Citizen Math lessons are appropriate for students with a range of skills and levels of mathematical understanding. The lessons are designed to be taught as whole-class or small group discussions that are facilitated by a teacher. When students approach questions with different levels of sophistication and use different methods, that enhances the conversation and can help students develop more complete conceptual understanding. Often a lesson/question lends itself most naturally to one or two methods of mathematical analysis -- say, writing and solving a linear equation -- but it could also be explored using basic arithmetic and some reasoning, by graphing, using a table, etc. Instead of funneling students toward exactly one mathematical approach, we suggest welcoming multiple approaches and comparing them. (You can read more about this approach in books like The Five Practices for Orchestrating Productive Mathematical Discussion.) Allow students to be creative and they may come up with more advanced methods that you could imagine or simpler, more intuitive ones, too.
Identifying the Difficulty Level of Lessons
The teacher guide for each lesson will identify the core mathematics used in the lesson, and that can be a guide for how appropriate it is for your students.
Additionally, the lesson tile for each lesson (see below) includes an icon in the bottom right corner that is rough signal for when along the continuum of conceptual development this lesson would be appropriate. Low - This lesson would be appropriate even before students have developed the math skills they'll be applying. The questions are sufficiently open and let students build on earlier skills while still "getting to" the target mathematics. High/red - These lessons/applications are best used after students have had some formal exposure and direct instruction around the mathematical ideas they'll need to employ in the lesson.
Using Citizen Math in Remedial Settings
There are two great ways to use Citizen Math to support students lacking on-grade level and below-grade concepts and skills proficiency:
Use earlier grade lessons to present mathematics in a new light. If students are struggling with something like ratios, it's possible that they've seen a related skill isolated (and out of context) many times leading to an expectation of struggle and sometimes and an attitude of indifference. Who can blame them? Well instead of going back to drill-and-kill materials, try an application that presents a need for the math in context and that allows a student to use their intuition to approach the question and then connect it to formal methods. If you use Citizen Math lessons for lower grades, there's still an opportunity to develop the mathematical practices like problem-solving, justifying your reasoning, etc.
Use an on-grade lesson/application that employs an important mathematical concept you know your students haven't otherwise mastered. Encourage and validate student approaches that are sound even if they initially lack grade-level sophistication. Have students make connections between intuitive/informal reasoning and more formal mathematical arguments made by other students.
Timing
The times on lessons are for an on-grade implementation. It may be appropriate to as much as double the time on the lesson. We suggest considering where you might naturally pause the conversation to infuse direct instruction and where it will be beneficial to allow for productive struggle.
Finding lessons based on difficulty