Math Forum - Problems Library - Middle School, Exponents, Roots

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Middle School: Exponents, Roots

In grades 6-8, students develop an understanding of large numbers and learn to recognize and use exponential, scientific, and calculator notation. They also study the inverse operations of squaring and finding square roots to simplify computations and solve problems, learning to find the approximate location of square roots between whole numbers on a number line.

Middle School Problems of the Week that allow students to practice these skills are found below. They address the NCTM Number and Operations Standard for Grades 6-8 expectation that students should understand numbers, ways of representing numbers, relationships among numbers, number systems, and meanings of operations and how they relate to one another.

For background information elsewhere on our site, explore the Middle School Exponents and Square Roots areas of the Ask Dr. Math archives, and see Large Numbers and Infinity and Square/cube roots without a calculator from the Dr. Math FAQ. To find relevant sites on the Web, browse and search Exponents/Roots in our Internet Mathematics Library; to find middle-school sites, go to the bottom of the page, set the searcher for middle school (6-8), and press the Search button.


Access to these problems requires a Membership.

Can You Find My Numbers? - Roya Salehi
Pre-Algebra, difficulty level 3. I have eight numbers in my list. Use the clues to find my numbers. ... more>>

The Complex Apartment Complex - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the number of apartments in a new building if each floor has twice as many apartments as the floor above. ... more>>

Inching Along Down the Football Field - Terrel Trotter
Math Fundamentals, difficulty level 3. Fred put his football down on a goal line of the 100-yard field. He then moved it forward half the field distance, over and over again. When did the distance first become less than one inch? ... more>>

Open and Shut Case - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the locker combination using mathematical clues. ... more>>

Palindrome Day - Judy Ann Brown
Pre-Algebra, difficulty level 2. How many Palindrome Days are there in a year? ... more>>

Santa's Little Helpers - Judy Ann Brown
Pre-Algebra, difficulty level 3. Help Santa to solve the puzzle created by the clever elves. ... more>>

Square Dancing - Judy Ann Brown
Pre-Algebra, difficulty level 2. The sum of each couple's numbers is a perfect square. Use other information in the problem to find the number of Ashley's partner. ... more>>

The Tower of Hanoi Puzzle - Roya Salehi
Pre-Algebra, difficulty level 4. Tower of Hanoi: What is the minimum number of moves it will take to transfer 25 disks from one post to another? ... more>>

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