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Middle School
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Middle School Logic: Reasoning and Proof
In grades 68, students continue to learn that mathematics involves
finding patterns and regularities, making conjectures, and evaluating
mathematical arguments. Through discussing their reasoning with a
teacher and with each other, they become more proficient in using
inductive and deductive reasoning. Mathematical argument at the
middleschool level may lack the formal quality of mathematical proof,
but it should include forming a plausible conjecture and testing it,
and showing the student's reasoning so that it can be understood and
evaluated by others, and so as to reveal the limitations as well as
the possibilities of inductive reasoning.
Middle School Problems of the Week that require logical thinking
skills are listed below. They address the NCTM
Reasoning
and Proof Standard for Grades 68.
For background information elsewhere on our site, explore the
Middle School Logic
area of the Ask Dr. Math archives. For relevant sites on the Web,
browse and search Logic
in our Internet Mathematics Library; to find middleschool sites,
go to the bottom of the page, set the searcher for middle school
(68), and press the Search button.
Access to these problems requires a Membership.

Balancing Mobiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
... more>>

Boxes of Stationery
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery?
... more>>

Cats, Dogs, and Kids Everywhere You Look
 Judy Ann Brown

Middle School, difficulty level 2. A Logic problem: Patty's dog and Oscar's cat are both namesakes of the owner of the cat named Oscar...Who owns the dog Patty?
... more>>

Club Competition
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Determine how many teams the Fibonacci Middle School Math Club can enter in their first competition.
... more>>

Ducky Promenade
 Leon Roland & class (poetry by Annie Fetter)

PreAlgebra, difficulty level 3. Find the weight of a duckling and two ducks after reading this poem.
... more>>

The Graduating Class
 Judy Ann Brown

PreAlgebra, difficulty level 3. Use the information about students with different grades to determine the number of students in Mrs. Smith's class.
... more>>

Happy Thanksgiving
 Judy Ann Brown

PreAlgebra, difficulty level 3. A logic puzzle to solve the ageold question, "Who will wash the dishes?"
... more>>

Label Shuffle
 Judy Ann Brown

PreAlgebra, difficulty level 3. There are three containers. Which one has the red marbles?
... more>>

Pegging Possibilities
 Michael Urbut

PreAlgebra, difficulty level 2. Explore the number of possible arrangements of pegs in this logic game.
... more>>

What Day Is It Today?
 Roya Salehi

Math Fundamentals, difficulty level 2. Sophie tells the truth only on Monday, Tuesday, Wednesday, and Thursday. Her sister tells the truth only on Monday, Friday, Saturday, and Sunday. If they both confess to their mom that "Yesterday I lied," what day is it today?
... more>>

Who Brought the Candy Corn?
 Judy Ann Brown

Middle School, difficulty level 3. Five children dressed in different costumes arrived for a Halloween party riding bicycles. Who drinks Root Beer? Who brought the candy corn? How did you figure this out?
... more>>
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