredths place is represented by five small flats.

By physically arranging these blocks, you create a visual representation of the decimal number.

Adding and Subtracting Decimals with Base Ten Blocks

Base ten blocks are fantastic for performing addition and subtraction with decimals. Let's try adding 1.24 and 0.56.

Adding Decimals:

Represent 1.24 with one large cube, two unit cubes, and four small flats.
Represent 0.56 with five unit cubes and six small flats.
Combine all the blocks. You'll have one large cube, seven unit cubes, and ten small flats.
Since ten small flats equal one unit cube, exchange them. Now you have one large cube, eight unit cubes, and zero small flats.
The result is 1.80 or 1.8

Subtracting Decimals:

Subtraction works similarly. Let's subtract 0.32 from 1.55.

Start with 1.55 represented by one large cube, five unit cubes, and five small flats.
You need to remove three unit cubes and two small flats.
After removing the blocks, you're left with one large cube, two unit cubes, and three small flats.
The answer is 1.23.

Converting Decimals to Fractions

Base ten blocks also help visualize the relationship between decimals and fractions. For example, one unit cube (0.1) represents one-tenth (1/10), and one small flat (0.01) represents one-hundredth (1/100).

Beyond the Basics

Base ten blocks are incredibly versatile. They can be used to teach more complex decimal concepts like multiplication and division. They help bridge the gap between abstract mathematical ideas and concrete visual representations.

Conclusion

Base ten blocks are invaluable tools for understanding decimals. Their hands-on nature allows students to visualize the place value of each digit and easily perform addition and subtraction. Mastering decimals becomes much simpler with the help of these versatile manipulatives. Using base ten blocks to learn about decimals provides a strong foundation for future mathematical concepts.