Math Forum - Problems Library - Pre-Algebra, Number Sense

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Pre-Algebra
operations with numbers
number sense
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Pre-Algebra
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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 6-8

Access to these problems requires a Membership.

Accuracy Please - Judy Ann Brown
Pre-Algebra, difficulty level 3. Considering precision, accuracy, and appropriateness in finding the volume of a cone. ... more>>

Anh's Code - Annie Fetter
Pre-Algebra, difficulty level 2. Decode the five mathematical operations symbolized in three equations, then evaluate an expression. ... more>>

Anjelica's Very Odd Magic Sweater - Cynthia Lanius, Suzanne Alejandre
Pre-Algebra, difficulty level 3. Find the shortcut Angelica's mother might have used to calculate the number of dimes. ... more>>

Baking Blackberries - Annie Fetter
Pre-Algebra, difficulty level 1. Which rectangular baking dish should I use? ... more>>

Bella's Bagel Bakery - Suzanne Alejandre
Pre-Algebra, difficulty level 1. How much more area is covered with cream cheese on the large bagel than on the small bagel? ... more>>

Building a Snow Statue - Judy Ann Brown
Pre-Algebra, difficulty level 3. Determine the height of a snow statue using the given information. ... more>>

Canadian Soccer - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps. ... more>>

Can You Find My Numbers? - Roya Salehi
Pre-Algebra, difficulty level 3. I have eight numbers in my list. Use the clues to find my numbers. ... more>>

Choosing Cs - Lisa Lavelle, Suzanne Alejandre
Pre-Algebra, difficulty level 3. Given the expression c^2 - 2, what is the probability that the result is composite for integers -10 through -2? ... more>>

The Complex Apartment Complex - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the number of apartments in a new building if each floor has twice as many apartments as the floor above. ... more>>

Divisible by a Dozen - Terry Trotter & Annie Fetter
Pre-Algebra, 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? ... more>>

Dollar Dealing - Suzanne Alejandre and Lillian Ray
Pre-Algebra, difficulty level 2. How much money did Hector and Larissa each have? ... more>>

Do you listen to WMTH or WALG? - Judy Ann Brown
Pre-Algebra, difficulty level 4. Each week listeners switch radio stations. Predict the long-term distribution of listeners for each station. ... more>>

Duke is Missing - Judy Ann Brown
Pre-Algebra, 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? ... more>>

Even Number Puzzle - Judy Ann Brown
Pre-Algebra, difficulty level 3. How many even four-digit whole numbers exist such that the thousands digit is odd, and all four digits are different? ... more>>

Falling Leaves - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Find the number of leaves that were falling. ... more>>

Fences for Fido and Friends - Annie Fetter
Pre-Algebra, difficulty level 2. Find the area of each rectangular dog pen. ... more>>

Flipping Over Pennies - Judy Ann Brown
Pre-Algebra, difficulty level 3. How many equally likely outcomes are there when flipping 10 coins? ... more>>

Guess My Number If You Can! - Judy Ann Brown
Pre-Algebra, difficulty level 4. Use division clues to reveal the secret number. ... more>>

Happy New Year! - Judy Ann Brown
Pre-Algebra, difficulty level 4. A puzzle for the new year: how is the grid designed? ... more>>

Kate's Combination - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Find Kate's locker combination using mathematical clues. Is there more than one possibility? ... more>>

Lucky Lollipops - Suzanne Alejandre & Maria Fung and her students
Pre-Algebra, difficulty level 3. Find the number of lollipops Logan the Leprechaun gives away using his "lucky" method. ... more>>

Mr. Carmel's Party Plan - Judy Ann Brown
Pre-Algebra, difficulty level 2. Help Mr. Carmel's class earn an ice cream party by counting the number of possible sundaes. ... more>>

Open and Shut Case - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the locker combination using mathematical clues. ... more>>

Palindrome Day - Judy Ann Brown
Pre-Algebra, difficulty level 2. How many Palindrome Days are there in a year? ... more>>

Partial Area - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the area of the portion of the circle that is not included inside the inscribed square. ... more>>

Pi Day - Let's Eat Cake! - Judy Ann Brown
Pre-Algebra, difficulty level 3. In honor of Pi Day we will be comparing the volumes of slices taken from round and rectangular cakes. ... more>>

Pi Day Treats - Judy Ann Brown
Pre-Algebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration. ... more>>

Prime Probability - Lisa Lavelle
Pre-Algebra, difficulty level 3. Given the expression n^2 - 5, what is the probability that the result is prime for integers between 2 and 12? ... more>>

Radical Darts - Steve Risberg
Pre-Algebra, difficulty level 2. How did Andruw get his total score playing Radical Darts? ... more>>

Reversal of Ages - Terry Trotter
Pre-Algebra, difficulty level 2. Using the clues given in the problem, how old are my dad and I today? ... more>>

Right Triangle, Which Legs? - Annie Fetter
Pre-Algebra, difficulty level 3. Find the possible lengths for the third side of a right triangle given the lengths of the other two sides. ... more>>

Santa's Little Helpers - Judy Ann Brown
Pre-Algebra, difficulty level 3. Help Santa to solve the puzzle created by the clever elves. ... more>>

The Scientific Notation Game - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Help Jay think about how points are calculated in the Scientific Notation Game. ... more>>

Scientific Sums - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the sum of a set of numbers written in scientific notation. ... more>>

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? ... more>>

Sizing Up Sequoias - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Compared to a given seed weight, find out how much an average mature sequoia weighs. ... more>>

Square Dancing - Judy Ann Brown
Pre-Algebra, 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. ... more>>

Super Bowl XXXIII - Judy Ann Brown
Pre-Algebra, difficulty level 2. Based on the winners and points scored during the past 15 Super Bowl games, which team should win Super Bowl XXXIII? ... more>>

Tiling Tables - Suzanne Alejandre
Pre-Algebra, 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. ... more>>

Timber! - Steve Risberg
Pre-Algebra, difficulty level 3. A tree breaks three-eighths 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? ... more>>

Time Is Power - Terry Trotter
Pre-Algebra, 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? ... more>>

The Tower of Hanoi Puzzle - Roya Salehi
Pre-Algebra, 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? ... more>>

Treasure Hunt Math - Judy Ann Brown
Pre-Algebra, difficulty level 3. Use clues to find the mystery palindrome. ... more>>

Valley Springs Snow Cream - Kelly Crisp
Pre-Algebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream. ... more>>

Waste Not, Want Not - Suzanne and Richard Alejandre
Pre-Algebra, difficulty level 2. Explain what you know about the number of bananas the store had at the beginning of the week. ... more>>

Wondering about Water - Annie Fetter
Pre-Algebra, difficulty level 3. Find the surface area of an Olympic-size ice hockey rink. ... more>>

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