In this Grade 6 lesson from Illustrative Mathematics Unit 5, students use base-ten block diagrams to represent and add decimal numbers, working with place values including tenths, hundredths, and thousandths. Students explore how the same decimal, such as 0.13 or 0.25, can be represented in multiple equivalent ways using ones, tenths, and hundredths blocks. The lesson builds toward adding decimals like 0.137 + 0.284 by connecting visual diagram-based reasoning to vertical calculation methods.
Section 1
Representing Decimals with Visual Models
To represent a decimal number such as using visual models, you match the digit in each place value to a specific number and type of block:
Section 2
Composing and Decomposing Decimal Units
Decimal place values are related by a factor of 10. Composing means bundling 10 smaller units to make 1 larger unit. Decomposing is the reverse.
Section 3
Modeling Decimal Addition with Regrouping
When adding decimals using a place value model, if a column contains 10 or more units (disks), you regroup 10 of those units to form 1 unit in the next larger place value to the left. This is also known as bundling.
Section 4
Relating Place Value Models to Vertical Addition
The standard vertical algorithm for addition is a written representation of adding on a place value chart. Each column in the algorithm corresponds to a place value column, and "carrying over" a digit is the written equivalent of regrouping (bundling) 10 place value disks into one disk of the next larger value.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter
Expand to review the lesson summary and core properties.
Section 1
Representing Decimals with Visual Models
To represent a decimal number such as using visual models, you match the digit in each place value to a specific number and type of block:
Section 2
Composing and Decomposing Decimal Units
Decimal place values are related by a factor of 10. Composing means bundling 10 smaller units to make 1 larger unit. Decomposing is the reverse.
Section 3
Modeling Decimal Addition with Regrouping
When adding decimals using a place value model, if a column contains 10 or more units (disks), you regroup 10 of those units to form 1 unit in the next larger place value to the left. This is also known as bundling.
Section 4
Relating Place Value Models to Vertical Addition
The standard vertical algorithm for addition is a written representation of adding on a place value chart. Each column in the algorithm corresponds to a place value column, and "carrying over" a digit is the written equivalent of regrouping (bundling) 10 place value disks into one disk of the next larger value.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter