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 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