Math Forum - Problems Library - Middle School, Algebraic Reasoning

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Middle School: Algebraic Reasoning

In grades 6-8, middle-school students study patterns using mathematical models such as tables, graphs, words, symbolic rules, and equations, investigating the nature of changes in quantities in linear relations. Students identify functions as linear or nonlinear and explore their properties, learning to represent problems using algebraic symbols, and developing an initial conceptual understanding of the different uses of variables. Students also learn to recognize equivalent forms for simple algebraic expressions, and they begin to solve linear equations.

The problems listed below offer opportunities to practice algebraic reasoning skills at the middle-school level, and address the NCTM Algebra Standard for Grades 6-8..

For background information elsewhere on our site, explore the Middle School Algebra and Word Problems areas of the Ask Dr. Math archives. To find relevant sites on the Web, browse and search Basic Algebra 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.

Balancing Mobiles - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile. ... more>>

Boxes of Stationery - Annie Fetter, Suzanne Alejandre
Pre-Algebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery? ... more>>

Buying Cola - Leon Roland & class
Pre-Algebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy? ... more>>

Car Rental Quandary - Judy Ann Brown
Pre-Algebra, difficulty level 3. Compare the car rental deals using the given information. ... more>>

Club Competition - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Determine how many teams the Fibonacci Middle School Math Club can enter in their first competition. ... more>>

Coding Conundrums - Mary DeYoung & class
Pre-Algebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle. ... more>>

Coin Count - Roya Salehi and Judy Ann Brown
Pre-Algebra, difficulty level 3. Use the given information to determine the number of nickels and dimes in Lisa's bank. ... more>>

Commuting Conundrum - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Help Suzanne and Richard decide which train tickets will give them the most value for their dollar. ... 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>>

Counting Chicken Wings - Annie Fetter, Suzanne Alejandre
Pre-Algebra, difficulty level 3. Figure out how many wings are in the Biggest Bucket O' Wings. ... more>>

Dishwasher Discounts - Pat Hagan
Pre-Algebra, difficulty level 2. Purchasing a new dishwasher can involve a lot of math. Help find the best deal. ... more>>

Distance Driving - Judy Ann Brown
Pre-Algebra, difficulty level 3. Write an expression that will help you determine how long it will take the car to travel any given number of kilometers. ... more>>

Dividing Daffodils - Suzanne Alejandre
Pre-Algebra, difficulty level 4. Help us plant our garden of daffodils. ... more>>

Ducky Promenade - Leon Roland & class (poetry by Annie Fetter)
Pre-Algebra, difficulty level 3. Find the weight of a duckling and two ducks after reading this poem. ... more>>

Duke is Missing - Judy Ann Brown
Pre-Algebra, difficulty level 3. Duke's head is 6 inches long, his tail is as long as his head plus half the length of his body, and his body is as long as the head and tail combined. How long is Duke? ... more>>

Football Figures - Judy Ann Brown
Middle School, difficulty level 2. This year we have already won as many games as we lost last year. How many games will the team play this year? ... more>>

Grandmother's Birthday Party - Judy Ann Brown
Middle School, difficulty level 1. Alice and Jessica are writing invitations for a surprise birthday party for their grandmother. Determine how many invitations they have written? ... more>>

How Old is Ms. Nelson? - Judy Ann Brown
Pre-Algebra, difficulty level 2. Ms. Nelson claims that she is three times as old as her little sister. However, six years ago she was five times as old as her sister was. How old is Ms. Nelson? ... more>>

The Math Club Holiday Party - Judy Ann Brown
Middle School, difficulty level 2. The Math Club is having a holiday party. If the presents are opened in 5 minute intervals starting at 1:00 p.m. the last gift will be opened starting at 5:35 p.m. How many club members are there? ... more>>

Mathematics Club Membership - Judy Ann Brown
Middle School, difficulty level 2. Find the number of students in the Mathematics Club using the given information. ... more>>

Membership Boom! - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the number of students involved in the Math Club, and the number of students in the school. ... more>>

Milk Madness - Suzanne Alejandre
Pre-Algebra, difficulty level 4. Help Georgina find out how much milk is left using the number pattern she describes. ... more>>

Mirror Musing - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Using the information given in a picture of Hagrid and Baby Norbert, find out how tall each of them is. ... more>>

Money in the Bank - Judy Ann Brown
Middle School, difficulty level 2. All but seven of the 49 coins in my bank are quarters and nickels. How much money could I have? ... more>>

New Home for Fibonacci and Fractal - Judy Ann Brown
Pre-Algebra, difficulty level 2. Determine how long it will take Jimal and Leslie to fill the new 15-gallon aquarium. ... more>>

Olympic Temperature - Judy Ann Brown
Pre-Algebra, difficulty level 3. Compare the difference in temperatures between Sydney, Australia at 14 degrees Celsius and Swarthmore, Pennsylvania, U.S.A. at 63 degrees Fahrenheit. ... more>>

Quilting Squares - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design. ... more>>

Seesaw - Suzanne Alejandre
Pre-Algebra, difficulty level 3. How did the four friends balance on the seesaw? ... more>>

Spring Garden Planning - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find the area as well as the length and width of my fractional garden. ... more>>

Where Does Mrs. Darien Live? - Judy Ann Brown
Middle School, difficulty level 2. Use clues to help Mrs. Darien's students find her house number. ... more>>

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