2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards

1. 2010 Alabama Course of Study: MathematicsCollege- and Career-Ready Standards Literacy Standards for Grades 6 – 12

2. APPENDIX CLiteracy Standards for Grades 6 – 12History/Social Studies, Science and Technical Subjects “These standards are designed to supplement students’ learning of the mathematical standards by helping them meet the challenges of reading, writing, speaking, listening, and language in the field of mathematics.”

3. It is essential for educators to: • select and develop resources that ensure students can connect their curriculum with the real world. • help students recognize and apply math concepts in areas outside of the mathematics classroom. • provide students with opportunities to participate in mathematical investigations. • help students develop problem-solving techniques and skills which enable them to interconnect ideas and build on existing content.

4. Basis of Literacy Standards The Literacy Standards for Reading and Writing are based on the College and Career Readiness (CCR) anchor standards as outlined in the English Language Arts (ELA) common core. Both of which are outlined in Appendix C.

5. Layout of the Literacy Standards Appendix C p. 128 College and Career Readiness Anchor Standards for Reading p. 129 Reading Standards for Literacy in History/Social Studies 6-12 p. 130 Reading Standards for Science and Technical Subjects 6-12 p. 131 College and Career Readiness Anchor Standards for Writing p. 132 Writing Standards for Literacy in History/Social Studies, Science and Technical Subjects grades 6-12 (through p. 134)

6. 1st Grade Mathematics / Standard 2 Course Standard: 2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. ELA Reading Standard: Grade 1, Standard 10: Ask and answer questions about key details in a text. Problem: I was cleaning the classroom. I found 5 pencils on the floor. I found 6 pencils under the window. I found 2 pencils on the desk. How many pencils did I find? • Teacher/Instructional Leader Notes: • Assess for student understanding by asking questions regarding details of the problem. • Reading problems provide the teacher with tremendous insight into students understanding.

7. 4th Grade Mathematics / Standard 11 Course Standard: 11. Find whole-number quotients and remainders with up to four-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. ELA Writing Standard: Grade 4, Standard 23d: Write informative or explanatory texts to examine a topic and convey ideas and information clearly. d. Use precise language and domain-specific vocabulary to inform about or explain the topic. Problem: Solve the division problem 56 ÷ 4. You may use cubes, grid paper, drawings, or other math tools to help you. Explain how you solved the problem. • Teacher/Instructional Leader Notes: • After students have computed the answer to the problem, ask them to write a story problem for the mathematical problem. • Requiring students to write an explanation of their answers provides insight for the teacher into student understanding.

8. Snapshot ViewNotice that the ten reading standards are in grade spans.6-89-1011-12A great layout to assist teachers in differentiating instruction!

9. A closer look: 1.Cite specific textual evidence to support analysis of science and technical texts. 1. Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions. 1. Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account.

10. Famous Mathematician Cards (aka: ‘The Baseball Card Project’) FRONT BACK

11. Another Reading Standard: Grades 6 – 8: Students should be able to read a word problem and create an image of some sort (diagrams, graphs, etc…) Grades 9 – 10: Students should ALSO be able to reverse this skill: translate diagrams and charts into meaningful problems or equations. Grades 11 – 12: Finally, they should expand this skill to other sources (video, data) and use it to address questions and solve problems.

12. Grade 8 Mathematics / Standard 22 CourseStandard: 22. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. ELA Standard: Reading Standard 7: Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually. Problem: Settlers in the Old West would often fashion tents out of a piece of cloth thrown over tent poles. They would secure it to the to the ground with stakes forming an isosceles triangle for the opening. How long would the cloth have to be so that the opening of the tent was 4 meters high and 6 meters wide?

13. Original Problem: Settlers in the Old West would often fashion tents out of a piece of cloth thrown over tent poles. They would secure it to the to the ground with stakes forming an isosceles triangle for the opening. How long would the cloth have to be so that the opening of the tent was 4 meters high and 6 meters wide? Solution: The vertical pole forms 2 right triangles, so I am using the Pythagorean Theorem. a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 5 = c But, there are two sides to the tent, so the material needs to be 10 meters long. Answer: The cloth needs to be 10 meters long. 4 6 3 (1/2 of 6) Teacher/Instructional Leader Notes: • Expressing answers as a complete sentence incorporates routine writing. • Continuallyexpress the importance of accuracy and clarity in diagrams. • Assess student ability to translate the word problem into a diagram separately from the ability to solve a problem. • It is vital to include word problems in mathematics instruction. • It is equally important students be given an opportunity to share idea’s or concerns about their work and to receive timely feedback.

14. Snapshot View : Writing Standards (page 1 of 3)

15. REVISITING: Grade8 Standard 22 CourseStandard: 22. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Original Problem: Settlers in the Old West would often fashion tents out of a piece of cloth thrown over tent poles. They would secure it to the to the ground with stakes forming an isosceles triangle for the opening. How long would the cloth have to be so that the opening of the tent was 4 meters high and 6 meters wide? NEXT Standard: Writing Standard #1: Write arguments focused on discipline-specific content. NEW ASSIGNMENT: The teacher presents solutions from the original assignment which were labeled incorrectly, had faulty logic and/or an incorrect solution. Randomly distribute and direct students to write a brief argument for each solution to either defend or dispute the logic used.

16. Snapshot View : Writing Standards p. 2 • Close-up: • 2. Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes: • Introduction • Development of ideas • Transitions • Vocabulary • Style • Conclusion

17. Writing Standard #3 In science and technical subjects, students must be able to write precise enough descriptions of the step-by-step procedures they use in their investigations or technical work so others can replicate them and (possibly) reach the same results.

18. Snapshot View : Writing Standards p. 3

19. A closer look: *The same for all three levels 10. Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for range of discipline-specific tasks, purposes, and audiences.

20. Grade 8 / Geometry Standard 18 • CourseStandard: • 18. Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. [G3] ELA Standard(s): • Reading Standard 7: Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually. • Writing Standard 2f: Provide a concluding statement that follows from and supports the information presented. Problem: Mr. Smith asked his students to plot the following points in order, connecting them to form a triangle: (3,0) (7, 1) (4, 5) (3,0). Here are the student responses. Which is correct? Describe the errors in logic made on the remaining three and the result of those errors. A B C D.

21. Possible Solution: A B C D • Triangle A is plotted correctly • In triangle B, the student switched the (x,y) coordinates. Instead of plotting (3,0) they plotted (0, 3). The student might be confused about which axis is the x and which axis is the y. • In Triangle C, the student went in the negative direction for the x coordinate but plotted the y correctly, this caused a reflection around the y-axis. • In triangle D the student plotted the x coordinate correctly but went in the negative direction for the y, this caused a rotation and a shift in the graph.

22. Teacher/Teacher Leader Notes • Is the student’s mathematical logic correct? • Can they describe errors found in others’ mathematical thinking? • Activities like this may be used as a bell ringer (sparking discussion prior to a lesson) or as an exit slip to assess understanding. • It is important that the responses are assessed by the teacher through grading or discussion.

23. Final Thought:The Literacy Standards Allow Flexibility in Reading and Writing Predictions Proofs Compare/Contrast methods Reflection Journals Word Problems Summarize Writing directions for replication by others Descriptions of Process or change

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25. Contact Information ALSDE Office of Student Learning Curriculum and Instruction Section Cindy Freeman, Mathematics Specialist Phone: 334.353.5321 E-mail: cfreeman@alsde.edu