ML Functions

COWculating – Picture Problem 8.F.B.4

hendrixky ML Functions, ML Modeling ,

This picture – taken from Freedom Works UK – becomes the center of a fun and highly interactive mathematics lesson where students get to think what it might be like to be a farmer! Students will be assigned a set number of cows that eat a set square footage of grass per day, and must determine how much land is needed in order to sustain the cows. Furthermore, students must consider the amount of time needed in order for grass to grow back, but they must have enough already grown for the cattle to eat in the meantime.

This lesson has students focus working on the 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.MP2
Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

This lesson correlates to the culture of the Ellensburg area, for a large portion of this area is populated by those in the agricultural profession. While most of them are in the hay production/distribution realm, students could connect to this rural lesson nonetheless.

Disneyland Drive! – 8.F.B.4, 8.F.B.5

hendrixky ML Functions, ML Modeling ,

Students are put to the test in this fun and highly interpretive summative review of the previous unit: linear functions!

You and your family are going on a trip to Disneyland, but you must drive there! Your parents have decided that they don’t want the wear-and-tear of such a trip on their own vehicle, so they have narrowed it down to two (2) rental vehicles. However, they are having a hard time figuring out which one would be the most efficient/economical choice. Your job is to gather all the information you can, and construct a minimum of five (5) equations, graph them on GeoGebra, and lastly must decide which car your parents should choose for your vacation!

In order to complete this lesson, students will be split into groups of 3-5 members. The class as a whole will have a set gas price, but each group will have different vehicles as well as a monetary cap that they must remain under.

ModelingLessonPlan

Rocket Math: 8.F.A.3, 8.F.B.5, MP4

natashasmith2 ML Functions, ML Modeling , , ,

 

 

Rocket Math

By: Natasha Smith, Mariana Rosas, Paloma Vergara, & Melisa Sanchez-Leyva

 

 

 

 

This modeling lesson is for an 8th-grade classroom and is focused on the standards CCSS.MATH.CONTENT.8.F.A.3 and CCSS.MATH.CONTENT.8.F.B.5. This lesson introduces students to the concept of nonlinear functions. In the lesson, students will be able to explore the concept of a nonlinear function and expand their knowledge of what a function can look like.

This lesson follows a similar format to Dan Meyers’ 3 Acts. Students will start by watching a video of a model rocket launch. Individually, they will quickly draw a graph of what they think the relationship between the height of the rocket and time is. Next, they will work in groups to plot the points estimating the relationship of the height of the rocket at each second. Lastly, the teacher will take them outside and launch a model rocket to prove or disprove students’ theories. The model rocket will have a Pocketlab attached to it which will provide an exact graph of the height of the rocket at each time point. Students will compare their graphs to the Pocketlab graph. We decided to launch the rocket again instead of providing students with a graph from the original launch in the final act as it adds an element of excitement to the activity and the students will enjoy going outside to watch the rocket launch.

This lesson incorporates multiple types of technology. For the video used in the lesson, teachers would achieve best results by filming their own rocket launch as they will want to use the exact same type of model rocket in both the video and the in-class launch. The video representation should be similar to this video. Students will also be using the website Desmos to graph points. Lastly, the teacher will be using a Pocketlab. The Pocketlab is a wireless sensor that can be attached to different objects and will record different types of data and output graphs. For this lesson, the Pocketlab can be attached to the model rocket and will record the height (altitude) of the rocket as time passes.

Lesson Plan and Worksheet.

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Fashion Drawing vs. Real Humans CCSS.MATH.8.F.B.4 & 5, MP4

almaguera ML Functions, ML Modeling, ML Ratios & Proportional Relationships ,

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This is an 8th grade modeling lesson aligned with linear function models and graphs. Are the fashion artist’s proportions right? This activity challenges students to analyze body proportions generated by a fashion illustrator, then compare them to the student’s own specific body proportions. Students will collect data into a table, plot it onto a graph, and generate an equation to determine the accuracy of the fashion illustration’s proportions.

 

Fashion Proportion vs Human Proportion