ML Functions

Cell Phone Companies Modeling 8.FB4 & 5

johnsonalyssa ML Functions, ML Modeling

Which cell phone plan is the best for me?

mobile-phone-emoji-emoticon-smiley-face-character-talking-happily-cell-60365046

In this lesson, students are given a scenario that requires them to create a linear equation, complete a table and graph the function. The problem presented to the students is as follows: I am sorry to inform you, but your parents have decided to take you off their cell phone plan. Three cell phone plans are provided to different groups in the class. Students are to work in small groups to create their equation, after which they move to larger groups to construct a poster to present to the class. After working in large groups the class will come together and discuss all three cell phone equations and compare. Finally, students will individually decided which cell phone company fits their lifestyle and justify their conclusion. In this activity students will model with mathematics and create linear equations through an interactive activity that appeals to their age group.

Cell Phone Company Lesson Plan

How Many Cups Does it Take? 8.FB.B

fischersh ML Functions, ML Modeling

styrofoam1

In this lesson, students are given the task to determine the number of cups needed to reach the height of their teacher. The only information given is the height of the teacher and the height of one Styrofoam cup. Students are to work with a partner to determine the number of cups with only the materials of four cups, a ruler, and their math journals. Once the number of cups is calculated, the next step is to come up with a linear equation to model what the students discovered. This interactive activity focuses on modeling and creating linear equations in an engaging way that challenges the minds of the students.

How Many Cups Does it Take

I Have a Dream – 8.FB.4&5

graymelissa Common Core State Standards Mathematics, ML Functions, ML Modeling

Are we any closer to equality than we were in 1963?

The civil rights leader Martin Luther KIng (C) waves to supporters 28 August 1963 on the Mall in Washington DC (Photo: AFP/Getty Images)
The civil rights leader Martin Luther King Jr. waves to supporters 28 August 1963 on the Mall in Washington DC (Photo: AFP/Getty Images)

Content and Practice Standards:
CCSS.Math: 8.F.B.4
CCSS.Math: 8.F.B.5
MP 4 – Model with mathematics.

Central Focus and Purpose:
Through experiment in mathematics and culture we will explore data in a series of graphs and evaluate whether we as a society are any closer to equality in the time that has passed. Students create models of linear functions and learn to recognize nonlinear function. They will find the slope of a linear function and evaluate what it means in terms of the economic, education, and social data in the interactive activity to determine whether we are any closer to equality.

Targets and Plan for Intended Learning:
Students will be able to calculate the rate of change and use the rate of change to interpret data in real-life graphs. Students will also be able to estimate a linear function over top of a graph that may not be perfectly linear.

Materials and Technology Needs:
For this assignment we will be using the classroom computer and projector to view short videos as well as read an article as a class. Worksheets for every student to complete (plus a few additional), calculators, pencil, and erasers. Students will be able to use the graphing calculator with the help of the teacher to find a line of best fit when appropriate to check their models.

Assessment Strategies:

  • The teacher will observe groups and look for possible student misconceptions to assure students are understanding what a linear function is and how to find the slope and ensure there are no problems caused by students making assumptions.
  • Help students with defining their variables correctly and answering the questions asked of them.
  • The teacher will ask groups to present their ideas and interpretations of the data. Other groups will be asked to comment and make connections to the material. Students must demonstrate they constructed a linear equation, and solve for the slope of the line.
  • Formative assessment will be the teacher’s evaluation of the written responses that are submitted at the end of class as well as their observations during the assignment. Students must show critical thinking and math reasoning. They must show a linear equation and evaluation of the line for its slope.

Relevant Multimedia Links:

A Half-Century After the March on Washington, Would King Be Satisfied? (Article).

“I have a dream” Martin Luther King Jr. the March on Washington (Short Version YouTube).

Graphical slope of a line | Linear equations and functions (Instructional Material YouTube).

Graph Shop – Graphing Lines Thrift Shop Parody (YouTube).

Lesson Plan and Materials:

Lesson Plan I Have a Dream.

I Have a Dream – Worksheet.

Graph Data for Lesson I Have a Dream.

Taylor Swift on Twitter 8.F.A.1

brittanystevens ML Functions, ML Modeling, Picture Problems, Technology Teaching Issues

twitter logoHow many Twitter followers does Taylor Swift gain every day? How many followers will she have next Friday if she keeps up the same rate?

Social media is everywhere in today’s society, especially for young people. Incorporating social media into a math lesson can be incredibly beneficial to student engagement and interest because social media is so embedded in teenage culture. In this activity, students monitor a popular celebrity on Twitter (or Instagram, Facebook, etc.) by recording how many followers he or she has each day. Students will record this data for several days and use these data points to create a scatter plot on the coordinate plane. After several days, students will be able to analyze the graph, identify trends, and maybe even use a linear model to estimate future values.

For this example, I chose to follow Taylor Swift because she is relevant to young adolescents, has a significant social media presence, and is generally appropriate in the content she posts (this last reason is very important!). If you would prefer to make this a one-day activity rather than a several-day process of collecting data, you can find existing data points at websites like Twitter Counter. However, the process of looking up new data each day and predicting new quantities is deeply valuable for student understanding and investment in the activity.

This lesson addresses CCSS.MATH.CONTENT.8.F.A.1, CCSS.MATH.CONTENT.8.F.B.4, and CCSS.MATH.CONTENT.8.F.B.5 in the Common Core State Standards for Math. The lesson also addresses GLE 1.1.2 in the 6th-8th Grade Washington State Standards for Educational Technology.

Walk This Way – An activity that can be adapted for grades 5-11

oursland HS Algebra, HS Functions, HS Modeling, ML Expressions & Equations, ML Functions, ML Modeling, Technology Teaching Issues

The Walk This Way activity uses a Motion Detector from Vernier and TI Calculators to connect student movement to graphical representations.

Notice each of the standards and cluster from the CCSS-Math.   

5.OA.B.3 Identify relationships between corresponding terms.

6.EE.C.9 Represent and analyze quantitative relationships between dependent and independent variables.

7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about quantitites.

8.F.B. Use functions to model relationships between quantities.

F-IF.A. Understand the concept of a function and use function notation.

A-CED.A. Create equations that describe numbers or relationships.

F-LE.B. Interpret expressions for functions in terms of the situation they model.

The Walk this Way activity includes both Lesson Guidelines and Student Handout.  Walk This Way – Lesson Guidelines

This activity engages students in modeling discourse – Student make and test predictions about graphical models of their classmates movement.

Screen Shot 2015-10-28 at 4.37.33 PMStudents work in groups of four: a. one person walks, b. another operates the calculator, c. another draws the graph on the calculator, and d. the graph of the peers walk, and the final person gives and writes the walking directions.  On the next walk the students switch tasks, so that everyone performs all tasks.

Students perform three different processes of modeling: Part 1. Physically walk from a graph given by the calculator (seen above); Part 2. Physically walk from a graph given on the work sheet (first two activities below); and Part 3. Draw and test a graph when given a walking story (final activity shown).

Screen Shot 2015-10-28 at 4.48.35 PMScreen Shot 2015-10-28 at 4.52.59 PMScreen Shot 2015-10-28 at 4.53.17 PM

Equipments Required

product.md-btd._hero.001.590.332TI- 83 or 84 calculator with Easy Data app (usually comes with the calculator)

Motion Detector from Vernier

Learning progression review of 8-F: Functions, Linear Equations, and Modeling Slope

ramppk Assessment of CCSS-Math, CCSS-Math Learning Progressions, Common Core State Standards Mathematics, ML Functions

Functions are the basis of algebra and future mathematics. This learning progression covers functions, linear equations, graphing, and generalizing all of it. The assessments will challenge students and ensure that the teacher knows their students have met the standard. The problems used are fun and engaging about real life situations where these concepts can be used. Also attached is a lesson plan about modeling how slopes change as lines change. This lesson uses a program called Geogebra to model the changing slopes for students. This lesson is great for a struggling Algebra class because students are able visually see how the slope changes from positive to zero and to negative. by using this program you are integrating technology into your classroom and grabbing your students attention. This learning progression address the common core standards CCSS.MATH CONTENT.8.F.A.1-A.3 and CCSS.MATH CONTENT.8.F.B.4-B.5. By using this leaning progression you students will learn about functions and have a good time while doing it.

Learning Progression technology lesson plan

6.EE – Healthy Heart

rykere Assessment of CCSS-Math, ML Expressions & Equations, ML Functions, Technology Teaching Issues

Students these days tend to lack exercise due to the constant use of technology. This real world problem engages students in a fun math activity that combines the use of technology with exercising. By monitoring their own heart rate students will have the opportunity to analyze the relationship between the dependent variable and the independent variables using graphs and tables, and relate these to equations that represent data applicable to real world problems.
On the livestrong.com website, Sarah Dray(2013) claims “Once you stop your workout, your heart rate should drop by about 20 beats during the first minute. People who have a reduction of 12 or less during that first minute are at a higher risk of suffering a heart attack later in life.” Are you at risk of suffering a heart attack later in life?

To have students answer this question they will need to monitor how fast their heart rate returns to normal after exercise with Vernier heart rate monitors and TI-84 graphing calculators.

http://www.vernier.com/products/sensors/hgh-bta/
As a class decide what type of exercise the students would like to partake in?(bunny hops, umping jacks, jogging in place, etc.)
After demonstrating how to use the technology. Have students break up into groups of four. The students should rotate taking turns monitoring their heart rate.
Students will see if their heart is in a health state by starting at rest, exercising for a minute, and then stopping and letting their heart return back to normal. Students will collect data of their heart rate every 10 seconds for the 2 minute period.
The common core standard of focus:
CSSI 6.EE.9 Use variable to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent variable and the independent variables using graphs and tables, and relate these to the equation.
To achieve the standard above have students make a table and graph of their data collected. Then with guided instruction have them write two equations. One equation reflecting how fast the heart rate accelerate during exercise and another equation reflecting how quickly the heart rate slowed during recovery.
To guide the student through the activity use the student handout attached and have the students fill out the handout as a group. By collaborating in groups they can learn how to respect each others thoughts and ideas, preparing them to be responsible citizens in a diverse society.
After the activity encourage students to bring their parents in during recess or lunch hour during the following day. Students can teach their parents how to use the equipment and test their parents heart health by monitoring the rate the parents’ heart recovers after a period of exercise.

Student Handout:
1. What is the independent variable?
2. What are the units of the independent variable?
3. What is the dependent variable?
4. What are the units of the dependent varibable?
5. What type of slope occurs when you begin to excersise?
6. What type of slope occurs when you let your heart rate return to its resting state?
7. What type of slope occurs if you just remain still.
Fill out the Table representing your heart rate. Make sure to include units
Time Heart Rate

Graph the the information on your table. Make sure to label your axis.

8. Write one equation reflecting how fast the heart rate acclerated during exercise.

9. Write a second equation reflecting how quickly the heart rate slowed during recovery.

10. Based on your data are you at risk of suffering a heart attack later in life? Explain.

8.F – Just A Little Salt Can Go A Long Way

genzlingec Assessment of CCSS-Math, Common Core State Standards Mathematics, ML Functions, ML Modeling, Technology Teaching Issues

Vernier_EasyTemp_large

There is no doubt that our society is advancing so much in the realm of technology.  It is our job as educators to integrate technology into our curriculum to prepare our students to be proficient and prepared for the future and able to understand technology when they are in their own careers.  It has also been a goal in the field of education to get students to learn how different subjects can be relatable to mathematics.  In this lesson, students must go beyond the task of computing numbers and creating a table of data to understanding the science behind why salt when added to water increases the overall time it takes for it to freeze or if it will freeze at all.  This may be a simple mathematics lesson, but it is an accurate example of what type of situations students will have to learn and understand if they are ever in the field of geology and understanding how elements of nature affects certain things.

Saltwater Vernier Probes Lesson

8.EE.B / 8.F.A. / HSA-CED.A Time to Sell Some Cars

genzlingec Algebra Teaching Issues, Assessment of CCSS-Math, Common Core State Standards Mathematics, Middle School Issues, ML Expressions & Equations, ML Functions, ML Modeling

With this problem, students are able to see an example of a real-world situation and understand how to answer a question about two different scenarios and see how they relate to one another.  It is important that students can see and understand that anything in the world can be related or traced back to math.  This is just one example.

Students in this lesson will have to understand proportional relationships between two linear equations then be able to create those equations from what they already know about what the equation for a line even looks like.  Students will be asked to graph their solutions in a table in order to see the comparisons of the two different car salesman and understand that even though an initial amount may be more than another, over a period of time the rate of change is more important to see who will make more at the end of the year.

Illustrative Mathematics Problem

8.EE-Using Geogebra to Model Slope

ramppk Algebra Teaching Issues, Common Core State Standards Mathematics, ML Expressions & Equations, ML Functions, Technology Teaching Issues

9_slope

 

Geogebra is one of the best modeling programs a math teacher can use. When trying to figure out new ideas for the classroom it can be difficult. A good way for new ideas is to integrate technology in to your lessons. Geogebra is a great free program that can be utilized by any teacher. When used correctly Geogebra can greatly aid any lesson and help your students fully understand the material. For a quick tutorial you can watch this video. http://www.youtube.com/watch?v=q2_FwCx83Jc

In this technology lesson plan I am modeling the slope of linear lines using Geogebra. I used Geogebra to show the class how the graph changes as the slope of the line changes. In Geogebra you can use a movable line to demonstrate this change. After students will do a worksheet about the relationship between the look, the slope and y-intercept of the graph. This will help students understand linear equations and how they are graphed. This lesson plan is great for students struggling with the understanding of linear lines and the way they look.