UEN Security Office
Technical Services Support Center (TSSC)
Eccles Broadcast Center
101 Wasatch Drive
Salt Lake City, UT 84112
(801) 585-6105 (fax)
This activity teaches students how to use formulas for dividing numbers. They will learn the formulas for multiples of 3, 2, and 5.
Invitation to Learn
The rules of divisibility are simple formulas for understanding how fair shares can be created from large numbers without practicing long or short division. Students usually come to fifth grade with an implicit understanding about why numbers are divisible by 2, 5, and 10, but it is important in fifth grade to make that understanding explicit. Additionally, the formulas for dividing numbers by 3 and 9 must be taught, since they are rarely discovered by children. It is helpful to separate the formulas for 2, 5, and 10 (which depend on the digit in the ones column) from the formulas for 3 and 9 (which depend on the sum of the digits and the formula for 6, which combines the rules for 2 & 3). Note that there are simple formulas for divisibility by 4, and 8, (as well as more complicated formulas for larger numbers) but they are not part of the Utah fifth grade Core Curriculum requirements. Information about these formulas is included in the curriculum extensions section for interested students.
This lesson should be sequenced after division with whole numbers has been reviewed and practiced, division with remainders has been reviewed and practiced, and students are familiar with vocabulary terms dividend, divisor, and quotient. It may also be used to review prime and composite, since every number greater than 2 that is divisible by 2, 3, 5, 6, 9, or 10 is composite; also, when discussing divisibility, students will probably remember that all numbers are divisible by one and themselves.
Invitation to Learn
Divide 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 0-9 on each card. Then, from the four choices of digits, the team makes a list of all the possible four-digit 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.
Furner, J.M., Yahya, N., Duffy, M.L. (2005). Teach mathematics: Strategies to reach all students. Intervention in school and clinic, Vol. 41, No. 1, 16-23.
In 2000 the National Council of Teachers of Mathematics identified equity as the first principle for school mathematics, meaning all children have the right to understand mathematical principles. This article offers 20 teaching strategies to reach the wide variety of learning styles and ability levels in our classrooms as we aim to meet the equity principle. Good lessons may incorporate several of these 20 strategies at one time: we may draw, explain verbally, organize conceptually, demonstrate manipulatively, and practice kinesthetically. Grouping heterogeneously and connecting culturally helps our lessons cross learning barriers and provide opportunities for children to help each other learn.
Ball, D., (1992). Magical Hopes: Manipulatives and the reform of math education: American educator, Summer 1992.
Although this article is 15 years old, its concerns are still valid: are we using manipulatives wisely when we teach mathematics to children? What are the relative merits of different concrete objects? Are lessons using manipulatives sensible to adults because we already understand the concepts they are designed to represent? As teachers it is important for us to understand the purpose behind the manipulatives we use when we design instruction, and it is vital for us to link the activities using manipulatives to the mathematical concepts explicitly for children to make important connections.