Lecture Notes: Representing Decimals with Base 10 Blocks

Introduction to Base 10 Blocks for Decimals

• Base 10 Blocks Representation:
  • Traditional naming vs. decimal naming.
  • Thousand block is referred to as a "one block" for decimals.

Understanding Base 10 Blocks

• One Block: Represents one whole.
• Tenth Block:
  • 10 flats make up one block.
  • Represented as 0.1 in decimal form.
• Hundredth Block:
  • 100 rods make up one block.
  • Represented as 0.01 in decimal form.
• Thousandth Block:
  • 1000 tiny cubes make up one block.
  • Represented as 0.001 in decimal form.

Connections Between Decimals and Fractions

• Decimal to Fraction Connection:
  • Tenth block resembles number 10 backwards (ignoring the decimal).
  • Hundredth block resembles number 100 backwards.
  • Thousandth resembles number 1000 backwards.

Place Value Chart and Reading Decimals

• Example Number: 1.234
  • Reading: Correct way is "1 and 234 thousandths".
  • Use of 'And': Represents the decimal point.

Expanded Form and Base 10 Blocks Example

• Number Representation:
  • Expanded Form: Showcasing as addition of place values.
  • Base 10 Blocks:
    • 1 ones,
    • 2 tenths (0.2),
    • 3 hundredths (0.03),
    • 4 thousandths (0.004).

Key Takeaways

• Base 10 blocks are an effective way to visualize and understand decimals.
• Recognizing the correlation between place value, decimal representation, and block structure is crucial.
• Proper reading of decimals includes understanding the placement and significance of each digit.