Virginia Department of Education
Slippery Slope
Explore slope using geometric patterns. Young mathematicians investigate towers built from cubes to develop a linear pattern. They move the data to a coordinate plane to connect the pattern to slopes.
Virginia Department of Education
Equations of Lines
Scholars connect slope-intercept form and standard form to the values of m and b by first matching a set of cards that have slope-intercept form, standard form, values of m, values of b, and graphs of linear equations. They then...
College Board
2006 AP® Calculus AB Free-Response Questions
Develop more than just a topical approach to the exam. The six free-response questions from 2006 reveal how the AP exam assesses topics. By using the questions, pupils practice topics such as velocity, sketch slope fields, solving...
West Contra Costa Unified School District
Point-Slope Application Problems
Create a linear equation for a problem when the intercept information is not given. The two-day lesson introduces the class to the point-slope form, which can be used for problems when the initial conditions are not provided. Pupils...
EngageNY
Constant Rates Revisited
Find the faster rate. The resource tasks the class to compare proportional relationships represented in different ways. Pupils find the slope of the proportional relationships to determine the constant rates. They then analyze the...
PBL Pathways
College Costs 2
What is the financial benefit for attending a community college for the first two years before transferring to a four-year college? The second part of the educational lesson asks young scholars to explore this question through data...
Inside Mathematics
Squares and Circles
It's all about lines when going around. Pupils graph the relationship between the length of a side of a square and its perimeter. Class members explain the origin in context of the side length and perimeter. They compare the graph to the...
Charleston School District
Equations of Linear Functions
Teaching linear function relationships using contextual information is beneficial to pupils' understanding. The lesson uses problem solving to build linear functions given different information for each problem. This is the second...
Georgetown University
Cup-Activity: Writing Equations From Data
Determine how cup stacking relates to linear equations. Pupils stack cups and record the heights. Using the data collected, learners develop a linear equation that models the height. The scholars then interpret the slope and the...
CCSS Math Activities
Smarter Balanced Sample Items: 8th Grade Math – Claim 2
Math can be a problem in eighth grade. Sample items show how problem solving exists within the eighth grade standards. Part of the Gr. 8 Claim 2 - 4 Item Slide Shows series, the presentation contains eight items to illustrate the...
Curated OER
Rates and Slopes: An Astronomical Perspective
In this rates and slopes worksheet, students solve 2 problems where they find the rate corresponding to the speed of the galaxies in a Hubble diagram for galaxies and they calculate the rate of the sunspot number change between indicated...
Balanced Assessment
On Averages and Curves
Determine the average on a curve. The class finds graphical representations of averages and expresses them both symbolically and on the graph. The assessment requires class members to justify using average to describe graphs.
West Contra Costa Unified School District
Derivative – Standard Definition
Making a clear connection to algebra concepts helps learners understand the definition of a derivative. The lesson begins with looking at limits of simple linear and rational functions, and leads to the definition of the...
Virginia Department of Education
Slope-2-Slope
Pupils build on previous experience with slope to investigate positive, negative, zero, and undefined slope. They complete a puzzle matching slope-intercept and standard forms of linear equations.
BW Walch
Creating and Graphing Linear Equations in Two Variables
This detailed presentation starts with a review of using key components to graph a line. It then quickly moves into new territory of taking these important parts and teasing them out of a word problem. Special care is...
Curated OER
A Steep Hike
Students explore slope. In this middle school mathematics instructional activity, students analyze and interpret graphs as they investigate slope as a rate of change. Students use a motion detector to collect data as they...
Curated OER
Forces and Graphing
Middle schoolers analyze graphs to determine relationships between variables and rates of change. They determine the basic concepts about static reaction forces. They determine the slope and equation of a line.
EngageNY
Exponential Growth—U.S. Population and World Population
Show how exponential growth can look linear. Pupils come to understand the importance of looking at the entire picture as they compare the US population to the world population. Initially, the populations look linear with the same rate...
Balanced Assessment
Oil Consumption
An assessment presents a chart displaying oil consumption Pupils use the chart to determine the greatest increase in consumption, and then apply that information to figure out when the consumption may reach 100 million barrels a day.
Nevada Outdoor School
Let It Snow! Let It Melt!
Winter weather offers a great opportunity to teach young scientists about the states of matter. This activity-based lesson includes a range of learning experiences, from experimenting with the rate at which ice melts...
Curated OER
Coffee: Differential Equation
In this differential worksheet, students read a word problem and write a differential equation and solve it. They draw the slope field for given problems. This two-page worksheet contains 9 multi-step problems.
Curated OER
Population: Logistically Speaking
In this population worksheet, students read word problems relating to population growth. They write the problem as a differential equation, create models and graphs of the solution. This three-page worksheet contains 10 multi-step...
Curated OER
Juggling Slopes
Students identify the slope of a line. In this algebra lesson, students label slopes as positive, negative, zero or undefined. They use the slope formula to find the slope algebraically and graphically.
Curated OER
Calculate the Slope of a Line Using Two Points
Find that slope! This video does an excellent job of demonstrating how to use the slope formula to find the slope of a line using two points. The instructor first reviews the definition of slope of a line, then works three problems using...