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Playing The Factor Game in Middle School Math

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Finding The Factor Game Again!

I was looking through my middle school math folders on my computer, and came across a document called “The Factor Game.” 

When I saw the document, it occurred to me that in trying to think of some new things to do with my classes, I forgot to play The Factor Game this year when we started talking about factors!

I was so disappointed. 

Of course, we can play The Factor Game next week, or any other time, since practice with factors is always helpful, but I just couldn’t believe that I had forgotten about it.

I’m sure many people know about The Factor Game, or use a version of it, but for those who don’t, I’ll explain how to use this math game. It’s great for 6th grade, but also upper elementary grades ~ and even 7th or 8th grades if students need factor practice!

How to Play The Factor Game in Middle School Math

1) Players start with a simple game board, with the numbers 1-30 

  • In the past I’ve alternated between giving students a pre-printed sheet and having them write their own numbers on their own paper
  • Sometimes I have them play at the whiteboard or with mini whiteboards, which they enjoy

2) Choosing Numbers

A. Player 1 chooses a number, and marks it on the game board

  • They might circle it, square it, triangle it, color it etc
  • Player 1 receives points equal to the number they chose

B. Player 2 then marks all of the remaining factors of Player 1’s choice

  • Player 2’s points are all of those remaining factors

3) Next, Player 2 chooses a number and gets the value of that number as their points

  • Player 1 identifies all of the remaining factors of that number, receiving those numbers as points

4) Play continues this way until all possible numbers have been used.
*Special rule – players can’t choose a number that has no factors available for the other player. If they do, they lose their turn, receiving no points.

The Factor Game ~ Example

Let’s look at this with actual choices and numbers.

When I introduce this game to my math classes, we play it on the whiteboard, and I always allow them to go first (the first time we play). 

Often, they will choose 30 as their number, since it’s the biggest and gives them lots of points.

When I go ahead and mark all the remaining factors of 30 (my points), they are shocked! 

  • In the images in this post, their points are circled in red and mine are squared in blue.

After the first turn, they have 30 points and I have 42! 

I normally have 2 students record our scores on the board, while 2 others keep running totals on a calculator, but points can all be tallied at the end if you want.

For my first turn in this example, my choice would be 27. 

This leaves students with only 9 as a remaining factor, since 1 and 3 are already gone. 

Needless to say, they’re usually a bit disappointed when they get so few points!

After their experience with 30 and its factors, students start thinking a bit more for their next turn.

They will often consider 25 or 23, but I remind them that they must leave a factor for me, and 1 and 5 are already taken. 

So, let’s pretend they choose 21. That leaves 7 for me.

The game continues, alternating turns, until all possible numbers are used, as shown in the “finished game” picture.

You can see, because of the way numbers were chosen, some numbers are not used.

Playing The Factor Game the Second Time

The second time we play as a group, I go first.

I choose 29 as my first number, and they are disappointed to only get 1 point!

We continue to play the second game, and they get a better idea of what makes a good choice. They start to look ahead and think about and discuss what factors I might get if they make a certain choice.

Students Play The Factor Game With a Partner

After our games as a class, I have the students work in partners, and they normally get one or two games played before we stop to discuss at the end of the period. 

  • We always talk about what the best and worst first choices are, and bring the idea of prime and composite into the discussion.

I’ve been playing this game with students for at least 15 years (I think), and every group of students has loved it

I found the game when I was involved with Mathline, so long ago. If you’d like to see the original lesson plan, with extension ideas, click here.

You can also watch the video of me explaining the Factor Game. I did this on a Facebook Live and then uploaded to YouTube:-)

Have you played the Factor Game in middle school math or upper elementary math? If not, I hope you’ll introduce it to your students!

Ellie

Welcome to Cognitive Cardio Math! I’m Ellie, a wife, mom, grandma, and dog ‘mom,’ and I’ve spent just about my whole life in school! With nearly 30 years in education, I’ve taught:

  • All subject areas in 4th and 5th grades
  • Math, ELA, and science in 6th grade (middle school)

I’ve been creating resources for teachers since 2012 and have worked in the elearning industry for about five years as well!

If you’re looking for ideas and resources to help you teach math (and a little ELA), I can help you out!

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