Differentiating in my Classroom during Math

Recently, one of my main goals in my classroom was to polish up my differentiation plan during math class. I had heard of several ways to accomplish this and techniques to use. To start, my class has 22 first grade students. I have about 2 students at a 2nd grade level for math, 4 at an end of year first grade level, 10 which are on-level and 6 that would be considered approaching. With this much diversity, the traditional "teach all" at once hasn't worked well. Of course, it is possible to do that, but it's at the expense of my more advanced math students as they sit through a lesson typically bored and ready to move on at any moment. Here are a few things I've been trying.

1. Math Journals: Math journals have been the topic of my action research. At first, I was anxious to use them because I was hoping they would give me more insight into what my students were understanding. To a point they do show this, but I've found that with an assignment scheduled most days, I've already gathered an understanding to each students knowledge. If anything, the math journals have supported a students current ability level in math. Currently, they act as more of a math vocabulary book. We put many things into them using illustrations and words to know. This has been somewhat difficult for my students who have trouble copying things from the board. I will use an iPad, take a picture of our SMART board, while we are completing it and I will place  the iPad next to those students who have trouble looking up and down. I'd like to start using journals to give me knowledge on what students prior knowledge is regarding future math topics, but haven't found time to get that in. I will hopefully work on that soon!
2. The second thing I've been using is our math curriculum's challenge cards. We use Math Expressions, which has a tiering model approach. It provides teachers with an on-level, challenge and approaching level learning plan each day. After we've discussed a new concept as a whole-group, I've got an "unofficial" idea of which students should be able to move on, with limited teacher support. I have also started asking them-"Do you think you'd be able to complete these sets of questions on your own?" or "Who thinks they need a little more help?" I've found that by giving them a little more accountability and independence, they've risen to a higher level of work during math. You need to use your teacher judgement on these questions! If they are ready, my students will take the tiering activity (best suited for them). I have the instructions already recorded via iPad. I will point students to the activity I think they will be the most successful, and they move to that "center." They watch the video for instructions. Students who need more guidance, work with me on the on-level assignment. Now, I'm not going to stay this model is perfectly clean and polished day in and day out. We are a work in progress, and it has taken some loosening of the reins on my behalf, but the expectations haven't changed. There is some noise during math, but the kids are learning and are engaged while applying math knowledge to their own work. Instead of sitting and going through examples of skill problems which they've already mastered. The biggest change I've noticed, is that we've moved from students listening, to students applying and creating.