Exponents RationalExpressions BoxMethod QuadraticEquations
PropertiesofEquality FractionsinEquations SumandProductPuzzles StandardFormofQuadraticFunction
LinearEquations SolvingInequalities MultiplyingPolynomials item2a
SquareRootsSquareNumbers HowtoFindSlope SystemsofEquations FactoringPolynomials item3a
PythagoreanTheorem xandyintercepts FactoringTrinomials item5a
Sum & Product Puzzles

Sum and product puzzles are awesome! If you can do these problems, then you are on your way to some intense algebra. Sum and product puzzles help get your brain to start thinking in a way that is necessary in problem solving. Check it out…


The goal in a sum and product puzzle (aka diamond problem) is to find THE pair of numbers that when you multiply them the product and sum fit nicely into this little puzzle shape.

What is so cool is that it really helps you practice your BASIC FACTS (hint, hint) and keeps you from getting lazy. Let's see how well you do with some practice puzzles, shall we? Don't worry, we'll start out really easy.


Step 1: Product (top number)

Look at the top number. This is your product.
Make a list of the pairs of factors for the product.
1, 6

Step 2: Sum (bottom number)

Look at your factors list.
Which pair, when you add them, are the addends that form the sum at the bottom?
2, 3

Step 3: Matching Pair

When you have found that matching pair, write them in your puzzle. That's it!

Helpful Hints

Hint #1: If the product (top number) is positive and the sum (bottom) is negative, then the two numbers (factors/addends) are going to both be negative.

Hint #2: It doesn't matter if you start with the sum or the product first…

Let's Practice!
bigx6 bigx6b

Try these sum and product puzzles.

Remember that you might need to use negative numbers!


Download a page to practice

Let's Practice! Sum & Product Practice worksheet

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