Math Forum - Problems Library - Pre-Algebra, Algebra: Variables

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Pre-Algebra
operations with numbers
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fractions, decimals,
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About the
PoW Library

Variables
The problems included here often can be solved using multiple methods, but students can be encouraged to try an algebraic approach using variables.

Related Resources
Interactive resources from our Math Tools project:
   Math 7: Algebra and Expressions
The closest match in our Ask Dr. Math archives:
   Middle School: Algebra
NCTM Standards:
   Algebra Standard for Grades 6-8

Access to these problems requires a Membership.

Accounting for Age - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Given a number trick, explain why the result is always the original number followed by your age. ... more>>

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

Bartering for Bananas - Suzanne Alejandre
Pre-Algebra, difficulty level 4. How many bananas can Byron get with five fish? ... 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>>

Building Fences - Judy Ann Brown
Pre-Algebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36-yard fence. ... more>>

Change Woes - suggested by a Western Oregon University mentor
Pre-Algebra, difficulty level 3. What coins did Lacey have before her money was mixed up with her brother's? ... more>>

Chirp! Chirp! - Annie Fetter
Pre-Algebra, difficulty level 3. Find the temperature when a cricket chirps a certain number of times a minute. ... 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>>

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>>

A Cranberry Craving - Claire Mead, Suzanne Alejandre
Pre-Algebra, difficulty level 2. Use the pattern to find out how many cranberries Carissa ate on Thanksgiving Thursday. ... 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>>

Election Day in Prealgpoweria - Steve Risberg, Suzanne Alejandre
Pre-Algebra, difficulty level 3. How many votes does each candidate in Prealgpoweria receive and how many eligible voters are there? ... more>>

Exploring Area - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find information about Pick's theorem and solve an area problem using this method. ... more>>

Falling into Sequences - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the 20th term in a sequence using both a recursive method and an explicit formula. ... more>>

Gearing Up - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Think about and explain the relationship between three different-sized gears. ... more>>

The Graduating Class - Judy Ann Brown
Pre-Algebra, difficulty level 3. Use the information about students with different grades to determine the number of students in Mrs. Smith's class. ... 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>>

Integer Images - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Use the four equations to figure out which integers the quadrilateral and the circle represent. ... more>>

It's A Secret - Judy Ann Brown
Pre-Algebra, difficulty level 2. In this puzzle, your job is to decode the secret message. ... more>>

Join Us for a Quarter-pound Burger - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Work with fractions and percents to help plan this cookout. ... more>>

Lemonade Fun - Maria Fung and her students
Pre-Algebra, difficulty level 2. How many cups of each size lemonade did Jose and Nick sell? ... more>>

Lucky Lollipops - Suzanne Alejandre & Maria Fung and her students
Pre-Algebra, difficulty level 3. Find the number of lollipops Logan the Leprechaun gives away using his "lucky" method. ... more>>

Measuring Melons - Suzanne Alejandre, Claire Mead
Pre-Algebra, difficulty level 3. Students determine how much each type of fruit weighs. ... 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>>

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>>

Mixing Marbles - Stephen Weimar
Pre-Algebra, difficulty level 3. Find how many marbles each person had at the beginning. ... more>>

Operating Diagonally - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Think about the effect of multiplication and addition on the numbers in the hundreds chart. ... more>>

Ostrich Llama Count - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Given the combined number of heads and legs of ostriches and llamas, help Raul and Esteban figure out how many ostriches and how many llamas there are. ... more>>

Peeling Potatoes - Terry Trotter
Pre-Algebra, difficulty level 2. How many potatoes did Annie and Steve have to peel? ... more>>

Pi Day Treats - Judy Ann Brown
Pre-Algebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration. ... 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>>

Sharing Birthday Cake - Ian Underwood
Pre-Algebra, difficulty level 2. Ian and his father have the same birthday, and share a cake based on the ratio of their ages. Determine when Ian will get certain amounts of cake. ... more>>

Study Hall Games - Judy Ann Brown
Pre-Algebra, difficulty level 4. I polled the students to find out which of the three games in my closet they might like to play. Then I created a math problem using the results of the poll. ... more>>

Timber! - Steve Risberg
Pre-Algebra, difficulty level 3. A tree breaks three-eighths of the way up the trunk, and the tip hits the ground 40 feet from the base of the trunk. How tall was the tree? ... more>>

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