Math Forum - Problems Library - Math Fundamentals, Algebraic Reasoning

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Algebraic Reasoning
Long before students begin learning formal algebra, they are encouraged to start using variables, expressions and equations to represent the thinking they do when solving problems. The problems in this subcategory can be solved in a variety of ways, including through the use of variables, expressions and equations.

Related Resources
Interactive resources from our Math Tools project:
   Math 4: Algebra
The closest match in our Ask Dr. Math archives:
   Elementary Word Problems
NCTM Standards:
   Algebra Standard for Grades 3-5

Access to these problems requires a Membership.

A Pound of Tea - Claire Mead
Math Fundamentals, difficulty level 3. Find out how long a pound of tea would last Hazel if she were alone. ... more>>

Baseball Cards - Claire Mead
Math Fundamentals, difficulty level 2. How many cards does each of the three boys have in his baseball card collection? ... more>>

Birthday Trip - Kristina Lasher
Math Fundamentals, difficulty level 3. Just how far is the trip to Aunt Mazie's house? ... more>>

Bouncing Babies - Lisa Lavelle
Math Fundamentals, difficulty level 3. Make predictions based on conversation at a recent baby shower. ... more>>

Building Barns * - Claire Mead
Math Fundamentals, difficulty level 3. How long will it take Amy's crew to build a barn? ... more>>

Building Bouquets - Amanda Knott and the Western Oregon University Mentors
Math Fundamentals, difficulty level 2. Help Jana determine how to divide her extra flowers for the flower shop special. ... more>>

Common Cents - Claire Mead
Math Fundamentals, difficulty level 2. How much money do Monique and Misty each contribute toward Mom's Valentine's candy? ... more>>

Crossing the River with Ogres - Claire Mead
Math Fundamentals, difficulty level 2. Find out how many times the boat must cross the river to get all the gnomes and ogres to the other side. ... more>>

Eating Grapes - Claire Mead
Math Fundamentals, difficulty level 3. How many grapes did Angela eat on Monday? ... more>>

Feathers and Fur - Lisa Lavelle
Math Fundamentals, difficulty level 3. Determine the number of pigeons and puppies Xiao has. ... more>>

Georg Tricks the Troll - Terry Trotter
Elementary, difficulty level 3. Georg decides to tangle with the troll and see if he can make some money. ... more>>

Greta's Garden - Claire Mead
Math Fundamentals, difficulty level 2. Find out how much money Greta made from each of her vegetables at the Farmers's Market. ... more>>

Growing Worms - Claire Mead
Math Fundamentals, difficulty level 3. Find a pattern to predict the growth of worms made of triangles. ... more>>

Imogene the Imp * - Claire Mead
Math Fundamentals, difficulty level 3. How many people have to get on the Ferris Wheel before Imogene is at the front of the line? ... more>>

Just the Facts * - Claire Mead
Math Fundamentals, difficulty level 3. It's not a good idea to guess in this game! Find out how many multiplication facts Zach got right. ... more>>

Lawn-Mowing Chore - Judy Ann Brown
Math Fundamentals, difficulty level 4. Find the area of the yard that Josh, Sam, and Mark must mow. ... more>>

March Madness! - Teaching the Young Learner Class
Math Fundamentals, difficulty level 3. Given four clues, figure out which pair of friends won a basketball game. ... more>>

Pauline the Plumber - Claire Mead
Math Fundamentals, difficulty level 2. Use the clues to find out how many widgets Pauline purchased. ... more>>

Pirate Treasure * - Claire Mead
Math Fundamentals, difficulty level 3. How many trips will it take to get the pirates and their treasure back to the ship? ... more>>

Pizza Dough - Claire Mead
Math Fundamentals, difficulty level 2. How much water does Mario need to use to make enough pizza dough for him and his friends? ... more>>

Pocket Change - Claire Mead
Math Fundamentals, difficulty level 1. How many dimes do I have in my pocket? ... more>>

Price Tag Repair - Teaching the Young Learner Group
Math Fundamentals, difficulty level 2. Can you use the clues to help Cathy repair the price tags for the family yard sale? ... more>>

Sharing Birthdays - Claire Mead
Math Fundamentals, difficulty level 2. How old will Alana be when her mother is three times Alana's age? ... more>>

Sharing Smelt - Claire Mead
Math Fundamentals, difficulty level 3. Find out how many smelt Larry caught Saturday morning. ... more>>

Shopping at the School Store - Claire Mead
Math Fundamentals, difficulty level 2. How much does a pencil cost at the school store? How much does an eraser cost? ... more>>

Shop 'Til You Drop * - Claire Mead
Math Fundamentals, difficulty level 3. Find out how much Jason spent on his first back-to-school shopping trip. ... more>>

Siblings - Claire Mead
Math Fundamentals, difficulty level 2. Use clues to find out how many boys and girls are in Alex's family. ... more>>

Tatianna and the Troll - Terry Trotter, revised
Elementary, difficulty level 3. Tatianna tests the troll... and neither loses nor gains. ... more>>

The Math of the Irish - Claire Mead
Math Fundamentals, difficulty level 3. Use the mean age of the group to find Uncle Paddy's age. ... more>>

The Teddy Bears' Banquet * - Claire Mead
Math Fundamentals, difficulty level 3. How many bears can be seated at the banquet? ... more>>

Timber!!! - Lisa and Judy Gardner
Math Fundamentals, difficulty level 3. Determine the lengths of two pieces of a damaged redwood tree. ... more>>

Trapezoid Teatime - Claire Mead
Math Fundamentals, difficulty level 3. Find out how many guests can sit at a row of trapezoid tables at the school volunteers' tea. ... more>>

Wheels R Us - Claire Mead
Math Fundamentals, difficulty level 2. How many bicycles does Danielle have in her cycle shop? ... more>>

Wooden Legs - Claire Mead
Math Fundamentals, difficulty level 2. How many different ways can Wendy use 31 legs to build wooden dollhouse furniture? ... more>>

You Think Your Teacher is Tough!* - Claire Mead
Math Fundamentals, difficulty level 2. Use Mr. Garcia's scoring system to find out how many problems Tyler got correct on his test. ... more>>

Zoo Train - Claire Mead
Math Fundamentals, difficulty level 3. How many passengers boarded the zoo train? ... more>>

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