Quad Fun: Daily Life Equation Adventures!

9th Grade Project 3 weeks

Quad Fun: Daily Life Equation Adventures!

Antonia R

CCSS.Math.Content.HSA-REI.B.3

CCSS.Math.Content.HSA-SSE.A.2

CCSS.Math.Content.HSA-SSE.B.3

CCSS.Math.Content.HSA-REI.C.7

CCSS.Math.Content.HSA-REI.B.4

+ 12 more

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Purpose

The purpose of this learning experience is to engage 9th-grade students in a practical exploration of quadratic functions through the lens of real-world applications, such as bridge design. By collaborating with community partners and participating in hands-on activities, students will develop a deep understanding of mathematical concepts while honing their problem-solving, communication, and reflection skills. This project-based approach aims to foster a meaningful connection between mathematics and its tangible impact on engineering and design, encouraging students to think critically and creatively about the world around them.

Learning goals

Students will deepen their understanding of quadratic functions by exploring their real-world applications in bridge design, focusing on graphing and interpreting key features. They will develop quantitative reasoning skills by solving quadratic equations and inequalities, and by analyzing data to make informed decisions about design choices. Students will enhance their collaborative and reflective abilities through peer feedback and digital reflection journals, fostering growth in problem-solving and communication.

Standards

[Common Core] CCSS.Math.Content.HSA-REI.B.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
[Common Core] CCSS.Math.Content.HSA-SSE.A.2 - Use the structure of an expression to identify ways to rewrite it.
[Common Core] CCSS.Math.Content.HSA-SSE.B.3 - Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
[Common Core] CCSS.Math.Content.HSA-REI.C.7 - Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
[Common Core] CCSS.Math.Content.HSA-REI.B.4 - Solve quadratic equations in one variable.
[Common Core] CCSS.Math.Content.HSF-LE.A.3 - Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
[Common Core] CCSS.Math.Content.HSF-IF.C.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
[Common Core] CCSS.Math.Content.HSF-IF.C.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
[Common Core] CCSS.Math.Content.HSF-IF.C.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Competencies

Reason Quantitatively - Pose and solve problems (RQ.1)
Reason Quantitatively - Represent and communicate information mathematically (RQ.3)
Reason Quantitatively - Analyze and interpret data (RQ.2)
Learn with Purpose - Develop a plan to pursue a goal (LI.1)
Learn with Purpose - Monitor progress and adjust (LI.2)
Learn with Purpose - Give and receive feedback (LI.3)
Learn with Purpose - Reflect (LI.5)
Learn with Purpose - Engage in discussion (LI.4)

Products

Students will design and construct a scale model of a bridge using materials such as popsicle sticks and string, applying quadratic functions to calculate the optimal arch for strength and stability. They will create a digital presentation that includes graphs, equations, and real-life examples of quadratic functions in bridge design. These models and presentations will be showcased at the Quadratic Expo, where students will engage with attendees and explain their design process and mathematical applications.

Launch

Begin the project with 'Bridge Builders Day,' where students engage in a hands-on activity to construct small-scale bridge models. Using quadratic functions, students will determine the optimal design for strength and stability. This interactive experience will set the stage for understanding the real-world application of quadratic functions in engineering.

Exhibition

Host a 'Quadratic Expo' where students present their digital presentations and models of bridge designs to parents, students from other grades, and community partners. Set up interactive stations where attendees can engage with the concepts of quadratic functions and their applications in bridge design. Encourage students to explain their design process, the mathematical principles they applied, and the real-world implications of their projects, fostering a collaborative and educational atmosphere.

Rubric

Competency Progression Rubric Competency-first rubric

Category	Learning Goal	Level 1	Level 2	Level 3	Level 4	Level 5	Level 6
Reason Quantitatively	Pose and solve problems	I can rephrase a problem in my own words and choose one way to solve it. Project-specific: I can explain a bridge design problem in my own words and choose a strategy to solve it, using quadratic equations to find the best arch for strength I can rewrite expressions to show the relationships between different parts of my bridge design and solve simple systems of equations that relate to my model	I can rephrase a simple problem in my own words and break it down into phases, steps, or parts. With guidance, I can try out a problem-solving strategy (e.g., tinker, look for patterns, visualize and draw it) to come up with an approach. I can explain or show my approach in words and/or pictures. Project-specific: I can break down a simple problem related to bridge design into clear steps and phases With some help, I can choose and use a problem-solving strategy, like looking for patterns or drawing it out, to explore how quadratic functions apply to my bridge model I can explain my approach using words and pictures, and I can use graphs and equations to show how I solved a problem involving quadratic and linear equations in my design	I can organize important information about a problem (e.g., using a chart, table, or graph) to help me identify a starting point for solving it. I can try out at least one problem-solving strategy to begin testing an approach. With guidance, I can test whether my approach and/or solution is reasonable. I can explain or show my approach in words and/or pictures. Project-specific: I can organize information about the bridge design problem using charts or graphs to find a starting point for my solution I can try out a problem-solving strategy by calculating the optimal arch of my bridge using quadratic functions With guidance, I can test and explain whether my approach is reasonable by showing my calculations and graphs	I can organize important information about a problem, ask questions to better understand its context and parts, and identify a starting point for solving it. I can identify the facts, precedents, or assumptions that I am bringing to the problem or my approach. I can choose problem-solving strategies to build an approach, making changes to my approach if I get stuck (e.g., solve a simpler problem, work backward, guess and test, try numerical cases). I can test whether my approach and/or solution is reasonable and accurate. I can illustrate and/or explain my approach and how it led to my solution. Project-specific: I can organize and analyze important information about my bridge design problem, ask insightful questions to understand its context, and identify an effective starting point for solving it I can apply my knowledge of quadratic functions to choose appropriate problem-solving strategies, making adjustments if needed, and use graphs and equations to illustrate my approach I can explain how my method led to my solution, ensuring my calculations are reasonable and accurate, and communicate my findings clearly during the Quadratic Expo	I can organize important information about a problem, ask questions to better understand its context and parts, and identify a starting point for solving it. I can evaluate the relevance and validity of facts, precedents, or assumptions that I am bringing to the problem and/or my approach. I can choose strategies, tools, or methods to develop an approach, experimenting with ideas and/or lines of reasoning. I can test my or others’ solutions and make corrections to ensure they are reasonable and accurate (e.g., attendant to the meaning of quantities; free from computational errors). I can illustrate and/or explain my solution and rationale. Project-specific: I can organize and evaluate key information about a bridge design problem by asking clarifying questions and identifying a starting point for solving it I can choose effective strategies and tools to design my bridge, experimenting with different ideas and lines of reasoning to determine the optimal quadratic function for strength and stability I can test my bridge model, make necessary adjustments to ensure accuracy, and clearly illustrate and explain my design choices and mathematical reasoning using graphs and equations	I can use a range of tools, strategies, or methods to frame, create, and/or evaluate a problem and its context and determine essential resources for exploring or solving it. I can choose and apply relevant and credible facts, precedents, or assumptions to bring to the problem and/or my approach. I can choose strategies, tools, or methods to generate a novel approach, experimenting with ideas, theories, or lines of reasoning. I can test my or others’ solutions in multiple ways to confirm the validity and accuracy of an approach and a solution. I can illustrate and/or explain my solution and rationale. Project-specific: I can effectively identify and frame complex problems related to bridge design, using a variety of mathematical strategies and tools to explore quadratic functions I confidently apply relevant facts and assumptions, generate innovative solutions, and test them through multiple methods to ensure their accuracy and effectiveness I clearly illustrate and explain my design choices and mathematical reasoning, demonstrating a deep understanding of quadratic functions and their real-world applications
Reason Quantitatively	Represent and communicate information mathematically	With guidance, I can draw pictures and/or use objects to help me explain a problem or situation. Project-specific: I can use pictures and objects to help explain my bridge design problem, showing how I applied quadratic functions to create a stable structure With guidance, I can illustrate how my model's arch relates to the mathematical concepts we've learned, using graphs and equations to support my explanations	I can draw pictures and/or use objects to record what I see and/or to explain my thinking about a problem or situation. I can make choices about the features of my visual representation (e.g., size, shape, color, relative placement) to show important quantities, relationships, or changes in a problem or situation. Project-specific: I can create a basic graph to show a quadratic equation and use it to explain how I chose the arch shape for my bridge model, identifying key features like the vertex and axis of symmetry I can describe, in simple terms, how these features influence the design's strength and stability	I can practice using different tools and techniques for visually representing information (e.g., diagrams, tables, graphs, flowcharts, formulas). I can provide descriptive information in my displays (e.g., title, labeled axes, units) to accurately depict patterns, quantities, relationships, or changes in a problem or situation. Project-specific: I can use diagrams and graphs to show how quadratic functions apply to my bridge design, making sure to include titles, labeled axes, and units I can explain how these visual tools help me understand the strength and stability of my bridge model and compare it to real-world examples	I can choose tools and techniques for organizing and displaying information based on the type and amount of data and/or what I want to communicate about it. I can provide descriptive information in my displays to accurately depict patterns, quantities, relationships, or changes in a problem or situation and, when applicable, offer interpretations or claims. Project-specific: I can effectively choose and use the appropriate tools and techniques to organize and display data about my bridge design I include detailed descriptions in my graphs and presentations to clearly show patterns and relationships of quadratic functions I confidently explain how these mathematical concepts support the strength and stability of my model, and I make interpretations or claims based on my data analysis	I can accurately organize and display data using tools and displays (e.g., tables, charts, graphs) aligned to my purpose. I can use descriptive vocabulary and analytical tools (e.g., best-fit functions, measures of central tendency) to discuss, illustrate, and offer interpretations of mathematical and/or conceptual relationships. Project-specific: I can effectively organize and display data using tables and graphs to illustrate my bridge design, and I can clearly explain how the quadratic functions apply to my design choices I can describe the mathematical relationships I used, such as solving quadratic equations and graphing functions, and discuss how these contribute to the strength and stability of my bridge model	I can accurately organize and display data using tools and displays aligned to my purpose, data set, audience, and context. I can use descriptive vocabulary and analytical tools to discuss and illustrate mathematical and conceptual relationships with clarity to make evidence-based claims and/or to evaluate others’ conclusions. I can represent data to demonstrate mathematical insight with novelty and/or elegance. Project-specific: I can skillfully organize and display data using graphs and digital tools to clearly illustrate the mathematical concepts behind my bridge design I use precise vocabulary and analytical techniques to explain how quadratic functions influence the strength and stability of my model, making informed, evidence-based claims My presentation reflects a deep understanding of mathematical relationships and showcases my ability to creatively and effectively communicate complex ideas
Reason Quantitatively	Analyze and interpret data	I can describe the patterns I see in a source of information. Project-specific: I can identify and describe the patterns I see in the data related to my bridge model's strength and stability Using graphs and equations, I can explain how different designs affect the structural integrity and show how quadratic functions are applied to solve real-world engineering problems	I can describe the patterns I see in a data set. I can explain or show what I think it means and why. Project-specific: I can identify some patterns in the data I gathered from my bridge model and explain what these patterns might indicate about its strength and stability I use graphs to show how changing the arch affects the bridge's performance and discuss my findings with my classmates using mathematical terms	I can identify and describe patterns and outliers in a data set. I can use reasoning and contextual information to explain what the data mean. Project-specific: I can identify patterns and outliers in the data from my bridge model tests and explain how these affect the strength and stability of my design I use graphs and equations to show key features of the quadratic functions I've applied, and I can discuss how different forms of the equations reveal important properties of my bridge's structure	I can identify and describe patterns and outliers in one or more sources of data. I can analyze data sets involving linear or nonlinear relationships and use details about the data to understand or investigate relationships. I can use reasoning, math skills, and contextual information to draw inferences about the data and/or explain phenomena. Project-specific: I can identify and describe patterns and outliers in data from my bridge model tests and use these insights to make informed improvements I can analyze both linear and quadratic relationships in my data, explaining how these relationships impact the strength and stability of my bridge design I use math skills and reasoning to draw conclusions about my design choices and share my findings clearly with others	I can apply concepts and methods of statistical analysis (e.g., slope, intercept, correlation coefficient for linear fits) to analyze and characterize data from an investigation. I can determine the relevance or significance of the data as they relate to a hypothesis, working explanation, or relevant theory, as well as limitations of my analysis. I can draw evidence-based inferences about the data to support a claim and/or evaluate others’ interpretations and/or analysis. Project-specific: I can effectively analyze the data from my bridge model investigation by applying quadratic and linear equations to interpret key features such as slope and intercept I determine the significance of this data in relation to my design hypothesis and use it to support my conclusions I can also evaluate and discuss the limitations of my analysis and make evidence-based inferences to strengthen my claims and understand others’ perspectives	I can lead an initiative or project involving the analysis and interpretation of data to address an important issue or need. I can select and apply advanced data analysis concepts, methods, and technologies to derive original insights and/or inform future research. I can determine the relevance or significance of the data as they relate to a hypothesis, working explanation, or relevant theory, as well as limitations of my analysis. I can draw evidence-based inferences about the data to support a claim and/or evaluate others’ interpretations and/or analysis. Project-specific: I can lead my bridge design project by effectively analyzing and interpreting data to solve complex problems using quadratic functions I confidently select and apply advanced mathematical concepts and technologies to explore and explain the properties of quadratic functions, ensuring my bridge model is both strong and stable I can evaluate the significance of my data in relation to my design hypothesis and limitations, and I draw evidence-based conclusions to support my design choices and communicate my findings clearly to others
Learn with Purpose	Develop a plan to pursue a goal	With guidance, I can set a goal for a project. With guidance, I can plan some steps to help me reach the goal. Project-specific: I can set a goal for my bridge design project with help from my teacher and identify some steps I need to follow, like choosing materials and planning the design, using quadratic equations to ensure the bridge's strength and stability	I can set a goal for a project and plan some steps to reach it, working alone or with others. I can help make sure that roles and/or steps are clear. Project-specific: I can identify a goal for my bridge design project and outline a few steps to achieve it, making sure to include solving quadratic equations to determine the best arch shape I can work with my team to clarify roles and use graphs to show how our design choices support strength and stability	I can create or co-create a specific, achievable goal for a project or task. I can create or co-create a plan for a project or task that breaks down the work into stages or steps and includes key dates or events. When working with others, I can discuss various preferences, needs, and/or strengths to help us develop our roles and work well together. Project-specific: I can set a realistic goal for my bridge model by understanding the key features of quadratic functions and how they apply to design I can create a step-by-step plan to build my model, identifying important deadlines and tasks needed to ensure my design is strong and stable I can work with my team by sharing our different strengths and preferences, so we effectively assign roles and collaborate on our project	I can create or co-create a specific, achievable goal and success criteria for a project or task. I can create or co-create a feasible plan (e.g., stages, tasks, assignees, time estimates, due dates) that accounts for task/project constraints and resources needed. When working with others, I can demonstrate care for various preferences, needs, and/or strengths to help us each contribute and work well together. When available, I can try using digital tools (e.g., scheduling communications and feedback, sharing work) to follow a plan and help reach a goal. Project-specific: I can create a clear and achievable goal for my bridge design project by considering the mathematical principles involved, such as quadratic functions, and outline a step-by-step plan that includes stages, tasks, and deadlines I can work collaboratively, valuing each team member's strengths and preferences to ensure our project is successful Additionally, I can utilize digital tools to organize our progress and communicate effectively with my team to achieve our shared goal	I can create or co-create specific, achievable goals and success criteria for a project or task. I can create or co-create a feasible plan and set of progress-monitoring tools that account for task/project constraints and resources needed. When working with others, I can demonstrate care for various preferences, needs, or strengths and help establish inclusive norms, routines, and/or structures that enable us to each contribute and work well together. When available, I can choose digital tools to meet a specific need for our project or team. Project-specific: I can create a detailed plan for my bridge model project that includes clear, achievable goals and criteria for success I can thoughtfully select digital tools and resources to enhance my design process and collaborate effectively with my team, ensuring everyone's strengths and ideas are valued and incorporated I can also demonstrate my understanding of quadratic functions by accurately graphing them and solving related equations to optimize my bridge design	I can create or co-create the purpose, goals, and success criteria for a project or initiative and develop strategies for anticipated issues. I can create or co-create a feasible plan and set of progress-monitoring tools that account for project constraints, resources needed, and other contextual factors. When working with others, I can demonstrate care for various preferences, needs, or strengths and help establish inclusive norms, routines, and/or structures that attend to cultural and/or power differences (e.g., gender, language, race, ability), and that enable us to each contribute and work well together. When available, I can choose and adapt digital tools to meet specific needs for our project or team. Project-specific: I can effectively create or co-create the purpose, goals, and success criteria for my bridge design project, developing a comprehensive plan that considers project constraints and available resources I can anticipate potential issues and devise strategies to address them, ensuring smooth progress I thoughtfully collaborate with my peers, respecting diverse needs and strengths, and help establish inclusive norms and structures within our team I adeptly choose and adapt digital tools to support our project's specific needs Additionally, I accurately apply quadratic functions to design an optimal bridge model, solve related equations, and clearly communicate my mathematical reasoning through graphs, equations, and presentations
Learn with Purpose	Monitor progress and adjust	With guidance, I can stop to check in with myself or my partners to see how it’s going. I/we can ask for help if needed. Project-specific: I can pause during my bridge model project to check my progress and talk with my partner about how our design is going If we need help with solving quadratic equations or graphing functions, we can ask our teacher or classmates for guidance to make sure our bridge is strong and stable	I can stop to check in with myself or my partners about how it’s going (e.g., Am I stuck? Do I need anything? Am I closer to my goal?). If I/we get stuck or distracted, I can come up with some ideas about how to move forward (e.g., ask for help, start over, use a new tool). Project-specific: I can regularly pause during my bridge design project to assess my progress and identify if I need to make any adjustments When I encounter challenges, I come up with practical strategies to overcome them, like asking for help or trying a new approach I can use the structure of quadratic expressions to rewrite them in different forms and solve equations, helping me refine my model's strength and stability	I can pause to check in on progress and practice positive self-talk and/or encouragement of my team or partner. If I/we get stuck or distracted, I/we can identify the cause of the issue and try out an idea about how to move forward (e.g., change the approach, adjust the environment, ask for the specific help needed to keep progressing). Project-specific: I can regularly pause to assess how well my bridge design project is progressing by reviewing my calculations and graphs for accuracy If I encounter challenges, I can identify the issue, encourage my team to stay positive, and suggest adjustments, such as trying a different mathematical approach or seeking feedback from a peer, to keep moving forward effectively	I can regularly pause to check in with myself and/or others about process and progress toward the goal(s). I can practice positive self-talk and/or encouragement of my team or partner. If an issue arises, I/we can recognize it promptly, analyze causes, and pursue a suitable solution. Project-specific: I can regularly pause to check my progress on constructing my bridge model and adjust my design as needed by analyzing quadratic equations and graphing the functions If I encounter any challenges, I can identify the issue quickly, explore different ways to solve it, and use my mathematical reasoning to choose the best solution	Puedo hacer pausas periódicas para comprobar conmigo mismo y/o con los demás el proceso y el progreso hacia el/los objetivo(s). Puedo hablarme a mí mismo y/o animar a mi equipo o compañero de forma positiva y adaptada a las necesidades o preferencias individuales. Puedo utilizar ciclos de retroalimentación para ayudar a mejorar el trabajo. Si surge un problema, sé/sabemos reconocerlo rápidamente, analizar las causas y buscar una solución adecuada basada en múltiples datos o perspectivas. Puedo entablar conversaciones difíciles para resolver conflictos o problemas del equipo, según sea necesario. Project-specific: I can regularly check my progress and that of my team towards our goals, and make positive adjustments based on feedback I can identify challenges quickly, discuss them with my team, and use data and different perspectives to find effective solutions I can confidently engage in important conversations to resolve any conflicts or issues that arise in our project	I can regularly pause to check in on process and progress toward the goal(s). I can practice positive self-talk and/or encouragement of my team or partner that is responsive to individual needs or preferences. I/we can use multiple feedback cycles to improve the work and foster shared learning. If an issue arises, I/we can recognize it promptly, analyze causes, and pursue a suitable solution informed by multiple data points or perspectives. I can engage in and/or facilitate difficult conversations to resolve team conflicts or issues, as needed, using a strengths-based approach. Project-specific: I can consistently check my progress toward the goal of designing a stable bridge by using quadratic equations and graphs I can effectively communicate with my team, offering positive support and encouragement that respects each member's preferences I can use feedback to enhance our design through multiple revisions, ensuring our bridge model is strong and stable If a problem occurs, I quickly identify the issue, explore its causes using data and perspectives, and lead my team in finding a solution I can also facilitate constructive conversations to resolve any conflicts within the team, focusing on our strengths to improve collaboration and learning
Learn with Purpose	Give and receive feedback	I can ask questions or express what I like about something someone else made or did. With guidance, I can listen to what others say about something I made or did and record or repeat some ideas I heard. Project-specific: I can ask questions about the bridge design choices and express what I like about my classmates' models, focusing on how quadratic functions are used for stability With guidance, I can listen to feedback about my own design and record or repeat the key ideas about how quadratic equations and graph features contributed to my project	I can ask questions to learn more about someone’s work. I can share some things I really like about it and why. I can listen to what others say about something I made or did and record or repeat some ideas I heard. Project-specific: I can ask thoughtful questions about a classmate's bridge design to understand their use of quadratic functions better I can identify specific elements I appreciate, like how they solved equations or chose certain graph features, and explain why I like them I can listen to feedback about my own bridge project and accurately note down some of the helpful ideas shared by others	I can ask questions to learn more about what someone made and how they made it. I can identify several strengths, using evidence or examples. I can ask for targeted feedback and record or repeat some ideas I heard, using a provided tool or process. Project-specific: I can thoughtfully ask questions to learn more about how peers constructed their bridge models and applied quadratic functions I can identify several strengths in their designs and use specific examples to support my observations I can seek feedback on my own bridge design, using a feedback tool to capture and reflect on constructive ideas shared by others	I can ask questions to learn more about what someone made and how and why they made it. I can identify strengths and possible improvements, using evidence or examples. I can reflect on my work to identify specific aspects I’d like to improve. I can ask for targeted feedback and determine the most important or interesting ideas I heard. Project-specific: I can ask insightful questions about someone's bridge model to understand their design choices, using examples from their presentation I can identify specific strengths and suggest improvements by referring to the quadratic functions they used I can reflect on my bridge design to pinpoint areas for enhancement and seek specific feedback on the mathematical strategies I applied, determining which feedback is most valuable for refining my work	I can ask questions to learn more about someone’s purpose, audience, and approach (e.g., style, craft, medium). I can use evidence or examples to identify strengths and prioritize suggestions. I can reflect on my work and use quality criteria to identify specific aspects to improve. I can ask for targeted feedback from others and decide which suggestions are most relevant and important. Project-specific: I can effectively ask questions to understand my peers' purposes and approaches in their bridge designs, and I use specific examples from their presentations to identify what they did well I can thoughtfully prioritize my feedback, suggesting improvements based on mathematical evidence When reflecting on my own work, I use quality criteria to identify areas for growth and seek targeted feedback from others, considering which suggestions will have the greatest impact on enhancing my design and presentation	I can ask questions to learn more about someone’s purpose, audience, approach, and feedback needs to focus my feedback. I can use evidence or examples to identify strengths and prioritize suggestions based on the maker’s purpose, audience, and/or approach. I can reflect on my work and use quality criteria to identify and prioritize specific aspects to improve. I can gather and integrate targeted feedback representing diverse perspectives and relevant expertise or insight. Project-specific: I can thoughtfully ask questions to understand the purpose and audience of my peers' bridge designs, focusing my feedback on their mathematical approach and real-world application I use specific examples and evidence from their work to highlight strengths and suggest improvements, ensuring my feedback aligns with their goals I reflect on my own design, using quality criteria to identify what could be enhanced, and actively seek diverse perspectives to refine my project based on expert insights and peer reviews
Learn with Purpose	Reflect	With guidance, I can share what I liked about something I did or created. With guidance, I can notice when something didn’t turn out how I wanted and describe what happened. I can notice and name when something is easy or hard for me (e.g., socially, academically, emotionally). Project-specific: I can describe what I enjoyed about building my bridge model and explain why I chose certain design features I notice when my calculations using quadratic functions didn't match my expectations and can describe how I adjusted my approach I can identify which parts of solving quadratic equations were easy for me and which parts required more effort	I can name and celebrate something I learned or did well. I can identify when something didn’t turn out how I wanted and describe what happened. With guidance, I can name something I want to try doing differently in the future based on what I learned or experienced. I can identify learning tasks that are easy or hard for me and share worries or wonders I have about learning/trying something. Project-specific: I can describe what I learned about using quadratic functions in my bridge design, celebrating parts of my project that worked well I can explain when my design didn't meet my expectations and what I learned from it With some help, I can think of new strategies to improve my bridge model next time I can also share which parts of the project I found easy or challenging and discuss any questions I have about using quadratic functions in real-world situations	I can name and celebrate something I learned or did well and explain the steps I took to achieve it. I can ask myself questions about my learning process (e.g., Did I follow my plan? Did I understand what was needed?) and name something I might do differently in the future based on what I learned or experienced. I can identify some of my learning strengths and challenges when presented with a task (e.g., steps I take, what is difficult or easy for me). Project-specific: I can recognize and celebrate my success in designing a bridge model by explaining how I used quadratic functions to improve its stability I can ask myself questions about my design process, like whether my calculations and graphs helped achieve the desired arch strength, and identify what I could do differently next time I can describe my strengths in solving quadratic equations and graphing functions, and acknowledge areas where I can improve, such as rewriting expressions to reveal important features	I can explain and critique something I learned or did, celebrating my strengths, contributions, and/or learning. I can ask myself questions about my learning process, connect the results of my actions to what I know about myself (e.g., I know I get distracted easily, so next time I’ll choose a quieter space to work), and generate ideas about what I might do differently in the future based on what I learned or experienced. I can identify some of my learning strengths and challenges and reflect on previous learning experiences to predict the resources of time, effort, and energy a new task will require. Project-specific: I can explain what I learned about using quadratic functions in bridge design and evaluate my progress by recognizing my strengths and areas for growth I can ask myself questions about how I solved quadratic equations and inequalities, and connect my experiences to improve future projects, like choosing better study environments I can identify my learning strengths, such as my ability to graph functions and interpret key features, and predict how much time and effort a new math task might require based on past experiences	I can explain and critique my learning experiences and celebrate my strengths, contributions, and learning. I can draw on my understanding of my learning process as well as my experience and/or interactions with others to generate ideas about what I might do differently in the future. I can identify my learning strengths and challenges; make informed predictions about the resources of time, effort, and energy a new task will require of me; and develop and practice strategies and systems to help manage my resources and any anticipated challenges. Project-specific: I can thoughtfully analyze and evaluate my bridge design project by explaining how I applied quadratic functions to enhance the strength and stability of my model I can celebrate my strengths and contributions, and I use my experiences and feedback from others to generate ideas for future improvements I am able to identify and articulate my learning strengths and challenges, predict the resources needed for future tasks, and develop strategies to manage any anticipated challenges effectively	I can explain and critique my learning experiences and celebrate my strengths, contributions, and learning, including my creative risk-taking. I can draw on my understanding of my learning process, experience, and/or interactions with others to generate ideas about what I want to learn, pursue, and/or do differently in the future. I can share and advocate for my learning strengths and needs, anticipate the resources of time and energy tasks will require, and routinely use learning strategies and systems with flexibility. I can reflect on multiple aspects of my learning process, identify how they influenced my results, and make a plan to strengthen or make changes to my process in the future. Project-specific: I can thoughtfully reflect on my bridge design project by analyzing how my use of quadratic functions influenced the strength and stability of my model I can identify and celebrate the creative risks I took and how they contributed to my learning and the final presentation I can clearly articulate my learning process and the strategies I used, and I can plan for future projects by identifying areas where I can improve, such as refining my mathematical calculations or enhancing my presentation skills
Learn with Purpose	Engage in discussion	When it’s my turn, I can share an idea or respond to the question or prompt. Project-specific: I can confidently share my ideas during discussions about bridge design and quadratic functions, using specific examples from my project, and I can respond thoughtfully to questions or prompts, demonstrating my understanding of how quadratic equations contribute to optimal bridge stability and strength	When it’s my turn, I can share my ideas or respond to the question or prompt. I can ask a question about the topic. Project-specific: I can participate in discussions by sharing my thoughts on how I used quadratic functions to design my bridge model I can ask questions about how different materials and design choices affect the strength and stability of a bridge	I can respond to a question or prompt in a way that shows my knowledge of and/or curiosity about the topic. I can pose a specific question related to the topic and demonstrate active listening (e.g., verbal and nonverbal affirmations, paraphrasing to show understanding, asking for clarification). Project-specific: I can respond to questions about quadratic functions and bridge design by demonstrating my understanding through clear explanations and examples I can ask thoughtful questions related to the project and actively listen to my peers' ideas, using verbal affirmations and paraphrasing to show I understand their points	I can respond to a question or prompt in a way that shows my knowledge of and/or curiosity about the topic. I can pose questions about the topic to learn more about other people’s ideas while demonstrating active listening. I can practice building on the ideas of others (e.g., elaborating on the idea, connecting to related ideas or evidence). Project-specific: I can confidently respond to questions about quadratic functions and bridge design, showcasing my understanding and curiosity I ask thoughtful questions to learn more about others' perspectives and actively listen to their responses I can build on others' ideas by making connections to mathematical concepts like solving equations or graphing functions, and I enjoy elaborating on these ideas during discussions	I can respond to a question, prompt, or comment in a way that shows my knowledge of and/or curiosity about the topic and that offers a new insight, perspective, or evidence-based connection. I can pose open-ended questions and use active listening to learn more about views/perspectives that differ from mine. I can build on the ideas of others and/or challenge them to enhance the discussion (e.g., asking probing questions, elevating minoritized perspectives, citing relevant evidence, addressing errors in data or logic). I can adjust my stance or opinion when presented with new information and/or perspectives and explain shifts in my thinking. Project-specific: I can actively engage in discussions about bridge design by responding with insights that connect quadratic functions to real-world applications I can ask open-ended questions to explore different perspectives on design choices, and I listen thoughtfully to others' ideas I can enhance the conversation by challenging assumptions with evidence from my mathematical calculations and graphs, and I am open to adjusting my views when presented with new information or perspectives	I can respond to questions, prompts, or comments in a way that exhibits deep knowledge and/or curiosity about the topic and that offers new insight, perspective, or evidence-based connections. I can monitor and adjust my engagement style to contribute to a balanced and inclusive discussion. I can pose questions to build my understanding or broaden my perspective (e.g., prompt elaboration, surface underlying issues or interests) while maintaining an affirming and inclusive tone. I can build on the ideas of others and/or challenge them to deepen the discussion or help move it forward. I can adjust my stance or opinion when presented with new information and/or perspectives, demonstrate humility with new understandings, and acknowledge and explain shifts in my thinking. Project-specific: I can actively engage in discussions about quadratic functions and bridge design by responding thoughtfully to questions and comments, offering new insights or connections based on my research and calculations I can pose questions to deepen my understanding and adjust my engagement to ensure everyone has a chance to contribute By building on others' ideas and considering different perspectives, I can enhance the conversation and adapt my views when presented with new information, demonstrating flexibility and openness in my learning

Learning Journey

Empathize

Students will engage with local engineers to explore real-life applications of quadratic functions in bridge design, fostering empathy and understanding of community needs and insights that will guide their project development.

Days 1 - 2