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CONTENT LITERACY INSTRUCTIONAL SHIFTS FOR MATH Facilitator Auddie Mastroleo ҉ OCM BOCES Network Team COMMON CORE SHIFTS ELA & CONTENT LITERACY Balancing Informational & Literary Texts (Grades PK-5) Knowledge in the Disciplines (Grades 6-12) Staircase of Complexity Text-based Answers Writing from Sources Academic Vocabulary BALANCING INFORMATIONAL & LITERARY TEXTS Range of Text Types Literature = Stories, Dramas, Poetry SHIFT 1 Grades PK-5 Informational = Literary Nonfiction, Historical, Scientific, & Technical Texts 12th grade 8th grade 4th grade 50% fiction 50% nonfiction 40% fiction 60% nonfiction 20% fiction 80% nonfiction Increase in teaching and learning with nonfiction text KNOWLEDGE IN THE DISCIPLINES Reading & Writing Literacy Standards Depending on text rather than referring to it • Complement, not replace content standards •Read a president’s speech & write a response •Read scientific papers & write an analysis SHIFT 2 Grades 6-12 Think sophisticated non-fiction •Analyze and evaluate texts within disciplines •Gain knowledge from texts that convey complex information through diagrams, charts, evidence, & illustrations Expectation of rigorous domain specific literacy instruction outside of ELA PreCCLS Core Text SHIFT 1 Balancing Informational and Literary Texts SHIFT 2 Building Knowledge in the Disciplines PostCCLS Core Texts SHIFT 1 Balancing Informational and Literary Texts SHIFT 2 Building Knowledge in the Disciplines Paired Texts: The Golden Ratio MATH PRE AND POST SHIFT NOTES TURN AND TALK With a partner… Share your initial thinking and reactions STAIRCASE OF COMPLEXITY Increase in text complexity at each grade level Qualitative Levels of meaning Structure Clarity of language Knowledge demands Quantitative Word length Sentence length Text cohesion Reader & Task SHIFT 3 Motivation Knowledge Experience Expectation of proficiency and independence in reading grade level text Appendix B: Text Exemplars and Sample Performance Tasks PRE-CCLS A ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b, a:b, or a/b, where b=0. For example, the rations 1 to 2, 1:2, and ½ all represent the same comparison. A proportion is an equation stating that two ratios are equal. In the proportion a/b=c/d, the values a and d are the extremes. The values b and c are the means. When proportion is written as a:b=c:d, the examples are the first and last positions. The means are in the two middle positions. SHIFT 3 Staircase of Complexity POST-CCLS In everyday life, we use the word ”proportion” either for the comparative relation between parts of things with respect to size or quantity or when we want to describe harmonious relationship between different parts. In mathematics, the term “proportion” is used to describe equality of the type: nine is to three as six is to two. The Golden Ratio has been used in [art, architecture, design, and music] to achieve what we might term as “visual (or audio) effectiveness.” One of the properties contributing to such effectiveness is proportion – the size and relationships of part to one another and to the whole. The history of art shows that in the long search for an elusive canon of “perfect” proportion, one would somehow automatically confer aesthetically pleasing qualities on all works of art, the Golden Ratio has proven to be the most enduring. SHIFT 3 Staircase of Complexity TEXT-BASED ANSWERS Questions tied directly to the text, but extend beyond the literal Students must cite text to support answers Personal opinions, experiences, and connections to the text are minimized in favor of what the text actually says or doesn’t say SHIFT 4 Questions are purposefully planned & direct students to closely examine the text PRE-CCLS A ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b, a:b, or a/b, where b=0. For example, the rations 1 to 2, 1:2, and ½ all represent the same comparison. A proportion is an equation stating that two ratios are equal. In the proportion a/b=c/d, the values a and d are the extremes. The values b and c are the means. When proportion is written as a:b=c:d, the examples are the first and last positions. The means are in the two middle positions. SHIFT 4 Text-based Answers Question: The ratio of the side lengths of a quadrilateral is 2:3:5:7, and its perimeter is 85ft. What is the length of the longest side? POST-CCLS In everyday life, we use the word ”proportion” either for the comparative relation between parts of things with respect to size or quantity or when we want to describe harmonious relationship between different parts. In mathematics, the term “proportion” is used to describe equality of the type: nine is to three as six is to two. The Golden Ratio has been used in [nature, art, architecture, design, and music] to achieve what we might term as “visual (or audio) effectiveness.” One of the properties contributing to such effectiveness is proportion – the size and relationships of part to one another and to the whole. The history of art shows that in the long search for an elusive canon of “perfect” proportion, one would somehow automatically confer aesthetically pleasing qualities on all works of art, the Golden Ratio has proven to be the most enduring. SHIFT 4 Text-based Answers Question: Describe how the idea of proportion can be applied to mathematical concepts as well as life and culture. Use specific examples from the text to support your answer. MATH PRE AND POST SHIFTS NOTES TURN AND TALK With a partner… Share your initial thinking and reactions WRITING FROM SOURCES Three Text Types Argument Informational/ Explanatory Writing Narrative Writing SHIFT 5 Supporting a claim with sound reasoning and relevant evidence Increase subject knowledge Explain a process Enhance comprehension Conveys experience i.e. fictional stories, memoirs, anecdotes, autobiographies Argumentative writing is especially prominent in the CCLS Appendix C: Samples of Student Writing Pre-CCLS 1. Is the ratio 6:7 the same as 7:6? Why or why not? 2. Susan wants to know if the fractions 3/7 and 12/18 are equivalent. Explain how she can use the properties of proportions to find out. 3. Copy and complete the graphic organizer. In the boxes, write the definition of a proportion, the properties of proportions, and examples and nonexamples of a proportion. SHIFT 5 Writing from Sources Post-CCLS Architect, mathematician, and engineer, Richard Buckminster Fuller once said, “When I am working on a problem, I never think about beauty. I think only of how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong.” Use your knowledge of proportions and the text, The Golden Ratio to agree or disagree with this quote. Define and explain the mystery of the golden ratio. Provide examples of mathematical and real life applications of the golden ratio. Show the mathematics of the golden ratio as it applies to your examples. SHIFT 5 Writing from Sources ACADEMIC VOCABULARY Tier One Words • Words of everyday speech Tier Two Words • Not specific to any one academic area • Generally not well-defined by context or explicitly defined within a text • Wide applicability to many types of reading Tier Three Words • Domain specific • Low-frequency • Often explicitly defined • Heavily scaffolded SHIFT 6 Ramp up instruction of Tier Two words Pre-CCLS ratio SHIFT 6 proportion extremes means Academic Vocabulary Post-CCLS Tier 3 Words Tier 2 Words ratio harmonious proportion intriguing extremes elusive means aesthetic SHIFT 6 Academic Vocabulary MATH PRE AND POST SHIFTS NOTES TURN AND TALK With a partner… Share your initial thinking and reactions QUESTIONS? CONCERNS? NOTICES?