Alabama Course of Study: Mathematics Building Mathematical ...

Alabama Course of Study: Mathematics Building Mathematical ...

2010 Alabama Course of Study: Mathematics College- and Career-Ready Standards Literacy Standards for Grades 6 12 APPENDIX C Literacy Standards for Grades 6 12 History/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. 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. 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) Snapshot View Notice that the ten reading standards are in grade spans. 6-8 9-10 11-12 A great layout to assist teachers in differentiating instruction! A closer look: 1.Cite specific 1. Cite specific textual

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

Famous Mathematician Cards (aka: The Baseball Card Project) FRONT BACK 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. Grade 8 Mathematics / Standard 22 Course Standard: 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? Solution: 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? The vertical pole forms 2 right

triangles, so I am using the Pythagorean 4 Theorem. a2 + b 2 = c 2 32 + 42 = c2 9 + 16 = c2 25 = c2 6 5=c But, there are two sides to the 3 (1/2 of 6) tent, so theNotes: material needs to Teacher/Instructional Teacher/Instructional Leader Leader Notes: Expressing answers as a complete be 10 meters long. sentence incorporates routine

Expressing answers as a complete sentence incorporates routine writing. writing. C of and clarity in Continually ontinually express express the the importance importance of accuracy accuracy andcloth clarity needs in diagrams. diagrams. Answer: The to be

A ssess student ability to translate the word problem into a diagram Assess student ability to translate the word problem into a diagram separately separately 10 meters long. from the ability to solve a problem.

from the ability to solve a problem. IItt is is vital vital to to include include word word problems problems in in mathematics mathematics instruction. instruction. IItt is is equally equally important important students students be be given given an an opportunity opportunity to to share share ideas ideas or or

concerns about their work and to receive timely feedback. concerns about their work and to receive timely feedback. Algebra I / Standard 11 Course Course Standard: Standard: 11. Create equations (inequalities) in one variable and use them to solve problems (linear, quadratic, simple rational, exponential) . ELA

ELA Standard: Standard: Reading #4: Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to their grade level. Problem: Identify the word problems below as linear, quadratic, simple rational or exponential stating evidence for your choice. Then, write an equation using variables when appropriate. Solve your equation. 1. A car travels 125 miles in 3 hours. How far would it travel in 5 hours? 2. At a concert, Nabila purchased three t-shirts and a concert program that cost $15. In total, Nabila spent $90. Find the cost of a single t-shirt if they were all the same price. 3. The product of two consecutive positive even integers is 14 more than their sum. Find the integers. Solution:

1.The first problem is a simple rational equation. It compares miles and hours: so, 3x = 625 and x = 208.3 miles * Answer: The car would travel 208.3 miles in 5 hours. 2.The second problem is linear because it has one unknown, the price of the tshirts. Let x be the number of t-shirts 3x+15 = 90 so, x = 25 Answer: The cost of each t-shirt is $25. 3.The final problem is quadratic because it has two unknowns but the second one is related to the first. Let x be the initial even number; (x+2) is the next consecutive even integer x(x+2) = 14 + x + (x+2) x2 + 2x = 16 + 2x x2 = 16, Answer: The first number is 4 and the second number is 6 . x = 4. Proof: 6+4 = 10 and 6(4) = 24 which is 14 more than 10.

Teacher/Instructional Leader Notes: Assess for student logic and ability to pull key vocabulary used in mathematical text. Reading problems provide the teacher with tremendous insight into students understanding. Snapshot View : Writing Standards (page 1 of 3) REVISITING: Algebra I, Standard 11 Original Original Problem: Identify the word problems below as Original Standard: Standard: 11. Create equations (inequalities in one variable and use them to solve problems (linear, quadratic,

simple rational, exponential) . Linear, quadratic, simple rational or exponential stating evidence for your choice. Then, write an equation using variables when appropriate. Solve your equation. 1. A car travels 125 miles in 3 hours. How far would it travel in 5 hours? 2. At a concert, Nabila purchased three t-shirts and a concert program that cost $15. In total, Nabila spent $90. Find the cost of a single t-shirt if they all had the same price. 3. The product of two consecutive positive even integers is 14 more than their sum. Find the integers. NEXT Standard: Writing Standard #1: Write arguments focused on discipline-specific content. NEW ASSIGNMENT: The teacher presents problems from the original assignment which were labeled incorrectly, had faulty logic and/or incorrect solutions. Randomly distribute and direct students to write a brief

argument for each problem to either defend or dispute the logic used. 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 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. Snapshot View : Writing Standards p. 3 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 disciplinespecific tasks, purposes, and audiences. Grade 8 / Geometry Standard 18 Course Course Standard: Standard: ELA Standard(s):

18. Describe the effect Reading Standard 7: Integrate of dilations, quantitative or technical information translations, expressed in words in a text with a rotations and version of that information expressed reflections on twovisually. dimensional figures Writing Standard 2f: Provide a concluding using coordinates. statement that follows from and [G3] 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.

Possible Solution: A B C D a) Triangle A is plotted correctly b) 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. c) 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. d) 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. Final Thought:

The Literacy Standards allow Flexibility in Reading and Writing t s Predictions a f r t n o C Proo / e r a p s s Reflect m d o o

C h i on met Journal rd s Summariz W o W em s ritin l g di e b o for r re c t Pr ions epli Descriptions of cati b on

Process or change y oth er s ?? Questions ?? Contact Information ALSDE Office of Student Learning Curriculum and Instruction Cindy Freeman, Mathematics Specialist Phone: 334.353.5321 E-mail: [email protected]

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