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Number Theory

These problems delve into prime and composite numbers, factors, multiples, and other properties of numbers.
Some of these problems are also in the following subcategories:
 Related Resources

Interactive resources from our Math Tools project:
Math 4: Number Theory
The closest match in our Ask Dr. Math archives:
Elementary Number Sense/About Numbers
NCTM Standards:
Number and Operations Standard for Grades 35
Access to these problems requires a Membership.

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>>

Assembly Seating
 Claire Mead

Math Fundamentals, difficulty level 2. What is Ben's plan for arranging chairs for the school assembly?
... more>>

Basketball Bargain
 Chad Tollefson from Western Oregon University

Math Fundamentals, difficulty level 1. Can Luis use the teacher's clues to figure out how many balls are in the closet? Can you?
... more>>

Birthday Probability
 Kristina Lasher & Lisa Lavelle

Math Fundamentals, difficulty level 3. What is the likelihood that someone is born on an even or odd day of
the month? Are you more likely to be born on a prime number day or a
multiple of 3?
... more>>

Building Bouquets
 Amanda Knott and the Western Oregon University Mentors

Math Fundamentals, difficulty level 2. Help Jana determine how to divide her extra flowers for the flower shop special.
... more>>

The Chocolate Allergy Revelation
 Antiquity (Steve Earth)

Math Fundamentals, difficulty level 5. Use metareasoning to deduce the ages of three people based on a product, a sum, and a seemingly irrelevant third piece of information.
... more>>

Cicada Circus
 Kristina Lasher and special thanks to John Cooley

Math Fundamentals, difficulty level 2. Use the table of information about periodical cicadas to figure out when
the next time is that there will be three years in a row without an
emergence.
... more>>

Crack the Code
 Christi Sather and Kristina Lasher

Math Fundamentals, difficulty level 2. Help Christi use the clues to figure out which code will unlock the vault.
... more>>

Darlene's Dart Board
 Claire Mead

Math Fundamentals, difficulty level 3. How many darts does it take to win on Darlene's dart board?
... more>>

Dragons and Tigers and Hares, Oh My!
 Claire Mead

Math Fundamentals, difficulty level 3. Use clues about the Chinese calendar to determine when Lin's greatgrandfather was born
and how old he is.
... more>>

Five Digits of Fun
 Lisa Lavelle

Math Fundamentals, difficulty level 4. Find a fivedigit number based on these clues.
... more>>

Football Fanfare
 Suzanne Alejandre and Kristina Lasher

Math Fundamentals, difficulty level 1. The students in the pep club are designing a "card stunt" for the halftime show for the next football game. What are the possible seating arrangements they can use?
... more>>

Four Playful Mathematicians
 inspired by Maria Fung's class at Western Oregon

Math Fundamentals, difficulty level 2. Follow the clues to help the four playful mathematicians return the lost watch.
... more>>

Holiday Ornaments
 Claire Mead

Math Fundamentals, difficulty level 3. How many holiday ornaments did each girl's mother make?
... more>>

How Old is Mia?
 Claire Mead

Math Fundamentals, difficulty level 3. Use Mia's clues to find how old she is.
... more>>

I Like to Palindrive!
 Kristina Lasher

Math Fundamentals, difficulty level 3. How many palindromic numbers will appear on Kristina's odometer in October, 2003?
... more>>

In Their Prime
 Claire Mead

Math Fundamentals, difficulty level 2. Use the clues about multiples and primes to figure out how old
Jonathan and Hazel are.
... more>>

A Jar of Coins
 Claire Mead

Math Fundamentals, difficulty level 2. Use fraction clues to discover how many pennies, nickels, dimes and quarters I have in my
jar.
... more>>

Jason's Piggy Bank
 Claire Mead

Math Fundamentals, difficulty level 2. How many nickels did Jason find in his piggy bank?
... more>>

Jellybean Fractions
 Lisa Lavelle

Elementary, difficulty level 2. Determine good and bad choices in playing the Jellybean Fractions Game.
... more>>

Jellybean Rectangles
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Have fun figuring out strategy in the Jellybean Rectangle game.
... more>>

Just the Facts *
 Claire Mead

Math Fundamentals, difficulty level 3. It's not a good idea to guess in this game! Find out how many
multiplication facts Zach got
right.
... more>>

Marble Mayhem
 Claire Mead

Math Fundamentals, difficulty level 2. Fred and his friends divide the marbles in several different ways, but
there is always one left
over.
... more>>

Monmouth Mountain Bikes
 Kristina Lasher

Math Fundamentals, difficulty level 1. How many mountain bikes will have the highest level of safety testing?
... more>>

Moons, by Jove!
 Claire Mead

Math Fundamentals, difficulty level 3. Find out how long it will take these 3 moons to return to a position
of alignment with their
planet.
... more>>

Mr. Lincoln's Line *
 Claire Mead

Math Fundamentals, difficulty level 3. Find out who's wearing glasses and carrying lunch boxes in Mr.
Lincoln's lunch line.
... more>>

Nova Scotia Quilt
 Claire Mead

Math Fundamentals, difficulty level 3. Use the area of a rectangular bed quilt to determine its dimensions.
... more>>

Odd (and Even) Dates
 Lisa Lavelle

Math Fundamentals, difficulty level 1. Can you figure out these curious dates?
... more>>

Odds vs. Evens
 Kristina Lasher

Math Fundamentals, difficulty level 3. Can Jerome and Kiya use what they know about probability to make their games fair?
... more>>

Peanut Butter and Jelly
 Lisa Lavelle

Math Fundamentals, difficulty level 3. How many sandwiches can we make before using up a package of bread and jars of jelly and peanut butter at the same time?
... more>>

Pondering Palindromes
 Mary DeYoung & class

Math Fundamentals, difficulty level 1. Explore 4digit palindromes and find something else they have in common.
... more>>

Puzzling Puzzle Pieces
 Lisa Lavelle

Math Fundamentals, difficulty level 2. Explore the ways 108 puzzle pieces can be arranged.
... more>>

Rabbit's Run
 Lisa Lavelle

Math Fundamentals, difficulty level 1. Help Regina develop options for building her rabbit's run.
... more>>

Set a Date
 Lisa Lavelle (with help from Judy Ann Brown)

Math Fundamentals, difficulty level 3. Explore an interesting detail about a given date, and find six more dates with the same quality.
... more>>

Sharing Birthdays
 Claire Mead

Math Fundamentals, difficulty level 2. How old will Alana be when her mother is three times Alana's age?
... more>>

She Counts Seashells *
 Claire Mead

Math Fundamentals, difficulty level 2. How many shells does Marcia have in her collection?
... more>>

Shopping at the School Store
 Claire Mead

Math Fundamentals, difficulty level 2. How much does a pencil cost at the school store? How much does an eraser cost?
... 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>>

Tangrams
 Claire Mead

Math Fundamentals, difficulty level 2. Discover some of the relationships among the pieces in a set of Tangrams.
... more>>

Toys To Go
 Claire Mead

Math Fundamentals, difficulty level 2. Help Sam determine the sale price of scooters at the toy store.
... more>>

Wheels R Us
 Claire Mead

Math Fundamentals, difficulty level 2. How many bicycles does Danielle have in her cycle shop?
... more>>

Wooden Legs
 Claire Mead

Math Fundamentals, difficulty level 2. How many different ways can Wendy use 31 legs to build wooden
dollhouse furniture?
... more>>
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