I. Patterns, Relationships, and Functions

 
  1. Patterns
  2. Variability and Change

 

Additional Links to General Mathematics Sites

 

2. Variability and Change

Middle School

  1. Benchmark 1. "Identify and describe the nature of change; recognize change in more abstract and complex situations and explore different kinds of change and patterns of variation."
    1. Bouncing Tennis Balls - Variability and Change (I.2.MS.1,4&5)
      This is a lesson plan that has the students graph information found by bouncing a tennis ball.  They will use this information to determine the dependant and independent variables.
    2. Number Pattern and Sequences - Variability and Change (I.2.MS.1)
      Students work through four different patterns, from Fibonacci's sequence, to geometry. With paper and pencil, they answer questions to describe the change that occurs in each pattern.
    3. Pathfinder: Measuring Wind Speed - Variability and Change (I.2.MS.1&6)
      Students create  their own anemometer, an instrument used to measure wind speed.  Students can plot and then analyze real world wind speed data collected by Pathfinder during one of its recent missions.  This is a teacher resource.
    4. Principles and Standards for School Mathematics:  Learning about rate of change…  - Variability and Change (I.2.MS.1,2&4)
      Students interact with 2 line graphs, one with a constant variable, the other with 2 changing variables.  They answer questions to learn about change and linear graphs.
    5. Sports and Math: Will Women Ever Surpass Their Male Counterparts? - Variability and Change (I.2.MS.1,2,3,4&6)
      Students interpret numerical and graphical data about athletic performance, derive equations, and make statistical predictions.
  2. Benchmark 2. "Connect an initial state to a final state and generalize a rule that describes a pattern of change."
    1. Mathline: The Yo-Yo Problem - Variability and Change (I.2.MS.2&5)
      Students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation and the graphing calculator.
    2. Mathline: Population Simulation with M&M's - Variability and Change ( I.2.MS.2)
      Students use M&M's to study population growth and decay.  They conduct experiments and record the data, then interpret the data.  Teacher resource.
    3. Principles and Standards for School Mathematics:  Learning about rate of change…  - Variability and Change (I.2.MS.1,2&4)
      Students interact with 2 line graphs, one with a constant variable, the other with 2 changing variables.  They answer questions to learn about change and linear graphs.
    4. Sports and Math: Will Women Ever Surpass Their Male Counterparts? - Variability and Change (I.2.MS.1,2,3,4&6)
      Students interpret numerical and graphical data about athletic performance, derive equations, and make statistical predictions.
    5. The Next Billion  - Variability and Change  (I.2.MS.2&6)
      Students predict when the  world population will reach 7 billion. Students will discuss things in the environment that are constantly changing.  They will use this information as well as other data to predict when the population will reach 7 billion.  They will discuss the reliability of their predictions, compare them to past trends, and discuss social factors that can affect population growth.
  3. Benchmark 3. "Begin to investigate applications in bivariate data and linear relationships and explore questions of what will happen to one quantity if another variable is changed."
    1. Best Practices of Technology Integration - Variability and Change (I.2.MS.3)
      Students will use the Internet to find a car they would like to buy if they were old enough.  They would then compute monthly payments and the total amount of interest paid on a typical auto loan.  This is a teacher resource.
    2. Functions Made Easy - Variability and Change (I.2.MS.3&5)
      Students will explore the concept of functions as relationships, as machines, s equations, and as graphs.  This is a teacher resource site.
    3. Learning about Rate of Change in Linear Functions Using Interactive Graphs: Constant Cost per Minute - Variability and Change (I.2.MS.3)
      This site allows students to manipulate a graph representing constant cost/minute of a phone contract.  There is also a link to a graph where the rate changes after a certain period of time ($.50/min for the first hour, $.10/minute thereafter).
    4. Sports and Math: Will Women Ever Surpass Their Male Counterparts? - Variability and Change (I.2.MS.1,2,3,4&6)
      Students interpret numerical and graphical data about athletic performance, derive equations, and make statistical predictions.
    5. The Hot Tub - Variability and Change (I.2.MS.3)
      This lesson uses the depth of water in a hot tub at various points.  Students need to describe the water level with positive or negative slope and function of depth of water over time.
  4. Benchmark 4. "Represent variability or change by ordered pairs, tables, graphs and equations."
    1. Bouncing Tennis Balls - Variability and Change (I.2.MS.1,4&5)
      This is a lesson plan that has the students graph information found by bouncing a tennis ball.  They will use this information to determine the dependant and independent variables.
    2. Online Graphing - Variability and Change  (I.2.MS.4)
      Outstanding - Will graph functions like a graphing calculator would do, only easier.  Great for those without access to graphing calculators.
    3. Points in the X - Y Plane - Variability and Change (I.2.MS.4)
      Interactive tool to manipulate coordinate points and to see how they move as the coordinates change.
    4. Principles and Standards for School Mathematics:  Learning about rate of change…  - Variability and Change (I.2.MS.1,2&4)
      Students interact with 2 line graphs, one with a constant variable, the other with 2 changing variables.  They answer questions to learn about change and linear graphs.
    5. Sports and Math: Will Women Ever Surpass Their Male Counterparts? - Variability and Change (I.2.MS.1,2,3,4&6)
      Students interpret numerical and graphical data about athletic performance, derive equations, and make statistical predictions.
    6. The Rich Get Rich - Variability and Change (I.2.MS.4)
      Students complete a chart which explains whether it would be better to take $1,000,000 or take $0.01 the first day and have it doubled every day after that. There is a story that the students follow to get to the answer.
  5. Benchmark 5. "Differentiate between functions and relationships such as linear vs. not linear or continuous vs. non-continuous."
    1. Bouncing Tennis Balls - Variability and Change (I.2.MS.1,4&5)
      This is a lesson plan that has the students graph information found by bouncing a tennis ball.  They will use this information to determine the dependant and independent variables.
    2. Function Machine - Variability and Change (I.2.MS.5)
      Students are able to enter a number to represent the variables and then determine what functionis taking place. The activity explains linear functions and allows the students to ask how, what, and why for solving the problem.
    3. Functions Made Easy - Variability and Change (I.2.MS.3&5)
      Students will explore the concept of functions as relationships, as machines, s equations, and as graphs.  This is a teacher resource site.
    4. Graphing and the Coordinate Plane - Variability and Change (1.2.MS.5)
      This lesson is designed to introduce students to graphing ordered pairs of numbers on the coordinate plane.  Students will be able to give the rise over run for slope.
    5. Linking Length, Perimeter, Area, and Volume - Variability and Change  (I.2.MS.5)
      This is a lesson plan where students will work with 2-dimensional rectangles to focus on the relationship between the scale factor and ratio of perimeters or area of similar figures.   Graphs are drawn for students to visualize the linear and non-linear relationships of perimeter, area, and scale factor .
    6. Mathline: The Yo-Yo Problem - Variability and Change (I.2.MS.2&5)
      Students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation and the graphing calculator.
  6. Benchmark 6. "Continue to explore relationships arising from interesting contexts and use variables and relationships to solve mathematical problems."
    1. Buying a Car   - Variability and Change  (1.2.MS.6)
      Students will use the internet as a resource to look for a car.  They will find a car that they would like to buy and will figure out the amount needed to buy the car, how much would be paid in interest, how much the loan would be for, as well as the many other factors need in buying a vehicle.
    2. Figure This! Math Challenges for Families - Variability and Change (I.2.MS.6)
      Figure This! Mathematics Challenges for Families provides interesting math challenges that middle-school students can do at home with their families. Each challenge features a description of the important math involved, a note on where the math is used in the real world, a hint to get started, complete solutions, a "Try This" section, additional related problems with answers, questions to think about, fun facts related to the math, and resources for further exploration. Math Challenge #7 and #11 are examples of problems that would help teach this particular objective.
    3. Pathfinder: Measuring Wind Speed - Variability and Change (I.2.MS.1&6)
      Students create  their own anemometer, an instrument used to measure wind speed.  Students can plot and then analyze real world wind speed data collected by Pathfinder during one of its recent missions.  This is a teacher resource.
    4. Sports and Math: Will Women Ever Surpass Their Male Counterparts? - Variability and Change (I.2.MS.1,2,3,4&6)
      Students interpret numerical and graphical data about athletic performance, derive equations, and make statistical predictions.
    5. The Next Billion  - Variability and Change  (I.2.MS.2&6)
      Students predict when the  world population will reach 7 billion. Students will discuss things in the environment that are constantly changing.  They will use this information as well as other data to predict when the population will reach 7 billion.  They will discuss the reliability of their predictions, compare them to past trends, and discuss social factors that can affect population growth.

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