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Wacky Water World Amusement Parks - Using Slope to Find the Better Deal

Lesson Plan

Wacky Water World Amusement Parks - Using Slope to Find the Better Deal

Grade Levels

8th Grade

Course, Subject

Mathematics
Related Academic Standards
A1.1.2.2.1 A1.1.2.2.1
Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).
A1.1.2.2.2 A1.1.2.2.2
Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).
A1.2.2.1.4 A1.2.2.1.4
Determine the slope and/or y-intercept represented by a linear equation or graph.
A1.2.2.2.1 A1.2.2.2.1
Draw, find and/or write an equation for a line of best fit for a scatter plot.
A1.2.3 A1.2.3

Data Analysis
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  • Big Ideas
    Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data.
    Degree and direction of linear association between two variables is measurable.
    Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
    Information to gain or expand knowledge can be acquired through a variety of sources.
    Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.
    Purpose, topic and audience guide types of writing
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
    Data can be modeled and used to make inferences.
    Mathematical relations and functions can be modeled through multiple representations and analyzed to raise and answer questions.
    Mathematical relationships among numbers can be represented, compared, and communicated.
    Mathematical relationships can be represented as expressions, equations, and inequalities in mathematical situations.
    Measurement attributes can be quantified, and estimated using customary and non-customary units of measure.
    Numerical quantities, calculations, and measurements can be estimated or analyzed by using appropriate strategies and tools.
    Patterns exhibit relationships that can be extended, described, and generalized.
  • Concepts
    Analysis of one and two variable (univariate and bivariate) data
    Functions and multiple representations
    Informational sources have unique purposes.
    Linear relationships: Equation and inequalities in one and two variables
    Linear system of equations and inequalities
    Organization of information facilitates meaning.
    Various types of writing are distinguished by their characteristics
    Categorical and Quantitative Data
    Equations and Inequalities
    Patterns, Relations, and Functions
  • Competencies
    Differentiate between primary and secondary source material.
    Display, analyze, and make predictions using univariate and bivariate data.
    Organize and present information and data that support and illustrate inferences and conclusions drawn from research.
    Represent functions (linear and non-linear) in multiple ways, including tables, algebraic rules, graphs, and contextual situations and make connections among these representations. Choose the appropriate functional representation to model a real world situation and solve problems relating to that situation.
    Write informational pieces, specific to a purpose and audience, which have a well developed main idea, includes cause and effect relationships or problem and solution, and contain precise language and specific detail, relevant graphics, and primary and secondary sources (e.g. letters, reports, instruction, essays, articles, interviews).
    Write, solve, and interpret systems of two linear equations and inequalities using graphing and algebraic techniques.
    Analyze a set of data for a pattern, and represent the pattern with an algebraic rule and/or a graph.
    Analyze and/or interpret data displays and/or use them to make predictions (circle graph, line graph, bar graph, box-and-whisker plot, stem-and-leaf plot, scatter plot).
    Construct and compare linear, quadratic, and exponential models and solve problems.
    Create a function and/or sequence that model a relationship between two quantities.
    Create and/or analyze functions using multiple representations (graph, table, and equation).
    Create new functions from existing functions (transformations of graphs).
    Define, evaluate, and compare functions.
    Interpret solutions to linear equations and inequalities.
    Interpret solutions to linear systems of equations and inequalities.
    Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.
    Summarize, represent, and interpret single-variable data and two-variable data.
    Use and/or identify algebraic properties.
    Use measures of dispersion to describe a set of data (range, quartiles, interquartile range).
    Use the concept and notation of function to interpret and apply them in terms of their context.
    Write, solve, and/or graph linear equations and inequalities using various methods.
    Write, solve, and/or graph systems of linear equations and inequalities using various methods.

Rationale

The students will be able to their knowledge of systems of equations to graph data based on two real life scenarios and determine the best cost.

Vocabulary

System of Equations

Objectives

  1. The students will use their knowledge of systems of equations to create an equation to determine the best cost of each plan and then graph each set of data.
  2. The students will use their graphs to make predictions, analyze the data and answer questions.

Lesson Essential Question(s)

How are relationships represented mathematically?
How can data be organized and represented to provide insight into the relationship between quantities?
How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
How can mathematics support effective communication?
How can patterns be used to describe relationships in mathematical situations?
How can probability and data analysis be used to make predictions?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How does the type of data influence the choice of display?
How is mathematics used to quantify, compare, represent, and model numbers?
How precise do measurements and calculations need to be?
In what ways are the mathematical attributes of objects or processes measured, calculated and/or interpreted?
What makes a tool and/or strategy appropriate for a given task?

Why spend more?  How can system of equations help us to make better spending choices? 

Duration

One 50 minute Class Period

Materials

Each pair of students will need the following:

  • Graph paper
  • Lab Sheets (see below)
  • Pencil
  • A calculator *This is an accommodation for lower level or English as a second language learners only*

Suggested Instructional Strategies

Students will learn a variety of skills such as conceptual understanding of linear equations, graphing and how to interpret data as well as procedural knowledge of how to use slope-intercept form, how to graph linear equations and make predictions based on their graphs.  In addition to the core standards, this lesson includes problem solving, reasoning and making connections.  The lesson can be adapted and enhance to meet the needs of all learners.  All instructional adaptations are marked with a yellow highlighter for lower level and English as a second language learners and a green highlighter for upper level learners/enhancements.  Middle level learners are not highlighted either yellow or green but will complete all yellow highlighted parts of this lesson.

Prior to this lesson, students should have a working knowledge of finding slope, using slope to graph and solving equations.  This should have been taught in previous lessons.  Based on the students’ performance on previous lesson, place the students in the appropriate groups.

Instructional Procedures

This lesson lends itself as an excellent opportunity, if a co-teacher is available in the class, to split the class into two equal groups to do a parallel teaching activity thus making smaller groups that allow the students to work closely with the teacher.  PLEASE NOTE:  This is not for the Learning Support teacher to have all of her students! The groups should be an equal mix of students from the class.

The teacher should be walking around throughout the lesson to answer students’ questions and monitor progress in order to ensure understanding and the success of the students during the lesson.

  1. Tell the students that two new water parks just opened up in your neighborhood and you and your friends can’t wait to go!! You don’t have much money so you want to know which park has the better deal that will allow you to ride more rides at a cheaper price.
  2. THINK-PAIR-SHARE:  Give the students the worksheet with the two plans and decide which park they think has the bigger deal.  Have the students first use a minute of “think” time (completely silent) to write down which park they would recommend and why.  Then turn to a partner and talk about which plan they choose and why for a minute.  Discuss this as a class, but tell the students no one is allowed to change from their original predication. 
  3. Have the students calculate how much it costs to ride the rides in each park and fill in the table on their worksheets.  (See lab sheet attached).

For learning support students, allow the use of a calculator if needed.

  1.  After this, have the students discuss their findings with a partner or as a class if preferred.  Ask the students if there is an equation that we can use to represent the total cost of the ride.

For learning support students, you may wish to give them the equation y = mx+b and explain to them that y is the total cost, m (or slope) is how many rides and b is the base cost it takes to get into each park.  Guide them through testing this by putting in the numbers to their calculator that they already have.  For example, for one ride in Park A you would fill in y = 1(1) + 5 which equals six.  It costs six dollars to ride one ride in Park A.  Whereas in Park B y=.50(1) + 10 which is $10.50 for one ride.

For higher level learners, have the students figure out the equation based on trial and error without giving too many hints.

  1.  Have the students graph each park in a different color on graph paper up to six rides. 

For learning support students, you may need to tell them that the number of rides will be the x axis and the total cost will be on the y axis, or give them a graph with these titles already in place.

For higher level learners, the directions for graphing are not as specific as other lab sheets

  1.  Have the students answer the remaining questions on their lab sheets based on their graphs. (See attached)

For learning support students, you may want them to work with a partner or guide them through the questions as a class discussion to make sure that they understand the concept being taught. 

For higher level learners, I would suggest working with one partner or alone for the remaining questions.  It should also be noted that there are more prediction questions for the students to answer than the other students. 

  1. Have the students create an advertisement for the amusement park with the best deal.  This can be done as a poster, commercial, etc . . . Have the students choose the project type they would like to do to generate higher interest among the students.

Their presentation needs to include

  1. Which park has the better price 
  2. It should include their graph as a point of reference for the audience to see.
  3. A detailed explanation, (in writing if doing a poster or other written advertisement) to explain their work.

In addition to the students advertisement have the students complete the following:

  • For below level and on level learners, have the students create a Facebook post or write an email to their friends to explain which park they should go to and why.
  • For above level learners, have them complete a blog post or write a newspaper article based on their findings.

See attached rubric below for details of how the students can be assessed.

Formative Assessment

  • Upon completion of this activity, all learners will be able to make predications and relate the information to a real life situation. 
  • In addition, the students will have gained an understanding of the system of equations and how to use equations to represent real life problems
  • All assessment of this activity is based on the students’ lab sheet responses as well as their graph and ability to make predictions based on the data presented.
  • The students will also be assessed on their advertisement for the amusement park with the best deal.  The rubric for this is attached.

Related Materials & Resources

Please see attached. The first lab sheet is for lower level learners (marked with a star), the middle for regular education students, (marked with a circle) and the last is enhanced for upper level or gifted students, (marked with a square).  Also attached is the rubric to assess the students' work.

Wacky Water World Lab Sheets.docx
Wacky Water World Rubric.docx

Author

Tina Warfel, TIU 11

Date Published

June 04, 2014
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