Learn on PengiPengi Math (Grade 5)Chapter 4: Decimal Multiplication and Division

Lesson 5: Dividing Decimals Using Models and Algorithms

In this Grade 5 Pengi Math lesson from Chapter 4, students learn to divide decimals by modeling the process with base-ten blocks and place value charts to represent sharing and regrouping. They then connect those visual models to the standard long division algorithm, developing a conceptual understanding of each step in the procedure.

Section 1

Modeling Decimal Division with Base Ten Blocks

Property

When modeling decimal division with base ten blocks, arrange the dividend blocks into equal groups of the divisor size.
If the divisor contains hundredths, convert tenths blocks to hundredths blocks by trading 11 tenth for 1010 hundredths to enable proper grouping.

Examples

Section 2

Model Decimal Division Using a Place Value Chart

Property

When dividing on a place value chart, if a place value has a remainder after sharing, unbundle each remaining unit into 10 units of the next smaller place value. This is based on the principle that 1 larger unit is equivalent to 10 of the next smaller unit (e.g., 1 one=10 tenths1 \text{ one} = 10 \text{ tenths}, 1 tenth=10 hundredths1 \text{ tenth} = 10 \text{ hundredths}).

Examples

Section 3

Connecting Place Value Actions to the Division Algorithm

Property

The steps of the long division algorithm are a symbolic representation of the actions performed on a place value chart.

  • Distributing disks into groups →\rightarrow Divide
  • Finding the total disks distributed →\rightarrow Multiply
  • Finding the leftover disks →\rightarrow Subtract
  • Decomposing leftovers and combining with the next place value →\rightarrow Bring Down

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Modeling Decimal Division with Base Ten Blocks

Property

When modeling decimal division with base ten blocks, arrange the dividend blocks into equal groups of the divisor size.
If the divisor contains hundredths, convert tenths blocks to hundredths blocks by trading 11 tenth for 1010 hundredths to enable proper grouping.

Examples

Section 2

Model Decimal Division Using a Place Value Chart

Property

When dividing on a place value chart, if a place value has a remainder after sharing, unbundle each remaining unit into 10 units of the next smaller place value. This is based on the principle that 1 larger unit is equivalent to 10 of the next smaller unit (e.g., 1 one=10 tenths1 \text{ one} = 10 \text{ tenths}, 1 tenth=10 hundredths1 \text{ tenth} = 10 \text{ hundredths}).

Examples

Section 3

Connecting Place Value Actions to the Division Algorithm

Property

The steps of the long division algorithm are a symbolic representation of the actions performed on a place value chart.

  • Distributing disks into groups →\rightarrow Divide
  • Finding the total disks distributed →\rightarrow Multiply
  • Finding the leftover disks →\rightarrow Subtract
  • Decomposing leftovers and combining with the next place value →\rightarrow Bring Down

Examples