This link doesn’t specifically answer your questions, but maybe it can help you think through how to work your curriculum into your plans.
https://www.thedailycafe.com/articles/Using-the-Math-Daily-3-Structure-with-your-Curriculum
I was thinking that if you choose some of the games you have out for the kids to do match the concepts you want them to practice, that may help. I’m not currently doing Math Daily 3, so I’m probably not the best person to give advise, but maybe this will help a bit.
Suzanne

Great questions! I hope my answers help.
Our focus lessons are chunked into 2-3 brief lessons that provides repeated practice of new material. Focus lesson one you are introducing a new concept (I do), focus lesson two you are revisiting that concept with a whole group practice (we do), and focus lesson three you are providing time for students to work with that concept to demonstrate their level of understanding (you do). These lessons don’t always have to be in this order. The goal is that the lessons are brain compatible in length and provide opportunity for repeated practice.
During the session of Math Daily 3 when students go out and work on their chosen task, the classroom teacher is meeting with small groups or individually with students who need extra support. The tasks children choose during the round include familiar games that reinforce previously taught concepts, exploration and problem solving of current concepts, and written expression of concept understanding. Day one of a new concept, a student may practice that concept during the three lessons and a small group, or during the three lessons and as an exploration during a Math Daily 3 session. Day two of a concept a student may practice that concept in a small group, one on one, or during task time. At some point a game might be introduced that reinforces the concept and helps develop student understanding.
When students choose a task, they are guided to choose tasks to help them meet their goals. For example, if a student needs multiplication practice, he/she is going to know one (or both) of their choices during Math Daily 3 sessions needs to provide practice of multiplication. We don’t choose for them, but we guide their choice by limiting their choice or explaining a certain task needs to be chosen during one of the rounds.
In my experience with Math Daily 3, students are given time to learn a concept and practice that concept until a solid understanding is developed and a new concept is layered on.