My students were engaged in the Four 4’s task, and we’re excited about going through the rest of their solutions tomorrow. I’ve seen this task other places, but most recently found it again on youcubed.org as part of the Inspiration Math lessons they have there.

Students were asked to express the numbers 1 – 20 using exactly four 4’s and any operation signs they wished. I’ll update this post tomorrow with all of their solutions.

One of the things I like to have my students do is MOVE in math class, and I realized yesterday, I hadn’t done any movement yet. We’ve done a lot of different activities, so the periods have past quickly each day, but no movement. I needed to add that in today and found the perfect spot to add it in the Four 4’s activity. I structured the task this way:

I told students that in honor of the 4th day of school, we were going to complete a challenge with the number 4. (In later periods, I asked students to tell me what day of school we were on and started there.) The challenge is to express every number from 1 to 20 using exactly four 4’s. We reviewed what a numerical expression was and with my regular students we created an Order of Operations page in our notebook that I didn’t think about making with my gifted first period. As First period worked through the problems, we discussed the order of operations since there was some disagreement and I saw the need to do it before starting with my other classes. Tomorrow, we’ll add the visual to first periods notebooks as well. After refreshing how the order of operations worked, we did one problem together and then everyone worked for about 3 minutes independently. Students needed a lot of clarification on the rules.

“Yes, four 4’s.”

“Only 4’s, you can’t use a 1.”

“Even if you’ve already used four 4’s, you can’t add another number.”

“Five 4’s aren’t allowed.”

“Two 4’s aren’t enough; you have to use all 4 for every expression.”

“Zero isn’t one of the numbers from 1 to 20.”

“Yes, you have to use all four 4’s in every expression.”

*(Student halfway through the activity, “How many 4’s do we have to use?”)*

“4.”

There was a lot of productive struggle. And I heard some students proudly exclaim when they got an expression to work out to one of the numbers. We found some useful facts in each class (4÷4=1) and (+4-4=0) proved to be helpful for students. A few also were relieved to hear they didn’t have to work in order, which meant trying anything out and have the result be a number between 1 and 20 resulted in success. One period had a student get the answer of 2 by showing (4/4) + (4/4), and she had written the division problems as factions, and I think the look of it was super impressive to the students. We had just decided two other expressions didn’t work for 2, and a few students were feeling like expressing 2 was going to be impossible. **I love anything that makes a student acknowledge the beauty of a math problem.** That was a nice moment. I’m excited to finish this activity up with students tomorrow.