Basic Facts:
Addition & Subtraction
CTL’s Basic Facts: Addition & Subtraction is a Kindergarten through Grade 2 supplemental curriculum that incorporates intentionally designed lessons, materials, assessment and professional development. Through explicit strategy instruction, game-based practice and the use of formative assessment, students develop fluency with the basic addition and subtraction facts. The kit provides a teacher guidebook and all materials needed for the included games, such as cards, spinners, counters, literacy connections, etc.
Multiple Representations
The vibrant materials were designed so that students have the opportunity to see quantities represented in multiple ways. Dot patterns, pictures, ten frames, as well as the standard and word form are included for each number 0 – 20. During game play, students build connections between the representations in order to further develop their number sense.
Explicit Strategy Instruction
Following the framework of Bay-Williams and Kling (2019) outlined in Math Fact Fluency, lessons begin with developing mastery with the foundational fact sets and progress to the selection and use of the derived fact strategies for unknown facts. Explicit strategy instruction is used to build students’ number sense as fluency with the remaining basic facts is developed. Each lesson follows the workshop model with three main components: mini lesson, workshop and closure. The brief mini lesson is delivered by the teacher and introduces students to the key work of the day. The main part of each lesson is the workshop where students are working collaboratively to practice known facts as well as choosing and applying strategies for solving unknown facts. Student reflection, which can take many forms, is the closure for each lesson. Supplemental activities and games included are meant to provide additional time for students to practice choosing and applying strategies.
game-based practice
As a primary focus of this resource, game-based practice provides numerous opportunities for all students to practice strategy application and develop a positive disposition towards mathematics. Rather than expecting students to respond correctly on timed tests, teachers shift their focus toward students who are engaged in strategy discussion with their peers. Each game is easily adapted for use with all students.
formative assessment
As small groups of students are engaged in playing games, the teacher will monitor accuracy, efficiency, and the appropriate and flexible use of strategies in each student. Using the provided Observation Checklists, teachers will be able to track individual student progress. Additional opportunities for assessment are created during class discussion when students are asked to share solutions and strategies. The game-based practice and formative assessment components emphasize the developmental and research-based approach of the curriculum.
Lesson Design
Each Procedural Fluency lesson follows the workshop model with three main components: mini lesson, workshop and closure. The brief mini lesson is delivered by the teacher and introduces students to the key work of the day. The main part of each lesson is the workshop where students are working collaboratively to practice known facts as well as choosing and applying strategies for solving unknown facts. Student reflection, which can take many forms, is the closure for each lesson.
Individual lessons outline a plan for explicit instruction on the foundational facts and/or derived fact strategies. Supplemental activities and games included are meant to provide additional support to students in developing mastery with the facts. Plan to spend multiple sessions for game play where students are given ample time to practice foundational facts and derived fact strategies. Moving ahead too soon to the next derived fact strategy will not lead to fluency. Expecting students to respond quickly and accurately such as in timed tests too soon can be detrimental (Beilock, 2010; Boaler, 2014; Isaacs & Carroll, 1999; Ramirez, Gunderson, Levine & Beilock, 2013). The lessons are outlined by strategy and most could be completed in one session. However, teachers should anticipate multiple days for students to practice strategy selection and application with game play. For example, students may require several sessions with the Making 10 strategy.
Professional Learning & coaching
All of CTL’s professional learning models meet the Learning Forward Professional Learning Standards for effective student learning. The most recent findings show a combination of curriculum and professional learning produce the greatest impact on student learning (Lynch, Gonzalez, & Pollard, 2018). Professional learning experiences focus on teacher understanding of the conceptual progression, analysis of instruction, and reflection. CTL offers a Foundational Training for all teachers.
While our approach brings educators together to regularly engage in collaborative professional learning, the program honors the individual needs of participating practitioners. CTL coaching provides a space for assessment, reflection, and refinement that is educator-driven, and proven to enhance engagement, motivation and instructional practices. Whether virtually or in-person, CTL staff engage in side-by-side instructional planning, pre/mid/post observations, reflection cycles, analysis of student work protocols, and other timely and relevant coaching experiences with teachers. CTL’s personalized professional coaching helps to create a school-wide culture of continuous improvement, which pays dividends both in the classroom and in the professional learning communities.
Where applicable, CTL also offers job-embedded coaching for school and district mathematics coaches as they develop their capacity to lead and support teachers in the program’s design.