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:

*      Model and describe patterns and functional relationships.

*      Model and analyze quantitative data.

*      Using algebraic symbols to represent and interpret data and physical phenomena.

 

National (NCTM) Standards:

*      Understand patterns, relations, and functions.

*      Represent and analyze mathematical situations and structures using algebraic symbols.

*      Use mathematical models to represent and understand quantitative relationships.

*      Analyze change in various contexts.

 

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…

  1. Patterns can be used to identify trends and made predictions.

 

 

 

 

 

 

  1. An equation or inequality may be written to describe the general relationship between two sets of data.

 

 

 

 

      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…

  1. Extend and compare arithmetic and geometric sequences.
  2. Represent and analyze a wide variety of geometric and numeric patterns using words, tables, verbal descriptions, graphs and equations.  State the rule for a given pattern in oral and written form.

 

  1. Express mathematical relationships using a variable in simple equations and inequalities.
  2. Write and solve simple equations and inequalities to solve problems.

 

  1. Organize data in tables, graphs and scatter plots.  Identify trends and analyze how a change in one variable relates to a change in a second variable.

 

 

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

Learning Center Work

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: