Lesson objective: Divide decimal numbers less than one using a variety of representations and strategies.

This lesson helps to build procedural skill with decimal division. The use of base 10 blocks and number lines supports the understanding of division as a grouping process. These pictorial representations are then replaced by the compensation method and partial quotient algorithm to prepare students for 6th grade decimal division. This work develops students' understanding that dividing decimal numbers less than zero is no different than dividing whole numbers.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they deepen and broaden their understanding of place value and the base 10 number system beyond whole numbers to decimals by extending their knowledge of decomposing larger units into smaller units. They also make the connection that if both the divisor and the dividend are multiplied by the same power of ten, then the value of the quotient is unchanged.

**Key vocabulary:**

- dividend
- divisor
- flat
- quotient
- reasonable
- rod

**Special materials needed:**

- base 10 flats and rods on paper
- colored pencils
- blank number lines