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Math Fundamentals
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Operations with Numbers
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Problems in this category can be solved using a combination of basic operations (addition, subtraction, multiplication, division). Problems requiring application of approximating skills (estimation, rounding) are also included in this category.
Problems that focus more specifically on each skill in this category can also be found in the following subcategories:
- Related Resources
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Interactive resources from our Math Tools project:
Math 4: Operations with Numbers
The closest match in our Ask Dr. Math archives:
Elementary Arithmetic
NCTM Standards:
Number and Operations Standard for Grades 3-5
Access to these problems requires a Membership.
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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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All Aboard!
- Claire Mead
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Math Fundamentals, difficulty level 3. How long will Sasha's train trip from Washington to Chicago take?
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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?
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Anthony's Famous Butter Rolls
- Kristina Lasher
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Math Fundamentals, difficulty level 2. How many rolls will Anthony need to bake for the family's Thanksgiving feast?
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Assembly Seating
- Claire Mead
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Math Fundamentals, difficulty level 2. What is Ben's plan for arranging chairs for the school assembly?
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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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Back-to-School Shopping
- Judy Ann Brown
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Math Fundamentals, difficulty level 2. Mrs. Bender noticed that the total of the items her children purchased was $155. Can you determine the cost of one pair of jeans?
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Back-to-school Supplies
- Lisa Lavelle
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Math Fundamentals, difficulty level 2. Help calculate the total bill for these back-to-school supplies.
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Baseball Cards
- Claire Mead
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Math Fundamentals, difficulty level 2. How many cards does each of the three boys have in his baseball card collection?
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Baseball Trivia
- Judy Ann Brown
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Math Fundamentals, difficulty level 2. How many runs do the Phillies have to score before the base runners have covered a mile?
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Basketball Bargain
- Chad Tollefson from Western Oregon University
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Math Fundamentals, difficulty level 1. Can Luis use the teacher's clues to figure out how many balls are in the closet? Can you?
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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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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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Birthday Probability
- Kristina Lasher & Lisa Lavelle
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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?
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Bobsled Sums
- Bob and Claire Mead
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Math Fundamentals, difficulty level 3. Find which men rode with driver number 1 on his four-man bobsled.
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Building Bouquets
- Amanda Knott and the Western Oregon University Mentors
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Math Fundamentals, difficulty level 2. Help Jana determine how to divide her extra flowers for the flower shop special.
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Building the Fence
- Steve Risberg & Kristina Lasher
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Math Fundamentals, difficulty level 3. Herta is building a fence. How wide will the gaps between the pickets be so that everything is spaced evenly?
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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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Buy the Numbers
- Claire Mead
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Math Fundamentals, difficulty level 3. How many apartments can Tabitha number with the digits she purchased?
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California Dreaming
- Judy Ann Brown
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Math Fundamentals, difficulty level 3. Determine the length of time that will be needed to drive from Allentown, Pennsylvania, to Los Angeles, California.
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Can You Drink That Swimming Pool?
- Kristina Lasher
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Math Fundamentals, difficulty level 3. Estimating the amount of water in a pool. About how long would it take
to drink that much water?
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Change You Can't Count On
- Claire Mead
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Math Fundamentals, difficulty level 2. What is the greatest amount of money I can have in my pocket?
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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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Chelsea's Number Puzzle
- Claire Mead
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Math Fundamentals, difficulty level 2. Help Chelsea solve this addition number puzzle using the numbers 1 through 9.
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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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Choose Your Challenge
- Kristina Lasher
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Math Fundamentals, difficulty level 2. Can Zak find a more precise measure of how much older his brother is than he is?
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Choosy Chooser's Choices
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Find out how many outfits Charlene can put together for a sunny day.
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Cicada Circus
- Kristina Lasher and special thanks to John Cooley
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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.
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Circles Around
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Use this exploration problem to discover the relation between circumference and diameter.
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Clock Work
- Claire Mead
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Math Fundamentals, difficulty level 2. How did Maria and Sammy arrange their pencils on the clock face?
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Common Cents
- Claire Mead
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Math Fundamentals, difficulty level 2. How much money do Monique and Misty each contribute toward Mom's Valentine's candy?
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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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Counting Cats and Dogs
- Claire Mead
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Math Fundamentals, difficulty level 2. How many students in Lin's school have both a dog and a cat?
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Count the Discount
- Kristina Lasher
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Math Fundamentals, difficulty level 3. The jacket on the clearance rack is marked down 20% more each day. How much will it cost after 5 days?
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Crack the Code
- Christi Sather and Kristina Lasher
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Math Fundamentals, difficulty level 2. Help Christi use the clues to figure out which code will unlock the vault.
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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.
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Cupcakes, Cupcakes!
- Kristina Lasher & Terry Trotter
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Math Fundamentals, difficulty level 1. Andrei needs to put icing on the cupcakes and get out the door to catch the bus. Will he and his sister be able to get them all iced in time?
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Dad's Cookies
- Diane Anderson's Teaching the Young Learner Class
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Math Fundamentals, difficulty level 3. Figure out how many cookies Dad baked for the family before they ate them all!
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Darlene's Dart Board
- Claire Mead
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Math Fundamentals, difficulty level 3. How many darts does it take to win on Darlene's dart board?
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Dashing Through the Snow
- Claire Mead
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Math Fundamentals, difficulty level 3. Use clues to determine the finishing order of the ski racers at Winter Carnival.
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A Dicey Situation
- Claire Mead
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Math Fundamentals, difficulty level 3. Determine the fairness of a game in which players score points
according to the difference between the values of two rolled dice.
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Dragons and Tigers and Hares, Oh My!
- Claire Mead
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Math Fundamentals, difficulty level 3. Use clues about the Chinese calendar to determine when Lin's great-grandfather was born
and how old he is.
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Driving Decisions
- Kristina Lasher
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Math Fundamentals, difficulty level 4. Help the Downings decide which car rental is the best option for their trip to Denver.
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Elevator Weigh-in
- Kristina Lasher
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Math Fundamentals, difficulty level 2. Would Melissa's family and neigbors exceed the maximum weight allowance of their apartment building elevator? If not, how many more would fit?
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Elizabeth's Cookies
- Inspired by Swarthmore College students
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Math Fundamentals, difficulty level 1. Can you help Elizabeth figure out how many times she'll need to use her cookie sheet to bake all of her cookies?
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Emmy's Action Figures
- Claire Mead
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Math Fundamentals, difficulty level 2. In how many different ways can Emmy arrange her Famous Mathematician
action figures?
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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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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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Filling the Freezer
- Kristina Lasher
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Math Fundamentals, difficulty level 4. How many cartons of ice cream can the Math Club fit in their freezer?
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Fish in a Barrel
- Claire Mead
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Math Fundamentals, difficulty level 3. Find out how many fish Jake, Herman and Luke each took home from their
fishing trip.
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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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Flying Time Zones
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Help me figure out what time my watch should show when I land in Denver.
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Football Fanfare
- Suzanne Alejandre and Kristina Lasher
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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?
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Four Dates
- Claire Mead
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Math Fundamentals, difficulty level 2. Anthony explores number patterns on a calendar.
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Four Playful Mathematicians
- inspired by Maria Fung's class at Western Oregon
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Math Fundamentals, difficulty level 2. Follow the clues to help the four playful mathematicians return the lost watch.
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Frog Farming
- Claire Mead
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Math Fundamentals, difficulty level 2. Help Farmer Mead build a rectangular pen that holds the greatest
number of frogs.
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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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Giving with Grapefruit
- Lisa Lavelle & Western Oregon University Students
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Math Fundamentals, difficulty level 1. How much will Cassie help raise for charity?
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Golden Gate Bridge *
- Claire Mead
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Math Fundamentals, difficulty level 2. Find out how much wire was used in the two main cables of the Golden
Gate Bridge.
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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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Greta's Garden
- Claire Mead
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Math Fundamentals, difficulty level 2. Find out how much money Greta made from each of her vegetables at the
Farmers's Market.
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Hauling Sand
- Claire Mead
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Math Fundamentals, difficulty level 2. How many tons of sand can Marty haul in his dump truck?
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Heidi's Hometown
- Claire Mead
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Math Fundamentals, difficulty level 2. How many people lived in Heidi's hometown at the end of 2007?
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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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Homework-Free Fridays
- Claire Mead
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Math Fundamentals, difficulty level 2. How many different ways can Donna roll the blue and red dice to win a weekend free of
homework?
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Horton's Clover Hunt
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Find out how fast Horton had to work picking clovers.
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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.
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How Old is Dad?
- Claire Mead
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Math Fundamentals, difficulty level 2. Use the clues to find out how old Dad is.
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How Old is Mia?
- Claire Mead
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Math Fundamentals, difficulty level 3. Use Mia's clues to find how old she is.
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I Get A Kick Out Of Soccer!
- Judy Ann Brown
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Math Fundamentals, difficulty level 3. How many laps of the soccer field would a team member need to complete to run more than a mile?
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I Like to Palindrive!
- Kristina Lasher
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Math Fundamentals, difficulty level 3. How many palindromic numbers will appear on Kristina's odometer in October, 2003?
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Inching Along Down the Football Field
- Terrel Trotter
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Math Fundamentals, difficulty level 3. Fred put his football down on a goal line of the 100-yard field. He then moved it forward half the field distance, over and over again. When did the distance first become less than one inch?
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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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Is There Really a Discount?
- Lisa Lavelle
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Math Fundamentals, difficulty level 3. Determine which friend is correct about the final price on a sales item.
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Jason's Piggy Bank
- Claire Mead
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Math Fundamentals, difficulty level 2. How many nickels did Jason find in his piggy bank?
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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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Just the Facts *
- Claire Mead
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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.
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The Kickball Tournament
- Diane Anderson's Teaching the Diverse Young Learner Class at Swarthmore College and Claire Mead
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Math Fundamentals, difficulty level 1. How many players will Ms. Emery put on each kickball team?
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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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Let the Chips Fall . . .
- Claire Mead
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Math Fundamentals, difficulty level 3. Use clues about sums to determine which digits are on the reverse sides of three
given chips.
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Lighting the Menorah
- Lillian Ray and Claire Mead
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Math Fundamentals, difficulty level 1. How many candles are used during Chanukah?
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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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Lucky Lettuce Land
- Kainoa Trotter, et al.
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Math Fundamentals, difficulty level 3. Help Farmer Lucky fence his lettuce land.
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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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Luscious Lemonade
- Judy Ann Brown
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Math Fundamentals, difficulty level 3. The label on the lemon concentrate says that I need to mix 2 cups of concentrate with 3 cups of water. How much lemon concentrate should I buy to make 25 gallons of lemonade?
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The Mad Hatter's Gone!
- Leanne Gater
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Math Fundamentals, difficulty level 4. Explore a coordinate plane and help the Cheshire Cat find his favorite cheese.
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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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Marble Mayhem
- Claire Mead
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Math Fundamentals, difficulty level 2. Fred and his friends divide the marbles in several different ways, but
there is always one left
over.
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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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Math Club Field Trip
- Claire Mead
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Math Fundamentals, difficulty level 3. How many people returned from the Math Club field trip in Miss Noether's van?
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Math Club Lollipop Profits
- Judy Ann Brown
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Math Fundamentals, difficulty level 3. The Math Club plans to sell lollipops. Help them to calculate their profit.
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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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