Divisibility Activity Plan
Materials

ExplorationDivide the class into teams of three members each. One member is the director, one the recorder, and one the materials coordinator. Each team takes four index cards and writes a different digit from 09 on each card. Then, from the four choices of digits, the team makes a list of all the possible fourdigit number combinations using each digit once. There will 24 possible number combinations. Next, have the students each take a graphic organizer, Divisibility Test, with columns for the numbers they created, plus the columns for 2, 3, 5, 6, 9, and 10 listed across the top. Using calculators if you wish, have the students divide each of their 24 numbers by 2, 3, 5, 6, 9, and 10 to decide if their numbers divide evenly without leaving remainders. If the number divides evenly, have the students write “yes” in the column on the graphic organizer. If the number does not divide evenly, have the students write “no” in the column on the graphic organizer. After the graphic organizer is complete, have each team record their “yes” examples on chart paper hanging around the room, one piece for each of the numbers 2, 3, 5, 6, 9, and 10. Once this is done, have each team make a hypothesis about a “rule” for divisibility for each of the numbers 2, 3, 5, 9, and 10. Have them record their hypotheses on the graphic organizer labeled Divisibility Rules. It is important that each child have his or her own copy of the two graphic organizers because the next part of the lesson is done as a whole class.

Bringing Our Experiences Together
 After teams have completed their Divisibility Test graphic organizer, recorded their numbers on the chart paper, and made hypotheses about divisibility on their Divisibility Rules graphic organizer, have them return to their individual seats for a wholeclass lesson.
 Using the chart paper lists as summaries of numbers generated by the class teams, discuss each chart and have the students share their hypotheses of divisibility rules. Guide their discussions to the correct rules for each number, and have them write them on the graphic organizer. Then have them trim the edges of their graphic organizers and glue them into their math journals for later referencing.
 Ask the students if it is possible to divide their rules into two main categories, using a Venn Diagram to compare and contrast the categories. Lead them to separate the numbers where the ones digit determines the divisibility (2, 5, 10) from the numbers that require adding all the digits (3, 9). Have them complete a Venn Diagram in their math journals while you model one on the board.
What would I do differently?
A lot of time was spent on trying to find all of the different combinations of numbers. In the future, I would have the number cards premade. This could save some time. I would either only require about a dozen different number combinations, or model a quick way to ensure that all number combinations are found.
Depending on my classroom setup and the materials available, I might also have the groups share out their numbers and have a recorder record all of the information in one place, instead of poster paper around the classroom.
The discussion we had while the students were sharing their hypotheses took a significant amount of time. However, I think by delving into these rules, instead of just handing out a cheat sheet, the students had a stronger hold on the information. Later during our fractions unit, I would recall back to this lesson while students were working with factors and multiples!
Depending on my classroom setup and the materials available, I might also have the groups share out their numbers and have a recorder record all of the information in one place, instead of poster paper around the classroom.
The discussion we had while the students were sharing their hypotheses took a significant amount of time. However, I think by delving into these rules, instead of just handing out a cheat sheet, the students had a stronger hold on the information. Later during our fractions unit, I would recall back to this lesson while students were working with factors and multiples!