Math & Nature  Geometry & Biology ◦ CCSS  MACC.912.G-MG.1.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).  MACC.K12.MP.1.1: Make sense of problems and persevere in solving them.  MACC.K12.MP.4.1: Model with mathematics
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Math & Nature  Geometry & Biology ◦ CCSS  MACC.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects (e.g. modeling a tree trunk or a human torso as a cylinder.)  MACC.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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MACC.912.G-MG.1.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). MACC.912.G-MG.1.3: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios)
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Math & Nature  Geometry & Biology ◦ CCSS  G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).  G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).  G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
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Example: Foundational Degree Requirements Communication - Oral: Recognize, send, and respond to communications for varied audiences both as speaker and listener. (LEAP Communication) (State Board Core, Communication) (HS Language Arts - Speech) Complete 3 credits ____ COMM 101 Critical/Creative Thinking and Problem Solving: Engage and demonstrate the ability to analyze and evaluate information and arguments; select or design appropriate frameworks and strategies to solve problems in multiple contexts individually and collaboratively. (LEAP Critical and Creative thinking) (Across the curriculum) (HS Humanities/Fine Arts/Interdisciplinary) Complete 3 credits. ____ ENGL 175 Introduction to Literature 3 ____ ENGL 257 Literature of Western Civilization 3 ____ ENGL 258 Literature of Western Civilization 3 ____ ENGL 267 Survey of English Literature 3 ____ ENGL 268 Survey of English Literature 3 ____ ENGL 271 Introduction to Shakespeare 3 (300 L) ____ ENGL 277 Survey of American Literature 3 (300 L) ____ ENGL 278 Survey of American Literature 3 ____ ENGL 285 American Indian Literature 3 (400 L) ____ ENGL 295 Contemp. U.S. Multicultural Literature 3 ____ FLAN 207 Contemporary World Culture 3 ____ INTR 200 Interdisciplinary Seminar 3 ____ PHIL 201 Logic and Critical Thinking 3 Communication – Written: Recognize, send, and respond to written communications for varied audiences as both writer and reader. (LEAP Communication and LEAP Information Literacy) (State Board Core, English Comp) (HS Language Arts - English) Complete 6 credits ____ ENGL 101 ____ ENGL 102 Mathematical and Symbolic Reasoning: Apply mathematical reasoning to investigate and solve problems. (LEAP Quantitative Literacy). (State Board Core, Mathematics) (HS Mathematics) Complete 3-4 credits ____ MATH 123 Contemporary Mathematics 3 ____ MATH 130 Finite Mathematics 4 ____ MATH 143 College Algebra 3 ____ MATH 144 Analytic Trigonometry 2 ____ MATH 147 Pre-Calculus 5 ____ MATH 160 Survey of Calculus 4 ____ MATH 170 Analytic Geometry & Calculus I 4 ____ MATH 175 Analytic Geometry & Calculus II 4 ____ MATH 187 Discrete Mathematics 4 ____ MATH 253 Principles of Applied Statistics 3 ____ MATH 275 Analytic Geometry & Calculus III 4
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References                 Bart, W. (1970). Mathematics Education: The Views of Zoltan Dienes. The School Review, Vol. 78, No. 3. 3. Brownell, W. (1945). The Natural Sciences and Mathematics. Review of Education Research, Vol. 15, No. 4. 4. Brownell, W. (1947). The Place of Meaning in the Teaching of Arithmetic. The Elementary School Journal, Journal, Vol. 47, No. 5. Bruner, J. (1966). Toward a Theory of Instruction. Instruction. W.W. Norton & Company, New York. Bruner, J. (1966). The Culture of Education. Education. Harvard University Press, Cambridge, MA. Bruner, J. (1966). The Process of Education. Education. Harvard University Press, Cambridge, MA. Dienes, Z. (1960). Building Up Mathematics. Mathematics. Hutchinson Educational LTD, London. Hiebert, J, Carpenter, T, & others. (1996). Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics. Educational Researcher, Vol. 25, No. 4. Hiebert, J, Carpenter, T, & others. (2000). Making Sense: teaching and learning mathematics with understanding. understanding. Kilpatrick, J., Wearver, J.F. (1977). The Place of William A. Brownell in Mathematics Education. Journal for Research in Mathematics Education, Vol. 8, No. 5 Noddings, N. (1994). William Brownell and The Search for Meaning. Journal for Research in Mathematics Education, Vol. 24, No. 5. 5. Schoenfeld, A. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics. Handbook on Research for Mathematics Teaching and Learning. Learning. Schoenfeld, A. (2005). Mathematics Teaching and Learning. . University of California, Berkeley. Learning Skemp, R. (1971). Psychology of Learning Math. Math. Penguin Books Ltd, Harmondsworth. Skemp, R. (1976). Relational Understanding and Instrumental Understanding. Understanding. Mathematics Teaching, 77. 77. Skemp, R. (1987). The Psychology of Knowing Math. Math. Lawrence Erlbaum Associates. Hillsdale, NJ.
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Math & Nature  Geometry & Biology ◦ CCSS  MACC.912.G-GMD.1.3 Use volume formulas for cylinders, pyramids, cones and spheres to solve problems.  MACC.912.G-GMD.2.4 Identify the shapes of twodimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
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Math & Nature  Geometry & Biology ◦ CCSS  MACC.912.G-GMD.1.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.  MACC.912.G-GMD.2.4: Identify the shapes of twodimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
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P16065 Antisense Copies of Light-Regulated Genes in Rice Abstract T Mike1, N Joshi1, J Bird1, K Margavage1,2, Bryant Morocho1, X-W Deng2, W Terzaghi1,2 Natural antisense transcripts (NATs) are RNAs complementary to sense RNAs that are known to play roles in gene regulation. We studied 21 genes with NAT that are involved in light-regulated pathways in Nipponbare rice (Oryza sativa japonica). Of these genes, 17 were detected by RT-PCR in shoots and roots of Nipponbare seedlings. RTPCR of the Os12g17600 rbcS gene detected multiple small antisense fragments rather than one continuous RNA. Quantitative RT-PCR of Os12g17600 identified 5-fold more sense than NAT in shoots of seedlings grown in light, but 14-fold more sense than NAT in darkgrown seedlings. qRT-PCR of the Os03g51030 PHYA gene indicated that all light treatments decreased the ratio of sense to antisense with the exception of far-red light, which increased the ratio. Several genes exhibited reciprocal regulation of NAT and sense RNAs according to light treatment. Low molecular weight RNA blots of the Os03g07300/ Os03g07310 gene pair identified a small RNA (~40 nucleotides) that was only observed in light-treated roots. These small RNAs might be used to down-regulate the expression of genes turned on by light in roots. 1 Wilkes University, Wilkes-Barre, PA - 2YaleUniversity, New Haven, CT Os03g07300/ Os03g07310 (ribulose-3-P epimerase/ axi protein) Os02g05830 (rbcS2) Conclusions  17 of 21 light-regulated genes examined have NATs, 5 of which are regulated by light  Several genes show reciprocal regulation of mRNA and NAT  Some NATs were processed into small RNAs which may help regulate sense/ antisense RNA transcription  qRT-PCR detected:  ~14-fold more rbcS mRNA than NAT transcripts in shoots grown in continuous darkness  ~5-fold more mRNA than NAT in shoots grown in continuous light  Roots grown 4hr in white light do not increase expression of rbcS mRNA  phyA NAT expression greatly increased upon exposure to white light for 4 Hr or to1mmol. m2 red light. Introduction Discussion  Natural Antisense Transcripts (NATs) RNA molecules complementary to other “sense” RNAs  Present in a variety of organisms, NATs are involved in RNA editing, genomic imprinting, viral defense, etc.  Sense-antisense RNA pairs may reciprocally regulate each other’s production: when production of one transcript increases, production of the other decreases  Prevalence of NATs in plants suggests that NATs may help regulate light responses  Light responses are regulated by complex networks of transcripts  Some antisense RNA is involved in circadian rhythms  Although NATs have been identified in model plant species, their functions are not clear  Tiling-path microarrays identified thousands of genes with NATs   17 of 21 NATs of light-regulated genes found by microarrays were confirmed, validating this high-throughput approach.  Reciprocal light regulation of sense and antisense transcripts was detected for several genes, providing a potential mechanism for regulating the abundance of specific transcripts in response to light. Figure 2: The Os03g07300/ Os03g07310 (ribulose-3-P epimerase/ axi protein) gene pair. A) Low molecular weight Northern showing a 40 nt, root-specific RNA derived from Os03g07310. B) RT-PCR confirming the presence of mRNA of both genes in the leaf tissues. LL: light-grown leaf; DL: dark-grown leaf.  Overlapping NATs initiated from several start sites were identified for Figure 3: Reciprocal regulation of Os02g05830 (rbcS2). In tissues expressing higher levels of NAT, the mRNA is found at lower levels, and vice versa, indicating reciprocal regulation. Os12g17600  Suggests that antisense is not initiated from a single promoter.  Small RNAs derived from several overlapping gene pairs were detected, which may help regulate their expression. LL: light leaf; DL: dark leaf; LR: light root; DR: dark root; 4hr. WL: 4 hour white light; 4hr. WR: 4 hour white root; RL: red leaf; RR: red root; FRL: far red leaf; FRR: far red root; BL: blue leaf; BR: blue root.  NATs are induced in greater magnitudes than sense mRNA in both rbcS and phyA leaves under various light treatments  Questions that still need answers:   Os03g51030 (PHYA) Os12g17600 (rbcS)    Which photoreceptors are involved? Do NATs help modulate light-regulated gene expression? How is NAT/ mRNA production regulated? Are NATs polyadenylated? Sequence of 40nt RNA product of 07300 gene? Methods Figure 1: Antisense and light regulation. High-throughput techniques identified large numbers of antisense and lightregulated transcripts. This research tested the hypothesis that antisense may play a role in light regulation.  Identified antisense transcripts from light-regulated genes in Japonica rice  Query microarray, MPSS, and cDNA databases  Treated seedlings to a variety of lighting conditions to determine effect on mRNA and antisense transcription Plants were grown: 10 days continuous white light or continuous darkness  10 days continuous darkness followed by 4 hours white light  10 days continuous darkness followed by either 1 mmol red light, 1 mmol far red light, or 1 mmol blue, then far red  RNA was extracted from roots and leaves using Ambion’s miRvana Total RNA Isolation kit.  Detection of mRNA and antisense utilized:  Northern blots to verify presence of RNA  Reverse Transcription using the 5’ or 3’ primer only  Real time PCR to quantify relative expression   Expression of Sense and Antisense phyA Transcripts Relative to DLAS in Shoots B) Table 1: Strength of detected antisense signals. The gene pairs in the red box overlap at their annotated 3’ ends and the snoRNA are transcribed from the opposite strands of RPT2 exons. The antisense strands of the remaining genes have no annotated functions. Blue Dark Far Red Light Red 4 hr White Antisense Sense Ratio S:A 1.2 156.0 130.9 1.0 152.1 152.1 0.8 132.2 172.6 2.0 81.9 41.8 4.9 112.3 23.0 2.5 186.9 75.3 B) Expression of Sense and Antisense rbcS Transcripts Relative to DLAS in Shoots Blue Dark Far Red Light Red 4 hr White Antisense 5.8 1.0 Sense Ratio S:A 85.3 14.7 13.9 13.9 5.5 100.6 11.0 57.4 527.3 122.5 10.4 5.2 11.2 40.2 284.0 7.1 Expression of Sense and Antisense rbcS Transcripts Relative to DRAS in Roots Blue Dark Far Red Light Red 4 hr White Antisense 0.4 1.0 Sense Ratio S:A 5.5 12.5 9.8 9.8 1.2 2418.4 153.8 15.7 16842.5 1854.2 12.9 7.0 12.1 0.1 2.5 19.4 Figure 4: Induction of Os03g51030 (phyA) in seedling shoots by various light treatments. Figure 5: Induction of Os12g17600 (rbcS) in seedling shoots by various light treatments. A) Graph of level of induction of sense and antisense standardized to the corresponding dark sample. A)Graph of level of induction of sense and antisense standardized to the corresponding dark sample. B) Expression levels of sense and antisense RNA in shoots relative to dark shoot antisense along with the ratio of sense to antisense. B)Expression levels of sense and antisense RNA in shoots (left) relative to dark shoot antisense and roots (right) relative to dark root antisense along with the ratio of sense to antisense. Acknowledgements This research was primarily supported by NSF grant DBI-0421675: Virtual Center for Analysis of Rice Genome Transcription (XingWang Deng, PI). Additional support from Wilkes University, Yale University, and the Howard Hughes Medical Institute is also gratefully acknowledged.
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CCSS-Math Coherence with Functions CCSS.MATH.CONTENT.6.EE.C.9 Grade 6 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable…. CCSS.MATH.CONTENT.7.RP.A.2.C Grade 7 Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. CCSS.MATH.CONTENT.8.F.B.4 Grade 8 HS Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Construct and compare linear, quadratic, and exponential models and solve problems. CCSS.MATH.CONTENT.HSF.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
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PLACEMENT HOW? Placement Placement Test Test Transfer Transfer Credits Credits SAT SAT or or ACT ACT Scores Scores High High School School AP AP Scores Scores (Mathematics) (Mathematics) WHAT TO DO? Take Take placement placement test test on on any any campus campus at at Testing Testing Center. Center. Accuplacer Accuplacer MATH MATH can can be be taken taken twice. twice. Students Students who who wish wish higher higher placement placement must must then then “appeal”. “appeal”. Appeal Appeal is is request to take a pencil-and-paper type test on material from the course they request to take a pencil-and-paper type test on material from the course they placed placed into. into. Bring Bring transcript transcript showing showing general general education education math math credits credits from from another another college college or or university university to to CCBC CCBC for for evaluation. evaluation. If If completed completed in in Maryland, Maryland, the the highest highest level level developmental math course, Intermediate Algebra can be used for placement. developmental math course, Intermediate Algebra can be used for placement. Placement Placement by by SAT SAT MATH MATH score score of of 500 500 or or higher higher (or (or by by ACT ACT MATH MATH score score 21 21 or or higher) places the student into an entry-level general education math course higher) places the student into an entry-level general education math course (MATH (MATH 111, 111, 125, 125, 131/2/3, 131/2/3, 135, 135, 163). 163). For For higher higher placement, placement, the the student student must must take take Accuplacer MATH. MATH. Accuplacer Students Students with with documentation documentation of of AP AP math math scores scores of of 3, 3, 4, 4, or or 5 5 from from high high school school can can be awarded college credit and placement according to this chart. be awarded college credit and placement according to this chart.
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Low Back Biomechanics of Lifting (cont.) M =W xh+W xb load & torso load torso Where: h – horizontal distance from load to L5/S1 disk b – horizontal distance from center of mass of the torso to the L5/S1 disk M back-muscle = F back-muscle x 5(N–cm) S(moments at L5/S1 disk = 0) F back-muscle x 5 = W load x h + W torso x b F back-muscle = (W load x h + W torso x b)/5 Assume h = 40 cm & b = 20 cm then F back-muscle = 8W load + 4W torso Assume W load = 300 N or 30kg (75lb) & W torso = 350 N (80lb) then
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Math & Nature  Geometry & Biology ◦ CCSS  MACC.912.G-SRT.3.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.  MACC.K12.MP.4.1 Model with mathematics
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