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X Puzzles Review Game

I love using X Puzzles to introduce factoring quadratics. These puzzles are also known as sum and product puzzles since the goal of the puzzle is to find the two numbers that have a given sum and product.

x puzzles review game to introduce factoring quadratics sum product puzzles

Years ago, I found a set of 5 pages of X Puzzles. I can no longer find them online, so I have uploaded the file below. The file says it was created by “cee13931.” If this is you, I’d love to give you proper credit!

X Puzzles Review Game

A few years ago when I was teaching Algebra 1, I wanted to turn these x puzzles into a sort of review game. When I’ve just used the worksheets in the past, students would often just copy answers off a neighbor. I wanted each student to be working different problems ON THEIR OWN!

x puzzles review game to introduce factoring quadratics sum product puzzles

I took the five worksheets and printed each set on a separate color of paper.

x puzzles review game to introduce factoring quadratics sum product puzzles

Then, I chopped up the worksheets so that each x puzzle was on a separate square of paper.

x puzzles review game to introduce factoring quadratics sum product puzzles

One of my favorite way to create an instant review game is Julie Morgan’s 1 to 100 game. All you need to play is a bank of questions (the worksheets I cut up) and a 100 grid.

I put up a hundred chart on my SmartBoard. Each student (or group of students depending on your class size) picks a color/shape/design.

x puzzles review game to introduce factoring quadratics sum product puzzles

Students came up to my desk and grabbed a puzzle card to start with. They went back to their desks and solve the puzzle on their individual dry erase boards.

x puzzles review game to introduce factoring quadratics sum product puzzles

Some students referenced the multiplication charts in the back of their interactive notebooks to help determine the correct two numbers with the given sum/product.

x puzzles review game to introduce factoring quadratics sum product puzzles

After finding the two magic numbers, students brought the puzzle card back up to my desk with their dry erase board. If the two numbers were correct, I took the puzzle card and gave the student a new puzzle. On the way back to their desk, the student stops by the SmartBoard to color in a number off the hundred chart with their specific color/shape/design.

I challenged my class to work through the entire deck of puzzle cards. So, as each puzzle was solved, I added the card to a pile.

x puzzles review game to introduce factoring quadratics sum product puzzles

When all of the cards were in the pile, it was time to figure out the winner (or winners if you prefer) of the game. Use a random number generator to pick a number between 1 and 100. I give candy to whichever student/group claimed that number on the hundred grid. If that number wasn’t claimed, I kept generating numbers until I found a winner.

Students love strategically picking their numbers even though the game is still completely luck-based. Of course, it is to a student’s advantage to have as many numbers claimed on the board as possible. I find this helps keep students on-focus throughout the game.

Other Resources for X Puzzles

Delta Math has three levels of these (called The X Game). I highly recommend it!

x puzzles review game to introduce factoring quadratics sum product puzzles

Shaun Carter has a related free download on his blog. He calls them diamond problems.

x puzzles review game to introduce factoring quadratics sum product puzzles
Image Source: https://primefactorisation.com/blog/2018/07/21/diamond-problems/

Free Download of X-Puzzles (Sum and Product Puzzles)


Sum and Product Puzzles (PDF) (2836 downloads)


Sum and Product Puzzles (WORD – ZIP) (717 downloads)