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MIDDLE SCHOOL

About Math

Algebra
   equations
   factoring expressions
   graphing equations

Arithmetic
   division
   exponents
   factorials
   factoring numbers
   fractions/percents
   logarithms

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Geometry
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     conic sections/
       circles
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   3D and higher
     polyhedra

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   calendars/
     dates/time
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Number Sense
   factoring numbers
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   pi
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Probability
Puzzles
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Word Problems

Browse Middle School Algebra
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Direct and indirect variation.
    Inequalities and negative numbers.
    Positive/negative integer rules.
    Solving simple linear equations.



How Much Does the Youngest Boy Get? [05/25/2000]
Five brothers, each born in a different year, share a gift of $100...

How Much Money Entering the First Store? [09/26/2002]
Timothy spent all of his money at five stores. At each store, he spent $1 more than half of the amount he had when entering the store. How much money did he have when he entered the first store?

How Much Popcorn did Paul Sell? [01/28/2002]
Paul made $44.14 selling 27 items (beer and popcorn). If he made $1.22 selling popcorn and $2.62 selling beer, how many boxes of popcorn were sold?

How Old Are John and Julia? [05/17/2001]
Julia is as old as John will be when Julia is twice as old as John was when Julia's age was half the sum of their present ages. John is as old as Julia was when John was half the age he will be 10 years from now. How old are John and Julia?

How Wide is the Garden? [01/06/1998]
A rectangular garden has a 136-ft. fence around it. The garden is 40 feet long. How wide is it?

Identifying Algebraic Properties [12/29/1996]
How do you identify which algebraic property has been used in each step of a simplification process?

Identity and Inverse Properties for Zero [01/07/2004]
If we subtract 0 from a number and get the same number, doesn't that make 0 an identity for subtraction? Also, can't a number be its own inverse for subtraction?

Implied Multiplication and TI Calculators [05/02/2008]
If I type 36/6(25-11*2) into my TI-85, I get an answer of 2. If I include a multiplication symbol to have 36/6*(25-11*2), I get an answer of 18. I thought that when the 6 is written right up against the parenthesis, the multiplication is implied. Why am I getting two different answers?

The Importance of Defining Variables Clearly in Algebra [11/01/2007]
A sample of dimes and quarters totals $18.00. If there are 111 coins in all, how many are there of each coin?

Incorrect Application of PEMDAS and Order of Operations [09/14/2006]
My students think PEMDAS means that all addition should be done before any subtraction is done. How can I show and convince them that they need to do both operations at the same time working from left to right?

Increasing the Average [02/25/2001]
Five members of a basketball team are weighed and an average weight is recalculated after each weighing. If the average increases 2 pounds each time, how much heavier is the last player than the first?

Inequalities [01/24/2001]
How do you add, subtract, multiply, and divide inequalities?

Inequalities: Add or Subtract? [10/21/2001]
Sometimes, when doing inequalities problems, I have to add or subtract one from the answer I have calculated. I don't understand when to add, subtract, or do nothing at all.

Inequalities and Absolute Value - Case Method [09/01/1998]
What is the case method? How does it apply to inequalities with absolute values?

Infinite Geometric Progression [10/02/1997]
How do you go about solving .27 repeating into a fraction?

Intercept Equation [10/07/1998]
I found a plane using the intercepts (4,0,0), (0,-5,0), and (0,0,3). Now I want an equation for those points using Ax + By + Cz = D.

Interpreting Slopes [09/14/1998]
Does the graph of each of these equations rise to the right, fall to the right, is it horizontal, or is it vertical?

Interpreting the Difference Between Two Numbers [09/22/2006]
If a question asks "What is the difference between 15 and 12" or "What is the difference between 12 and 15," would your responses be +3 and -3 respectively? Or would they both be +3?

Interval Notation [11/01/1997]
Solve for x and write the answer in interval notation: -3 < -x < 2 / 3.

Interval Notation for the Number Line [03/04/2009]
What does the interval [-4,10] mean on the number line? How do I graph it?

Is y the Same on Both Sides? [9/4/1996]
3/4 + y = 0.75 + y

Jack is Older than Jill [11/16/2001]
If you reverse the digits in Jack's age, you get Jill's age. The sum of their ages equals 11 times the difference between them. Jack is older than Jill. What are their ages?

Just Plain Algebra [01/07/1998]
Do you have any advice or any programs you might recommend for learning algebra?

K-triple [9/15/1996]
Which of these is a "k-triple", defined as (k/2, k, 3/2k)?

Learning Addition and Multiplication with Algebra [3/16/1996]
How do you know what the (a) is in algebra? I saw this on a picture: a(1/a) = 1/a(a) = 1...

Learning Algebra [6/3/1996]
How do you solve for: x(x+1) + 2 (x + 1) = ?

Length, Width of Rectangle Given Perimeter [9/4/1996]
If the perimeter of a rectangle is 300 and the length is two times the width...

Letters for Variables [11/19/2001]
Why do we use letters for variables?

Linear Equations in One Variable [10/11/2001]
Solve: 35 = 17 + 3(x-2).

Linear Systems of Equations in Two Variables [06/18/1999]
How can I find the length of AE, EB and DC, given that parallelogram ABCD has a perimeter of 50, trapezoid AECD has a perimeter of 39, and AE = EC?

Linear Transformations [6/13/1996]
Determine the image of (2,-6) under (x,y) -> (x+3, y+5)

Logarithmic Problem [2/22/1995]
Can you help me solve this: log 3^x = 6 + (1/2)log 9^x?

Magic Triangle Puzzle [09/24/2001]
The numbers in the squares are the sums of the numbers in the circles to which they are connected. Discover a method to help you find the numbers to put in the circles.

Magic Triangle Puzzles, Expanded [11/17/2012]
In the archives, a parent finds a discussion of magic triangles — but the puzzles assigned his daughter go beyond the counting numbers. Doctor Peterson walks through a range of strategies, from guess-and-check to algebraic.

Magic Triangle Sums [02/04/2003]
Find 6 consecutive odd numbers such that their magic triangle sum is 25. Find 6 consecutive numbers such their magic triangle sum is 4.

Magic Wheel [03/20/2002]
Given a wheel with 16 spokes and a hub, enter the whole numbers 1-17 in the hub and at the end of spokes. The sums of the 3 numbers along the spokes must be equal.

Making the Grade [04/13/2001]
After three tests, Amanda's average score is 88. What grade does she need on her next test to score a four-test average of 90?

Man Crossing a Bridge [09/27/2001]
A man is jogging across a bridge at 8 mph. When he is 3/8 of the way across...

Mapping Functions in the Real World [3/20/1995]
What is the purpose of learning to map a function? What is it used for in the real world?

Marble Collection Fraction Problem [9/9/1996]
3/4 of Tim's marble collection is the same size as 3/5 of Danny's collection...

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