10th-11th Grade Math – Stephanie Ludwig
PRE-PLANNING / AIM & OBJECTIVEOverarching Aim: Students are developing and internalizing skills required for solving equations with logarithms. In addition, students are learning to use mathematical language clearly and accurately as they describe their thinking.
Objective: Today, students will be able to solve logarithmic equations using the laws of logarithms.
ASSESSMENT
I will assess students informally by listening to their answers and explanations of those answers, during whole group activities and partner work. I will assess students formally using a “Ticket to Leave” at the end of class, with this problem: Solve and simplify log5(x+1) – log5 (x-1) = 2.
KEY TERMS & PRINCIPLES
A logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Rules of logarithms allow for logarithms to be expanded, simplified and more easily solved.
- Product rule: logbAC = logbA + logbC
- Quotient rule: logb(A/C) = logbA − logbC
- Power rule: logbAC = C(logbA)
LESSON CYLCE / OPENING & INTRODUCTION TO NEW MATERIAL (15 min)
Teacher will…
-Project Do Now problem, objective and homework solutions on the Smart Board.
-Work pre-designated homework problems with input from students, responding as necessary to students’ particular needs for reinforcement.
-Solve Do Now on the board.
-Throughout reworking of homework problems and review of Do Now, emphasize
- Rules of logarithms (see key terms)
- Importance of showing work
- Steps of expanding, solving, and simplifying problems
-Copy down and work on the Do Now problem and check their homework, reflecting on gaps in understanding.
-Answer teacher’s questions as problems are worked (e.g., giving and explaining next steps, offering alternative processes).
-Self-correct and turn in homework, circling problems that are still giving them trouble (if any).
GUIDED PRACTICE (15 min)
Teacher will…
-Work #1-3 on the worksheet, reinforcing what students have already learned about laws of logarithms.
-Use student input to guide problem solving (e.g., ask students to explain steps). / Students will…
-Follow along, taking notes.
-Ask questions to clarify their understanding.
-Answer teacher’s questions about the processes (e.g., give explanations for why certain steps are taken; offer next steps, referring to the rules).
STUDENT PRACTICE (20 min)
Teacher will…
-Instruct students to move into usual pairs and solve problems #4, 8, 11, 13, as well as 12 if time allows.
-Circulate to check on students’ progress and listen in on conversations, offering support as needed.
-Choose students to write each problem and solution on the board.
-Lead discussion of problems. / Students will…
-Split into pairs to solve problems.
-Work together, having conversations about their problem solving processes, specifically the rules they are using.
-Designated to solve problems at the board, help with explanations if other students do not yet understand.
CLOSING (10 min)
Teacher will pass out and take up “Tickets to Leave,” for immediate review and reflection before tomorrow’s lesson. / Students will fill out and pass in “Tickets to Leave” as a daily assessment.
DIFFERENTIATION
Pairings are designed so more advanced students can help those who struggle. Hard copies of Smart Board notes are available upon request or IEP stipulation.