Slope Discovery Power Point Activity by C. Hogan
Virginia Department of Education resource titled, "Slope Discovery," which is an activity resource in which the student will determine slope, write the equation in slope-intercept form, and graph a line.
This final lesson in the unit culminates with the Go Public phase of the legacy cycle. In the associated activities, students use linear models to depict Hooke's law as well as Ohm's law. To conclude the lesson, students apply they have learned throughout the unit to answer the grand challenge question in a writing assignment.
In this simulation of a doctor's office, students play the roles of physician, nurse, patients, and time-keeper, with the objective to improve the patient waiting time. They collect and graph data as part of their analysis. This serves as a hands-on example of using engineering principles and engineering design approaches (such as models and simulations) to research, analyze, test and improve processes.
Student pairs are given 10 minutes to create the biggest box possible using one piece of construction paper. Teams use only scissors and tape to each construct a box and determine how much puffed rice it can hold. Then, to meet the challenge, they improve their designs to create bigger boxes. They plot the class data, comparing measured to calculated volumes for each box, seeing the mathematical relationship. They discuss how the concepts of volume and design iteration are important for engineers. Making 3-D shapes also supports the development of spatial visualization skills. This activity and its associated lesson and activity all employ volume and geometry to cultivate seeing patterns and understanding scale models, practices used in engineering design to analyze the effectiveness of proposed design solutions.
Students lean about proportions, ratios, and unit rate. It is important for connections to be made among ratio tables, graphing points, and slope of a line. Students make these connections through the first activity provided by the VDOE. The second task by Illustrative Mathematics is a way to assess student understanding.
This lab demonstrates Ohm's law as students set up simple circuits each composed of a battery, lamp and resistor. Students calculate the current flowing through the circuits they create by solving linear equations. After solving for the current, I, for each set resistance value, students plot the three points on a Cartesian plane and note the line that is formed. They also see the direct correlation between the amount of current flowing through the lamp and its brightness.
This is a lesson that introduces kids to the concepts of slope and y-intercept as they relate to multiplicative and additive relationships.
Students are introduced to the "Walk the Line" challenge question. They write journal responses to the question and brainstorm what information they need to answer the question. Ideas are shared with the class (or in pairs and then to the class, if class size is large). Then students read an interview with an engineer to gain a professional perspective on linear data sets and best-fit lines. Students brainstorm for additional ideas and add them to the list. With the teacher's guidance, students organize the ideas into logical categories of needed knowledge.
This is a remix of Color Week from Illustrative Mathematics, https://tasks.illustrativemathematics.org/content-standards/tasks/1110. The purpose of this activity is to give students practice in collecting data and answering questions related to the gathered data that is displayed in a picture graph to support sol K.11a and K.11b. Students wear a different color shirt each week to represent the color of the week, collect the data by coloring a shirt, place it on the graph, and count how many were worn of that color.
Students compare slope as it relates to distance vs. time. Using a simulation on Desmos, students find that faster speeds create steeper slopes on a graph.
Students learn about complex networks and how to represent them using graphs. They also learn that graph theory is a useful mathematical tool for studying complex networks in diverse applications of science and engineering, such as neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Topics covered include set theory, defining a graph, as well as defining the degree of a node and the degree distribution of a graph.
Students will identify the parts of the coordinate plane and graph ordered pairs in all four quadrants of the coordinate plane. There are strategies embedded within the handout to support an enduring understanding. For example, in order to plot points, you can use an Elevator relation: Choose the door "x", then the floor "y")
Extension: Virginia Department of Education resource document titled, "Coordinate Plane", which is a remediation lesson. Students identify, and graph ordered pairs in the four quadrants of a coordinate plane. Visual aid handout, exit ticket, and lesson plan are included.
A brief refresher on the Cartesian plane includes how points are written in (x, y) format and oriented to the axes, and which directions are positive and negative. Then students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points.
Using a website simulation tool, students build on their understanding of random processes on networks to interact with the graph of a social network of individuals and simulate the spread of a disease. They decide which two individuals on the network are the best to vaccinate in an attempt to minimize the number of people infected and "curb the epidemic." Since the results are random, they run multiple simulations and compute the average number of infected individuals before analyzing the results and assessing the effectiveness of their vaccination strategies.
Exploring data collection and graphing -- Mathematics Instructional Plans (MIPs) help teachers align instruction with the 2016 Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.
Students design and build model landfills using materials similar to those used by engineers for full-scale landfills. Their completed small-size landfills are "rained" on and subjected to other erosion processes. The goal is to create landfills that hold the most garbage, minimize the cost to build and keep trash and contaminated water inside the landfill to prevent it from causing environmental damage. Teams create designs within given budgets, test the landfills' performance, and graph and compare designs for capacity, cost and performance.
Student teams design and create LEGO® structures to house and protect temperature sensors. They leave their structures in undisturbed locations for a week, and regularly check and chart the temperatures. This activity engages students in the design and analysis aspects of engineering.
Students quantify the percent of light reflected from solutions containing varying concentrations of red dye using LEGO© MINDSTORMS© NXT bricks and light sensors. They begin by analyzing a set of standard solutions with known concentrations of food coloring, and plot data to graphically determine the relationship between percent reflected light and dye concentration. Then they identify dye concentrations for two unknown solution samples based on how much light they reflect. Students gain an understanding of light scattering applications and how to determine properties of unknown samples based on a set of standard samples.
Students use two different methods to determine the densities of a variety of materials and objects. The first method involves direct measurement of the volumes of objects that have simple geometric shapes. The second is the water displacement method, used to determine the volumes of irregularly shaped objects. After the densities are determined, students create x-y scatter graphs of mass versus volume, which reveal that objects with densities less than water (floaters) lie above the graph's diagonal (representing the density of water), and those with densities greater than water (sinkers) lie below the diagonal.
Students drop water from different heights to demonstrate the conversion of water's potential energy to kinetic energy. They see how varying the height from which water is dropped affects the splash size. They follow good experiment protocol, take measurements, calculate averages and graph results. In seeing how falling water can be used to do work, they also learn how this energy transformation figures into the engineering design and construction of hydroelectric power plants, dams and reservoirs.