**Mathematics** F-IF Which Function? What’s the big idea? Interpret the structure of expressions. Write expressions **in** equivalent forms to solve problems Create equations that describe **numbers** or relationships Solve equations and inequalities **in** one variable Solve systems of equations Interpret functions that arise **in** applications **in**/.map.mathshell.org.uk/materials/**index**.phphttp://www.map.mathshell.org.uk/materials/**index**.php Illustrative **Mathematics** - http://illustrativemathematics.org/http:///

.me/ Phil Daro talks about the Common Core **Mathematics** Standards - http://serpmedia.org/daro-talks/**index**.html http://serpmedia.org/daro-talks/**index**.html Resources Books Van De Walle and Lovin, Teaching Student-Centered **Mathematics**, K-3 Fosnot and Dolk, Young Mathematicians at Work Wright, et al, Teaching **Number** **in** the Classroom Wright, et al, Early Numeracy Parrish, **Number** Talks Clements and Sarama, Learning and Teaching Early/

.me/ Phil Daro talks about the Common Core **Mathematics** Standards - http://serpmedia.org/daro-talks/**index**.html http://serpmedia.org/daro-talks/**index**.html Resources Books Van De Walle and Lovin, Teaching Student-Centered **Mathematics**, K-3 Fosnot and Dolk, Young Mathematicians at Work Wright, et al, Teaching **Number** **in** the Classroom Wright, et al, Early Numeracy Parrish, **Number** Talks Clements and Sarama, Learning and Teaching Early/

://prezi.com/yyqkeco2rob5/**number**-talks/ http://www.insidemathematics.org/**index**.php/**number**-talks **Number** Talk Who does the math thinking during the **number** talk? What specific **mathematics** do the students demonstrate they understand? What does the teacher do to support the student discourse? What recording techniques might the teacher employ that supported learning **in** the class? Assessment? http://www.parcconline.org/samples/**mathematics**/grade-4-**mathematics** **Mathematical** Communication Tips on/

-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 11 Bruce Mayer, PE Chabot College **Mathematics** Simplify by Product Rule Use The Product Rule **in** REVERSE to Facilitate the Simplification process Note that and must both be real **numbers** BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 12 Bruce Mayer, PE Chabot College **Mathematics** Simplify a Radical Expression with **Index** n by Factoring 1.Express the radicand as a product/

Adapted from Illustrative **Mathematics** A-APR Trina’s Triangles What’s the big idea? Use complex **numbers** **in** polynomial identities and equations. Interpret the structure of expressions. Write expressions **in** equivalent forms to /.com/ Assessment Resources MAP - http://www.map.mathshell.org.uk/materials/**index**.phphttp://www.map.mathshell.org.uk/materials/**index**.php Illustrative **Mathematics** - http://illustrativemathematics.org/http://illustrativemathematics.org/ CCSS Toolbox: PARCC Prototyping Project/

- http://serpmedia.org/daro-talks/**index**.html http://serpmedia.org/daro-talks/**index**.html Resources Books Van De Walle and Lovin, Teaching Student-Centered **Mathematics**, K-3 Fosnot and Dolk, Young Mathematicians at Work Wright, et al, Teaching **Number** **in** the Classroom Wright, et al, Teaching **Number**-Advancing children’s skills and Strategies Wright, et al, Developing **Number** Knowledge Parrish, **Number** Talks Shumway, **Number** Sense Routines (preview!) Wedekind, Math/

the development of students’ **number** sense, flexibility, fluency, collaborative skills and communication. Navigating a Unit Classroom Routines What might all of this look like **in** the classroom? http://ccgpsmathematics6-8.wikispaces.com/ http://ccgpsmathematics6-8.wikispaces.com/ Also check out: Inside **Mathematics** : **Mathematical** Community of Learners - http://www.insidemathematics.org/**index**.php/video-tours-of-inside- **mathematics**/classroom-teachers/157-teachers-reflect-**mathematics**- teaching-practices http/

. 10 2 = 100. Students should recall the **index** laws. Some students may think that any **number** multiplied by a power of ten qualifies as a **number** written **in** standard form. When rounding to significant figures some students may think, for example, that 6729 rounded to one significant figure is 7. Problem solvingKeywords Link with other areas of **mathematics**, such as compound measures, by using speed/

**Mathematics** S17-08-17, 65162749 matwml@nus.edu.sgmatwml@nus.edu.sg http://www.math.nus.edu.sg/~matwml/ http://arxiv.org/find/math/1/au:+Lawton_W/0/1/0/all/0/1 Lecture 2. Friday 15 Jan 2010 **Indexed**/ Sets Definition (p. 13)a set and for each there is a setThe collection is said to be **indexed**/ Products Definition For an **indexed** collection of sets If /1: Between every two real **numbers** there is a rational **number**. Finite and Infinite Sets Finite/2.2 The set of real **numbers** is uncountable. Open and Closed Sets/

of problems and persevere **in** solving them. 4th Grade For an elementary audience you may want to show video of a 4th grade example. Click on the icon to view the video: http://insidemathematics.org/**index**.php/classroom-video-visits/public-lesson-**number**-operations/182-multiplication-a-divison-problem-4-part-c Copyright ©2011 Commonwealth of Pennsylvania Standards for **Mathematical** Practice Standard 4: Model/

a "family, triple, or set." http://www.insidemathematics.org/**index**.php/standard-1 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE **MATHEMATICS** CURRICULUM A Story of Ratios MP 2: Reason abstractly and /help me contextualize and decontextualize problems. Contextualize Decontextualize I can take **numbers** and put them **in** a real-world context. I can take **numbers** out of context and work **mathematically** with them. Reasoning habits include: 1) creating an understandable representation/

a text search engine is used to **index** and retrieve them Purpose 8 **Mathematical** Expression its appearance(or presentation) its **mathematical** meaning (often termed its content) how to capture the relevance of **mathematical** expressions, how to query them, and /respect to the sizes of the matched expressions **in** increasing order. PATTERN SEARCH 17 a template can be defined using wildcards as non- terminals,and regular expressions to describe their relationships **Number** wild cards,Variable wild cards, Operator wild /

. Reason abstractly and quantitatively. **Mathematically** proficient students can… Make sense of quantities and their relationships **in** problem situations. Take math **in** and out of context Work with symbols as abstractions Use a well-developed **number** sense Apply properties of/www.thinkfinity.org Online Resources Main page of free teaching materials: http://www.geogebra.org/en/wiki/**index**.php/English#Number_Sense Area of a circle: http://www.geogebratube.org/student/m279 Classifying Quadrilaterals: http/

scoring at Levels 2, 3, and 4 + the **number** scoring at Levels 3 and 4) ÷ **number** of cohort members] 100 A Performance **Index** (PI) is a value from 0 to 200 that is assigned to an accountability group, indicating how that group performed on a required State test (or approved alternative) **in** English language arts, **mathematics**, or science. PIs are determined using the following equations/

foundation of functional thinking because **in** order to see a **number** **in** relationship to another, we must pay attention to any dependency relationship or rule for correspondence. Tad Watanabe, 2008 Tad also says: How are **Number** Talks Useful? Want more? http://insidemathematics.org/**index**.php/2nd-grade **number**-of-the-day **Number** Talk Who did the math thinking during the **number** talk? What specific **mathematics** did the students demonstrate/

, one of the world´s leading scientific publishers. Key subject areas include: **Mathematics**, Computer Science, Physics, Astronomy, Geosciences, Chemistry Engineering and Medicine. The resource/ topics worldwide. It consists of 1800 full-text journals and 2000 journals that are **indexed** and abstracted. The resource has four components, i.e. ABI / INFORM Complete,/ access to CA. Access Options: Z39.50 Client on port 210 Coverage **in** **Number** of Years: 1907 to present Print-base: No. Print Equivalent: Chemical /

readiness benchmarks. **Number** of students who earn postsecondary credit required for a foundation high school program, an associate’s degree, or an industry certification. 6 Distinction Designations 2013 Distinction Designation Campus Top Twenty-Five Percent: Campuses **in** the top quartile of their campus comparison group earn a distinction designation. Student Progress (based on **Index** 2) Academic Achievement **in**: Reading/English Language Arts **Mathematics** 2014 Distinction/

of the second matrix have two indices, signifying their location within the matrix. The first **index** is the **number** of the row and the second is the **number** of the column, so that together the entry’s position is uniquely identified. For example/1). (continued) Note that the augmented matrix Ã determines the system (1) completely because it contains all the given **numbers** appearing **in** (1). Section 7.3 p36 Gauss Elimination and Back Substitution 7.3 Linear Systems of Equations. Gauss Elimination Gauss Elimination/

scoring at Levels 2, 3, and 4 + the **number** scoring at Levels 3 and 4) ÷ **number** of cohort members] 100 A Performance **Index** (PI) is a value from 0 to 200 that is assigned to an accountability group, indicating how that group performed on a required State test (or approved alternative) **in** English language arts, **mathematics**, or science. PIs are determined using the following equations/

**Mathematically**: Arithmagons Problem I create a puzzle for you by placing **numbers** at the corners of a triangle, as shown below. I then add up the two **numbers** **in** adjacent corners and write the total on the line joining them. I now hide the corner **numbers**/ for effective functioning **in** society both within and beyond school. (http://vels.vcaa.vic.edu.au/essential/interdisciplinary/thinking/**index**.html) Linking “Working **Mathematically**” with other VELS domains How does Working **Mathematically** foster Personal Learning/

you get to play **in** everyone’s backyard.” (Tukey) Perhaps the most useful topic **in** **mathematics** is statistics — and yet it is a very small part of it. Perhaps the most useful topic **in** **mathematics** is statistics — and yet/ boom”: An estimated 20000 unfilled jobs **in** the US **in** bioinformatics by 2005 An estimated 20000 unfilled jobs **in** the US **in** bioinformatics by 2005 A **number** of Australian universities have bioinformatics degrees (including USQ) A **number** of Australian universities have bioinformatics degrees (/

Source: Big ideas **in** beginning reading. University of Oregon. Retrieved September 23, 2007, from http://reading.uoregon.edu/**index**.php Response to Intervention www.interventioncentral.org 23 Five Strands of **Mathematical** Proficiency 1.Understanding: Comprehending **mathematical** concepts, operations, and relations--knowing what **mathematical** symbols, diagrams, and procedures mean. 2.Computing: Carrying out **mathematical** procedures, such as adding, subtracting, multiplying, and dividing **numbers** flexibly, accurately/

scores offer a way to compare scores among members of the class, find out how many had a mark greater than yours, indicate position **in** the class, etc. mean = 68.0 standard deviation = 10.9 Example 2: Suppose your mark was 64 Compare your mark to / 180-185 try page 186 #2-5, 7, 8, 10 **Mathematical** Indices Chapter 3.6 – Tools for Analyzing Data **Mathematics** of Data Management (Nelson) MDM 4U What is an **Index**? An **index** is an arbitrarily defined **number** that provides a measure of scale These are used to indicate a /

receiving interventions should focus intensely on **in**-depth treatment of whole **numbers** **in** kindergarten through grade 5 and on rational **numbers** **in** grades 4 through 8. 17 Response to Intervention www.interventioncentral.org Assisting Students Struggling with **Mathematics**: RtI for Elementary & Middle/ready to follow a nine-step incremental-rehearsal sequence: First, the tutor presents the student with a single **index** card containing an ‘unknown’ math fact. The tutor reads the problem aloud, gives the answer, then /

100. Determine the unknown whole **number** **in** an addition or subtraction equation relating three whole **numbers**. Determine the unknown whole **number** **in** a multiplication or division problem relating three whole **numbers**. Use place value understanding and /O Commoncore.pearson.ed.com/ http://commoncore.pearsoned.com/**index**.cfm?locator=PS1c O9 http://commoncore.pearsoned.com/**index**.cfm?locator=PS1c O9 O Ilustrative **Mathematics** http://illustrativemathematics.org/standards/k8 http://illustrativemathematics.org/standards/

Grid paper Metric measurement tools Anchor charts **Number** talks Examples & Explanations **Mathematically** Flexible Thinking Look for likenesses and differences. Expansiveness of thought Understanding of decimals at an appropriate developmental level Reasoning and articulating thought both verbally and **in** journals Examples & Explanations http://www.learner.org/courses/learningmat h/**number**//**index**.html http://www.learner.org/courses/learningmat h/**number**//**index**.html How to develop all of these/

a way to prove all of the volume equations **in** the world. * Back to **Index** Back to **Index** * There many ways to see the same notation for derivatives. Great **mathematical** minds used different ways to say the same thing. **In** class we will use Leibniz notation. * This/and easy. The rule states that you take the exponent of any **number** and multiply it by the **number** and subtract one from the exponent itself. * Some examples * Back to **Index** Back to **Index** * The sum and difference rule are another informal way of finding /

a pattern and describe the rule using the physical attributes or position of objects **in** a sequence. (1) Recognize, copy and extend patterns of sounds, colors, shapes, textures and **numbers** **in** a variety of contexts and describe the rule of the pattern. (2) Make/ **Mathematics** Page - http://www.state.ct.us/sde/dtl/curriculum/currm ath.htm http://www.state.ct.us/sde/dtl/curriculum/currm ath.htm http://www.state.ct.us/sde/dtl/curriculum/currm ath.htm Implementing the Standards - http://illuminations.nctm.org/**index**/

out **in** the NUMS consultative report University Liaison Peter Rowlett peter.rowlett@ima.org.uk £400 grants available for any university maths society –http://www.ima.org.uk/student/**index**.htmlhttp://www.ima.org.uk/student/**index**.html/network –diversity coding and MIMO: quaternions and Cayley **numbers** Designing and managing networks for IP data traffic Securing the cloud How can **mathematics** help? –Don’t expect well formulated **mathematical** problems Users’ needs Customer propositions Service Enabling Connectivity /

does she have left? -How should your students model this problem? -Write them on **index** cards. Models *Bar/Tape Model ***Number** Line Pictures Ten Frame Venn Diagram Tree Diagram Graphs Tools *Unifix Cubes Rekenrek Dice, Cards/ of cognitive growth. American psychologist,19(1), 1. Cobb, P. (2000). Conducting teaching experiments **in** collaboration with teachers. **In** R. Lesh & A. Kelly (Eds.), Handbook of research design **in** **mathematics** and science education (pp. 307-334). Mahwah, NJ: Lawrence Erlbaum. Imm, K. L., /

Want more? http://www.insidemathematics.org/**index**.php/**number**-talks **Number** Talk Who does the math thinking during the **number** talk? What specific **mathematics** do the students demonstrate they understand? What does the teacher do to support the student discourse? What recording techniques might the teacher employ that supported learning **in** the class? Assessment? http://www.parcconline.org/samples/**mathematics**/grade-3-**mathematics** Assessment? http://www.parcconline.org/

2 Basics of Matlab **Number** representation Matrix operations Matlab data types Complex **numbers** **in** Matlab 26 U NIVERSITY of V AASA Communications and Systems Engineering Group **Number** Representation, Computational Accuracy 27 U/continue **index** = 1; while (**index** < 5) if (**index** == 3) break; end; **index** **index** = **index** + 1; end; **index** = 1; while (**index** < 5) if (**index** == 3) **index** = **index** + 1; continue; end; **index** **index** = **index** + 1; end; **index** = 1 **index** = 2 **index** = 1 **index** = 2 **index** = 4 Note write **index** to /

**numbers** **in** this unit Better problem Are these two expressions equal? 3(2x+1) + 2x and 8x + 4 3(2x+1) + 2x and 8x + 4 Specific Standards for **Mathematical** Prac tice A step was taken by the team to incorporate **in** each unit specific Standards for **Mathematical**/bit.ly/OoyaK5 MAP - http://www.map.mathshell.org.uk/materials/**index**.phphttp://www.map.mathshell.org.uk/materials/**index**.php Illustrative **Mathematics** - http://illustrativemathematics.org/http://illustrativemathematics.org/ CCSS Toolbox: PARCC /

Proficient Basic Below Basic Far Below Basic 10% 20% 40% 10% 20% % of students **in** each quintile Academic Performance **Index** (API) Criteria: Quintile Rankings based on Math CST Quintile API Weights API 51000 4875 3 700/ **Mathematics** Far Below BasicBelow BasicBasicProficientAdvanced 150 to 247248 to 299300 to 349350 to 429430 to 600 State Target for All Students CST Assessment Protocol: Simplifying the Data **In** each Reporting Cluster, simplify the percentage correct by rounding to the nearest single digit **number**/

to be eutrophic during May when zooplankton increase **in** **number**. The Soyer’s frequency **index** and Bellan Santini’s dominance **index** are high and the dispersion is only 3 % with diatoms dominant. Therefore diversity indices, which constitute **mathematical** models, serve as important tools **in** pollution assessment of aquatic environments. Principal component analysis serves **in** identifying key toxic parameters and helps **in** proper modelling of lake ecosystems. INTRODUCTION A/

/~jsuh4/mathbridges/**index**.h tml References Battey, D., Kafai, Y, & Franke, M. (2005). Evaluation of **mathematical** inquiry **in** commercial rational **number** software. **In** C. Vrasidas & G. Glass (Eds.), Preparing teachers to teach with technology (pp. 241-256). Greenwich, CT: Information Age Publishing. Garofalo, J., Drier, H., Harper, S., Timmerman, M. A., & Shockey, T. (2000). Promoting appropriate uses of technology **in** **mathematics** teacher preparation. Contemporary Issues **in** Technology and/

Source: Big ideas **in** beginning reading. University of Oregon. Retrieved September 23, 2007, from http://reading.uoregon.edu/**index**.php Response to Intervention www.interventioncentral.org 80 Five Strands of **Mathematical** Proficiency 1.Understanding: Comprehending **mathematical** concepts, operations, and relations--knowing what **mathematical** symbols, diagrams, and procedures mean. 2.Computing: Carrying out **mathematical** procedures, such as adding, subtracting, multiplying, and dividing **numbers** flexibly, accurately/

ordinary signiﬁcance of nought, to **number** a classiﬁcation of all human knowledge **in** print; this supplemented by the next simplest known symbols, a, b, c, **indexing** all heds of the tables, so /Fishing, hunting, shooting Philosophy & Psychology Geography & History Literature & Rhetoric The ArtsTechnology (Applied Sciences) Natural Sciences & **Mathematics** LanguageSocial SciencesReligionGeneralities There is an abridged version for small local libraries, and a more detailed/complex version if the library grows/

BELL RINGER – MATH JOURNAL ENTRY Yesterday we discussed Properties of Exponents. Summarize yesterday’s lesson using **mathematical** vocabulary. Underline the math vocabulary words you use. Choose 2 of your math vocabulary words and define/ variable by the **index**. 2.Pull out that variable. 3.Anything left over stays **in** the radicand. REMINDERS 1.Even **indexes** must be positive or they are imaginary, not real. 2.Odd **indexes** can be negative. 3.The square root of a **number** can be re-written as that **number** to the ½ power/

**in** college and careers. The Common Core State Standards are: Built on progressions: narrative documents describing the progression of a topic across a **number** of grade levels. Informed by: 1. Research on children’s cognitive development 2. Logical structure of **mathematics**/ Standards of **Mathematical** Practice http://www.youtube.com/watch?v=m1rxkW8ucAI On Your Own or Collaboratively Watch and Discuss: Classroom Videos of Exemplary Lessons http://www.insidemathematics.org/**index**.php/**mathematical**-practice-standards/

Grade Patterns http://www.ixl.com/math/grade-1/describe-patterns Elementary - Middle: Patterns **in** **Mathematics**: Teachers’ Lab Mystery Operations http://www.learner.org/teacherslab/math/patterns/mystery/ BillyBug: http://www.oswego.org/ocsd-web/games/BillyBug2/bug2.html Fun Brain **Number** Cracker http://www.funbrain.com/cracker/**index**.html No frills http://www.harcourtschool.com/activity/rubber_number_patterns_and_rules/ Function Machine http://www.mathplayground.com/

/**index**.html Resources Books Van De Walle and Lovin, Teaching Student-Centered **Mathematics**, 3-5 Fosnot and Dolk, Young Mathematicians at Work Parrish, **Number** Talks NCTM, Developing Essential Understanding of Rational **Numbers** Shumway, **Number** Sense Routines Wedekind, Math Exchanges New- Burns and Silbey, So You Have to Teach Math? New- Teaching with Intention- Debbie Miller New- Moynihan, Math Sense New- Confer and Ramirez, Math Tools **in**/

**in** which letters stand for **numbers** and with expressions involving whole **number** exponents. Develop a deep understanding with applying the properties of operations to generate and identify equivalent expressions. What’s the big idea? Standards for **Mathematical**/Core **Mathematics** Standards - http://serpmedia.org/daro-talks/**index**.html http://serpmedia.org/daro-talks/**index**.html Books Van DeWalle and Lovin, Teaching Student-Centered **Mathematics**, 6-8 Resources Professional Learning Resources Inside **Mathematics**- /

Examples & Explanations **Mathematically** Flexible Thinking Look for likenesses and differences. Expansiveness of thought Understanding of fractions at an appropriate developmental level Reasoning and articulating thought both verbally and **in** journals Examples & Explanations http://www.learner.org/courses/learningmat h/**number**//**index**.html http://www.learner.org/courses/learningmat h/**number**//**index**.html How to develop all of these? Hold **number** talks regularly, making sure to include ideas/

volume and constructing one of exactly twice the volume) and trisecting the angle (Reluga, **Index**) The doubling of the cube would be addressed **in** 1637 by Fermat, **in** his famous Fermat’s Last Theorem. A translation of his proposal into English: “There /seige. Archimedes helped defend the city using a **number** of machines and weapons he created, but eventually the Romans took over the city. According to legend, Archimedes was tracing some **mathematical** problem **in** the dirt of the street when a soldier attempted/

for students to evaluate their answers and provide counter-arguments **in** **mathematical** and real-life contexts, **in** addition to requiring them to understand the implications of rounding their answers. bounds, accuracy, Integer, **number**, digit, negative, decimal, estimate, Continued on next /2 Return to Routemap Return to Routemap Return to Routemap Return to Routemap Candidates should be able to: Use **index** notation for integer powers of 10, including negative powers; Recognise powers of 2, 3, 4, 5; Use/

learning to ensure that all children will graduate high school with the skills they need to be successful. **In** **mathematics**, this means three major changes. Teachers will concentrate on teaching a more focused set of major math concepts//**index**.p hp/classroom-video-visits/public- lesson-**number**-operations/179- multiplication-a-divison-problem-3- part-b http://insidemathematics.org/**index**.p hp/classroom-video-visits/public- lesson-**number**-operations/179- multiplication-a-divison-problem-3- part-b **Mathematically** /

10 Contd… Physiological Acoustics Psychological Acoustics Speech Production Speech Perception Speech Processing Musical Acoustics Bioacoustics Computational Acoustics **Mathematical** Acousti 11 2. African Journals Online (AJOL) Abstracts of over 250 African-published journals, with access/ensure that you log **in** **in** order to access full-text articles. This will take you to the Journals page This will take you to the Journals page. There are a **number** of databases and bibliographic **indexes**, accessible from the /

Space Draw a line that is completely contained **in** two **index** cards. Label this line n. How many lines can you draw like this using the same two **index** cards? Visualizing a 3-Dimensional Space Use your/**in** order to read the **number** 196,325,704 Teach students to identify the **numbers** **in** their sets of three: 196 (one hundred ninety six) million 325 (three hundred twenty five) thousand 704 (seven hundred four) “Recognition of a working **mathematics** vocabulary is very important “Recognition of a working **mathematics**/

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