Division: Solving for Unknown Factors
Students will be able to solve for the unknown factors in division problems.
- Invite students to bring their math journals and a pencil to the class meeting area.
- Have students place their supplies on the floor next to them.
- Tell students that today they're going to learn strategies for solving division problems.
- Let the students know that to solve for the unknown factor in a division problem, they must have a strong grasp of some multiplication strategies and multiplication facts.
- On the board write “Multiplication Strategies.”
- Ask students to share with the class some multiplication strategies they already know. As the students share, list the strategies on the board under the term “Multiplication Strategies.”
- Some strategies students may share are repeated additions, arrays, skip counting, or grouping.
Explicit Instruction/Teacher modeling(15 minutes)
- Direct the students’ attention to the board.
- Write a few division problems on the board with an unknown factor. For example, 36÷__= 4 and __÷5= 8.
- Tell the students that the first thing we want to do is rewrite the problem as a multiplication problem. For this example, 4x __ = 36 and 5x8 = __.
- Next, tell the students that we need to decide which multiplication strategy to use to solve for the unknown factor. This is an important step as you want the students to choose a strategy they know as well as one that is efficient.
- With student input, solve one of the above problems, using at least three of the strategies referred to above.
Guided Practice(15 minutes)
- Tell the students to pick up their supplies and write down and solve the other problem using what they think is the most efficient strategy on the board.
- Ask for volunteers to raise their hands and share with the class the steps involved in solving the problem.
- Give the students time to solve the problem.
- As the problem is being solved aloud by the class write down the steps volunteered by the students on the white board.
- When the problem is finished, review it with the class for accuracy. Make sure everyone has the problem written down to use as a reference for completing their assignment during independent work time.
Independent working time(20 minutes)
- Send the students back to their seats.
- Give students the Solve for the Unknown worksheet.
- Walk around and observe the students as they work on completing the assignment.
- Monitor the students as they work, making sure the problems are done correctly, in that they are justifying their answers by showing their work in coming up with the answers for the “Unknown Factor” in each division problem assigned.
- During this time, the teacher will ask questions of the students to make sure they understand the concept of solving for the unknown factor to solve division problems.
- The teacher will also answer questions posed by the students to help them clarify any misconceptions they may have.
- Give advanced students more challenging problems with higher dividends and lower factors to solve.
- Observe and monitor these students more closely. Get involved in helping the students solve the problems. Use of manipulatives show the students visually how to solve the problems.
- Assess students based on comments and feedback received during the lesson.
- Utilize the worksheet to determine accuracy and proficiency in solving for the uknown factors.
- Give each student a sticky note and tell them that they will write the unknown factor for a problem on it. They will also show their work. When they have completed the sticky note, they will put it in a designated place in the room (i.e., on the board, on a section of the wall, etc.)
- Write the problem 18 ÷ = 6 on the board.
- Instruct students to complete the task.
Review and closing(5 minutes)
- Ask for a choral response of the unknown factor students wrote on their sticky notes.
- Call on nonvolunteers to share their strategy, and have others agree or disagree with the strategy used.
- Have students turn and talk to a partner about which multiplication strategy they believe is the best to use when solving for the unknown factor in a division problem.