# One of my favorite number activities is the 4 4s

I heard a colleague say recently, that math was good for three things:  “…making predictions about the world, making models of the world, and because math is beautiful.”  One of my favorite number activities, the 4 4s is low entry, and high ceiling, and the mathematical context by itself gives us a place to explore the beauty of numbers and relationships.

I created this floor to ceiling white board last year in my classroom with 4 x 8 paneling. Kids LOVED being able to draw and work on this scale!

I remember doing this myself as a student, and I was so glad for the reminder when I came across the Four 4’s activity at CAS Musings.  In a nutshell, the problem asks students to use four 4’s and any operations they can think of to get to each target number – I asked them to solve for every integer from 1 and 100.  The basic arithmetic operations +, -, ×, ÷ along with exponents, roots, decimals (4.4 or .4), concatenation (44), percentages, repeating decimals (.44…), are all allowed – and some funky ones are necessary (just try to get to 73 or 77!).  Depending on the level you’re teaching, you might include more advanced operations.  This was easily differentiated as well– I previewed the activity and assigned some specific numbers to students who needed quick success or more challenging work.

There are many ways of getting to each number, and the multiple solutions leave room for kids to create and to DO math. Depending on the needs of your group, you could do this in a competitive or a collaborative way – for my group of 7th and 8th graders last year, collaborative worked better.  I think that my 10th and 11th graders would benefit from the competition this year, so I’ll add some structure and a prize this time – I’m thinking of awarding points for the most complex solutions as well as the most elegant solutions.  I’ll allow students to work together, and make sure to honor and highlight different ways of getting to each solution.

Last year, this worked really well for reviewing and cementing proper notation, order of operations, factorial, multiplying exponents, and general number sense.  There were great student conversations.  My notes included snippets like “…wait.  Dividing by .4 is the same as multiplying by 2.5!”  I’ve included the worksheet I used below.

If you’re looking for a beautiful follow up, Fawn has of course upped everyone’s game with Foxy Fives

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## 13 thoughts on “One of my favorite number activities is the 4 4s”

1. Laura Hawkins

This just looks like a great time. (And nice pictures!) I’m trying to talk more about the mathematical idea of “elegance” this year, and this creates great opportunities to do that.

1. Nat Post author

I agree with you about the pictures – they describe the activity much better than I could. And the idea of honoring elegance with students is important to me as well. I plan to ask them to come up with a “hierarchy of elegance” to categorize their 4 4s answers. Thanks for your thoughts.

2. David

This is a wonderful activity, and seems like a great way to assess the fundamental math skills of one’s students early in the year. I’m going to use it!

1. Nat Post author

I found this very revealing in terms of fundamental skills. But I also found that there was room for the most advanced students to be challenged. You can introduce arithmetic as complex as they can handle. So glad that you found something you could use.

3. Jason Ermer

The Four Fours is a classic and a favorite of mine! In a bit of shameless self-promotion, I’ll suggest that you check out Challenge 06 over at http://www.CollaborativeMathematics.org. It’s related in the sense that the challenge is to make an expression from a given set of building blocks. If your students like the four fours, they might like “Pieces of Eight”! :)

1. Nat Post author

The “pieces of eight” is a nice extension. I found 19 ways to make 1000 (so far). I’m looking forward to checking out the other challenges. Thanks for your thoughts.

4. Fawn Nguyen

Such a showoff, Nat, with your floor-to-ceiling whiteboard. :) Okay, our display is more ghetto, but I tape poster size papers up, one for each number from 1 to 20. This is for my 6th graders only. So each paper has 10 lines (for 10 different ways), and one can only write down his/her four 4s if it’s UNIQUE from the other ones already on the paper.

Math Forum (I think it was them) used to have a yearly online submission of using the digits in that year to make the numbers 1 to 100. For example, this is 2013, so the digits 0, 1, 2, and 3 are used.

Thank you for sharing, Nat.

1. Nat Post author

Yeah, that whiteboard wall was SWEET. This year, I’m roaming, and don’t have my own classroom, much less a whiteboard wall. Tough to get used to. I may use a version of your posters this year.

Math Forum is still running their activity: http://mathforum.org/yeargames/ Thanks for the heads-up. I remember reading about someone doing this with the Ramanujan Numbers too, but I haven’t tried it myself.

So nice to hear from you, and thanks for your thoughts.

5. @cheesemonkeysf

I love this! What a great idea, especially for one of those “rainy day” type days when you need an activity a roomful of crazy people can get excited about.

Thank you!

– Elizabeth (@cheesemonkeysf)

1. Nat Post author

This is a perfect rainy day activity. You can do it with almost no prep, so you can be spontaneous too – I actually left it as a sub plan once when I needed something quick and good to do. You can always create the visual piece later on if the work is successful. Thanks for visiting!