Task Title: Navigating the Current: Vector Addition and Relative Velocity
Grade: High School
Date: March 2024
SEP: Using Mathematics and Computational Thinking
DCI: PS2.A: Forces and Motion
CCC: Systems and System Models
Task Purpose: Determining whether students can apply what they have learned to a similar but new context
What was in the task, where was it, and why is this evidence?
The scenario is the interactive simulation itself, where manipulating boat speed, river speed, and heading causes real-time changes in the boat’s resultant velocity and crossing path.
Students cannot complete the analysis without actively using this phenomenon to visualize vector addition.
Features of engaging, relevant, and accessible tasks:
| Features of scenarios | Yes | Somewhat | No | Rationale |
|---|---|---|---|---|
| Scenario presents real-world observations | [x] | [ ] | [ ] | Navigating a boat across a moving river is a common real-world scenario. |
| Scenarios are based around at least one specific instance, not a topic or generally observed occurrence | [x] | [ ] | [ ] | The specific instance is a boat trying to reach a specific point across a flowing river. |
| Scenarios are presented as puzzling/intriguing | [x] | [ ] | [ ] | It is counterintuitive that aiming straight across a river results in landing far downstream. |
| Scenarios create a “need to know” | [x] | [ ] | [ ] | Students need to know how to calculate the correct heading to reach their intended destination. |
| Scenarios are explainable using grade-appropriate SEPs, CCCs, DCIs | [x] | [ ] | [ ] | Explainable using high school level vector mathematics and forces/motion concepts. |
| Scenarios effectively use at least 2 modalities (e.g., images, diagrams, video, simulations, textual descriptions) | [x] | [ ] | [ ] | The task uses an interactive simulation and textual descriptions. |
| If data are used, scenarios present real/well-crafted data | [x] | [ ] | [ ] | The simulation provides realistic resultant velocity and time data based on vector addition. |
| The local, global, or universal relevance of the scenario is made clear to students | [x] | [ ] | [ ] | Navigating moving water and understanding relative velocity are universally relevant in physics, transportation, and engineering. |
| Scenarios are comprehensible to a wide range of students at grade-level | [x] | [ ] | [ ] | The visual, interactive nature makes abstract concepts accessible. |
| Scenarios use as many words as needed, no more | [x] | [ ] | [ ] | Instructions are concise and action-oriented. |
| Scenarios are sufficiently rich to drive the task | [x] | [ ] | [ ] | Multiple variables can be altered, generating complex data for analysis. |
| Evidence of quality for Criterion A: [ ] No | [ ] Inadequate | [x] Adequate | [ ] Extensive |
Suggestions for improvement of the task for Criterion A:
Provide explicit real-world examples (like a hot air balloon or car tires) in the introduction to strengthen local/global relevance.
Consider in what ways the task requires students to use reasoning to engage in sense-making and/or problem solving.
Students must reason about why the boat’s path and arrival point change when its heading or the river’s current are altered, using vector addition to explain the macroscopic resultant velocity.
Evidence of SEPs (which element[s], and how does the task require students to demonstrate this element in use?)
Using Mathematics and Computational Thinking: Students use an interactive computational model to explore relationships and generate data.
Evidence of CCCs (which element[s], and how does the task require students to demonstrate this element in use?)
Systems and System Models: Students analyze the boat and river as a system, identifying how the individual velocity components interact to determine the overall system behavior.
Evidence of DCIs (which element[s], and how does the task require students to demonstrate this element in use?)
PS2.A: Forces and Motion: Students connect individual velocity vectors to determine the resultant motion and position of an object within a frame of reference.
Consider in what ways the task requires students to use multiple dimensions together.
Students use computational thinking and mathematics (SEP) to analyze the system model (CCC) regarding how individual velocity vectors (DCI) combine to determine resultant motion.
Consider in what ways the task explicitly prompts students to make their thinking visible (surfaces current understanding, abilities, gaps, problematic ideas).
Students must provide written explanations and draw vector diagrams connecting the individual velocity components to the resultant path, making their mathematical reasoning visible.
| Evidence of quality for Criterion B: [ ] No | [ ] Inadequate | [x] Adequate | [ ] Extensive |
Suggestions for improvement of the task for Criterion B:
Require students to explicitly draw the vector addition triangle (head-to-tail method) alongside their written explanation to further surface their mathematical thinking.
Consider specific features of the task that enable students to make local, global, or universal connections to the phenomenon/problem and task at hand. Note: This criterion emphasizes ways for students to find meaning in the task; this does not mean “interest.” Consider whether the task is a meaningful, valuable endeavor that has real-world relevance–that some stakeholder group locally, globally, or universally would be invested in.
Understanding vector addition and relative velocity is essential for various engineering, aviation, and maritime applications, providing universal relevance.
Describe what modes (written, oral, video, simulation, direct observation, peer discussion, etc.) are expected/possible.
Expected modes are written responses and interaction with the simulation.
| Features | Yes | Somewhat | No | Rationale |
|---|---|---|---|---|
| Task includes appropriate scaffolds | [x] | [ ] | [ ] | Step-by-step data collection guides the process. |
| Tasks are coherent from a student perspective | [x] | [ ] | [ ] | The progression from observation to data collection to analysis is logical. |
| Tasks respect and advantage students’ cultural and linguistic backgrounds | [x] | [ ] | [ ] | Uses standard scientific representations and accessible language. |
| Tasks provide both low- and high-achieving students with an opportunity to show what they know | [x] | [ ] | [ ] | All students can collect data, while analysis allows for varying depths of explanation. |
| Tasks use accessible language | [x] | [ ] | [ ] | Terminology is standard and visually supported by the UI. |
Consider how the task cultivates students interest in and confidence with science and engineering, including opportunities for students to reflect their own ideas as a meaningful part of the task; make decisions about how to approach a task; engage in peer/self-reflection; and engage with tasks that matter to students.
The immediate visual feedback and dynamic graphs build confidence by allowing students to quickly test hypotheses.
Consider the ways in which provided information about students’ prior learning (e.g., instructional materials, storylines, assumed instructional experiences) enables or prevents students’ engagement with the task and educator interpretation of student responses.
The task assumes some prior introduction to the concepts of vectors, speed, and velocity, which is standard for HS physical science.
Describe evidence of scientific inaccuracies explicitly or implicitly promoted by the task.
The simulation accurately models vector addition and relative velocity.
| Evidence of quality for Criterion C: [ ] No | [ ] Inadequate | [x] Adequate | [ ] Extensive |
Suggestions for improvement of the task for Criterion C:
Provide explicit options for peer discussion during the analysis phase.
Before you begin:
Assessing student ability to use a computational model to understand the relationship between vector components and relative velocity (PS2.A, Systems and System Models).
Consider the following:
Yes, students must use the provided model to answer the analysis questions.
No extraneous knowledge is strictly required; the simulation provides the necessary data.
Yes, the written explanations will demonstrate if students can connect the resulting vector components to relative velocities.
Consider what student artifacts are produced and how these provide students the opportunity to make visible their 1) sense-making processes, 2) thinking across all three dimensions, and 3) ability to use multiple dimensions together [note: these artifacts should connect back to the evidence described for Criterion B].
The required written analysis of the vector data and relative velocity behavior serves as direct evidence of 3D integration.
Consider how well the materials support teachers and students in making sense of student responses and planning for follow up (grading, instructional moves), consistent with the purpose of and targets for the assessment. Consider in what ways rubrics include:
Teachers should evaluate if students successfully use the model’s data and mathematics (SEP) to show system relationships (CCC) related to forces and motion (DCI).
Partial understanding might be shown if a student can describe the resultant path but cannot explain why based on the underlying vector components.
Responses can guide future instruction on non-perpendicular vectors or real-world applications (like aviation).
Consider any confusing prompts or directions, and evidence for too much or too little scaffolding/supports for students (relative to the target of the assessment—e.g., a task is intended to elicit student understanding of a DCI, but their response is so heavily scripted that it prevents students from actually showing their ability to apply the DCI).
The step-by-step data collection provides scaffolding, while the open-ended analysis questions maintain cognitive demand.
| Evidence of quality for Criterion D: [ ] No | [ ] Inadequate | [x] Adequate | [ ] Extensive |
Suggestions for improvement of the task for Criterion D:
Include a formal scoring rubric aligned to the three dimensions.
Consider the task purpose and the evidence you gathered for each criterion. Carefully consider the purpose and intended use of the task, your evidence, reasoning, and ratings to make a summary recommendation about using this task. While general guidance is provided below, it is important to remember that the intended use of the task plays a big role in determining whether the task is worth students’ and teachers’ time.
The Navigating the Current task effectively leverages an interactive simulation to engage students in three-dimensional learning. By manipulating velocity variables and observing real-time vector changes, students use computational thinking to understand system relationships related to relative velocity. The task is accessible and directly supports its intended summative purpose.
Final recommendation (choose one):