1. Who is Number 3? Arnoldo Salas, Deborah Stephens, & Evan Willig
Long Division Lesson
Who is Number 3?
Arnoldo Salas, Deborah Stephens, & Evan Willig
Arnoldo

2. Learners & Goal
Designed to teach long division to students in the fourth grade.
Students will find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.
Based on California Common Core Standard: Mathematics, Grade 4.
Arnoldo

3. Design & Development Based on Dick & Carey model
Cognitive learning theory
Gagné’s nine events
Arnoldo
Cognitive learning theory from Silber.

4. Gain Attention
Show students a division problem that they cannot complete.
Arnoldo
because it is not on the multiplication table and is impractical for repeated subtraction.

5. State Objectives
“Today we will learn long division, which will allow you to solve problems like these.”
Evan
Must let students know what they will be able to do by the end of the day.
This helps the learner keep a goal in mind.

6. Stimulate Recall “How did we divide 15 by 3 in the past?” 15 - 3 = 12
= 9
9 - 3 = 6
6 - 3 = 3
Evan
The students will also be reminded how to use a multiplication table in reverse.
The purpose is to remind students that they can do simpler division problems, and they will be using the simple division in the long division algorithm.
3 - 3 = 0

7. Present Content Introduce the outline of the algorithm. Divide
Multiply
Subtract
Bring down
Repeat or Remainder
Evan
Show the students a set of examples, with no remainders. Describe the steps of the algorithm.
As the lesson series progress there will change the algorithm between to include a remainder.
The students will write answers identifying the quotient and remainder or as mixed numbers.

8. Provide Guidance Lead the students in guided practice.
Model use of “Math Facts” job aid. 1 2 3 4 6 8 9 12 16
Evan
Lead the students in guided practice. First say the step, and have a non-volunteer student respond. And So on.
On subsequent examples have students tell you which step comes next and do the calculations for them.
Students will be provided with a “Math Facts” job aid containing an addition/subtraction table, multiplication tables, and the mnemonic for the long division algorithm.

9. Elicit Performance Students practice on a problem set. Deborah
Students practice on a problem set. The first two problems of the set will be solved with all steps shown to provide additional guidance for the students. Students will use individual dry-erase boards to practice the examples with the teacher.

10. Provide Feedback Students share worked problems with class.
Provide students with positive and constructive feedback.
Students learn from peer performances.
Deborah
The teacher will be using a class-centered dry-erase board, or projection, to deliver the examples to the students in the class. Correct a portion of the assignment with peers; allow students to share their worked problems (correct and incorrect) with the class and provide positive and constructive feedback.

11. Assess performance Students finish assignment on their own.
Use results to evaluate their understanding.
Deborah
Let students finish the assignment. This will result in a set of questions to evaluate their understanding. Answer keys for the assessments show the correct use of the algorithm to allow teachers to identify what part of the algorithm the students had trouble with. Students will also be evaluated using a posttest at the end of the long division unit.

12. Enhance Retention Teach Dad, Mom, Sister, Brother, Rover mnemonic.
Students keep “Math Facts” job aid.
Deborah
Teach the Dad (Divide), Mom (Multiply), Sister (Subtract), Brother (Bring down), Rover (Repeat or Remainder) mnemonic for the algorithm. Students will also keep the “Math Facts” job aid for future reference.

14. References:
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors.
Dick, W., Carey, L., & Carey, J. O. (2009). The systematic design of instruction (7th ed.). Upper Saddle River, NJ: Pearson.
ousia (Designer). (2013). Family (b&w version) [Graphic]. Retrieved December 12, 2013, from family.png. Modified by Evan Willig.
nehtaeh79 (Designer). (2012). Standing dog silhouette [Graphic]. Retrieved December 12, 2013 from
Silber, K. H. (1998). The cognitive approach to training development: A practitioner's assessment. Educational Technology Research and Development, 46(4),

15. Thank You