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Elementary
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Elementary:
Arithmetic/Early Mathematics:
Number and Operations
At the elementary level students study numbers and ways of
representing them, including different number systems, and
learn to understand relations among numbers, place value,
simple fractions, and equivalent forms of common fractions,
decimals, and percents. They become familiar with the number
line, learn to understand the meanings of operations
(addition, subtraction, multiplication, and division)
and how they are related, and practice so as to be able
to compute easily.
Many of the Elementary Problems of the Week allow students
to exercise these skills, and address the NCTM
Number
and Operations Standard for Grades 3-5. Below are some of them.
For background information elsewhere on our site, explore the
Elementary
area of the Ask Dr. Math archives (see, in particular,
About Numbers).
To find relevant sites on the Web, browse and search
Arithmetic/Early
Mathematics 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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Across Europe
- Lisa Lavelle
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Elementary, difficulty level 3. Calculate Tray's gift "budget" during her first year working for Capital City Guidebooks (requires a bit of geography research). Initially a two-week problem.
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Across the Netherlands
- Maggie Hos-McGrane
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Math Fundamentals, difficulty level 5. Help sort out this bike trip through the Netherlands (requires a bit of map reading). Initially a two-week problem.
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Across Wisconsin
- Jo Wenzler
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Math Fundamentals, difficulty level 2. Determine how long it will take this athletic math teacher to bike across Wisconsin (requires a little map reading). Initially a two-week problem.
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Aidan's Millimeter Measurements
- Lisa Lavelle
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Math Fundamentals, difficulty level 1. Calculate Aidan's height and age based on his well-baby measurements at the doctor's office.
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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?
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At the Movies
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Explore the changes in movie and theater prices.
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A Barrel of Fun
- Lisa Lavelle
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Elementary, difficulty level 3. How much apple juice did the man keep?
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The Big Balloon Blowup
- Leon Roland & class
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Math Fundamentals, difficulty level 3. Help Ulrike and Lars determine the number of balloons in each bag.
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Birds in Trees
- Steve Maurer
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Elementary, difficulty level 3. Can you figure out the number of trees in the courtyard?
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Birthday Beach Bash
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Help determine how many balloons were needed for party favors at the end of this celebration.
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Borrowed Books
- Teaching the Young Learner Group
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Elementary, difficulty level 2. Determine the number of books in the borrowing library created by three friends.
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Bunches of Basil
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Determine the maximum number of basil plants I will have after I finish thinning the garden.
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Calculator Double Vision
- Lisa Lavelle
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Elementary, difficulty level 2. Enter a 3-digit number twice on a calculator and use division to get the original number.
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Cat Walk
- Math Olympiad Problem (revised)
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Elementary, difficulty level 2. Using the ratio of dog steps to cat steps and the length of a dog step, calculate the number of feet a cat walks in 24 steps.
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Charlene Goes Shopping
- Lisa Lavelle
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Math Fundamentals, difficulty level 2. Charlene needs to add some items to her winter collection. Help her determine where she should shop.
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Chicken Little's Eggs
- Jody Newman
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Elementary, difficulty level 3. How many eggs did Chicken Little have in her basket at the start of her trip to town?
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Chime Time
- Lisa Lavelle (adapted)
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Elementary, difficulty level 3. Determine how long it takes a clock to chime.
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The Chocolate Allergy Revelation
- Antiquity (Steve Earth)
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Math Fundamentals, difficulty level 5. Use meta-reasoning to deduce the ages of three people based on a product, a sum, and a seemingly irrelevant third piece of information.
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Cool Cubes
- Heather Cool and Lisa Lavelle
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Math Fundamentals, difficulty level 3. Can Jackie really mark her cubes so that each sum from 1 to 36 is possible?
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Erika's Rock Collection
- Elisabeth and Stephen Baseman and Chamberlain
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Math Fundamentals, difficulty level 2. Find out how many rocks Erika has collected over the years.
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Expressions of One Hundred
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Find a way to express one hundred with the given digits.
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Farmer Fever's Hay
- Ed Levinson
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Elementary, difficulty level 4. Determine the weights of the four pieces of Farmer Fever's broken 40-pound rock.
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Feathers and Fur
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Determine the number of pigeons and puppies Xiao has.
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Five Digits of Fun
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Find a five-digit number based on these clues.
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Frugal Flooring
- Marita Paynter
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Math Fundamentals, difficulty level 2. Help Graeme determine how many tiles he needs to decorate his new bedroom and whether or not he can afford them.
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Frugal Freeda
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Help Freeda decide which store has the best buy.
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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.
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Garden Fresh Fruit
- Shrawan Khanna's Ninth Grade Class
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Math Fundamentals, difficulty level 4. Help the poor farmer predict his revenue (if he can sell all his fruit).
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Georg Tricks the Troll
- Terry Trotter
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Elementary, difficulty level 3. Georg decides to tangle with the troll and see if he can make some money.
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Golf Anyone?
- Phil Marchal
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Math Fundamentals, difficulty level 3. Kyle needs some help in figuring out how many buckets of golf balls were hit at the Hook and Slice Driving Range.
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Good Fences
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Design a fence that will keep the animals happy.
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The Great Flood
- Jon Basden
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Elementary, difficulty level 3. How much "flood" water did Mr. Basden clean up with his shop vac?
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Growing Pains
- Lisa Lavelle
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Elementary, difficulty level 4. Predict the height and weight of a child after ten years.
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Holiday Shopping and Surfing
- Lisa Lavelle
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Math Fundamentals, difficulty level 2. Help Charlene calculate the change she'll have left for holiday card supplies after she completes her online shopping.
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Idle Ivan and the Troll
- Lisa Lavelle
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Elementary, difficulty level 2. Idle Ivan makes a deal with a troll... to his disappointment he discovers he knows less math than he thought.
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Irish Specials
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Calculate the final bill for our St. Patrick's Day dinner last week.
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It's an open and shut case! Or is it?
- Lisa Lavelle
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Elementary, difficulty level 3. A Razzle Dazzle Elementary School locker problem.
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Jellybean Fractions
- Lisa Lavelle
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Elementary, difficulty level 2. Determine good and bad choices in playing the Jellybean Fractions Game.
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Jellybean Rectangles
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Have fun figuring out strategy in the Jellybean Rectangle game.
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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?
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Lawn-Mowing Chore
- Judy Ann Brown
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Math Fundamentals, difficulty level 4. Find the area of the yard that Josh, Sam, and Mark must mow.
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Lost in Space
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Figure out how big an error the engineers made when they mixed up their units.
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Lunch Bunch Budgets
- Lisa Lavelle
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Math Fundamentals, difficulty level 2. Determine the number of children needed for the lunch bunch budget to balance.
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Magic Square Jumble
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Help straighten out this magic square.
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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.
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The Math Teacher's Ties
- Brentwood College School - Math 12(1)
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Math Fundamentals, difficulty level 3. Read the rhyme and determine the number of ties the math teacher has in his wardrobe.
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McPrincipal's Night at McDee's
- Antonietta D.
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Elementary, difficulty level 4. Just how much did the teachers from Mathematics Elementary School sell (and earn) in their charity drive?
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A Million in Time
- Lisa Lavelle
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Math Fundamentals, difficulty level 2. "Human beings can expect to live a million..." Use your conversion skills to determine which unit of time best completes this statement.
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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?
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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.
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More Mowing Madness
- George Miller and Lisa Lavelle
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Math Fundamentals, difficulty level 4. Where should Matt and Georgette change places to evenly split their "Matt-mowing" work?
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Movie Line Madness
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Determine what time it will be when Odysseus and Penelope finish taking care of their movie customers.
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Mr. W. Goes Across Australia
- Lisa Lavelle
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Math Fundamentals, difficulty level 5. Help Mr. W figure out when he needs to start his trip in order to meet Mrs. W on time (requires a bit of map reading).
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Ms. Newton's Secret
- Jeanne Fitzgerald
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Math Fundamentals, difficulty level 2. Can you discover the secret of Ms. Newton's age?
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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.
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Mystery Numbers
- CanSchoolNet - revised
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Math Fundamentals, difficulty level 2. Fill in the missing numbers on an ancient scroll.
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Neighborhood Watch
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Find out how many trips will be made around the neighborhood in this watch program.
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The New Rug
- Lisa Lavelle
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Elementary, difficulty level 3. Find the number of squares needed to cover the Reading area.
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Odd (and Even) Dates
- Lisa Lavelle
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Math Fundamentals, difficulty level 1. Can you figure out these curious dates?
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Oh, Brother!
- Lisa Lavelle
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Math Fundamentals, difficulty level 1. Aidan is how many days younger than T.J.?
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The Olympic Distance
- Shrawan Khanna & Class
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Elementary, difficulty level 4. Determine how many kilometres the Russian Olympic team members will travel in attending the 2002 Winter Olympics.
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Operation Challenge
- Lisa Lavelle
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Elementary, difficulty level 2. Help Inger and Tarik complete Ms. Madril's multiple-choice challenge.
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Our Favorite Balloon Colors
- Lisa Lavelle
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Elementary, difficulty level 4. Determine the number of submitters who listed blue as their favorite balloon color.
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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.
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Peanut Butter and Jelly
- Lisa Lavelle
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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?
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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?
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Penny Space
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Determine the space needed to store a million pennies.
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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.
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Pondering Prescriptions
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Help calculate the amount of antibiotic in each dose of my prescription.
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Presidential Timepieces
- Mary DeYoung & class
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Math Fundamentals, difficulty level 4. Develop a sense of time by exploring presidential events.
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Rabbit's Run
- Lisa Lavelle
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Math Fundamentals, difficulty level 1. Help Regina develop options for building her rabbit's run.
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Railroad Crossing
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Determine how far apart Division Junction and Logarithm Square are, based on the time Emily and Edward Engineer cross paths.
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Raisin Nut Cookies
- Marsha May
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Math Fundamentals, difficulty level 4. Sarah needs to convert her cookie recipe for her cousin.
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Sacagawea Cheerios
- Stephen Maurer
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Math Fundamentals, difficulty level 3. Determine how many Sacagawea coins the government will give away during this Cheerios promotion.
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Saline Solutions
- Lisa Lavelle
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Elementary, difficulty level 3. Measure the ingredients needed to mix the saline solutions.
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School, Who Has Time?
- Lisa Lavelle (old remembered puzzle)
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Math Fundamentals, difficulty level 3. Given all the time we spend doing other things, how do we have time for school?
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Something Fishy
- Basden's 8th Hour MathDogs
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Math Fundamentals, difficulty level 3. Find the maximum number of goldfish and koi for the schoolyard garden pond.
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Special Stars
- Lisa Lavelle
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Math Fundamentals, difficulty level 2. Calculate the number of pipe cleaners Leah used to create a Star of David chain.
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Speeders, Beware!
- Stephen Maurer (and Chief Brian Craig)
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Elementary, difficulty level 4. Evaluate the method the Swarthmore Borough Police Department uses for catching speeders.
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Splish Splash
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Determine the ratio of my volume to T.J.'s volume.
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Sprinkler Spray
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Compare the radii of three sprinklers in Lily's garden.
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Stained Glass Window
- Jackson First Year Algebra Class
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Elementary, difficulty level 5. Find the size of a stained glass window for my front door.
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The Sum of Four Numbers
- Lisa Lavelle
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Math Fundamentals, difficulty level 1. Determine the truth about four numbers, given some information about their sum.
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Super Deal Salsa
- Lisa Lavelle
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Math Fundamentals, difficulty level 2. Determine how much money was saved by buying salsa in bulk.
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Tatianna and the Troll
- Terry Trotter, revised
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Elementary, difficulty level 3. Tatianna tests the troll... and neither loses nor gains.
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Timber!!!
- Lisa and Judy Gardner
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Math Fundamentals, difficulty level 3. Determine the lengths of two pieces of a damaged redwood tree.
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A Very Special Number
- Lisa Lavelle
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Elementary, difficulty level 2. Find a number with some interesting divisibility properties - can you put them all together?
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Video Viewing
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Just how much television will Frank and Lisa watch?
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Water Fun?
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Determine how long it would take for a 30-gallon water heater to empty.
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Water Park Adventure
- Leon Roland & class
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Math Fundamentals, difficulty level 2. How much does each member of the class need to earn to fund the field trip?
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What a Move!
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Determine the number of hours it took the movers to move the Lavelles to their new home, as well as the number of man-hours.
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What Was That Score?
- Lisa Lavelle
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Math Fundamentals, difficulty level 2. Determine the football (not soccer!) score.
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Wordy Problems
- Lisa Lavelle
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Elementary, difficulty level 4. Convert these word addition problems into numbers.
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