Math Forum - Problems Library - Middle School, Logic

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Middle School Logic: Reasoning and Proof

In grades 6-8, 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 middle-school 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 6-8.

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 middle-school sites, go to the bottom of the page, set the searcher for middle school (6-8), and press the Search button.


Access to these problems requires a Membership.

Balancing Mobiles - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile. ... more>>

Boxes of Stationery - Annie Fetter, Suzanne Alejandre
Pre-Algebra, 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
Pre-Algebra, 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)
Pre-Algebra, difficulty level 3. Find the weight of a duckling and two ducks after reading this poem. ... more>>

The Graduating Class - Judy Ann Brown
Pre-Algebra, 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
Pre-Algebra, difficulty level 3. A logic puzzle to solve the age-old question, "Who will wash the dishes?" ... more>>

Label Shuffle - Judy Ann Brown
Pre-Algebra, difficulty level 3. There are three containers. Which one has the red marbles? ... more>>

Pegging Possibilities - Michael Urbut
Pre-Algebra, 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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