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Lines and Linear Equations

Explore components of a formative assessment lesson, engineer effective classroom activities, analyze student learning, and activate students as active learners and resources. Engage in activities like "The Race" and "Graphs Working Together" to strengthen understanding of lines and linear equations.

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Lines and Linear Equations

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  1. Lines and Linear Equations Projector Resources

  2. Formative Assessment Lesson Lines and Linear Equations Mathematics Assessment Resource Service University of Nottingham & UC Berkeley For more details, visit http://map.mathshell.org Facilitated by: Jenny Ray, Mathematics Specialist Kentucky Dept. of Education / NKCES www.JennyRay.net

  3. Participant Learning Target • I can analyze components of a Formative Assessment Lesson • After engaging in a formative lesson from a student’s perspective, participants will determine how teachers can • Engineer effective classroom discussions, questions, activities, and tasks that elicit evidence of students’ learning, • Provide feedback that moves learners forward, • Activate students as owners of their own learning, • Activate students as learning resources for one another.

  4. Assessment Task The Race Read through the questions and try to answer them as carefully as you can. Please work independently. (This is important.)

  5. Important Note: • Due to time constraints, the next component of the Formative Assessment Lesson must be envisioned by participants. • After the initial assessment, the teacher must collect student responses and note what their work reveals about their current levels of understanding, as well as different approaches. • Help students make further progress by summarizing their difficulties as a list of questions.

  6. Examples of Common Issues & Questions • Student assumes Maggie is running the fastest because at 5 seconds her line is above Emma’s. • Student fails to notice the distance increases by 5’s, not 1’s. • How can you figure out the speed of each runner? • What is the scale on the vertical and horizontal axes for each graph?

  7. Lesson Introduction • Please use white paper and a pen/pencil to show me your responses to my questions.

  8. Flowing Liquid

  9. Flowing Liquid

  10. Liquid flowing out of the top prism 1

  11. Liquid flowing out of the top prism 2

  12. Liquid flowing out of the top prism 3

  13. Liquid flowing out of the top prism 4

  14. Liquid flowing out of the top prism 5

  15. Liquid flowing out of the top prism 6

  16. Graphs

  17. Working Together The graphs represent the flow of a liquid either out of the top prism or into the bottom prism of the container. Take turns to match two cards that represent the movement of water in the same container. Place the cards next to each other, not on top, so that everyone can see. When you match two cards, explain how you came to your decision. Your partner should either explain that reasoning again in his or her own words, or challenge the reasons you gave. Some graphs are missing information, such as a scale along an axis. You will need to add this scale. You both need to be able to agree on and explain the match of every card.

  18. Sharing Work If you are staying at your desk, be ready to explain the reasons for your group’s graph matches. If you are visiting another group, copy your matches onto a piece of paper. Go to another group’s desk and check to see which matches are different from your own. If there are differences, ask for an explanation. If you still don’t agree, explain your own thinking. When you return to your own desk, you need to consider as a group whether to make any changes to your own work.

  19. Whole Class Discussion

  20. Extension: • Consider the equation: h = 5t + 1 This equation describes the flow of liquid in one of the prisms of the container. On your whiteboards write an equation that describes the flow of the liquid in the other prism of the same container.

  21. Extension: • Consider the equation: h = 5t + 1 This equation describes the flow of liquid in one of the prisms of the container. Write an equation that describes the flow of the liquid in this prism that takes half the time.

  22. Reviewing the Assessment Task • Look again at your original, individual solutions to the problems and consider the comments on your paper. • Make some notes on what you have learned during the lesson. • Use what you have learned to complete the new assessment task / revise your answers.

  23. Participant Learning Target • I can analyze components of a Formative Assessment Lesson • After engaging in a formative lesson from a student’s perspective, participants will determine how teachers can • Engineer effective classroom discussions, questions, activities, and tasks that elicit evidence of students’ learning, • Provide feedback that moves learners forward, • Activate students as owners of their own learning, • Activate students as learning resources for one another. REVISITED

  24. CONTACT INFORMATION Jenny.Ray@education.ky.gov www.JennyRay.net Thank you for your active participation! Please let me know if I can assist you in any way.

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