Math Forum - Problems Library - Elementary, Logic

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Elementary Logic: Reasoning & Proof

In grades 3-5, students learn to formulate conjectures and to assess them on the basis of evidence. They learn that a few examples are not enough to establish the truth of a conjecture and that counterexamples can be used to disprove a conjecture. By considering a range of examples, they reason about general properties and relationships they find, exploring the structure of a pattern, similarities and differences between two classes of shapes, or the overall shape of a data set. They move from considering individual mathematical objects to thinking about classes of objects, reasoning about the relations that apply to the numbers, shapes, or operations about which they are learning. At this level, posing and justifying conjectures should be an expected part of mathematical activity.

Elementary Problems of the Week that require logical thinking skills are listed below. They address the NCTM Reasoning and Proof Standard for Grades 3-5.

For background information elsewhere on our site, explore the Elementary Logic area of the Ask Dr. Math archives. To find relevant sites on the Web, browse and search Logic 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.

Alien Operations - Teaching the Young Learner Group
Elementary, difficulty level 2. Can you help scientists decipher the operation symbols on this alien artifact? ... more>>

Anderson's Pumpkin Patch - Teaching the Young Learner Group and Lisa Lavelle
Math Fundamentals, difficulty level 2. How many students are there in Ms. Juncos's fourth grade class? ... more>>

Cubic Changes - Lisa Lavelle
Math Fundamentals, difficulty level 4. Determine how the volume and surface area of a cube change when the edge length is changed. ... more>>

Funny Money - Lisa Lavelle (adapted)
Math Fundamentals, difficulty level 2. Determine the amount of money Divya has in her bank. ... more>>

High School Reunion - Western Oregon University Pre-service
Elementary, difficulty level 2. Use logic to discover the arrangement of person, car, city, and occupation. ... more>>

Hot Dog Day! - Jeffrey Mo
Math Fundamentals, difficulty level 3. Determine how many large hot dogs have been ordered for this special day. ... more>>

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

Mini-Movie Theater Seating - Chrissy Stewart (adapted)
Elementary, difficulty level 3. How many rowdy kids can sit in the Mini-Movie Theater? ... more>>

More Balloons - Lisa Lavelle
Math Fundamentals, difficulty level 5. Here's a more difficult problem based on our balloon color preferences. ... more>>

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

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

Penguin Confusion - Lisa Lavelle
Elementary, difficulty level 2. Four penguins have lost their nametags. Help them sort out who's who. ... more>>

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

Perfect Passengers - Mrs. Clark's Sixth Grade Stars
Elementary, difficulty level 2. See if you can determine who's who using clues to their eye color and luggage. ... more>>

Pondering Palindromes - Mary DeYoung & class
Math Fundamentals, difficulty level 1. Explore 4-digit palindromes and find something else they have in common. ... 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>>

Summer Shoe Leftovers - Teaching the Young Learner Group
Math Fundamentals, difficulty level 4. Determine which of the leftover shoes might satisfy three shoppers' needs. ... more>>

Team Tag - Corinne MacPherson (adapted from Faces of Mathematics by A. Wayne Roberts)
Elementary, difficulty level 3. In the game of Team Tag, each kid (excluding Allison) earned a different number of points. How many points did Allison's teammate Jenny earn? ... more>>

Tourists in Turkey - Arda Antikacioglu
Elementary, difficulty level 4. Analyze tourism data from Turkey to discover how many people visited specific areas of the country last year. ... more>>

True Lies - Lisa Lavelle
Elementary, difficulty level 2. Test your logic skills with a citizen of the City of Truth. Or is it the City of Lies? ... more>>

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