Mathematics Lesson Sequence

introduction

This three lesson sequence is designed to meet 3rd grade Colorado Academic Standard: 3.NF.A. Number & Operations- Fractions: Develop understanding of fractions as numbers. This is a mid to year-end 3rd-grade standard, that is supported by previous standards.


  1. Monday: Express whole numbers as fractions and recognize equivalence with different units.

  2. Tuesday: Express whole number fractions on the number line when the unit interval is 1.

  3. Wednesday: Explain equivalence by manipulating units and reasoning about their size.

The following professional connections and implications discuss the techniques that support students' development in academic and content language across all subjects. These techniques are also specifically used in the mathematics lesson sequence that follows.

The three-unit lesson sequence is based on EngageNY curriculum that meets Colorado's Academic Standards. The lesson sequence has been modified to meet CLD learner's unique needs, support students below grade-level expectations, and create understanding for ELL students that are native Spanish speakers.

Professional Connections & Implications

From your fieldwork and other work for this class, describe the specific approaches that helped your students in their development of academic language and content learning.

    • While this lesson sequence specifically focused on mathematics, similar techniques can be applied to other subjects for the development of academic language and content learning.

      1. Assessment's

        • Assessments are a valuable tool to understand students learning, especially when they are well designed with the student in mind. Using formative assessments has been the most important tool to understand students' development of language and content learning because they are a continual process. Formative assessments allow you to gauge where your students' current understanding is, and modify lessons to support their unique needs.

      2. Scaffolding

        • Scaffolding is another helpful technique that supports students through their development of academic language and content learning. Scaffolding breaks down concepts into understandable chunks that then build off of each other. This technique is especially important for language learners because they can apply what they previously learned to new concepts.

      3. Language Cognates

        • Supporting CLD students that are bilingual is incredible and complicated. Students learning two languages can build foundations of connections between the two languages. They can apply concepts from one language and build off of those concepts in another language. This creates a foundational connection where language cognates can be used as a tool to strengthen their understanding across both languages.


What additional experiences might be helpful for your students’ language development for social and academic purposes?

    • Understanding a student's background and home life is a very important element in understanding the student holistically. Having a connection with the student and their family is an experience that enriches the student's language development for social and academic purposes.


What insights and implications for action does this experience provide for your professional practice as a teacher of culturally and linguistically diverse learners?

  • Teachers and teacher educators must respect all learners and themselves as individuals with culturally defined identities.

  • Students bring funds of knowledge to their learning communities, and, recognizing this, teachers and teacher educators must incorporate this knowledge and experience into classroom practice.

  • Socially responsive and responsible teaching and learning requires an anthropologically and ethnographically informed teaching stance; teachers and teacher educators must be introduced to and routinely use the tools of practitioner/teacher research in order to ask difficult questions about their practice.

  • Students have a right to a variety of educational experiences that help them make informed decisions about their role and participation in language, literacy, and life.

  • Educators need to model culturally responsive and socially responsible practices for students.

  • All students need to be taught mainstream power codes/discourses and become critical users of language while also having their home and street codes honored.

  • Teachers and teacher educators must be willing to cross traditional personal and professional boundaries in pursuit of social justice and equity.

  • Teaching is a political act, and in our preparation of future teachers and citizens, teachers and teacher educators need to be advocates for and models of social justice and equity.

*These insights are taken from: https://ncte.org/statement/diverselearnersinee/ my teaching pedagogy aligns heavily with NCTE's work and beliefs surrounding language learning, supporting CLD learners, and their families.

Lesson Sequence

Reflections

This lesson sequence was implemented in 3rd grade at Silverthorne Elementary, a dual language (Spanish & English) elementary school in Silverthorne Colorado.

Considerations...

This lesson was given in April 2021. The students in this specific class had been quarantined 5 times due to COVID during this school year. Due to their disrupted learning schedule, the students missed some of the foundational skills that were needed to understand some of the concepts in this lesson sequence.

This became apparent during Monday's lesson, and we spent more time in the beginning of the lesson building skills and concepts. The "Exit Ticket" from the first lesson showed that Tuesday's lesson needed to be modified, and we needed to spend more time in small groups working on fluency and concept development. Tuesday's "Exit Ticket" showed that the students were understanding how to "express whole fractions on the number line when the unit interval is 1", but that additional support was needed in vocabulary for English and Spanish. Wednesday's was modified with more vocabulary support at the beginning of the lesson, and then a continuation of the lesson as planned.