RPM+Throughlines+Clark

Connections with “common core” Mathematical Content appears in below. || C. Walker’s Candidates proposed at last meeting working on through-lines. || Standards for Mathematical Practice || Standards for Mathematical Content || 1) Reasoning/Problem Solving (1,4,5,8,9-14,20,21) || Number Sense ||  1) Make sense of problems and persevere in solving them. || 1) Operations & Algebraic Thinking || 2) Communication (1-21) || Balance || 2) Reason abstractly and quantitatively. || 2) Number & Operations in Base 10 & Fractions || 3) Connections (1-21) || Proportionate Reasoning ||  3) Construct viable arguments and critique the reasoning of others. || 3) Measurement & Data  4) Geometry || 4) Number Sense (2,3) || Multiplicative Thinking ||  4) Model with Mathematics || 5) Ratios/Proportionate Relationships || 5) Geometry (4) || Structure || 5) Use appropriate tools strategically. ||  6) The Number Systems 7) Expressions/Equations || 6) Probability/Statistics (8) || Doing and undoing || 6) Attend to precision || 8) Statistics &Probability || 7) Algebra (1,2,5,6,7,18-20) || Concept of a variable ||  7) Look for and make use of  structure. || 9) Functions  10) Interpreting Functions || 8) Functions (9-12) || ||  8) Look for and express regularity in repeated reasoning. || 11) Building Functions  12) Linear, Quadratic & Exp. Functions || || ||  13) Trigonometric Functions  14) Quantities – Reasoning quantitatively || || ||  15) Real Number System  16) Complex Number System || || ||  17) Vector & Matrix Quantities  18) Seeing Structure in Expressions || || ||  19) Arithmetic of Polynomials & Rational  Expressions || ||  ||  20) Creating Equations || || ||  21) Reasoning with Equations & Inequalities || BillMonroe’s proposed augmentations to existing Washington State College Readiness Mathematics Standards.  1) Include __Algebraic Thinking__ to from Common Core Mathematical content to augment Mathematics Standards 4) Number Sense.  Use descriptions of __Algebraic Thinking__ from the website **“** [] ”.  __Algebraic Thinking__ is linked to operations with numbers and is covered in grades 1 – 5.  Some topics covered are:  The cardinality of a set of objects – determine which sets have 8 objects and which do not..  Filling in a missing number in an expression so is equal to a given value.  Example:Fill in a number above the underline in the expression3 + 2( __- 4)so it has avalue of 11.  The Division Algorithm – build understanding of the relationship between division and multiplication. Equivalent fractions – be able to reason why two fractions represent the same size using a visual model and a number line. Comparing the size of two fractions with either the same numerator or denominator.(use equality or inequality symbols) Distinguish multiplication comparison with addition comparison. Ex. Show that both statements are true.35 is 5 times as many as 7.versus35 is 28 more than 7. Gain familiarity with factors and multiples. Generate and analyze patterns. Ex. Given the rule “add 3” generate a sequence of numbers that begins with 1. Observe the pattern of the appearance of “even” numbers.Many explorations can occur at this point. Ex. Given two sequences of numbers determined by different rules compare and contrast patterns of each. This could be done by creating a coordinate graph. Introduce grouping symbols and evaluate expressions using grouping symbols. Ex. Have students explain reasoning why3(12,345 + 9,821) is three times the sum 12,345 + 9,821 without calculating. 2)Include __Expressions and Equations__from Common Core Mathematical content to augment Mathematics Standards 7) Algebra. Use descriptions of __Expressions and Equations__ from the website **“** [] ”. __Expressions and Equations__ cover grades 6-8. Some topics covered are: Apply properties of operations to generate equivalent expressions.Identify when two expressions are equivalent. Rewrite a given expression with two or more quantities in a different form to gain insight into how the quantities are related. Understand the underlying question when solving an equation. Recognize that a variable can stand for a specific number or, in given cases, any number. Solve real world problems using equations that include one or more variables. Use an inequality as a constraint in solving a real world problem. Recognize and analyze quantitative relationships between dependent and independent variables. Solve real-life problems that in multiple-steps.Ex.Place a towel rack that is 9 ¾ inches long in the center of a door that is 27 ½ inches wide. Understand the connections between proportional relationships, lines and linear equations. Graph proportional relationships.Interpret unit rate as the slope. Ex. Compare a distance-time graph with a distance-time equation for two different objects and determine which has the highest speed. Solve real world and mathematical problems leading to two linear equations in two variables. BillMonroe’s proposed Through-Line Concepts/Content 1) Proportionate Relationships and Reasoning Mathematical Concept fraction, ratio, percent, rate, slope  Use these concepts to reinforce understanding of proportionate relationships.  Use proportionate reasoning to solve real world problems.  2) Modeling Quantitative Relationships Use two or more quantities Use graphical, tabular, linguistic and symbolic representations. Describe relationship using the four representations. Given one representations, generate the other three. Use real-world problems/situations. Student builds model based on real world information and assesses reasonableness of the model. Use models to interpolate and extrapolate values. Connect quantitative relationships to the concept of functions. 3) Determining Symbolic Meaning and Contextual Influence on Symbolic Meaning Ascertain with clarity the meaning of operation symbols within the context of the expression/equation.  4) Creating Algebraic Equivalence Gain fluency writing equivalent expressions and/or equations. 5) Recognizing Pattern and Structure(3.4 in WA State Standards) repeated operations (sequences),  application of the same principles/procedures when solving problems,  components of expressions and equations.  Structure appears in the Common Core Standards as a Math Practice Standard  “Look for and make use of structure.”Below are some descriptions of what this means.  Step back from a problem or expression for an overview and shift perspective.  See equivalences in reordering of steps.  See complicated expressions as single objects or as composed of several objects.  Ex:See the expressionas 5 subtract a quantity squared and realize the value of the expression could never be greater than 5.  6) Procedural Understandingsource: Jon Hasenback email hasenban.jon@wulax.edu Understand the overall goal of the algebraic process and know how to predict or estimate the outcome. Understand how to carry out an algebraic process and know alternative methods and representations of the process. Understand and communicate to others why the process is effective and leads to valid results. Understand how to evaluate the results of an algebraic process by invoking connections with a context or with other known math. Understand and use mathematical reasoning to assess the relative efficiency and accuracy of an algebraic process compared with alternative methods. Understand why an algebraic process empowers him/her as a problem solver.
 * Washington State College Readiness Mathematics Standards ** ||
 * Candidates For Through-Line Concepts/Content ** ||||
 * Common Core State Standards Initiative **
 * Standards for Practice and Content have intersections. **
 * Source: “http://www.corestandards.org/the-standards/mathematics” ** ||
 * Source: “http://www.corestandards.org/the-standards/mathematics” ** ||