UbD 2.0 - Linear Functions
Overview
A lesson plan outlining the teaching of linear functions at a Grade 8-9 level.
Stage 1 - Desired Results
ESTABLISHED GOALS |
Students will show understanding of the following standards according to the Common Core curriculum:
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Transfer
Students will be able to independently use their learning to… |
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Meaning
UNDERSTANDINGS | ESSENTIAL QUESTIONS |
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Aquistion
Students will know… | Students will be skilled at… |
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Stage 2 - Assessment Evidence
Evaluative Criteria | Assessment Evidence |
| Students will show their understanding of these concepts by completing problems using the concepts in question. | PERFORMANCE TASK(S):
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| OTHER EVIDENCE:
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Stage 3 - Learning Plan
Learning Activities:
Summary of Key Learning Events and Instruction
What learning experiences and instruction will enable students to achieve the desired results? How will the design
W = Help the students know Where the unit is going and What is expected? Help the teacher know Where the students are coming from (prior knowledge, interests)?
H = Hook all students, and Hold their interest?
E1 = Equip students, help them Experience the key ideas and Explore the issue?
R = Provide opportunities to Rethink and Revise their understandings and work?
E2 = Allow students to Evaluate their work and its implications?
T = be Tailored (personalized) to the different needs, interests, and abilities of learners?
O = Be Organized to maximize initial and sustained engagement as well as effective learning?
1.00 Bell Ringer - Review of Algebra at the previous level [W, H, E1, R]
- Problems having students plug a number into an expression for "x" and solving for "y."
- Problems having students graph a linear function from a given equation in slope-intercept form.
1.03 Go over Bell Ringer as a class, students asked to talk through problems. [W, H, E1, R]
2.00 Manipulating Equations - Solving an equation for the dependent variable [W, E1, R, E2, T]
2.01 Work through examples to show different methods/rules of manipulating equations., solving equations for "y." [W]
2.02 Students work on example problems using these methods by themselves or in pairs. [E1, R]
2.03 The solutions to problems are given by students verbally. Any contradictions or questions are worked out on the board by teacher or students. [E1, R, E2, T]
3.00 Graphing Linear Functions [W, E1, R, E2, T]
3.01 Work through examples to show manipulation of functions to solve for "y" to then graph the lines on coordinate planes. [W]
3.02 Students work on example problems using these methods by themselves or in pairs. [E1, R]
3.03 Student volunteers draw their solutions on the board. Any contradictions or questions are discussed as a class. [E1, R, E2, T]
4.00 Creating an Equation from the Graph of a Line [W, E1, R, E2, T]
4.01 Work through examples to show how the graph of a line can be analyzed to find the slope ("m") and y-intercept ("b") to write the function in slope-intercept form ("y=mx+b"). [W]
4.02 Students work on example problems using these methods by themselves or in pairs. [E1, R]
4.03 The solutions to problems are given by students verbally. Any contadictions or questions are settled/shown on the board by teacher or students. [E1, R, E2, T]
5.00 Transformations of a Line [W, E1, R, E2, T]
5.01 Work through examples to show how adding/subtracting a constant to the independent variable or the y-intercept shifts the line left/right or up/down. [W]
5.02 Work though examples to show how scalars can increase, decrease, or flip the slope of a line. [W]
5.03 Students work on example problems using these methods by themselves or in pairs. [E1, R]
5.04 Student volunteers draw their solutions on the board. Any contradictions or questions are discussed as a class. [E1, R, E2, T]
6.00 Inverse of Linear Functions [W, E1, R, E2, T]
6.01 Work through examples to show manipulating linear functions to solve for the independent variable, now making it the dependent variable, then show how the graph of this inverse function is the reflection of the original function across the line y=x. [W]
6.02 Show that a linear function and its inverse are perpendicular to each other. [W]
6.03 Show via substitution of one function into the other solves for the point of intersection of the two lines. [W]
6.04 Students work on example problems using these methods by themselves or in pairs. [E1, R]
6.05 Student volunteers work out and draw their solutions on the board. Any contradictions or questions are discussed as a class. [E1, R, E2, T]
7.00 Real World Problems [W, E1, R, E2, T]
7.01 Work through an example to show what to look for in a real world problem to write an equation for the function required to find the solution asked for. [W]
7.02 Students work on two example problems by themselves or in pairs using the methods shown. [E1, R]
7.03 The solutions to problems are given by students verbally. Any contadictions or questions are settled/shown on the board by teacher or students. [E1, R, E2, T]
8.00 Homework Practice [E1, R, E2, O]
8.01 Students are assigned problems using the concepts of the lesson to practice for homework. Solutions are made available for students to check their work. [E1, R, E2]
8.02 Students will be graded at the beginning of next class based on completion. [O]
8.03 Any further questions or clarifications that students require on particular homework problems will be answered by student volunteers, who will work out their solutions on the board and explain their work. [E1, R, E2, T]
9.00 Quiz [O]
- Students complete an quiz that requires them to show their work and solutions to problems where the skills learned in this lesson are required to solve the problems in question.