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SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 1 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics Prerequisite Grade Kindergarten Skills Represent, compare, and order whole numbers, and join and separate small sets of numbers or objects. Order objects by measurable attributes, such as length and weight, and indirectly compare lengths to a third object to solve problems. Identify, name and describe a variety of two and three dimensional shapes presented in different sizes and orientations, as well as combining those shapes to construct more complex shapes. Identify, duplicate, and extend simple number, sequential and growing patterns. Sort and re-sort objects using one or more attributes to solve problems. Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 2 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics – Grade 1 Represent, compare, and order whole numbers up to 100, including using the number line and grouping in tens and ones. Use properties (commutative, associative) and a variety of models to develop understanding of two digit addition and subtraction, and the relationship between them, as well as develop strategies for basic addition facts and related subtraction facts. Use standard and non-standard units of measurement to find lengths and subsequently solve problems. Decompose, as well as compose, two- and threedimensional shapes, describing their properties in order to build understanding of part-whole relationships. Apply, as well as identify and describe number patterns and properties such as odd and even. Represent measurements and discrete data in picture and bar graphs involving counting and comparing. These should provide meaningful connections to number relationships. Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 3 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics – Grade 2 Represent, compare, and order whole numbers up to 1000, and their equivalents (e.g. 35 is 3 tens and 5 ones or two tens and 15 ones), including using the number line and expanded notation, while grouping in hundreds, tens and ones. Develop extended understanding of multiple models, and properties of addition and subtraction, leading to fluency with efficient, accurate and generalizable methods to add and subtract multi-digit whole numbers and develop quick recall of addition and related subtraction facts. Select and apply appropriate methods to estimate sums and differences or to calculate them mentally. Extend concepts and procedures for estimating and measuring length, area, volume, weight, time and elapsed time. Use processes (e.g. partitioning, transitivity, inverse relationships) to estimate, measure, and compute lengths to solve problems involving data, space and movement, including standard measures such as centimeter and inch. Use number patterns to extend knowledge of properties of numbers and operations (skip counting as a foundation for understanding multiples) Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 4 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics – Grade 3 Develop an understanding of multiplication and division of whole numbers by building on knowledge of the base ten system/operations and through the use of representations (e.g., equal-sized groups, arrays, area models, equal “jumps” on number lines, successive subtraction, partitioning, and sharing) in order to describe relationships, make estimations, and solve problems. Develop an understanding of the size, meaning, and uses of fractions to represent parts of a whole, parts of a set, or points/distances on a number line, and that fractions are used to represent numbers that are equal to, less than, or greater than one. Extend the concepts of measurement to include perimeter as a measurable attribute and select appropriate units, strategies, and tools to solve problems involving perimeter. Describe, analyze, compare, and classify two- and three-dimensional shapes/figures using their attributes. Use congruence and symmetry to decompose, compose, and transform twodimensional figures. Construct and analyze frequency tables, bar graphs, picture graphs, and line plots and use them to describe data and solve problems. Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 5 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics – Grade 4 Apply increasingly sophisticated strategies to solve multiplication and division problems that include and go beyond basic facts and one-digit multiplier problems, using properties of addition and multiplication. Select and apply appropriate strategies to estimate and/or solve a variety of problems including problems involving addition and subtraction of decimals and of fractions with like denominators. Read, represent, interpret the representation, compare and order fractions in various forms (e.g., area model, fraction of a set, fraction notation). Relate understandings of fractions to reading and writing of decimals and understand decimal notation as an extension of the base-ten system. Understand area as a measurable attribute and select appropriate units, strategies (e.g., decomposing) and tools to solve problems or make estimations. Use properties of 2-dimensional shapes to find the area of polygons, connect the area/array model of multiplication to the area formula for rectangles, and use this connection to justify the formula. Expand symmetry and congruence to describe basic transformations, including reflections, rotations, and translations (i.e., flips, turns, and slides). Use transformations to design and analyze simple tilings Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 6 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics – Grade 4 and tessellations. Identify a rule to describe and extend a sequence of numbers, objects, and/or relationships observed in a variety of contexts. Continue to represent and analyze problems by making frequency tables, bar and picture graphs, and line plots; apply the concept of place value to develop an understanding and use of stem-and-leaf plots. Use plots to predict the likelihood of events. Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 7 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics –Grade 5 Develop fluency with and an understanding of efficient strategies for division (models, place value, properties of operations, and the relationship between multiplication and division) and use them to solve problems. Develop an understanding of and fluency with addition and subtraction of fractions and decimals (models, place value, properties of addition and subtraction of decimals) to solve problems in a variety of contexts, including measurement. Develop understanding of negative integers using concrete objects. Extend informal understanding of volume of solids to the measurement of capacity and weight or mass. Understand volume as a measurable attribute and select appropriate units, strategies and tools to solve problems or make estimations. Relate 2-dimensional shapes to 3-dimensional figures and analyze polyhedra solids, describing them by their attributes. Use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities, and graph simple equations Construct and analyze double-bar and line graphs and use ordered pairs on coordinate grids. Use basic concepts of probability to predict the likelihood of event occurring. Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 8 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics –Grade 6 Expand the meaning of multiplication and division of fractions and decimals and their inverse relationships to compute fluently and solve real world problems. Use a variety of models to represent percents. Extend previous understandings of the characteristics of 2-d and 3-d shapes including the measures of area and volumes by exploring, solving and interpreting real world problems. Write mathematical expressions and equations that correspond to given situations, evaluate expressions and use expressions and formulas to solve problems. Understand ratios as part to part and part to whole comparisons, and as comparisons of two different quantities (e.g., rates). Represent part to whole comparisons in fraction, decimal and percent formats. Understand the concepts of the measures of central tendency of a data set, calculate accurately the measures of central tendency, and interpret these measures in the context of the given situation. Use elementary probability and proportions to make appropriate predictions. Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 9 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics – Grade 7 Extend computational fluency, estimation strategies and problem solving to include problems involving positive and negative rational numbers (including integers). Extend previous understandings of the characteristics of 3d-shapes to develop an understanding of and use formulas to determine surface areas and volumes. Apply a variety of strategies for proportional reasoning and use them to solve real world problems including problems dealing with similarity and rates of change. Recognize problem situations in which two or more variables have a linear relationship to each other. Understand the connections between linear equations and the patterns in the tables and graphs of those equations: rate of change, slope, and yintercept. Answer questions regarding a data set using measures of center and spread and interpreting the graphical representation (including box-and-whisker plots) of the data set. Determine the sample space for one-stage experiments and determine, when possible, the theoretical probabilities for events defined in the sample space. Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 10 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics – Pre-Algebra Extend understanding of numbers (rational and irrational), and operations, equivalent forms, (integers, fractions, decimals, percents, roots, exponents and scientific notation) and be able to use these understandings in problem solving situations. Understand and apply the Pythagorean Theorem to find distances between points in a coordinate plane and to analyze polygons and polyhedra. Use fundamental facts about distances and angles to describe and analyze figures and situations in 2- and 3-dimensional spaces and to solve problems including those with multiple steps. Use linear functions, linear equations, and linear inequalities to represent, analyze, and solve a variety of problems. Use the appropriate graphical data representation and extend understanding of the influence of scale in data interpretation. Extend understanding of probability to make comparisons of empirical probability and theoretical probability for the experiment. Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 11 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics – Algebra 1 Use algebraic properties and processes in mathematical situations and apply them to solve real world problems. Represent functions (linear and non-linear) in multiple ways, including tables, algebraic rules, graphs and contextual situations, and make connections among these representations. Choose the appropriate functional representation to model a real world situation and solve problems relating to that situation. Write, solve, graph, and interpret linear equations and inequalities to model relationships between quantities. Write, solve and interpret systems of two linear equations and inequalities using graphing and algebraic techniques. Display, analyze, and make predictions using univariate and bivariate data. Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 12 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics - Geometry Define and describe types of geometrical reasoning and proof, using them to verify valid conjectures as they surface in the study of geometry; develop a counterexample to refute an invalid conjecture. Define, describe, and analyze 2- and 3-dimensional figures, their properties and relationships, including how a change in one measurement will affect other measurements of that figure. Use concepts of congruence and similarity to relate and compare 2- and 3-dimensional figures, including trigonometric ratios. Use coordinates and algebraic techniques to interpret, represent and verify geometric relationships. Apply geometric properties of length or area to represent and calculate probabilities. Prerequisite Skills Resources Available Resources Needed Professional Development Needs SAS-Math Competencies With Backmapping What all students should be able to do at the end of this year or course… Page 13 SAS-Math Core Team – Jim Bohan – [email protected] Competencies – Mathematics – Algebra 2 Extend algebraic properties and processes to quadratic, exponential, and polynomial expressions and equations and to matrices, and apply them to solve real world problems. Represent exponential functions in multiple ways, including tables, graphs, equations, and contextual situations, and make connections among representations; relate the growth/decay rate of the associated exponential equation to each representation. Represent a quadratic function in multiple ways, including tables, graphs, equations, and contextual situations, and make connections among representations; relate the solution of the associated quadratic equation to each representation. Represent a polynomial function in multiple ways, including tables, graphs, equations, and contextual situations, and make connections among representations; relate the solution of the associated polynomial equation to each representation. Distinguish between independent and dependent events in order to calculate compound probabilities within real world situations. Prerequisite Skills Resources Available Resources Needed Professional Development Needs