LESSON PLAN TEMPLATE
TITLE: Family Portraits: Function
Introduction and Linear Functions
CONTENT AREAS (What areas of mathematics
does this lesson cover?):
GRADE LEVEL: 8 &
MATERIALS NEEDED: graph paper,
KEY CONCEPTS: Simple
functional relationships, equations of the form y=kx, and y=k/x, the
slope and y-intercept of the equation y=mx+b
Component 1.5: Understand and apply concepts and procedures from algebraic sense.
Patterns, functions, and other relations
1.5.1 Apply understanding of linear and non-linear relationships to analyze patterns, sequences, and situations. W
· Extend, represent, or create linear and non-linear patterns and sequences using tables and graphs. [RL]
· Explain the difference between linear and non-linear relationships. [CU]
· Predict an outcome given a linear relationship (e.g., from a graph of profit projections, predict the profit). [RL]
· Use technology to generate linear and non-linear relationship. [SP, RL]
1.5.6 Understand and apply a variety of strategies to solve multi-step equations and one-step inequalities with one variable. W
· Solve multi-step equations and one-step inequalities with one variable.
· Solve single variable equations involving parentheses, like terms, or variables on both sides of the equal sign.
· Solve one-step inequalities (e.g., 2x<6, x+4>10).
· Solve real-world situations involving single variable equations and proportional relationships and verify that the solution is reasonable for the problem. [SP, RL, CU]
Component 2.2: Apply strategies to construct solutions.
2.2.2 Apply mathematical tools to solve the problem. W
· Implement the plan devised to solve the problem or answer the question posed (e.g., in a table of values of lengths, widths, and areas find the one that shows the largest area; check smaller increments to see if this is the largest that works).
· Identify when an approach is unproductive and modify or try a new approach (e.g., if an additive model didn’t work, try a multiplicative model).
· Check the solution to see if it works (e.g., if the solution for a speed of 19 feet per second is 5 steps per second, perhaps the assumption of linearity was incorrect).
Component 1.1: Understand and apply concepts and procedures from number sense.
1.1.4 Apply understanding of direct and inverse proportion to solve problems. W
· Explain a method for determining whether a real-world problem involves direct proportion or inverse proportion. [SP, CU, MC]
· Explain a method for solving a real-world problem involving direct proportion. [CU, MC]
· Explain a method for solving a real-world problem involving inverse proportion. [CU, MC]
· Solve problems using direct or inverse models (e.g., similarity, age of car vs. worth). [SP, MC]
· Explain, illustrate, or describe examples of direct proportion. [CU]
· Explain, illustrate, or describe examples of inverse proportion. [CU]
· Use direct or inverse proportion to determine a number of objects or a measurement in a given situation.
GOALS (Remember the difference between goals and
Part B- Linear Functions: Students will be able to understand and apply the definition of a slope as the ratio of rise to run. Students will be able to calculate the slope of a line through two given points. Students will be able to identify the slope and the y-intercept of an equation in the form y=mx+b. Students will be able to compare slopes and y-intercepts of graphs by looking at their equations. Students will be able to write equations that satisfy given conditions and y-intercepts.
OBJECTIVES: Part A: Students will demonstrate their understanding of function equations by working out examples that take place in real life. They will give examples of direct and inverse variation.
Part B: Students will complete a homework assignment that will provide evidence of their ability to identify the slope of a line, compute a rise to run ratio, and solve and check linear equations.
PROCEDURES: (Label each step in the process: Activating Prior Knowledge, Disequilibration, Elaboration, Crystallization)
POST-ASSESSMENT : Each student should
have include a written definition of the functions covered, the corresponding
equation, and a graph of the function. They should also include how
to solve and check equations of the form y=mx+b.