Lesson objective: Solve problems by reasoning about fractions as division.
This lesson provides an opportunity for students to apply their knowledge and understanding of interpreting fractions as division and division results as fractions in a fair share situation. Students are asked to compare two different division problems, which are actually the same situation, but with different numbers.
Key Concept students will use:

Fractions can be interpreted as the division of the numerator by the denominator; if the numerator is divided by the denominator, the quotient is located at the same place on the number line as the original fraction.
Skills students will use:
 interpret quotients of whole numbers as a number of shares and a number of groups. (Grade 3, Unit 7, 3.OA.1.2)
 use drawings and equations to represent and solve division situational problems involving equal groups. (Grade 3, Unit 7, 3.OA.1.2)
Students engage in Mathematical Practice 8 (Look for and express regularity in repeated reasoning) as they use solve a variety of similar situations that require them to express a remainder as a fairly shared amount.
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.
 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.
 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.
 divisor: the name for the number that divides another number. For example, in the equation 36 ÷ 4 = 9, the divisor is 4.
 quotient: The result of dividing one number by another number. For example, in the equation 36 ÷ 4 = 9, the quotient is 9.