Using Positive And Negative Numbers In Context ✓ Solved

Using Positive and Negative Numbers in Context: This lesson

Using Positive and Negative Numbers in Context: This lesson unit assesses students' ability to understand and use directed numbers (positive and negative integers) in context, focusing on ordering, comparing, adding, and subtracting with number-line representations (e.g., temperature problems). Compose three discrete program objectives or goals relating to the intent of this learning experience. For each program objective: choose an appropriate Bloom’s Taxonomy verb and justify the choice. For each program objective, compose one to three learning objectives aligned to that program objective and relate each to the intent of the learning experience. Present objectives, verbs, justifications, and aligned learning objectives in clear scholarly prose, supporting assertions with credible references.

Paper For Above Instructions

Introduction

This lesson unit, "Using Positive and Negative Numbers in Context," targets students' conceptual and procedural understanding of directed numbers using real-world contexts such as temperature changes and city elevations. The design emphasizes formative assessment, number-line modeling, collaborative tasks, and pre/post assessment to reveal and remediate common student misconceptions (Shell Centre, n.d.; CCSS, 2010). The following presents three program objectives, the Bloom’s Taxonomy verbs selected for each (with justification), and one to three aligned learning objectives that relate directly to the lesson intent. Rationale and brief instructional/assessment strategies accompany each objective, grounded in research on formative assessment and meaningful learning (Fink, 2013; Black & Wiliam, 1998).

Program Objective 1 — Conceptual Understanding

Program Objective: Students will develop accurate conceptual understanding of directed numbers and their representation on number lines.

Bloom’s Verb (chosen): Explain. Justification: "Explain" aligns with Bloom’s taxonomy at the understanding/analysis level in its revised form (Anderson & Krathwohl, 2001). This verb requires students to articulate relationships between representations (number-line, symbolic, context) and to make sense of operations with negatives rather than simply performing procedures (Anderson & Krathwohl, 2001).

Aligned Learning Objectives:

  • LO1.1: Given a temperature-change scenario, explain using a number line how the starting temperature, change, and final temperature relate algebraically and spatially.
  • LO1.2: Compare and explain differences between adding a negative number and subtracting a positive number using concrete and pictorial representations.

Relation to Intent and Instructional Strategy: These objectives target robust conceptual understanding that supports transfer across contexts (Fink, 2013). Use the pre-assessment to identify misconceptions, then enact guided number-line activities and think-alouds so students can construct verbal explanations (Shell Centre, n.d.; Wiliam & Thompson, 2007). Formative questioning and student explanations during group tasks will be used as evidence of achievement (Black & Wiliam, 1998).

Program Objective 2 — Procedural Fluency and Application

Program Objective: Students will apply procedures for ordering, comparing, adding, and subtracting positive and negative integers accurately in contextual problems.

Bloom’s Verb (chosen): Apply. Justification: "Apply" requires students to use learned procedures in new but similar contexts, consistent with real-life tasks in the lesson (Anderson & Krathwohl, 2001). It emphasizes correct execution within meaningful scenarios (e.g., temperature calculations, city elevation comparisons).

Aligned Learning Objectives:

  • LO2.1: Solve temperature-change problems by computing final, starting, or change values using directed-number operations with 90% accuracy on a formative task.
  • LO2.2: Order and compare a set of city temperatures (including negatives) and justify the ordering with numerical and number-line reasoning.

Relation to Intent and Assessment: These objectives operationalize the lesson’s emphasis on contextual problem solving. Practice via card-matching activities and poster creation fosters repeated reasoning and procedural fluency (Shell Centre, n.d.). Immediate feedback on mini-whiteboard work and post-lesson assessment measure growth (Wlodkowski & Ginsberg, 2017; Black & Wiliam, 1998).

Program Objective 3 — Reasoning and Communication

Program Objective: Students will construct and critique mathematical arguments about directed-number calculations and communicate reasoning clearly to peers and whole class.

Bloom’s Verb (chosen): Analyze. Justification: "Analyze" requires breaking down reasoning, critiquing claims, and examining structure—a higher-order skill central to constructing and critiquing arguments (MP3) and attending to precision (MP6) in the Common Core Mathematical Practices (CCSS, 2010).

Aligned Learning Objectives:

  • LO3.1: Given a peer's solution to a temperature-change problem, identify an error or a strength, and articulate a corrective question or extension in a written feedback comment.
  • LO3.2: Produce a poster that models a set of directed-number problems and includes a written justification connecting number-line, symbolic, and contextual representations.

Relation to Intent and Classroom Practices: Emphasizing argumentation and critique mirrors formative assessment cycles where feedback propels learning (Black & Wiliam, 1998). Structured peer review protocols and facilitator mini-conferences promote engagement and inclusion, which is particularly important for diverse learners (Wlodkowski & Ginsberg, 2017).

Assessment and Evidence of Learning

Formative evidence: pre- and post-assessments, mini-whiteboard responses, group poster artifacts, and teacher feedback questions. The pre/post comparison demonstrates growth in conceptual and procedural domains (Shell Centre, n.d.). Success criteria include accurate explanations, correct computations in contextual tasks, and meaningful peer critiques as outlined in the learning objectives.

Instructional Alignment and Rationale

These objectives integrate Bloom’s taxonomy with the lesson’s formative structure to promote durable learning (Anderson & Krathwohl, 2001; Fink, 2013). The blend of conceptual explanation, applied procedure, and analytic communication supports multiple CCSS standards (7.NS, 7.EE) and mathematical practices (CCSS, 2010). Strategies such as homogeneous pairing, mini-conferences, and explicit framing of tasks help scaffold learning while preserving productive struggle (Shell Centre, n.d.; Wlodkowski & Ginsberg, 2017).

Conclusion

The three program objectives—with their selected Bloom verbs and aligned learning objectives—provide a coherent framework that matches the intent of the "Using Positive and Negative Numbers in Context" lesson. By focusing on explanation, application, and analysis, the design supports conceptual understanding, procedural fluency, and communicative reasoning, all assessed formatively to guide instruction and student growth.

References

  • Anderson, L. W., & Krathwohl, D. R. (Eds.). (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom's taxonomy. Longman.
  • Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), 7–74.
  • Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. http://www.corestandards.org
  • Fink, L. D. (2013). Creating significant learning experiences: An integrated approach to designing college courses (Rev. ed.). Jossey-Bass.
  • Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.
  • Shell Centre for Mathematical Education. (n.d.). Using Positive and Negative Numbers in Context: Lesson Guide and resources. University of Nottingham.
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Pearson.
  • Wiliam, D., & Thompson, M. (2007). Integrating assessment with instruction: What will it take to make it work? In C. A. Dwyer (Ed.), The future of assessment: Shaping teaching and learning (pp. 53–82). Erlbaum.
  • Wlodkowski, R. J., & Ginsberg, M. B. (2017). Enhancing adult motivation to learn (4th ed.). Jossey-Bass.
  • National Council of Teachers of Mathematics. (2014). Principles to Actions: Ensuring Mathematical Success for All. NCTM.

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