Learn on PengiEureka Math, Grade 5Chapter 4: Adding and Subtracting Decimals

Lesson 1: Add decimals using place value strategies, and relate those strategies to a written method.

In this Grade 5 Eureka Math lesson, students learn to add decimals by working with tenths, hundredths, and thousandths as like units using place value disks and charts, then connect those concrete strategies to the standard vertical written method. The lesson builds on students' understanding of decomposing decimal units and aligning place values to add numbers such as 2 tenths 5 thousandths + 6 hundredths accurately. Part of Chapter 4 on Adding and Subtracting Decimals, it reinforces why like units must be aligned when recording decimal addition vertically.

Section 1

Composing and Decomposing Decimal Units

Property

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.

10 tenths=1 one10 \text{ tenths} = 1 \text{ one}
10 hundredths=1 tenth10 \text{ hundredths} = 1 \text{ tenth}
10 thousandths=1 hundredth10 \text{ thousandths} = 1 \text{ hundredth}

Examples

Section 2

Modeling Decimal Addition with Regrouping

Property

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.

10×hundredths=1×tenth10 \times \text{hundredths} = 1 \times \text{tenth}
10×tenths=1×one10 \times \text{tenths} = 1 \times \text{one}

Section 3

Relating Place Value Models to Vertical Addition

Property

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.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Composing and Decomposing Decimal Units

Property

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.

10 tenths=1 one10 \text{ tenths} = 1 \text{ one}
10 hundredths=1 tenth10 \text{ hundredths} = 1 \text{ tenth}
10 thousandths=1 hundredth10 \text{ thousandths} = 1 \text{ hundredth}

Examples

Section 2

Modeling Decimal Addition with Regrouping

Property

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.

10×hundredths=1×tenth10 \times \text{hundredths} = 1 \times \text{tenth}
10×tenths=1×one10 \times \text{tenths} = 1 \times \text{one}

Section 3

Relating Place Value Models to Vertical Addition

Property

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.

Examples