Author: brittanystevens

Logging On 8.F.B.4 and 8.F.B.5

brittanystevens ML Functions, ML Modeling, Technology Teaching Issues

Which Internet plan is better?

High-Speed-Internet

During this lesson, students explore linear relationships in real-world problems to determine the best plan for their Internet needs. The lesson relies heavily on student discourse and reasoning in comparing scenarios as well as procedural fluency in creating tables, graphs, and equations to represent data.

Students will receive a brief scenario about someone shopping for an Internet access plan. One plan includes an initial usage fee followed by a constant rate per minute of Internet access. Rather than receiving these rates in the problem, students are expected to find them using a few given data points. Once these rates are found, students will be presented with a new plan that contains different rates and fees. Students will repeat the process (working toward procedural fluency) and compare the two plans. Because this is a modeling activity, students will be largely left alone with their groups to find solutions. The teacher should play a passive role, asking guiding questions and helping students discover new knowledge for themselves rather than lecturing and giving out answers.

Through the practices of modeling and discourse, students will be better able to grasp the concepts in the CCSS content standards. Students are not only expected to solve the problem accurately, but to model the problem using multiple methods and justify their answers using mathematical reasoning. As students work to solve the problem, they will be expected to model their data using an x-y table, a graph, and a linear equation. Students will share their findings with their peers and work together to compare both Internet plans. More discussion will ensue as students decide which life factors will affect their choice of Internet plan (how much Internet a person would use in a month, etc.). These discussions and group-oriented work will help students attain a deeper, more holistic understanding of linear relationships.

The lesson addresses the following Common Core State Standards:

CCSS.MATH.CONTENT.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change  and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

CCSS.MATH.CONTENT.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

Follow our lesson plan here: Modeling Linear Functions Lesson Plan.

By Brittany Stevens, Samantha Hibbard, Juliana Golding, and Bill Munson

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.

Super Bear 6.RP.A.3

brittanystevens ML Modeling, ML Ratios & Proportional Relationships

How many regular size gummy bears would it take to equal one Super Bear? How about mini bears?

super bear

Students explore concepts of proportions and rates as they determine the relationships between three different sizes of gummy bears. The lesson uses a series of short multimedia videos that provide small amounts of information in a real-world problem to create intrigue. Specifically, the first video shows someone placing three different sizes of gummy bears on a table: a “mini” bear, a “regular” bear, and a “super” bear. The video ends with the three bears aligned in a row, without posing a question or providing information. The video inspires students to solve a problem by formulating their own instinctive questions and seeking out missing information.

Throughout the lesson, students guide their own learning by deciding how to solve the problem and what information they will need to do so. Working in groups, students will arrive at a solution and then share their process with the rest of the class. Students may be given guiding questions or ideas if they seem lost, but the lesson should rely on students’ abilities to discover and problem solve within groups. Once each group has shared their own ways of solving the problem, the teacher will show the whole class a new method for finding the answer using ratios and proportions. The lesson provides several opportunities for extension, including solving for both mini and regular size bears, as well as determining which option of bear provides the most gummy for the least amount of money. The lesson meets CCSS.MATH.CONTENT.6.RP.A.3, MP.1, and MP.4 in the Common Core State Standards.

super bear2

Find the videos for the lesson here.

Follow our lesson plan here: Super Bear Modeling Lesson

By Brittany Stevens, Devyn Hunter, Kelly Yingling, and Enrique Gudino