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Elementary: Algebraic Reasoning

In grades 3-5, elementary students lay the groundwork for the more formal study of algebra in middle and high school mathematics classes. They first study patterns, relations, and functions, making generalizations and analyzing patterns using graphs, words, and tables. They use algebraic symbols to represent variables as unknown quantities, and express mathematical relations using equations. Students use models and objects to represent quantitative relations and draw conclusions, and they study change and how a change in one variable can relate to a change in a second variable.

The problems listed below offer opportunities to practice algebraic reasoning skills at the elementary level, and address the NCTM Algebra Standard for Grades 3-5.

To find relevant sites on the Web, browse and search Basic Algebra in our Internet Mathematics Library; to find elementary sites, go to the bottom of the page, set the searcher for late elementary level (3-5), and press the Search button.

Access to these problems requires a Membership.

A Barrel of Fun - Lisa Lavelle
Elementary, difficulty level 3. How much apple juice did the man keep? ... more>>

Borrowed Books - Teaching the Young Learner Group
active problem Elementary, difficulty level 2. Determine the number of books in the borrowing library created by three friends. ... more>>

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

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

Growing Pains - Lisa Lavelle
active problem Elementary, difficulty level 4. Predict the height and weight of a child after ten years. ... more>>

Idle Ivan and the Troll - Lisa Lavelle
Elementary, difficulty level 2. Idle Ivan makes a deal with a troll... to his disappointment he discovers he knows less math than he thought. ... more>>

Jumping Rope - Leon Roland & class
active problem Math Fundamentals, difficulty level 2. Just how long was the rope with which we started? ... more>>

Lunch Bunch Budgets - Lisa Lavelle
active problem Math Fundamentals, difficulty level 2. Determine the number of children needed for the lunch bunch budget to balance. ... more>>

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

Multiplication Mystery - Ya. I. Perelman (translated from Russian by Valentina Sokolskaya)
active problem Math Fundamentals, difficulty level 3. Decipher this cryptic multiplication problem to uncover the final product. ... more>>

Payment in Kind - Lisa Lavelle (adapted)
active problem Elementary, difficulty level 3. Determine the spouses of three kind women based on the details of their inheritance. ... more>>

Penguin Fun - Bob Coulter
active problem Elementary, difficulty level 2. Three penguins go to an amusement park. Can they all take the same ride? ... more>>

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

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

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