Thinking Mathematically: Algebraic Thinking

MOBILE PUZZLES

These puzzles show mobiles balanced with different kinds of objects of different weights. Students use algebraic thinking to reason about what value each weight has.

Puzzle #1:

Puzzle #2:

Puzzle #2 (numbers up to 60)

Puzzle #3:

Puzzle #3 (consecutive integers)

INEQUALITIES

The idea for these wonderful puzzles came from Paul Salomon. His own "imbalance puzzles" can be found on his website: http://lostinrecursion.wordpress.com.

see-saw puzzles (easiest kind)

LETTER PUZZLES

Students reason their way through these puzzles, gaining practice with important concepts along the way, including understanding the "equals sign" as a balance of equivalent values, the idea of multiplication as repeated addition, and also implicitly practicing division even if they have not formally learned it.

PATTERNS AND FUNCTIONS

THE SHEEP AND CHICKEN PROBLEM

The Sheep and Chicken Problem

THE TROLL PROBLEM

The Troll Problem

What is Mathematics?

While there is no simple definition of mathematics, it is clear that young children and mathematicians have very different ideas about what math is. For young students whose experience with math is often limited to learning "math facts" and practicing algorithms, it is easy to think that mathematics is nothing more than routine arithmetic. It becomes evident only much later that mathematics is not really about numbers at all, but about reasoning.

The problem sets and activities available here are meant to supplement the regular curriculum for students in the early grades (approximately K to 3). They are meant to emphasize mathematical reasoning and problem solving over content knowledge.

About Me

Sian was a practicing lawyer when she decided to return to school to explore her latent interest in mathematics. She holds a degree in law from the University of Texas and an MA in math education from Teachers College Columbia University. Sian is the Associate Director of the Center for Mathematical Talent at the Courant Institute of Mathematical Sciences, New York University. She also teaches math at the Speyer Legacy School in New York City and works with various other schools as a math education consultant. Sian's interest is in helping young people to discover and develop their own interest and ability in mathematics through extracurricular activities that focus on mathematical reasoning and problem solving. For comments, questions, or suggestions email Sian at sianzelbomath@gmail.com.

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Algebraic Thinking