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Algebra Professional Development

Linear Sentences. Algebra Professional Development. End of the Year Assessments. Technology Enhanced (TE). As you look at the sample items, identify: One mathematical practice needed to answer this type of items

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Algebra Professional Development

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  1. Linear Sentences Algebra Professional Development

  2. End of the Year Assessments

  3. Technology Enhanced (TE) As you look at the sample items, identify: • One mathematical practice needed to answer this type of items • One thing you have to address with your students so they are better prepared for this type of assessment item

  4. Constructed Response (CR) As you look at the sample items, identify: • One mathematical practice needed to answer this type of items • One thing you have to address with your students so they are better prepared for this type of assessment item

  5. Performance Task As you look at the sample items, identify: • One mathematical practice needed to answer this type of items • One thing you have to address with your students so they are better prepared for this type of assessment item

  6. MODULE 2 Desired Outcome: Participants will experience a rigorous concept task

  7. CCSS Domains on Linear Sentences (Equations) • Algebra - Creating Equations • Algebra – Reasoning with Equations and Inequalities • Functions – Interpreting Functions • Functions – Linear, Quadratic, and Exponential Models

  8. CCSS on Linear equations • A-CED.1 F-IF.5 • A-CED.2 F-IF.6 • A-REI.1 F-IF.7a • A-REI.10 F-LE.1b • F-IF.1 F-LE.2 • F-IF.4 F-LE.5 • F-LE.1a

  9. Algebra 1 Progression 8EE5 7EE4a ACED 2 8EE8 FIF 6 8F1 6EE5 8F2 7RP2 AREI 10 FLE 1b 8F5 7G1 FIF 4 8F4 FIF 7a 6SP2 8SP2 6NS8

  10. CCSS on Linear equations A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

  11. CCSS on Linear equations F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

  12. CONCEPTUAL CATEGORY: ALGEBRADOMAIN: CREATING EQUATIONSCLUSTER: CREATE EQUATIONS THAT DESCRIBE NUMBERS OR RELATIONSHIPS • As a table/ group, discuss: • What is the purpose of the cluster? • What is the connection between the cluster and the standards? • What is one thing you notice that stands out about the standards? • What is one thing you are wondering about?

  13. Mathematical Practice 3 Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

  14. Concept Lesson: “Tying the Knot!”

  15. Concept Lesson: “Tying the Knot!” Your task is to explore the relationship between the length of a rope and the number of knots tied in the rope. a) By measuring the length of the rope after you tie each knot, investigate the relationship between the number of knots and the length of the rope. b) Express this relationship in a table, a graph, a written description, and an algebraic formula.

  16. Extension 1 What is always true about the values of p and q if p= a certain number of knots in the rope and q=the corresponding length of the knotted rope ? What is sometimes (but not always) true about values of p and q ? What is never true about values of p and q ?

  17. Extension 2 Given a point (m, n), create an equation for a linear function that falls above this point.  Create an equation for a linear function that falls below this point. Pass your equations to a partner and challenge them to determine – without graphing – which equation is above and which equation is below (m, n). If Jane came up with an equation that has point (3,110) and above a given point on the line (2,100) and Jose argues that the equation is below. Who do you think is right and why?

  18. Using Mathematical Practice 3 • How might you use Math Practice 3 to help students answer more questions like the one we used today? • Be specific about the experiences you will provide students, including EL’s, SEL’s, GATE, and SWD. Lesson Debrief: “Tying the Knot!” What EL/SEL strategies were modeled? How did they contribute to building the important conceptual understandings of the task?

  19. MODULE 3 Desired Outcome: Participants will work with the Thinking Through a Lesson Protocol (TTLP) to plan the implementation of the Tying the Knot concept task

  20. Thinking Through a Lesson Protocol How will we set upthe lesson? How will the students explorethe concept? How will the students share, discuss, and analyzetheir solutions?

  21. Thinking Through a Lesson Protocol

  22. Planning for Implementation Thinking Through a Lesson Protocol (TTLP) • Read through the lesson and discuss how the TTLP was used to design it. • What instructional strategies could be added to the lesson that would contribute to increased access for all learners? • EL • SEL • Gifted • SWD

  23. Reflect • How would the use of the TTLP and Concept Task help you provide access to rigor and SMP 1 and SMP 3?

  24. MODULE 4 Desired Outcome: Participants will learn about explicit strategies that foster the development of academic language and increase students’ access to core mathematics content

  25. Access to Math Content Strategies • Use of Multiple Representations • Four Fold Graphic Organizer • Compare and Contrast • Comparing Linear Graphs • Comparing Multiple Representations • Patterns & Functions

  26. Strategy: Comparing Representations “Matching Representations” Activity • Y is always 4x more

  27. Comparing Multiple Representations Take the cards out of your envelope and spread them out on your table. Match together the verbal descriptions, tabular representations, graphs, and symbolic representation.

  28. Comparing Multiple Representations In a small group, discuss: What helped you to identify the members of each set? Each group will then share one set of four representations and explain how they identified the members of that set.

  29. Comparing Multiple Representations How does this activity enrich the students’ understanding of different linear representations? How might you use a similar type of activity in a different unit of study?

  30. Promoting MathematicalDiscourse in the Classroom • Let’s Talk Article Share with your triad the “most important thing” about the section you read.

  31. Reflect & Summarize • What are some of strategies used that will specifically address EL needs? • How might the strategies modeled today be used with other concepts? • What changes do you foresee in your students’ understanding after utilizing these strategies? • How will you make time in your day-to-day lessons to incorporate these strategies?

  32. Thank you for ALL you do to improve achievement for ALL of our students!

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