2. Why a New Curriculum for Algebra I ? P.A.10-111 Secondary School Reform; including “model” curricula and end of course exams CCSSM Common Core State Standards for Mathematics (adopted by Connecticut in 2010)

3. New High School Requirements (P.A. 10-111) Starting with class of 2020. 25 credits for graduation with 8 credits in STEM subjects. 4 credits in mathematics (including Algebra I, geometry, and Algebra II or probability/statistics). Model curricula to be developed for 8 courses. Common final examinations for Algebra I, geometry, biology, grade 10 English, American history.

4. Breakdown of Credits

5. Algebra I

6. A Brief History 2009 – State of CT awarded the Mathematics and Science Partnership Grant to the CT Academy of Science and Engineering to develop a model curriculum for Algebra I Curriculum supported CT Secondary Education Reform Aligns with Common Core State Standards Field-tested 2010-2013

7. CT Algebra One Partners (Curriculum Writing 2009) Associated Teachers of Mathematics in Connecticut (ATOMIC) Connecticut Academy for Education in Mathematics, Science & Technology, Inc. Connecticut Council of Leaders of Mathematics (CCLM) Mathematics Basic Skills Council of Connecticut (MBSCC) Mathematical Association of Two-Year Colleges of CT (MatyCONN) Project to Increase Mastery of Mathematics and Science (PIMMS)

8. Mathematics and Science Partnership Grant 2010-2013 Field testing in 3 phases. 80 teachers involved. Curriculum was continually improved on the basis of feedback from the field test sites. In the 3 rd year, the Education Development Center conducted a comparative study.

9. Year 1: red Year 2: blue Year 3 experimental group: green Year 3 control group: orange (adopting curriculum in 2013-14)

10. Common Core State Standards K-12 Emphasis on Focus, Coherence, Conceptual Understanding. HS standards for “College and Career Readiness”. Most HS standards identified as “CORE” with additional standards for “STEM”. Eighth grade curriculum will place major emphasis on algebra and geometry. The model curriculum developed by Connecticut is well-aligned with these standards.

11. Algebra 1 Curriculum Components 1. Guiding principles (framework) 2. Enduring understandings (critical concepts) 3. Course-level expectations 4. Pacing guidance for all eight units 5. Assessments – formative and summative 6. Unit investigations and activities 7. Culminating experience: A performance-based project 8. End-of-course exam

12. Guiding Principles of the Algebra 1 Curriculum Reasoning Principle: The curriculum must develop deep understanding of mathematical concepts and principles. Teaching Principle: The curriculum must support and illustrate effective pedagogical practices. Assessment Principle: The curriculum envisions assessment as an integral part of instruction. Technology Principle: The curriculum must make full use of technologies that increase the productivity of instruction and enrich students’ experiences.

13. Guiding Principles of the Algebra 1 Curriculum Scope Principle: The curriculum must focus on the essential ideas and processes of mathematics. Connections Principle: The curriculum must effectively organize and integrate important mathematical ideas. Context Principle: The curriculum must include situations, applications and contemporary problems, interdisciplinary in nature, that illustrate the usefulness of mathematics. Differentiation Principle: The curriculum must provide a balance of shared experiences for all students.

14. Enduring Understandings 1. The fundamental structure of algebra provides a systematic method for identifying, describing, analyzing and generalizing patterns. 2. Algebra provides a way to use numbers, symbolic notation and arithmetic operations to model, transform, simplify and solve problems efficiently. 3. Information may be represented by physical models, diagrams, data tables, graphs and symbolic expressions.

15. Enduring Understandings 4. Algebra facilitates correlation among these different representations which may give different insights to the solution of a problem. 5. Algebra provides ways to describe and classify relationships and functions and use the classifications to derive models that have practical real-world applications. 6. Algebra provides a way to explore and understand the effects of parameter changes on any function and its various representations.

16. Enduring Understandings 7. Algebra provides the underlying structure to make connections among all branches of mathematics, including measurement, geometry, calculus and statistics. 8. Innovations in technology allow users to explore and deepen their understanding of new and long- standing mathematical concepts and applications of algebra.

17. CCSS Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

18. Algebra I - Scope and Sequence Unit 1: Patterns Unit 2: Linear Equations and Inequalities Unit 3: Functions Unit 4: Linear Functions Unit 5: Scatter Plots and Trend Lines Unit 6: Systems of Linear Equations Unit 7: Introduction to Exponential Functions Unit 8: Quadratic Functions

19. Sample Group Activity Quadratics in the Kitchen The cross sections of many kitchen bowls and some cups are in the shape of a parabola. (Actually a paraboloid). Your teacher may have a right circular cone and be able to show you how you can cut it with a plane to generate a “perfect” parabola. In this experiment you will keep adding water to your bowl and will measure the depth of the water using a wooden stirrer and the diameter of the surface of the water using a thick but not stretchy string. Measure everything in millimeters (mm). Use the table below and record your measurements. Materials: Bowls, string, wooden toothpicks or coffee stirrers, colored water, ruler in (mm) and graph paper. Diameter (mm) Radius (mm) Height of Water (mm)

20. Quadratics in the Kitchen Instructions for the Experiment: 1. If the bottom of the bowl is flat, measure the diameter of the bottom before you pour in any water into the bowl. Record the diameter and radius in the table and set the corresponding height of water to 0. 2. Put a little water containing food coloring into the bowl or cup. Measure the diameter of the surface in millimeters using your string. Measure the depth at that moment. Record your measurements above. 3. Add a little more water and repeat your measurements. Record your measures above. 4. Keep repeating this step until the bowl is almost full or you have completed all 7 rows of the table. Be careful not to overflow.

21. Quadratics in the Kitchen Analyze the Data: 1. Using the graph paper your teacher provides, graph the height of the water on the vertical axis (y-axis) against the radius on the horizontal axis (x-axis). 2. Compare and contrast your graph with the graph created by another group. Does the data appear to be a linear function? Explain any similarities or differences. 3. In step one, you were asked you to plot the radius on the x axis and the height on the y axis. Based upon your knowledge about the independent and dependent variables, determine if this configuration makes sense. 4. Justify your answer by writing a logical argument that clearly incorporates your complete understanding of functions. Be sure to use appropriate mathematical vocabulary and notation in your argument.

22. Unit 8 – Investigation One Quadratics in the Kitchen

26. Sample - End of Unit Exit Ticket The Guinea Road Bridge in Stamford CT is built on a parabolic arch of stone. The function that models the archway is y = -.01x 2 +.8x +10 When applying this function, you notice that the bridge is built 10 feet above the road’s surface on both sides of the road. The x is the horizontal ground distance in feet. The y is the height of the arch above the ground (in feet). Use the picture below and your knowledge of the graphs of parabolas to answer the following questions: a. Find the maximum height of the bridge. b. Find the coordinates of the point on the road that lies directly below the vertex. c. What is the approximate length of the 4 lanes, including the lane - divider. d. Convert the given equation of this parabola to the vertex form of a quadratic function.

27. Connecticut Algebra I Curriculum - Tips for Parents The Algebra I curriculum is designed to help students develop their comprehension of algebra topics rather than simply learn step-by-step procedures. Students study algebra in the context of real-world application problems. The curriculum will help prepare students for college and career readiness and for the Smarter Balanced Assessment This curriculum was tested and revised by teachers in 21 Connecticut school districts over the past 3 years.

28. Connecticut Algebra I Curriculum - Tips for Parents Students will be working with his/her peers in class and for some projects. Students will be using a graphing calculator in class. Students will use the computer for some investigations. Students may not take as many traditional notes as in the past; notes are embedded in many activities.

29. Connecticut Algebra I Curriculum - Tips for Parents Students do not have a textbook. All activities used for classwork and homework can be accessed online at the following Moodle site: sde-cthsmoodle.cthss.cen.ct.gov/moodle/course/view.php?id=526 1.Click “Login as Guest” 2.Input passcode: csde