# 3. Practice connecting fractions and division (FP)

teaches Common Core State Standards CCSS.Math.Content.5.NF.B.3 http://corestandards.org/Math/Content/5/NF/B/3
teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4

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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 equal-size 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.

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