This lesson is on division of a fraction by a whole number, focusing on the meaning of the operation. It was conducted at Spinghurst Elementary in New York.

1. Grade 5 Lesson on Division of Fractions by Whole Numbers at Springhurst Elementary School, New York.

2. The Anchor Problem – to make a correct division sentence using one set of digit tiles 0 to 9. Why do you think the teacher provided the restriction of not repeating any of the digits?

3. Students were given time to make some sentences on their own. It was evident that the students were already familiar with the algorithm. The purpose of this lesson was for students to make sense of the algorithm. Three approaches were used by the students.

4. First, the teacher wanted to discuss an incorrect use of notation. One pair has thought that 2/0 = 2 and made the sentence 8/4 ÷ 1 = 2/0 This example is interesting because it involves the idea of division by 1 which results in the two fractions being equal. It was agreed that 8/4 = 2 and that the right-hand side is equal to 2. Other students offered that 2 can also be written as 2/1 and, incorrectly 2 (2/0). The teacher explained that 2/0 is not 1. 2/1 is. And that division by zero is not defined. Subsequently, students offered the right-hand side can be 4/2 and 6/3. 4/2 was rejected because they realized the condition of the problem – no repetition of digits.

5. The first explanation a student gave for the algorithm is the fact that 2 fourths shared equally by 3 is equal to each getting 1/3 of 2 fourths. The second explanation was based on the idea of division of whole numbers. If 2 divided by 2 is 1 then 2 fourths divided by 2 is 1 fourth. If 4 divided by 2 is 2 then 4 fourths divided by 2 is 2 fourths. The rest of the lesson was focused on the whole class grasping these two ideas.

6. In discussing the other responses forwarded by the students, the teacher challenged the students to use the second method to explained cases such as 8 fourths divided by 6 where 8 is not divisible by 6. In the case of ¾ divided by 8, students were able to suggest changing the numerator to 24, writing ¾ as 24/32 before dividing by 8 since 24 is divisible by 8.

7. The third approach used was the bar model that the students have become familiar with. The teacher was pleased that a student who seemed unsure of himself found his voice to explain to the class why 1/5 ÷ 4 = 1/20. The lesson ended with students reflecting on the methods used to explain division of a fraction by a whole number.