COURSE: Topics

TOPIC: Real Number System

STAGE 1: IDENTIFY DESIRED RESULTS

Content Standard(s)

Generalizations about what students should know and be able to do

Established Goals:

 

CT Frameworks:

a)     The number system extends from natural numbers to include integers, rational numbers, and real numbers.

b)     Properties of number systems are used to develop strategies for computation and estimation and judging the reasonableness of results.

c)     Multiplication, division and power properties of exponents can simplify calculations with expressions and scientific notation.

 

NCTM Standards:

a)     Compare and contrast the properties of numbers and number systems including the rational and real numbers.

b)     Use number-theory arguments to justify relationships involving whole numbers.

c)     Develop fluency in operations with real numbers.  Using mental computation or paper-and-pencil calculations for simple cases and technology for more complicated cases.

 

Enduring Understandings

Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)

Essential Questions

Inquiry used to explore generalizations

 The student will understand that:

1.       The real number system has subsystems.

2.      The real number system is a mathematical field.

3.      There is a specific order of operations in the real number system that must be followed for all computations.

4.      There are laws of real number exponents that are used to simplify and evaluate algebraic expressions.

 

1.     What are the subsystems of the real number system?

2.     What are the field properties of the real number system?

3.     What is the order of operations for simplifying an algebraic or numerical expression?

4.     How do you use the laws of real exponents to evaluate algebraic expressions?

Knowledge and Skills

What students are expected to know and be able to do

Students will know…

1.       The real number system has subsystems that include the natural, whole, integers, rational and irrational numbers.

2.     The field properties of the real number system.

3.     The order of operations (PEMDAS).

4.     The laws of real number exponents.

 

 

Students will be able to…

1.     Identify the subsystems of the real number system.

2.     List, identify and use the field properties of the real number system.

3.     Use the order of operations to simplify numerical and algebraic expressions.

4.     Use the laws of real number exponents to simplify numerical and algebraic expressions.

 

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

As a researcher for the Southeastern Connecticut Tourism Council, you must update the travel brochure that provides temperature information for Waterford.  You must include the average daily temperature for the month of January in Fahrenheit and Celsius, the range of temperatures for that month, the median temperature and the mode of the temperatures.  Your report will be made to the head of the council in the form of a poster.

 

In addition to tests and quizzes, one or more of the following will be used:

  1. Cooperative learning activities.
  2. Graphing calculator activities.
  3. Informal and formal checks: homework checks, problem of the day and review worksheets.
  4. Flash cards.

 

STAGE 3: DEVELOP LEARNING PLAN

Learning Activities:

  1. Cooperative learning activities.
  2. Graphing calculator activities.
  3. Homework and review worksheets.
  4. Work stations.

 

 

COURSE: Topics

TOPIC: EQUATIONS, INEQUALITES AND GRAPHS

 

STAGE 1: IDENTIFY DESIRED RESULTS

Content Standard(s)

Generalizations about what students should know and be able to do

Established Goals:

 

CT Frameworks:

a)     Tables, graphs, and equations can be used to analyze linear functions. 

b)     Functions are used in a variety of situations including to model data, to make predictions, and to find the rate of change.

c)     A wide variety of functions can be used to model real world situations,

d)     Geometric relationships may be verified and proved using synthetic and coordinate methods.

 

NCTM Standards:

a)     Understands patterns, relations and functions.

b)     Represent and analyze mathematical situations and structures using algebraic symbols.

c)     Use mathematical models to represent and understand quantitative relationships.

d)     Analyze change in various contexts.

e)     Apply and adapt a variety of appropriate strategies to solve problems.

f)      Use the language of mathematics to express mathematical ideas precisely.

g)     Recognize and use connections among mathematical ideas.

h)      Select, apply and translate among mathematical representations to solve problems.

 

Enduring Understandings

Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)

 

Essential Questions

Inquiry used to explore generalizations

 The student will understand that:

1.     Equations and inequalities can be represented by graphs that reveal patterns and enable predictions and solutions.

2.     Graphs of linear equations, linear inequalities, and absolute value equations are constructed using data and algebraic rules.

3.     Equations and inequalities are solved systematically by using inverse operations.

4.     Real-world situations can be modeled and solved by using equations and inequalities.

 

1.   How are equations and graphs related?

2.   What strategies can you use to graph linear equations, linear inequalities and absolute value equations?

3.   How do you solve equations or inequalities algebraically?

4.   How can you use equations, inequalities and linear systems to solve real-life problems? 

 

 

 

 

 

Knowledge and Skills

What students are expected to know and be able to do

Students will know…

1. How to interpret the graphs of linear equations, linear inequalities, absolute value equations and systems of equations and inequalities.

2. How to solve and graph linear equations, inequalities, absolute value equations and systems of equations and inequalities.

3. How to determine the slope and intercepts of a line.

4. How to write the equation of a line.

5. How to write and use an equation, inequality or linear system as a real life model to solve problems and answer questions.

6.  How to relate algebraic and geometric representations of equations, systems of equations, and inequalities.

 

Students will be able to…

1. Describe, analyze and generalize patterns using tables, rules, algebraic equations and graphs.

2. Model, solve and graph linear equations.

3. Use a table of values; intercepts and slope- intercept form to graph a linear equation.

4. Find the slope of a line.

5. Interpret the slope as a rate of change.

6. Find x and y intercepts.

7. Write the equation of a line given a graph, given the slope and one point, or given two points in slope-intercept form, point slope form and standard form.

8. Model, solve and graph inequalities and absolute value equations.

9. Model, solve and graph systems of linear equations and inequalities by graphing, substitution, and linear combinations.

10.Translate real- life problems into linear equations or inequalities and solve.

11. Interpret algebraic equations and inequalities geometrically and describe geometric relationships algebraically using Cartesian coordinates.

STAGE 2: DETERMINE ACCEPTABLE EVIDENCE

Performance Task(s)

Authentic applic