Lesson objective: Practice determining an equal share in a situation where a remainder is present.
This lesson helps to build procedural skill in working with fractional remainders. A tape diagram and a number line are used to help highlight how a remainder is shared equally. This work develops students' understanding that there are situations where it is appropriate to share a remainder, and then presents a procedure for determining how to find and name such quotients.
Students engage in Mathematical Practice 4 (modeling with mathematics) as they use both a tape diagram and a number line to build fluency in their work with fractional remainders.
Key vocabulary:

denominator: the number of equalsize parts into which the whole has been partitioned. For example, in the fraction \({3 \over 8}\), 8 is the denominator. The denominator is written below the horizontal bar in a fraction. It is also the divisor.

dividend: the name for the number into which you are dividing in a division problem. For example, 36 is the dividend in the equation 36 ÷ 4 = 9.

division: A mathematical operation based on sharing or separating into equal parts.

divisor: the name for the number that divides another number. For example, in the equation 36 ÷ 4 = 9, the divisor is 4.

equal: exactly the same in value

fractional remainder: the amount left over when values are divided into equal shares, expressed as a fraction. In the division equation 16 ÷ 3 = 5 R1 the remainder is 1, which can also be expressed as \({1 \over 3}\).

numerator: the number of equal parts being considered. For example, in the fraction \({3 \over 8}\), 3 is the numerator. The numerator is written above the horizontal bar in a fraction. It is also the dividend.

quotient: The result of dividing one number by another number. For example, in the equation 36 ÷ 4 = 9, the quotient is 9.

remainder: The amount left over when values are divided into equal shares. In the division equation 16 ÷ 3 = 5 R1 the remainder is 1.