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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.
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Alien Operations
- Teaching the Young Learner Group
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Elementary, difficulty level 2. Can you help scientists decipher the operation symbols on this alien artifact?
... more>>
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Anderson's Pumpkin Patch
- Teaching the Young Learner Group and Lisa Lavelle
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Math Fundamentals, difficulty level 2. How many students are there in Ms. Juncos's fourth grade class?
... more>>
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Cubic Changes
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Determine how the volume and surface area of a cube change when the edge length is changed.
... more>>
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Funny Money
- Lisa Lavelle (adapted)
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Math Fundamentals, difficulty level 2. Determine the amount of money Divya has in her bank.
... more>>
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High School Reunion
- Western Oregon University Pre-service
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Elementary, difficulty level 2. Use logic to discover the arrangement of
person, car, city, and occupation.
... more>>
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Hot Dog Day!
- Jeffrey Mo
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Math Fundamentals, difficulty level 3. Determine how many large hot dogs have been ordered for this special day.
... more>>
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Jumping Rope
- Leon Roland & class
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Math Fundamentals, difficulty level 2. Just how long was the rope with which we started?
... more>>
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March Madness!
- Teaching the Young Learner Class
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Math Fundamentals, difficulty level 3. Given four clues, figure out which pair of friends won a basketball game.
... more>>
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Mini-Movie Theater Seating
- Chrissy Stewart (adapted)
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Elementary, difficulty level 3. How many rowdy kids can sit in the Mini-Movie Theater?
... more>>
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More Balloons
- Lisa Lavelle
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Math Fundamentals, difficulty level 5. Here's a more difficult problem based on our balloon color preferences.
... more>>
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Multiplication Mystery
- Ya. I. Perelman (translated from Russian by Valentina Sokolskaya)
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Math Fundamentals, difficulty level 3. Decipher this cryptic multiplication problem to uncover the final product.
... more>>
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Payment in Kind
- Lisa Lavelle (adapted)
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Elementary, difficulty level 3. Determine the spouses of three kind women based on the details of their inheritance.
... more>>
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Penguin Confusion
- Lisa Lavelle
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Elementary, difficulty level 2. Four penguins have lost their nametags. Help them sort out who's who.
... more>>
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Penguin Fun
- Bob Coulter
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Elementary, difficulty level 2. Three penguins go to an amusement park. Can they all take the same ride?
... more>>
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Perfect Passengers
- Mrs. Clark's Sixth Grade Stars
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Elementary, difficulty level 2. See if you can determine who's who using clues to their eye color and luggage.
... more>>
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Pondering Palindromes
- Mary DeYoung & class
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Math Fundamentals, difficulty level 1. Explore 4-digit palindromes and find something else they have in common.
... more>>
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Price Tag Repair
- Teaching the Young Learner Group
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Math Fundamentals, difficulty level 2. Can you use the clues to help Cathy repair the price tags for the family yard sale?
... more>>
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Summer Shoe Leftovers
- Teaching the Young Learner Group
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Math Fundamentals, difficulty level 4. Determine which of the leftover shoes might satisfy three shoppers' needs.
... more>>
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Team Tag
- Corinne MacPherson (adapted from Faces of Mathematics by A. Wayne Roberts)
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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>>
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Tourists in Turkey
- Arda Antikacioglu
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Elementary, difficulty level 4. Analyze tourism data from Turkey to discover how many people visited specific areas of the country last year.
... more>>
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True Lies
- Lisa Lavelle
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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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