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...
Curated OER
Finding Equivalent Forms For Positive Rational Numbers
Learners discuss the relationship between and the equivalent forms of rational numbers. They will convert numbers from decimals to fractions, understanding they are equivalent, but just different forms.
Illustrative Mathematics
Comparing Rational and Irrational Number
Algebra learners must know how to use rational numbers to approximate irrationals. This resource asks participants to decide which number is larger without using a calculator. It makes a great exercise to use as a five-minute transition...
EngageNY
Comparing Rational Expressions
Introduce a new type of function through discovery. Math learners build an understanding of rational expressions by creating tables and graphing the result.
Illustrative Mathematics
Irrational Numbers on the Number Line
There are four irrational numbers that participants need to graph. Pi(π), -(½ x π), and √17 are easy to approximate with common rational numbers. On the other hand, the commentary describing the irrational number 2√2 is not clear. It...
Curated OER
Worksheet, Chapter 1: College Prep Algebra (Integers, Rational Numbers)
In this algebra worksheet, students evaluate equations, identify the inverse of numbers, translate words into a number sentence, compare expressions, and solve radicals. This six page worksheet contains a variety of 67 problems.
Charleston School District
Pre-Test Unit 7: Real Numbers
Don't be irrational! Use this pre-test to assess your classes' ability to work with all types of real numbers. The lesson asks learners to estimate value, evaluate roots, and order numbers. This begins a series of lessons on the real...
EngageNY
Multiplying and Dividing Rational Expressions
Five out of four people have trouble with fractions! After comparing simplifying fractions to simplifying rational expressions, pupils use the same principles to multiply and divide rational expressions.
Illustrative Mathematics
Graphing Rational Functions
The slider feature on Desmos excellently shows how graphs change based on different variable values. Learners look at two similar rational functions and compare and discuss what happens when the numbers go from positive to zero to...
Virginia Department of Education
Complex Numbers
Build on your class' understanding of real numbers as they begin working with complex numbers. Pupils begin with an exploration of i and the patterns in the powers of i. After developing a definition for i, they simplify complex number...
Alabama Learning Exchange
As If Numbers Weren't Complex Enough Already!
The class explores the concept of complex numbers on a website to generate their own Mandelbrot sets. They will practice performing operations with complex numbers and then to get a visual understanding, graph the absolute value of a...
Charleston School District
Comparing and Ordering Irrational Numbers on a Number Line
Estimating the value of numbers is much harder than it sounds! Scholars compare and order the value of numbers presented in different forms including fractions, decimals, roots, integers, and pi. This builds on the previous lessons in...
EngageNY
Complex Numbers and Transformations
Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...
EngageNY
Polynomial, Rational, and Radical Relationships
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...
EngageNY
Comparing Methods—Long Division, Again?
Remember long division from fifth grade? Use the same algorithm to divide polynomials. Learners develop a strategy for dividing polynomials using what they remember from dividing whole numbers.
Curated OER
Rational and Irrational Numbers 2
Is the circumference of a circle always, sometimes, or never rational? Learners answer questions individually and also work in groups to look at sums and products of rational and irrational numbers. They must also be able to use the...
Curated OER
Lesson 3: Number Sense
Learners solve word problems using number sense. They convert fractions to decimals and mixed numbers. Pupils determine if a given fraction is greater or less than another fraction, and order numbers on a number line.
Curated OER
Rational and Irrational Numbers 1
You'll need scissors, glue sticks, and mini whiteboards for this activity on rational and irrational numbers. Learners work in groups to classify a variety of expressions as rational or irrational. They are also given a mock discussion...
Concord Consortium
Last Digit Arithmetic
Mathematics involves a study of patterns. The exploratory lesson has learners consider the addition pattern in different sets of numbers. Each set has a different pattern that pupils describe mathematically. The patterns involve both...
Curated OER
Worksheet Chapter 1, 1.2-1.8 College Prep Algebra
In this algebra worksheet, pupils complete a variety of basic algebra problems. They compare integers, identify sets of numbers, simplify equations, translate words into numerical expressions, and identify properties. This worksheet...
Curated OER
Exploring Real Numbers
In this algebra worksheet, 11th graders classify numbers as rational, irrational, integral and whole. They solve the equations and graph i ton a number line. There are 26 questions with an answer key.
Balanced Assessment
Smaller, Larger, In-Between
Build a solid understanding of rational number relationships by asking class members to use various skills to order decimals, fractions, and numeric power expressions. Using the resource, they find that the fractions do not have an...
Curated OER
Rational Equations
In this rational equations worksheet, 9th graders solve 10 different problems that include various forms of rational equations. First, they determine the least common denominator in each equation. Then, students compare numerators and...
Curated OER
Cartesian Coordinates
Students investigate rational numbers through data analysis and statistics. In this algebra lesson, students represent, rename, compare and order rational numbers. They collect and represent data correctly on a graph.