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Number Sense

These problems require knowledge of number meanings, relationships among numbers, recognition of the relative magnitude of numbers, or the effect of operations on numbers.
Some of these problems are also in the following subcategories:
 Related Resources

Interactive resources from our Math Tools project:
Math 7: Number Sense
The closest match in our Ask Dr. Math archives:
Middle School: Number Sense/About Numbers
NCTM Standards:
Number and Operations Standard for Grades 68
Access to these problems requires a Membership.

Accuracy Please
 Judy Ann Brown

PreAlgebra, difficulty level 3. Considering precision, accuracy, and appropriateness in finding the volume of a cone.
... more>>

Anh's Code
 Annie Fetter

PreAlgebra, difficulty level 2. Decode the five mathematical operations symbolized in three equations, then evaluate an expression.
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Anjelica's Very Odd Magic Sweater
 Cynthia Lanius, Suzanne Alejandre

PreAlgebra, difficulty level 3. Find the shortcut Angelica's mother might have used to calculate the
number of dimes.
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Baking Blackberries
 Annie Fetter

PreAlgebra, difficulty level 1. Which rectangular baking dish should I use?
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Bella's Bagel Bakery
 Suzanne Alejandre

PreAlgebra, difficulty level 1. How much more area is covered with cream cheese on the large bagel
than on the small bagel?
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Building a Snow Statue
 Judy Ann Brown

PreAlgebra, difficulty level 3. Determine the height of a snow statue using the given information.
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Canadian Soccer
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps.
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Can You Find My Numbers?
 Roya Salehi

PreAlgebra, difficulty level 3. I have eight numbers in my list. Use the clues to find my numbers.
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Choosing Cs
 Lisa Lavelle, Suzanne Alejandre

PreAlgebra, difficulty level 3. Given the expression c^2  2, what is the probability that the result
is composite for integers 10 through 2?
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The Complex Apartment Complex
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the number of apartments in a new building if each floor has twice as many apartments as the floor above.
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Divisible by a Dozen
 Terry Trotter & Annie Fetter

PreAlgebra, difficulty level 3. If you take any three consecutive integers, multiply the first times the square of the second, then multiply by the third, is 12 a factor of the product?
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Dollar Dealing
 Suzanne Alejandre and Lillian Ray

PreAlgebra, difficulty level 2. How much money did Hector and Larissa each have?
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Do you listen to WMTH or WALG?
 Judy Ann Brown

PreAlgebra, difficulty level 4. Each week listeners switch radio stations. Predict the longterm distribution of listeners for each station.
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Duke is Missing
 Judy Ann Brown

PreAlgebra, difficulty level 3. Duke's head is 6 inches long, his tail is as long as his head plus half the length of his body, and his body is as long as the head and tail combined. How long is Duke?
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Even Number Puzzle
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many even fourdigit whole numbers exist such that the thousands digit is odd, and all four digits are different?
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Falling Leaves
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Find the number of leaves that were falling.
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Fences for Fido and Friends
 Annie Fetter

PreAlgebra, difficulty level 2. Find the area of each rectangular dog pen.
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Flipping Over Pennies
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many equally likely outcomes are there when flipping 10 coins?
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Guess My Number If You Can!
 Judy Ann Brown

PreAlgebra, difficulty level 4. Use division clues to reveal the secret number.
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Happy New Year!
 Judy Ann Brown

PreAlgebra, difficulty level 4. A puzzle for the new year: how is the grid designed?
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Kate's Combination
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Find Kate's locker combination using mathematical clues. Is there more than one possibility?
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Lucky Lollipops
 Suzanne Alejandre & Maria Fung and her students

PreAlgebra, difficulty level 3. Find the number of lollipops Logan the Leprechaun gives away using his "lucky" method.
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Mr. Carmel's Party Plan
 Judy Ann Brown

PreAlgebra, difficulty level 2. Help Mr. Carmel's class earn an ice cream party by counting the number of possible sundaes.
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Open and Shut Case
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the locker combination using mathematical clues.
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Palindrome Day
 Judy Ann Brown

PreAlgebra, difficulty level 2. How many Palindrome Days are there in a year?
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Partial Area
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the area of the portion of the circle that is not included inside the inscribed square.
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Pi Day  Let's Eat Cake!
 Judy Ann Brown

PreAlgebra, difficulty level 3. In honor of Pi Day we will be comparing the volumes of slices taken from round and rectangular cakes.
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Pi Day Treats
 Judy Ann Brown

PreAlgebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration.
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Prime Probability
 Lisa Lavelle

PreAlgebra, difficulty level 3. Given the expression n^2  5, what is the probability that the result is prime for integers between 2 and 12?
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Radical Darts
 Steve Risberg

PreAlgebra, difficulty level 2. How did Andruw get his total score playing Radical Darts?
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Reversal of Ages
 Terry Trotter

PreAlgebra, difficulty level 2. Using the clues given in the problem, how old are my dad and I today?
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Right Triangle, Which Legs?
 Annie Fetter

PreAlgebra, difficulty level 3. Find the possible lengths for the third side of a right triangle given
the lengths of the other two sides.
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Santa's Little Helpers
 Judy Ann Brown

PreAlgebra, difficulty level 3. Help Santa to solve the puzzle created by the clever elves.
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The Scientific Notation Game
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Help Jay think about how points are calculated in the Scientific Notation Game.
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Scientific Sums
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the sum of a set of numbers written in scientific notation.
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A Simple Reversal
 Judy Ann Brown

Math Fundamentals, difficulty level 1. The product of 3 and 24 is 72. The sum of 3 and 24 is 27, which is the reverse of 72. Can you find other pairs of numbers such that their product is the reverse of their sum?
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Sizing Up Sequoias
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Compared to a given seed weight, find out how much an average mature sequoia weighs.
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Square Dancing
 Judy Ann Brown

PreAlgebra, difficulty level 2. The sum of each couple's numbers is a perfect square. Use other information in the problem to find the number of Ashley's partner.
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Super Bowl XXXIII
 Judy Ann Brown

PreAlgebra, difficulty level 2. Based on the winners and points scored during the past 15 Super Bowl games, which team should win Super Bowl XXXIII?
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Tiling Tables
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Find a method to quickly calculate the dimensions of a rectangular table top with a given area so that it has the smallest possible perimeter.
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Timber!
 Steve Risberg

PreAlgebra, difficulty level 3. A tree breaks threeeighths of the way up the trunk, and the tip hits the ground 40 feet from the base of the trunk. How tall was the tree?
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Time Is Power
 Terry Trotter

PreAlgebra, difficulty level 2. During which hour of the day am I most likely to see a square number
on my computer
time display? How many times total during the day does this happen?
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The Tower of Hanoi Puzzle
 Roya Salehi

PreAlgebra, difficulty level 4. Tower of Hanoi: What is the minimum number of moves it will take to transfer 25 disks from one post to another?
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Treasure Hunt Math
 Judy Ann Brown

PreAlgebra, difficulty level 3. Use clues to find the mystery palindrome.
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Valley Springs Snow Cream
 Kelly Crisp

PreAlgebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream.
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Waste Not, Want Not
 Suzanne and Richard Alejandre

PreAlgebra, difficulty level 2. Explain what you know about the number of bananas the store had at the
beginning of the
week.
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Wondering about Water
 Annie Fetter

PreAlgebra, difficulty level 3. Find the surface area of an Olympicsize ice hockey rink.
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