Illustrative Mathematics
Converting Decimal Representations of Rational Numbers to Fraction Representations
A rational number is a ratio of two integers. Discuss with your class how to convert the rational numbers of repeating decimals to fractions. A good commentary on letting x equal the repeating decimal and multiplying each side of such...
New York City Department of Education
Rational Numbers
Order up a unit on rational numbers. A unit overview gives a basic outline of instruction and activities on rational numbers for the 7.NS domain. A performance task on profits at pizzerias assesses understanding of the concepts in the...
Flipped Math
Rational Equations
Take a rational look at solving equations. Learners watch a video presentation on solving simple rational equations that shows solving the equation along with finding excluded values. Viewers then practice the skill with the worksheets...
University of Utah
Rational and Irrational Numbers
Conquer any irrational fears you might have of irrational numbers. As class members investigate how to represent numbers geometrically, they learn about rational and irrational numbers, including approximating and ordering rational...
Willow Tree
Rational vs. Irrational Numbers
Build an understanding of rational numbers and their counterpart irrational numbers. Lead learners through an explanation of rational numbers and the ways they can be expressed. Then introduce them to irrational numbers and make...
EngageNY
Rational Functions
Make a connection between rational expressions and rational functions. Pupils review simplifying and performing operations on rational expressions and recall what it means for two rational expressions to be equivalent based on their...
K20 LEARN
Driving Rationally: Introduction To Rational Functions And Asymptotes
Calculating average speeds is not as simple as finding an average. The lesson introduces class members to rational functions by presenting a problem about finding an average speed for the rest of a trip. Pupils develop an equation to...
EngageNY
Graphing Rational Functions
Put everything together in a picture. Scholars take what they learned in the previous three lessons in the 15th segment of a 23-part unit to graph rational functions. They find the end behavior, the horizontal and vertical asymptotes if...
Utah Education Network (UEN)
Probability, Percent, Rational Number Equivalence
Start seventh grade with a bang with the first chapter of an eight-part seventh-grade workbook series that asks learners to work through problems involving simple probability, percents, and rational number equivalence.
EngageNY
Ordering Integers and Other Rational Numbers
Scholars learn to order rational numbers in the seventh lesson in a series of 21. Reasoning about numbers on a number line allows for this ordering.
EngageNY
Ordering Integers and Other Rational Numbers II
Individuals build on prior knowledge to order a set of rational numbers from least to greatest or greatest to least. As part of the lesson, they order rational numbers written in different forms.
EngageNY
Rational Numbers on the Number Line
Individuals learn how to plot rational numbers on the number line in the sixth lesson plan of a 21-part module. They identify appropriate units and determine opposites of rational numbers.
EngageNY
Comparing Integers and Other Rational Numbers
The ninth installment of a 21-part module has pupils compare integers and rational numbers in decimal and fraction form. They match stories to number lines and compare values in the stories.
EngageNY
Writing and Interpreting Inequality Statements Involving Rational Numbers
Statements often have multiple interpretations — but not these inequality statements. Scholars compare rational numbers and write inequality statements symbolically. The lesson includes problems that require comparing three numbers.
EngageNY
The Structure of Rational Expressions
Find out when rational expressions are closed. Pupils review adding, subtracting, multiplying, and dividing with rational numbers to make the connections to operations with rational expressions. Using specific examples, learners notice...
EngageNY
Transforming Rational Functions
Move all rational functions—well, maybe. Learners investigate the graphs of the reciprocals of power functions to determine a pattern between the graph and the power. Pupils graph rational functions where transformations are clearly...
Utah Education Network (UEN)
Operations with Rational Numbers
Add an engaging resource to your lessons on rational numbers and watch your pupils' understanding multiply. Learners determine rules for adding, subtracting, multiplying, and dividing integers. Individuals then extend these rules to all...
CK-12 Foundation
Infinite Limit Type: Evaluating Limits of Rational Functions
Rational functions become less mysterious when you know about limits. Individuals use an interactive to move a rational function on a coordinate plane and to investigate function values for certain x-values. They see how the limit...
EngageNY
End Behavior of Rational Functions
Connect end behavior to previous learning. Pupils connect finding the end behavior of rational functions to finding end behavior of polynomial functions. The 13th segment in a 23-part unit starts with finding the end behavior or power...
EngageNY
Horizontal and Vertical Asymptotes of Graphs of Rational Functions
Get close to your favorite line. Scholars use end behavior to help find horizontal asymptotes. With the understanding of domains of rational functions, learners find vertical asymptotes and then use graphing calculators to verify the...
West Contra Costa Unified School District
Solving Rational Equations
Scholars first learn to solve two-step equations with fractional coefficients and constants by traditional methods and by clearing the denominator. They continue by learning another approach to solve two-step equations that have decimal...
Virginia Department of Education
Rational Speed Matching
Ready, set, go! Individuals practice converting rational numbers between fractions, decimals, and percents. A speed game has teams match the three forms of rational numbers on a number line.
National WWII Museum
Rationing by the Numbers: Quantitative Data as Evidence
What was it like to live on wartime rations in the United States during World War II? Young historians find out by exploring how those on the home front bought food thanks to the ration system. Other data includes statistics on car sales...
West Contra Costa Unified School District
Work Problems – Bar Models
Why do we have to do so much work? Scholars learn how to set up bar models to represent a situation involving work. They use these bar models to help set up equations with rational coefficients to solve the problem situation.
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