EngageNY
Constant Rate
Two-variable equations can express a constant rate situation. The lesson presents several constant rate problems. Pupils use the stated constant rate to create a linear equation, find values in a table, and graph the points. The resource...
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 rates...
Howard County Schools
Constant Rate Exploration
Question: What do rectangles and bathtub volume have in common? Answer: Linear equations. Learn how to identify situations that have constant rates by examining two different situations, one proportional and one not proportional.
EngageNY
Graphs of Linear Functions and Rate of Change
Discover an important property of linear functions. Learners use the slope formula to calculate the rates of change of linear functions. They find that linear functions have constant rates of change and use this property to determine if...
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 taken to discuss...
Natinal Math + Science Initative
Slope Investigation
Context is the key to understanding slope. A real-world application of slope uses a weight loss scenario with a constant rate of change to introduce the concept of slope of a line, before it makes a connection to the ordered pairs and...
EngageNY
Introduction to Simultaneous Equations
Create an understanding of solving problems that require more than one equation. The lesson introduces the concept of systems of linear equations by using a familiar situation of constant rate problems. Pupils compare the graphs of...
Balanced Assessment
Bathtub Graph
Represent the relationship between independent and dependent variables through a modeling situation. The activity expects learners to graph the volume of water in a bathtub during a given scenario. The graph should result in two areas of...
EngageNY
Interpreting Rate of Change and Initial Value
Building on knowledge from the previous lesson, the second lesson in this unit teaches scholars to identify and interpret rate of change and initial value of a linear function in context. They investigate how slope expresses the...
West Contra Costa Unified School District
Average Rate of Change
Learners investigate average rates of change for linear functions and connect the concept to slope. They then determine average rates of change in quadratic and exponential functions.
EngageNY
Graphs of Simple Nonlinear Functions
Time to move on to nonlinear functions. Scholars create input/output tables and use these to graph simple nonlinear functions. They calculate rates of change to distinguish between linear and nonlinear functions.
Balanced Assessment
A Run for Two
Develop a graph to represent the distance between two cars. The assessment task presents a scenario in which two cars are traveling at constant speeds with one faster than the other. Pupils develop graphical representations to show the...
EngageNY
Linear Functions and Proportionality
Connect linear equations, proportionality, and constant rates of change to linear functions. Young mathematicians learn how linear equations of the form y = mx + b can represent linear functions. They then explore examples of linear...
Curated OER
Worksheet 14 - Rates
In this rate worksheet, students draw and label given situations, determine the rates and the relationship between them. This two-page worksheet contains 7 multi-step problems.
EngageNY
Graphs of Functions and Equations
Explore the graphs of functions and equations with a resource that teaches scholars how to graph functions as a set of input-output points. They learn how the graph of a function is the graph of its associated equation.
Curated OER
Dragonfly
The speed of a dragonfly brings math into the real world as your learners collaboratively see the value in calculating unit rates in direct proportion problems. This six-phase lesson encourages you, as the teacher, to only ask questions...
InqueryPhysics
Interpreting Motion Graphs
Every movement in the world can be measured and even motionless objects can be significant indicators of movement. Focus on motion graphs that feature distance vs. time, speed vs. time, and positive and negative acceleration.
Texas Instruments
Is It or Isn't It Proportional
How can you tell if number relationships are proportional? Mathematicians investigate proportional relationships. They compare and contrast functions and graphs to determine the characteristics of proportional relationships, as well as...
Curated OER
Mathematical Modeling and constant Rate Equations
In this rates instructional activity, students solve five story (word) problems related to rate and time. In two of the problems students are directed to create a graph of the problem.
Curated OER
Tight Rope
Learn how to explore the concept of linear functions. In this linear functions lesson, students collect linear data from a motion detector. Students walk to create a linear function. Students plot the points on a graph and determine a...
Curated OER
Rate of Change
High schoolers observe and calculate slopes. In this algebra lesson, students graph equations and determine the pace at which the slope is changing. They use the navigator to see the change as they graph the lines around.
Curated OER
Every Graph Tells A Story
Seventh graders explore linear equations. In this graphing lesson, 7th graders explore constant rates of change. Students discover the real-life application of graphs and demonstrate their ability to read graphs and write corresponding...
Illustrative Mathematics
Logistic Growth Model, Abstract Version
Here learners get to flex some serious algebraic muscles through an investigation of logistic growth. The properties of the constant terms in the logistic growth formula are unraveled in a short but content-dense activity. Moving...
EngageNY
Increasing and Decreasing Functions 1
Model situations with graphs. In the fourth installment of a 16-part module, scholars learn to qualitatively analyze graphs of piecewise linear functions in context. They learn to sketch graphs for different situations.