Click here for a Quick Guide for Observing Classroom Content and Practice Content (Math Intermediate CCRSAE Levels C and D)

The examples below feature several Indicators from the ABE Professional Standards. These Indicators are just a sampling from the full set of the ABE Professional Standards and were chosen because they create a sequence: the teacher plans a lesson that sets clear and high expectations, the teacher then delivers high quality instruction, and finally the teacher uses a variety of assessments to see if students understand the material or if re-teaching is necessary. These examples highlight teacher and student behaviors aligned to these Indicators that you can expect to see in a rigorous ABE intermediate level Math class.


(Indicators P1.1, P1.2, C1.1)

The teacher plans and implements CCRSAE-aligned, academically rigorous, differentiated lessons that include clear content and language objectives, set high expectations for all learners, cultivate a safe classroom environment, encourage productive struggle, and motivate all students to succeed.
Virtual/Hands-On Tools: a problem to engage with at arrival; thinking tools (unit cubes and 3D objects) and materials (graph paper or strips of colored paper) accessible to students; options to process new information (drawings, visual models); non-routine math problems and experiences
What is the teacher doing?What are adult learners doing?
Communicating a lesson’s connections to unit essential questions and goalsUnderstanding what they will learn in a lesson and how it connects to prior learning
Creating or selecting culturally responsive lessons that engage and sustain student attentionPersistently applying mathematical strategies and concepts when engaging with meaningful real-world problems
Establishing classroom routines that support students to communicate their thinkingUsing mathematical language precisely to convey meaning and understandings of concepts
Representing and relating solution methods orally, visually, and with concrete objectsRepresenting problems and solution methods using visual models, virtual manipulatives, or number sentences


(Indicators P1.3, P1.4)

The teacher delivers high quality, culturally responsive instruction that meets the diverse needs of all students and engages them with meaningful topics and tasks that develop students’ critical thinking and problem-solving skills.
Virtual/Hands-On Tools: number lines, 1” square tiles, grid paper, virtual (or paper) sticky notes, area models, bar models, pattern blocks, base 10 blocks.
What is the teacher doing?What are adult learners doing?
Selecting meaningful problems with opportunities to apply their learning and solve problems in collaboration with peersWorking cooperatively on a shared activity – developing an understanding or applying knowledge and skills to solve problems
Encouraging students to interpret structures and formulate conjectures about mathematical situationsInterpreting structures and formulating conjectures about mathematical situations
Providing opportunities to evaluate different approaches, including using digital tools such as Desmos or TinkerPlotsExplaining how multiple representations of numbers, operations, and shapes relate to one another


(Indicators P2.1, P2.2, P2.3)

The teacher uses a variety of formative and summative assessments to measure student learning and understanding, evaluate the effectiveness of instruction, develop differentiated and advanced learning experiences, and inform future instruction.
Virtual/Hands-On Tools: exit tickets, math journals or logs, My Favorite No, checklists for teacher observation of objectives being demonstrated or evidence of learning.
What is the teacher doing?What are adult learners doing?
Prompting students’ reasoning; listening to responses to gauge their understandingDemonstrating their thinking by drawing, using manipulatives (either physically or using virtual manipulatives), and discussing and sharing their work
Conducting frequent checks for understanding and adjusting instruction accordinglyRevising their thinking based on their engagement with peers, the teacher, or the math