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M.S. Problems
Middle School
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Middle School: Algebraic Reasoning
In grades 68, middleschool 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 middleschool level, and address the NCTM
Algebra
Standard for Grades 68..
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 middleschool sites, go to
the bottom of the page, set the searcher for middle school (68), and
press the Search button.
Access to these problems requires a Membership.

Balancing Mobiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
... more>>

Boxes of Stationery
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery?
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Buying Cola
 Leon Roland & class

PreAlgebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy?
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Car Rental Quandary
 Judy Ann Brown

PreAlgebra, difficulty level 3. Compare the car rental deals using the given information.
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Club Competition
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Determine how many teams the Fibonacci Middle School Math Club can enter in their first competition.
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Coding Conundrums
 Mary DeYoung & class

PreAlgebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle.
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Coin Count
 Roya Salehi and Judy Ann Brown

PreAlgebra, difficulty level 3. Use the given information to determine the number of nickels and dimes in Lisa's bank.
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Commuting Conundrum
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Help Suzanne and Richard decide which train tickets will give them the most value for their dollar.
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The Complex Apartment Complex
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the number of apartments in a new building if each floor has twice as many apartments as the floor above.
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Counting Chicken Wings
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. Figure out how many wings are in the Biggest Bucket O' Wings.
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Dishwasher Discounts
 Pat Hagan

PreAlgebra, difficulty level 2. Purchasing a new dishwasher can involve a lot of math. Help find the best deal.
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Distance Driving
 Judy Ann Brown

PreAlgebra, 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.
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Dividing Daffodils
 Suzanne Alejandre

PreAlgebra, difficulty level 4. Help us plant our garden of daffodils.
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Ducky Promenade
 Leon Roland & class (poetry by Annie Fetter)

PreAlgebra, difficulty level 3. Find the weight of a duckling and two ducks after reading this poem.
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Duke is Missing
 Judy Ann Brown

PreAlgebra, 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?
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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?
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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?
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How Old is Ms. Nelson?
 Judy Ann Brown

PreAlgebra, 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?
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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?
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Mathematics Club Membership
 Judy Ann Brown

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

PreAlgebra, difficulty level 3. Find the number of students involved in the Math Club, and the number of students in the school.
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Milk Madness
 Suzanne Alejandre

PreAlgebra, difficulty level 4. Help Georgina find out how much milk is left using the number pattern she describes.
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Mirror Musing
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Using the information given in a picture of Hagrid and Baby Norbert, find out how tall each of them is.
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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?
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New Home for Fibonacci and Fractal
 Judy Ann Brown

PreAlgebra, difficulty level 2. Determine how long it will take Jimal and Leslie to fill the new 15gallon aquarium.
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Olympic Temperature
 Judy Ann Brown

PreAlgebra, 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.
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Quilting Squares
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design.
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Seesaw
 Suzanne Alejandre

PreAlgebra, difficulty level 3. How did the four friends balance on the seesaw?
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Spring Garden Planning
 Judy Ann Brown

PreAlgebra, 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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