GRADE: 5
TOPIC: Algebraic Reasoning:
Patterns and Functions
|
STAGE 1:
IDENTIFY DESIRED RESULTS |
|
|
Content Standard(s) Generalizations about what students should know and be able to do |
|
|
Established Goals: State Standards:
National (NCTM)
Standards:
|
|
|
Enduring Understandings Insights learned from
exploring generalizations via the essential questions (Students will
understand THAT…) |
Essential Questions Inquiry used to explore generalizations |
|
1. Patterns and functions help us describe data and physical phenomena and solve a variety of problems. 2.
Patterns help with description, understanding,
and communication about the world. 3. Data can be used to interpret real life events and situations. 4.
Rules can be written to describe and extend
patterns. 5. When data is looked at in a variety of ways, our understanding of a problem, situation, or event becomes more meaningful. 6. Data can be used to uphold or defeat an opinion. |
1. What kind of patterns are in the world around us? 2. What are solutions of equations? 3. When is an equation an appropriate problem solving model? 4. How does data shape our understanding of a situation or event? 5. How and why do people use patterns? 6. Why do variables change the value? 7. Do variables have a value? 8. Why do we simplify equations? |
|
Knowledge and Skills What students are expected to know and be able to do |
|
|
Students will know…
C. Pairs of numbers can be represented
as a location on a coordinate plane defined by horizontal and vertical number
lines. (axes) |
Students will be able to…
|
|
STAGE 2:
DETERMINE ACCEPTABLE EVIDENCE |
|
|
Performance Task(s) Authentic application in
new context to evaluate student achievement of desired results designed
according to GRASPS (Goal, Role, Audience, Setting Performance, Standards) |
Other Evidence Application that is
functional in a classroom context only to evaluate student achievement of
desired results |
|
Goal: To
determine which salary will permit you to reach $1000 the fastest based on
what the patterns of the graph displays. Role: You are an employee at a video game company. Audience: Your boss. Situation: Your boss at the video game company where you work has given you two choices of salary schemes. You have to decide which of the choices will permit you to reach your goal of $1000 the fastest. Product Performance and Purpose: Using the information provided on the worksheet “What’s the Best Deal”, you are to calculate both salary schemes and record your data results on the table provided. During your calculations, stop at Day 5 and answer the question, “What choice is the best at this point? Why? Write a short paragraph justifying your choice. Continue to compute, but stop at Day 10. Answer the following questions: “Which choice is the best? Why? What happened?” Using the data, plot the results on a centimeter graph paper and record your responses to the following questions: “For what days does the choice 1 yield better total earnings than choice 2? For what days does choice 2 yield better total earnings than choice 1? Which plan is the slowest in achieving the earnings objective? Why? Which format – the table or the graph – would you use to communicate the results of this investigation? Why? What were the rules that generated the function for the daily salary for each choice?” Remember, you will need to support your choice by describing the graphs for each situation with specifics. Standards and
Criteria for Success Scoring Rubric The student: Score of 3: Meets or exceeds the objectives of the
task. Demonstrates a high level of
understanding. Student
demonstrates understanding of the task.
Written explanations are thoughtful and complete. Calculations are correct. The graph represents the data results
accurately. Score of 2: Partially meets the objectives of the
task. Demonstrates a high level of
understanding. Student
demonstrates understanding of the task.
Written explanations are brief.
Calculations are made with some errors. The graph does not quite represent the data
results, but the explanations do represent understanding. Score of 1: Does not meet the
objectives of the task. Demonstrates
poor or incorrect understanding. Student
demonstrates little understanding of the task. Written explanations are unclear. Calculations are made with several
errors. The graph does not represent
the data results and the explanations are incorrect. Score of 0: Shows no understanding of the problem or
how to arrive at a solution. Student demonstrates no understanding of
the task. There are no written
explanations and many calculations errors.
The graphs were not created. |
State Assessments District Assessments Topic Assessments Teacher Observations Daily Class Work Skills Check-ups Math Journal Responses Self-Reflection Homework |
GRADE: 5
TOPIC: GEOMETRY AND MEASUREMENT
|
STAGE 1:
IDENTIFY DESIRED RESULTS |
|
|
Content Standard(s) Generalizations about what students should know and be able to do |
|
|
Established Goals: State Standards: |