EngageNY
The Decimal Expansion of Some Irrational Numbers
Develop a definition of irrational numbers through an exploration of square roots. The 11th lesson plan in this series of 25 asks scholars to estimate the value of a square root. Learners observe as the estimation extends further and...
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...
EngageNY
Rational and Irrational Numbers
Back to the basics: learning how to add numbers. The 17th installment of a 35-part module first reviews addition techniques for rational numbers, such as graphical methods (number line) and numerical methods (standard algorithm). It goes...
EngageNY
Irrational Exponents—What are 2^√2 and 2^π?
Extend the concept of exponents to irrational numbers. In the fifth installment of a 35-part module, individuals use calculators and rational exponents to estimate the values of 2^(sqrt(2)) and 2^(pi). The final goal is to show that the...
EngageNY
Mid-Module Assessment Task: Grade 8 Module 7
Assess pupil understanding of rational and irrational numbers with a mid-module assessment that is the 15th lesson in the 25-part series. The questions represent the objectives in the first half of the series. Topics include decimal...
Mathematics Vision Project
Module 4: Rational Functions
Time to study the most sensible function — rational functions! The seven-lesson unit develops the concept of a rational function through a connection to rational numbers and fractions. Scholars graph functions, solve equations, and...
Curated OER
The Real Number System
Learners analyze the real number system. They discuss real numbers, rational and irrational numbers, integers, whole numbers, natural numbers and more of the real number in the system. They differentiate between all these numbers.
EngageNY
Converting Repeating Decimals to Fractions
Develop a process with your classes for converting repeating decimals to fractions. Through this process, pupils understand that any repeating decimal can be written as a fraction. The 10th lesson in this 25-part module helps reinforce...
Curated OER
Numbers, Numbers Everywhere!
Explore properties of integers! For this algebra lesson, pupils add, subtract, divide and multiply using integers correctly. They differentiate between rational and irrational numbers.
Curated OER
Number Sense: Real Numbers
Using a scientific calculator and an 11-page guide sheet, middle schoolers investigate real numbers and problem-solving properties. The publisher links this resource to Common Core standard for seventh grade math, but you may find it a...
Ohio Department of Education
Number Subsets: Winning the Number Game - Grade Eight
Young leearners identify subsets of the real number system and play a number game to identify natural numbers, whole numbers, integers, rational and irrational numbers.
EngageNY
The Long Division Algorithm
Two methods are always better than one! The eighth installment in this series asks pupils to convert decimals to fractions using two approaches. Individuals first use the more traditional approach of long division and then use reverse...
EngageNY
Infinite Decimals
Can you support the argument that the decimal 0.99999 ... is equivalent to the number one? The seventh installment in this 25-part module gives convincing support for this conclusion. Pupils write infinite decimals using powers of 10....
Curated OER
Meter Marker Mania
Students identify integers as rational and irrational numbers. In this algebra lesson plan, students measure and construct number lines using positive and negative integers. They convert between decimals and fractions.
Curated OER
Real Number System
Ninth graders discuss the real number system and its' properties. In this algebra lesson, 9th graders discuss rational, irrational, closure, real numbers and the distributive property of algebra. They solve problems using these...
EngageNY
Decimal Expansions of Fractions, Part 2
Develop your pupils' understanding of fractions and their decimal equivalence using the 12th lesson in this series. Scholars learn an alternative to long division that results in converting fractions to decimals that emphasize fractional...
5280 Math
Decimal Patterns
Find patterns in the process instead of the result. Learners convert series of decimals and fractions identifying patterns along the way. The lesson includes nine problem tasks with progressively more involved patterns.
EngageNY
Finite and Infinite Decimals
Explore the patterns of fractions that produce finite and infinite decimals. The sixth lesson plan of the series asks learners to determine a similar feature of fractions that produce finite decimals. Using the patterns, pupils create...
Curated OER
Discriminating Against the Zero
Students explore the concept of quadratic equations. In this quadratic equations instructional activity, students find the roots or zeros of quadratic equations using the quadratic formula. Students give examples of functions with 2...
EngageNY
Decimal Expansions of Fractions, Part 1
Is it possible to add infinitely long decimals? As pupils complete the examples in the ninth lesson of this 25-part series, they determine that adding these decimals cannot be done without error. Their task is then to determine the size...
Curated OER
Square Roots and Exponents
Eleventh graders solve problems with roots and exponents. In this algebra instructional activity, 11th graders use the properties of powers to help them multiply, add, subtract and divide exponential functions. They take the square root...
Curated OER
Coordinates
Students identify and label the coordinate planes by the four different quadrants. In this geometry lesson, students plot an ordered pair correctly. They identify and differentiate between rational and irrational numbers.
Curated OER
Special Right Triangles
Students identify the different parts of a right triangle. In this geometry lesson, students use the Pythagorean Theorem to identify missing sides and angles of a right triangle. They work with irrational and rational roots.
EngageNY
Integer Exponents
Fold, fold, and fold some more. In the first installment of a 35-part module, young mathematicians fold a piece of paper in half until it can not be folded any more. They use the results of this activity to develop functions for the area...